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High-resolution optical instrumentation for biosensing and biomechanical characterization
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High-resolution optical instrumentation for biosensing and biomechanical characterization
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1 High-resolution optical instrumentation for biosensing and biomechanical characterization By Alexa W. Hudnut A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL at the UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements of the Degree DOCTOR OF PHILOSOPHY Biomedical Engineering August 2018 2 Acknowledgements Coming into graduate school with the enthusiasm only a first year can have, I underestimated what a PhD entailed. Now on the other end, I appreciate the support success requires. I would like to take this space to thank everyone who has been there throughout the process. I would not have been able to complete my PhD without the constant encouragement and advisement from my mentors, colleagues, family, and friends. There are several people I would like to specifically thank. Professor Andrea Armani, thank you for finding interesting problems for us to solve and taking the time to develop me as a researcher, writer, leader, and human. You have a unique approach to supporting your students, and I have appreciated being part of the research group you have created. Within the group I have always felt my time could be used to focus on experiments and learning. I value your encouragement to explore new fields from optics, to biomechanics, to computational analysis. From these endeavors I have a much better appreciation for what other people do and how much can be learned from a deep literature review. I look forward to watching the research group thrive under your leadership. I have had countless wonderful teachers in my academic career. I would like to thank them all for their support, patience, and encouragement. Special thanks to my committee members: Dr. David Agus, Professor Eun Ji Chung, Professor Mike Kassner, and Professor Pin Wang. Thank you for being open to cross-disciplinary discussions and generous with your time. Thank you to my collaborators: Professor Qiming Wang, Dr. David Agus, Professor Shannon Mumenthaler, and Dr. George Hatch. I will always appreciate your patience in explaining different fields and sharing your facilities with me. 3 Thank you to George Tolomiczenko, Terry Sanger, and Nadine Afari for building the HTE program and giving me a second home within the University to learn about entrepreneurship and medical device development. Outside of USC, I would like to thank Professor Christian Franck (Brown), Professor Guy Genin (Washington University in St. Louis), and Professor Chelsey Simmons (University of Florida) for graciously responding to emails from a panicked graduate student you’d never met. Finally, I would like to thank Professor Norberto Grzywacz for always being my biggest cheerleader. I would not have pursued a PhD without your support. To the other Post Doctoral researchers and PhD students of the Armani Research Group, you are the best. You have been an open ear and excellent hive mind throughout my PhD. In order directly related to where your office was located in VHE, I would like to thank Victoria Sun, Michele Lee, Erick Moen, Lauren Lopez, Sam McBirney, Andre Kovac, Eda Gunor, Rene Zeto, Arsenii Epishin, Xiaoqin Shen, Akshay Panchavati, Xiaomin Zhang, Dongyu Chen, Simin Mehrabani, Maria Chistiakova, Amanda Cordes, Kelvin Kuo, Vinh Diep, Soheil Soltani, Hyungwoo Choi, and Tushar Rane. Special thanks the masters, undergraduate, and high school students who I was able to mentor and who in return taught me more than I could possibly have taught them: Lea, Gumi, Brock, Danny, Martin, Lili, Max, Alex, John, Joelle, Daniel, Kristina, Celeste, Gabe, and Bernard. There is no substitute for the support I have received from my family. I will never fully understand your intuition for what will motivate me, but I appreciate it every day. Thank you for always reminding me to celebrate my accomplishments and valuing the 4 work and failure that goes into every success. I truly am a sum of your best parts and for that I am eternally grateful. To my friends, it’s finally over! Thank you for always being there for a walk, last minute outing, hug, hot chocolate, or phone call. Please send any suggestions for a constructive outlet for my curiosity and energy. 5 Table of Contents Acknowledgements ………………………………………………………...2 Abstract…………… .................................................................................... 28 Chapter 1. Chapter Overview ................................................................... 29 1.1. Motivation ........................................................................................................... 29 1.2. Chapter Overview ............................................................................................... 30 1.3. References .......................................................................................................... 34 Chapter 2. Background .............................................................................. 36 2.1. Sensor Theory .................................................................................................... 36 2.1.1 Sensitivity ...................................................................................................... 37 2.1.2 Specificity ...................................................................................................... 38 2.1.3 False Positive/Negative Rate ........................................................................ 39 2.1.4 Response Time .............................................................................................. 40 2.1.5 Signal to Noise Ratio .................................................................................... 40 2.2 Optical Sensors .................................................................................................... 42 2.2.1 Refractive Index ............................................................................................ 42 2.2.2 Optical Waveguides ...................................................................................... 44 2.2.2.1 Power Loss within Waveguides ................................................................................. 45 2.2.3 Optical Polarization ...................................................................................... 47 2.2.4 Optical Birefringence .................................................................................... 49 2.2.5 Photoelastically-induced Polarization Detection ......................................... 51 2.3 Mechanical Characterization of Viscoelastic Materials .................................... 54 2.3.1 Viscoelastic Materials ................................................................................... 54 6 2.3.2 Biomaterials .................................................................................................. 55 2.3.3 Mechanical Testing ....................................................................................... 58 2.4 References ........................................................................................................... 60 Chapter 3. Optical Fiber Polarimetric Elastography Sensor Design .... 65 3.1 Introduction ............................................................................................................ 65 3.2 OFPE Instrument Configurations ..................................................................... 66 3.2.1 Single Fiber OFPE Instrument Setup ............................................................ 66 3.2.1.1 Compressive Stage ..................................................................................................... 67 3.2.1.2 Optical Fiber Sensor ................................................................................................... 69 3.2.1.3 Example Data Set ....................................................................................................... 71 3.2.2 Multi-Fiber OFPE Instrument Setup ............................................................. 71 3.2.2.1 Compressive Stage ..................................................................................................... 73 3.2.2.2 Optical Fiber Sensor Array ........................................................................................ 73 3.2.2.3 Example Data Set ....................................................................................................... 77 3.3 Data Analysis ....................................................................................................... 78 3.3.1 Loading-Unloading Curves ........................................................................... 78 3.3.2 Normalizing Loading-Unloading Curves ...................................................... 79 3.3.3 Maximum Phase Difference .......................................................................... 79 3.3.4 Energy Loss ................................................................................................... 80 3.4 Sample Preparation ............................................................................................. 81 3.5 Conclusion ........................................................................................................... 83 3.6 References ........................................................................................................... 85 Chapter 4. OFPE - Animal Results ........................................................... 87 4.1 Introduction ......................................................................................................... 87 7 4.2 Salmon Skeletal Muscle Testing with OFPE ..................................................... 88 4.2.1 Salmon Sample Preparation .......................................................................... 89 4.2.2 Salmon Testing Protocol ............................................................................... 90 4.2.3 Salmon Data Analysis ................................................................................... 90 4.2.4 Salmon Results and Discussion ..................................................................... 91 4.2.4.1 Uniform Sample ......................................................................................................... 91 4.2.4.2 Sample with a Single Collagen Membrane ................................................................ 93 4.2.4.3 Sample with Two Collagen Membranes .................................................................... 95 4.3 Porcine Tissue Testing with OFPE .................................................................... 97 4.3.1 Porcine Sample Preparation ......................................................................... 99 4.3.2 Porcine Testing Protocol ............................................................................. 100 4.3.3 Porcine Data Analysis ................................................................................. 100 4.3.3.1 Quasi-Linear Viscoelastic Fit ................................................................................... 101 4.3.3.2 Mechanical Deformations ........................................................................................ 104 4.3.4 Porcine Results and Discussion .................................................................. 105 4.3.4.1 Pathology Imaging Analysis of Soft Tissues ........................................................... 105 4.3.4.2 Porcine Liver Results and Discussion ...................................................................... 107 4.3.4.3 Porcine Kidney Results and Discussion ................................................................... 109 4.3.4.4 Porcine Pancreas Results and Discussion ................................................................ 111 4.3.4.5 Porcine Heart Results and Discussion ...................................................................... 114 4.3.4.6 Porcine Cartilage Results and Discussion ................................................................ 117 4.4 Comparison of Data Analysis Methods ............................................................ 126 4.4.1 Maximum Phase Difference Analysis .......................................................... 127 4.4.2 Energy Loss Analysis .................................................................................. 128 4.4.3 Quasi-Linear Viscoelasticity Analysis ......................................................... 130 8 4.4.4 Mechanical Deformation Analysis .............................................................. 133 4.5 Conclusion ......................................................................................................... 135 4.6 References ......................................................................................................... 137 Chapter 5. OFPE – Cancer Results ........................................................ 142 5.1 Introduction ....................................................................................................... 142 5.2 Patient Clinical Testing Methods with OFPE ................................................. 144 5.3 OFPE Testing Protocol ..................................................................................... 145 5.3.1 Tissue Preparation ...................................................................................... 145 5.3.2 OFPE Experimental Parameters ................................................................ 146 5.3.3 Downstream Molecular Analysis ................................................................ 147 5.4 Data Analysis ..................................................................................................... 151 5.5 Patient Clinical Samples Results and Discussion ............................................ 152 5.5.1 Liver Cancer Patient (CCTU-12935) ......................................................... 152 5.5.2 Colon Cancer Patient (CCTU-12982) ........................................................ 157 5.6 Downstream Molecular Analysis Results ......................................................... 163 5.7 Conclusion ......................................................................................................... 165 5.8 References ......................................................................................................... 166 Chapter 6. 3D Printed Biomimetic Structures ....................................... 171 6.1 Introduction ....................................................................................................... 171 6.2 Methods ............................................................................................................. 172 6.2.1 Pancreatic Tissue Sample Preparation ....................................................... 172 6.2.2 Biomimetic Structure Design ....................................................................... 173 6.2.3 FEM Modeling ............................................................................................ 174 9 6.2.4 Biomimetic Structure Fabrication ............................................................... 175 6.2.5 Compressive Testing Methods ..................................................................... 177 6.3 Results and Discussion ..................................................................................... 178 6.3.1 Results from Compressive Testing of Pancreatic Tissue ............................. 178 6.3.2 Modeling Results ......................................................................................... 179 6.3.3 Results from Compressive Testing of the Biomimetic Structures ................ 183 6.3.4 Comparison of Pancreatic Tissue and Biomimetic Structure Results ......... 184 6.4 Conclusion ......................................................................................................... 185 6.5 References ......................................................................................................... 187 Chapter 7. Future Work .......................................................................... 190 7.1 OFPE Instrument Design ................................................................................. 190 7.2 Animal Testing with OFPE .............................................................................. 192 7.3 Clinical Testing with OFPE ............................................................................. 193 7.4 Modeling of Tissue Biomechanics with 3D Printed Structures ...................... 193 Chapter A1. Additional Preliminary Investigations ............................. 194 A1.1 Introduction ....................................................................................................... 194 A1.2 Time Course Testing with OFPE ...................................................................... 195 A1.2.1 Time Course Sample Preparation ............................................................... 196 A1.2.2 Time Course Testing Protocol ..................................................................... 197 A1.2.3 Time Course Data Analysis ......................................................................... 197 A1.3 Time Course Results and Discussion .............................................................. 198 A1.3.1 Liver Results and Discussion ....................................................................... 198 A1.3.2 Articular Cartilage Results and Discussion ............................................... 200 10 A1.3.3 Fibrocartilage Results and Discussion ...................................................... 202 A1.3.4 Frozen Cartilage Results and Discussion .................................................. 204 A1.4 Conclusion ........................................................................................................ 206 A1.5 References ........................................................................................................ 208 Chapter A2. Asymmetric Toroid Optomechanics ................................ 209 A2.1 Introduction ...................................................................................................... 209 A2.2 Methods ............................................................................................................ 211 A2.2.1 Modeling ...................................................................................................... 211 A2.2.2 Fabrication .................................................................................................. 214 A2.2.3 Device Characterization .............................................................................. 215 A2.3 Results ................................................................................................................ 216 A2.3.1 Finite Element Method Modeling Results ................................................... 216 A2.3.2 Asymmetric Crown and Cantilever Mode ................................................... 217 A2.3.3 Dependence of Threshold on Asymmetry .................................................... 218 A2.4 Conclusion ........................................................................................................ 219 A2.5 References ........................................................................................................ 220 Chapter A3. Malaria Diagnostic .............................................................. 223 A3.1 Introduction ...................................................................................................... 223 A3.2 Sensor Design ................................................................................................... 225 A3.2.1 Magnetic Manipulation ............................................................................... 226 A3.2.2 Optical Scattering ........................................................................................ 227 A3.2.3 Optical Polarization .................................................................................... 228 A3.2.4 Theory .......................................................................................................... 229 11 A3.3 Instrument Configurations .............................................................................. 229 A3.4 Sample Characterization ................................................................................. 232 A3.5 Conclusion ........................................................................................................ 233 A3.6 References ........................................................................................................ 234 Chapter A4. VCSEL and Cell Scattering ............................................. 238 A4.1 Introduction ...................................................................................................... 238 A4.2 Methods ............................................................................................................ 240 A4.2.1 Device Setup ......................................................................................... 240 A4.2.2 Experimental Methods .......................................................................... 241 A4.3 Results .............................................................................................................. 242 A4.3.1 VCSEL Detection Results ..................................................................... 242 A4.4 Conclusion ........................................................................................................ 245 A4.5 References ........................................................................................................ 246 Chapter A5. Associated Matlab Codes ................................................. 248 A5.1 Calculating ΔPol .............................................................................................. 248 A5.1.1 LoadingUnloading.m ................................................................................... 248 A5.2 Quasi-Linear Viscoelastic Fitting ................................................................... 251 A5.2.1 Run_QLV_viscoelastic_model_triangle_loading.m .................................... 251 A5.2.2 fminsearchbnd.m ........................................................................................ 252 A5.2.3 solver_sawtooth_quasilinear_viscoelastic.m ............................................. 258 A5.2.4 nnls.m .......................................................................................................... 260 12 Figures Figure 2-1: Schematic of Snell’s Law representing how the difference in refractive index in material one (n 1 ) and the refractive index of material two (n 2 ) impacts the angle of incidence and the angle of refraction . ...................................................................... 43 Figure 2-2: Schematic representing total internal reflection in an optical waveguide. Within an optical waveguide if the light travels at a small enough angle it will remain within the core of the waveguide and propagate. The cladding and the core of the optical waveguide have different refractive indices (n 1 and n 2 respectively). ........................................................ 45 Figure 2-3: A polarized electromagnetic wave depicting the single orientation in the E and B fields of coherent polarized light. The E and B field are perpendicular and dependent on the direction of propagation, z. The wavelength of the light is labeled by λ. ........................................................................................................................... 49 Figure 2-4: Schematic of unpolarized light passing through a birefringent material (blue). The parallel (pink and black dots) and perpendicular (blue arrows) polarizations see different refractive indices and the light is refracted at two different angles. .......... 50 Figure 2-5: Visual representation of the loading and unloading cycle of one compressive test by graphing the circle trace of the three Stokes parameters <s 1 , s 2 , s 3 > on a unit sphere. ....................................................................................................................... 52 Figure 2-6: Schematic of an optical path within an optical polarimetry sensor setup as light travels through the system. ............................................................................... 54 Figure 2-7: Graphical representation of a loading and unloading curve generated by a representative biomaterial using a triangle method of compressive testing. The loading curve is the response of the material due to the initial load. The unloading 13 curve is the response of the material to the load being removed. The loading and unloading curves shown demonstrate hysteresis, characteristic of viscoelastic materials. ................................................................................................................... 59 Figure 3-1: Rendering of the single fiber configuration of the OFPE instrument setup for testing including all of the components of both the compressive stage (micrometer controlled) and the optical fiber sensor. The disposable optical fiber sensing region is the portion of the optical fiber between the bare fiber adapters. ................................................................. 67 Figure 3-2: Image of the single fiber configuration of the OFPE instrument during compressive testing of a porcine cartilage sample. ............................................................................. 70 Figure 3-3: Example loading and unloading curve generated with the single fiber configuration of the OFPE instrument. Data set from compression testing of a porcine kidney sample at 30% strain. .................................................................................................................. 71 Figure 3-4: Rendering of the multi fiber configuration of the OFPE instrument setup for testing including all of the components of both the compressive stage and the optical fiber sensor. The disposable optical sensing region is the portion of the optical fiber between the splitter and the MEMS switch. ................................................................................................ 72 Figure 3-5: Image of the multi-fiber configuration of the OFPE instrument during compressive testing of a human pancreatic cancer sample. ................................................................. 74 Figure 3-6: (a) Rendering of the 3D printed fiber array holder. The entire part is 15mm x 25mm x 10mm (w x l x h). The notches for holding the fibers are 500µm wide. The spacing between the notches is 1mm. (b) Image of the 3D printed fiber array holder. ................................................................................................................................... 75 14 Figure 3-7: Example of the (a) raw data and (b) parsed data recorded by the polarizer/photodiode/powermeter system implemented to replace the polarizer. This data was recorded during compression testing of a salmon skeletal muscle at 30% strain. ........ 77 Figure 3-8: Example loading and unloading curve generated with the multi-fiber configuration of the OFPE instrument. Loading and unloading curves from: (a) fiber one, (b) fiber two, (c) fiber three, and (d) fiber four. Data set from compression testing of a salmon skeletal muscle sample at 30% strain. ................................................................................................... 78 Figure 3-9: Graphical representation of a loading and unloading curve with the maximum phase difference highlighted. The y-axis is labeled as both stress and ΔPol because the stress is proportional to the ΔPol due to the photoelastic effect. ........... 80 Figure 3-10: Graphical representation of a loading and unloading curve with the energy loss shaded in blue. A value proportional to the energy loss can be calculated by taking the area between the two curves because the stress is proportional to the ΔPol photoelastic effect. .................................................................................................... 81 Figure 3-11: Rendering of the different types of tissue samples cut from multiple biomaterial types for OFPE testing: (a) salmon skeletal muscle – 9 mm × 9 mm × 5 mm (l×w×h), (b) porcine pancreatic tissue – 7 mm × 7 mm × 4 mm (l×w×h), and (c) porcine cartilage tissue – 7 mm × 7 mm × 4 mm (l×w×h) ............................................................................... 82 Figure 3-12: Analysis of the impact of the interaction length on the loading and unloading curves for a sample of uniform salmon skeletal muscle. (a) Loading and unloading curves for a uniform salmon sample of salmon with an interaction length of 5mm, 10mm and 20mm. (b) Analysis of the phase difference for three different 15 interaction lengths at the three different strain rates. (c) Analysis of the energy loss for the three different interaction lengths at the three different strain rates. ............. 83 Figure 4-1: Summary of the Young’s Modulus of the biomaterials profiled with the OFPE instrument in animal models (liver, colon, kidney, pancreas, heart, muscle, and cartilage tissue). The values of the biomaterials tested vary by six orders of magnitude [6-18]. ...................................................................................................... 87 Figure 4-2: Diagram of a section of salmon skeletal muscle used for OFPE testing. Dimensions of the tissue sample are 9mm x 9mm x 5mm (l x w x h). ..................... 90 Figure 4-3: Loading and unloading curves for a uniform salmon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is 2.3E-3, 1.5E-2 and 4.1E-2 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a uniform sample of salmon skeletal muscle. ......................................................................................................... 92 Figure 4-4: Loading and unloading curves for a salmon sample divided in half by a single collagen membrane, where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is 1.1E-2, 2.2E-2 and 2.1E-2 for 10%, 20%, and 30% strain, respectively. (c) Image of OFPE testing of a salmon skeletal muscle sample divided in half by a collagen membrane. ................................................................................................................................... 94 Figure 4-5: Loading and unloading curves for a salmon sample divided in thirds by two collagen membranes, where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is 1.4 E-3, 2.4 E-2 16 and 1.6 E-2 for 10%, 20%, and 30% strain, respectively. (c) Image of OFPE testing of a salmon skeletal muscle sample divided by two collagen membranes. .............. 96 Figure 4-6: Diagram of a section of porcine pancreatic tissue used for OFPE testing. Dimensions of the tissue sample are 7mm x 7mm x 4mm (l x w x h). These dimensions are used for testing of all porcine tissue sub-types. ............................. 100 Figure 4-7: Graphical representation of a QLV fit of the loading and unloading curves of a pancreatic tissue sample compressively tested to 20% strain. ............................. 102 Figure 4-8: Cartoons of three common forms of mechanical deformation within viscoelastic materials: (a) buckling, (b) delamination, and (c) bridging. The red lines represent the individual load bearing elements. The blue line denotes the difference between the material before compression and during compression. ...................... 105 Figure 4-9: H&E images from tissues before and after compressive testing with OFEP: (a) uncompressed liver sample, (b) compressed liver sample, (c) uncompressed kidney sample, (d) compressed kidney sample, (e) uncompressed pancreas sample, (e) compressed pancreas sample. The arrows indicate the microstructures from each organ that would be most likely to be destroyed due to compression. These structures remain intact across all three tissue types, indicating OFPE is non- destructive. .............................................................................................................. 106 Figure 4-10: (a) Loading and unloading curves for a porcine liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 2.8E-8, 1.2E-8, and 5.0E-8 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine liver. . 108 17 Figure 4-11: (a) Loading and unloading curves for a porcine kidney sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 2.8E-8, 1.2E-8, and 5.0E-8 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine kidney. ..................................................................................................................... 110 Figure 4-12: (a) Loading and unloading curves for a porcine pancreas sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.1E-8, 2.8E-8, and 4.5E-8 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine pancreas. .................................................................................................................. 112 Figure 4-13: (a) Loading and unloading curves for a porcine heart sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 5.6E-9, 8.8E-8, and 2.9E-8 for 10%, 20% and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine heart. 115 Figure 4-14: H&E images from heart tissues before and after compressive testing with OFEP: (a) uncompressed heart sample and (b) compressed heart sample. The H&E images demonstrate the repeated units within the muscle. The elasticity of the individual heart cells is hypothesized to be the reason for the unique behavior of the heart at high strain. .................................................................................................. 117 Figure 4-15: Gross anatomy of the porcine knee: (a) Schematic of the knee demonstrating the three locations of the cartilage resected for OFPE testing. (b) Photo of the articular cartilage of the femoral condyles with a box marking the location where the cartilage is harvested. (c) Photo of the articular cartilage of the 18 patella with a box marking the location where the cartilage is harvested. (d) Photo of the fibrocartilage of the meniscus with a box marking the location where the cartilage is harvested. .............................................................................................. 118 Figure 4-16: (a) Loading and unloading results for a sample of porcine Articular Cartilage from the Femoral Condyles where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 4.0E-8, 9.2E-8, and 1.0E-7 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of Articular Cartilage from the Femoral Condyles. .................................................................................................. 119 Figure 4- 17: Loading and unloading results for a sample of porcine Articular Cartilage from the Patella where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 3.8E-8, 1.4E-7, and 1.0E-7 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of Articular Cartilage from the Patella. ................................... 122 Figure 4-18: Loading and unloading results for a sample of porcine Fibrocartilage from the Meniscus where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 6.2E-8, 1.2E-7, and 2.3E-7 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of Fibrocartilage from the Meniscus. ....................................................... 125 Figure 4-19: (a) Maximum phase change for a uniform sample for the five consecutive runs at three different strain rates where the maximum error is 1.7 E-2, 4.9 E-2 and 8.4 E-2 for 10%, 20% and 30% strain respectively. (c) Maximum phase change for the five consecutive runs at three different strain rates where the maximum error is 19 1.1 E-1, 9.4 E-2 and 8.0 E-2 for 10%, 20% and 30% strain respectively. (e) Maximum phase change for the five consecutive runs at three different strain rates where the maximum error is 2.0 E-2, 2.6 E-2 and 4.2 E-2 for 10%, 20% and 30% strain respectively. .................................................................................................. 127 Figure 4-20: (a) Energy loss for the five consecutive runs at three different strain rates where the maximum error is 2.3 E-3, 1.5 E-2 and 4.1 E-2 for 10%, 20% and 30% strain respectively. (b) Energy loss for the five consecutive runs at three different strain rates the maximum error is 1.1 E-2, 2.2 E-2 and 2.1 E-2 for 10%, 20% and 30% strain respectively. (c) Energy loss for the five consecutive runs at three different strain rates where the maximum error is 1.4 E-3, 2.4 E-2 and 1.6 E-2 for 10%, 20% and 30% strain respectively. .................................................................. 129 Figure 4-21: Representative QLV fit for one the loading and unloading curve for liver, kidney, and pancreatic tissue. ................................................................................. 130 Figure 4-22: Coefficients of the QLV fit of the loading and unloading curves for liver, kidney, and pancreatic tissue. ................................................................................. 131 Figure 4-23: Mechanical Buckling Location: (a) Primary loading buckling point indicated by an absolute maximum in our loading curves. (b) Secondary loading buckling point indicated by a local maximum in our loading curves. (c) Unloading buckling point indicated by an absolute maximum in our unloading curves. ........ 134 Figure 4-24: Mechanical Deformation: (a) Delamination point indicated as a local minimum in the unloading curves. (b) Bridging point indicated as a local minimum in the unloading curves. .......................................................................................... 135 20 Figure 5-1: Summary of the Young’s Modulus of patient tissues profiled with the OFPE instrument: liver, liver cancer, colon, colon cancer, pancreas, and pancreatic cancer. The values of the biomaterials tested vary by three orders of magnitude [1, 10-15]. ................................................................................................................................. 143 Figure 5-2: Diagram of a section of patient tissue used for OFPE testing. Dimensions of the tissue sample are 7mm x 7mm x 4mm (l x w x h). These dimensions are used for testing of all human tissue sub-types. ..................................................................... 145 Figure 5-3: Schematic of the OFPE instrument used for testing. Either the single fiber or arrayed system can be used for patient testing, depending on the experimental parameters of interest. ............................................................................................. 146 Figure 5-4: Flow chart of planned future downstream molecular analysis of patient samples after they have been characterized with OFPE. The biological assessment is performed by collaborators or in core facilities. ..................................................... 148 Figure 5-5: (a) Loading and unloading curves for a normal liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.66E-7, 1.43E-8, and 1.86E-8 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the normal liver. ........................ 153 Figure 5-6: (a) Loading and unloading curves for one region of the cancerous liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 2.46E-7, 1.46E-7, and 1.95E-8 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the one region of the cancerous liver. .................................................................................. 154 21 Figure 5-7: (a) Loading and unloading curves for one region of the cancerous liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.33E-7, and 3.12E- 7, for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the one region of the cancerous liver. ................................................................................................. 155 Figure 5-8: (a) Loading and unloading curves for a normal colon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 7.05E-9, 6.28E-9, and 6.97E-9 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the normal colon. ....................... 159 Figure 5-9: (a) Loading and unloading curves for one region of the cancerous colon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.05E-8, 1.81E-8, and 1.79E-8 for 10%, 20%, and 30% strain respectively. (c) H&E Image of the one region of the cancerous colon. ................................................................................ 160 Figure 5-10: (a) Loading and unloading curves for one region of the cancerous colon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.71E-8, 1.86E-8, and 1.79E-8 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the one region of the cancerous colon. ................................................................................ 161 Figure 6-1: (a) Sections of pancreatic tissue are stained with hematoxylin and eosin (H&E) and imaged using a light microscope to inform the design of a model of the ECM structure within the pancreas. (b) Simplified structures are drawn in SolidWorks based on the H&E 22 images and past results from the literature. This geometry is subsequently used for FEM modeling and fabricating biomimetic structures. .......................................................... 173 Figure 6-2: Fabricating the biomimetic structures has three primary steps. (a) Step 1: a scaffold is 3D printed using projection microstereolithography, (b) Step 2: the scaffold is filled with a silicone elastomer and cured for 12 hours, and (c) Step 3: the scaffold is dissolved using an NaOH bath for 6 hours, freeing the silicone elastomer. ................................................................................................................................. 176 Figure 6-3: Schematics of the two different compressive testing methods used: (a) the Instron system used for mechanical testing of the biomimetic structures and (b) the OFPE system used for mechanical testing of the pancreatic tissue samples. ......... 177 Figure 6-4: OFPE testing results from compressive testing of pancreatic tissue at 10%, 20%, and 30% strain. .............................................................................................. 179 Figure 6-5: Images from FEM simulation of the buckling of the biomimetic structure with a D/L ratio of 0.21. As the strain increases, buckling begins to occur. The structure undergoes several unique regimes during the mechanical testing (a) before compression occurs, (b) during compression but before buckling, (c) during compression when buckling occurs, and (d) during compression after buckling has occurred. .................................................................................................................. 180 Figure 6-6: Simulation results for buckling characteristics of five biomimetic structures with variable D/L ratios. (a) Loading curves for five simulated structures. (b) Linear fit of the buckling strain for the five simulated structures vs. the D/L ratio. .......... 181 Figure 6-7: A suite of six silicone elastomer structures with known defects are modeled and subsequently fabricated. The structures are modified by removing the support 23 beams of one of the faces of the lattice structure. The removed support beams are indicated in purple. (a) Structure where all the support beams remain intact. (b) Structure where all the support beams are removed. (c) Structure where the middle support beam is removed. (d) Structure where one outer support beam is removed. (e) Structure where both the middle support beam and one outer support beam are removed. (f) Structure where both the outer support beams are removed. ............. 181 Figure 6-8: Loading curves generated from simulation results for all six biomimetic structures. The structure names correspond to Figure 6-7. The D/L ratio is held constant at 0.25. ...................................................................................................... 182 Figure 6-9: Instron Loadframe testing results from compressive testing of the biomimetic structure (e) tissue at 10%, 20%, and 30% strain. .................................................. 183 Figure 6-10: Linear fit of the buckling strain for the five simulated structures vs. the D/L ratio. The buckling point for five pancreatic tissue samples, determined with OFPE, plotted alongside the theoretical results. This method provides us with a system for quantifying what components of the ECM of the tissue cause specific mechanical behaviors. ................................................................................................................ 184 Figure A1-1: Diagram of a section of porcine pancreatic tissue used for OFPE testing. Dimensions of the tissue sample are 7mm x 7mm x 4mm (l x w x h). These dimensions are used for testing of all porcine tissue sub-types. ............................. 197 Figure A1-2: Loading and unloading curves for a porcine liver sample that has been tested for five hours and is stored at RT between tests. .......................................... 199 Figure A1-3: (a) Loading and unloading results for a sample of porcine Articular Cartilage from the Femoral Condyles from the first four hours of compression 24 testing. (b) Loading and unloading results for a sample of porcine Articular Cartilage from the Femoral Condyles from hours five through eight of compression testing. ..................................................................................................................... 201 Figure A1-4: (a) Loading and unloading results for a sample of porcine fibrocartilage from the meniscus from the first four hours of compression testing. (b) Loading and unloading results for a sample of fibrocartilage from the meniscus from hours five through eight of compression testing. ..................................................................... 203 Figure A1-5: (a) Loading and unloading results for a sample of porcine fibrocartilage from the meniscus from the first four hours of compression testing. (b) Loading and unloading results for a sample of fibrocartilage from the meniscus from hours five through eight of compression testing. ..................................................................... 205 Figure A2-1: Integrated optical devices can be fabricated on a silicon wafer. One example is a microtoroid where silica toroids are fabricated onto a silicon wafer. This figure depicts a scanning electron microscope (SEM) image of one such microtoroid. ............................................................................................................. 210 Figure A2-2: (a) Rendering of an asymmetric microtoroid device. (b) Schematic of an asymmetric microtoroid device with parameters labeled including: minimum minor radius (r min ), maximum minor radius (r max ), maximum major radius (R max ), minimum major radius (R min ), and total diameter (D). (c) SEM cross section of an asymmetric microtoroid device. ................................................................................................. 211 Figure A2-3: Rendering of the microtoroid device fabrication process. (a) Silica pads with a diameter of 150µm were fabricated using photolithography. (b) XeF 2 etching was used to create microdisks, which were silica pad on a silicon pillar created by 25 etching away the silicon under the silica pad. (c) Symmetric CO 2 reflow was used to create a symmetric microtoroid with a uniform torus. (d) Asymmetric CO 2 reflow was used to create an asymmetric microtoroid with a non-uniform torus by offsetting the laser during reflow. ........................................................................................... 214 Figure A2-4: Rendering of the testing setup used to measure the mechanical properties of the asymmetric toroids. A 1550nm tunable laser was used as a light source. A tapered optical fiber was used to couple light into the cavity. An oscilloscope was used to track the peaks of the laser. An ESA was used to measure the frequency and threshold power of the optomechanical modes of the toroid. ................................. 216 Figure A2-5: Subset of the FEM simulation results of the optomechanical modes of an asymmetric cavity. The lowest threshold modes for the asymmetric devices were the asymmetric crown mode and the asymmetric cantilever mode. The crown mode and cantilever mode still exist within the fourteen mechanical mode profile of the asymmetric device; however, the input power needed to excite them increases. ... 217 Figure A2-6: (a) Bright field microscope image of an asymmetric device. (b) ESA spectra data for the asymmetric crown mode. (c) ESA spectra data for the asymmetric cantilever mode. (d) Threshold curve for the asymmetric crown mode. (e) Threshold curve for the asymmetric cantilever mode. Modified from Soltani et al [17]. ......................................................................................................................... 218 Figure A2-7: (a) Plot of the normalized threshold vs. pillar offset for graph for an asymmetric crown mode. (b) Plot of normalized threshold vs. pillar offset for an asymmetric cantilever mode. Modified from Soltani et al [17]. ............................. 219 26 Figure A3-1: Optical path for the first configuration of the malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the first configuration of the PODS depicting the same configuration as the rendering. .................................................................................... 231 Figure A3-2: Optical path for the second configuration of the malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the second configuration of the PODS depicting the same configuration as the rendering. .................................................................................... 231 Figure A3-3: Optical path for the third configuration of the optical malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the third configuration of the PODS depicting the same configuration as the rendering. ...................................................................... 232 Figure A3-4: Optical path for the fourth configuration of the malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the fourth configuration of the PODS depicting the same configuration as the rendering. .................................................................................... 232 Figure A4-1: Cartoon outlining how the change in current can be used as a detection signal to measure optical scattering. By comparing the change in current over time, the dwell time, and the relative number and position of particles can be detected within a heterogeneous sample. Difference in the current indicated by A, B, and C can be a result of multiple factors such as the number of cells in the chamber or the distance between the cell and the laser. 239 27 Figure A4-2: Schematic of the integrated VCSEL and photodetector systems proposed. (a) SiPD system with integrated VCSEL used for preliminary testing. (b) GaAs photodetector system built, but not tested. .............................................................. 241 Figure A4-3: Example data from the SiPD-VCSEL system. (a) Differential normalized current plotted over time (sec). The flow was switched between cells (red) and media (black). The concentration was too high (~15 cells) in the sensing region of the chamber to definitively claim single cell detection. (b) Plot of each minute interval of either media or cells+media plotted on top of each other in terms of frequency. These plots can be used to statistically show if single cell detection occurs. ............................................................................ 243 Figure A4-4: Statistical analysis of the relative current to determine if single cell detection occurs. (a) Histogram of counts from only cell events. (b) Reorganization of counts and fit to a Poisson distribution. The fit is shifted to the right, indicating that there were multiple cells within the well during each measurement. ........................................................... 244 Figure A4-5: Example data from the GaAsPD-VCSEL system. (a) Differential normalized current plotted over time (sec). The flow was switched between cells (red) and media (black). (b) Plot of each minute interval of either media or cells+media plotted on top of each other in terms of frequency. ................................................................................ 244 28 Abstract One fundamental challenge in developing medical devices is that the same platform can rarely be used to diagnose or characterize multiple diseases. This is because highly specific chemical sensing methods are introduced to increase the signal, which has been necessary in the majority of traditional medical devices and diagnostics. By leveraging the fundamental properties of optics, I have overcome this limitation and developed a suite of medical device and diagnostic technologies based on optical polarization. The main platform discussed in this dissertation is an optical fiber polarimetric elastography (OFPE) instrument for determining the biomechanical properties of tissues. To demonstrate the flexibility of this platform, it is used to characterize a variety of biomaterials that range in Young’s modulus by three orders of magnitude. The following work details the experiments and results for how the instrument was designed, fabricated, and validated. Additional instruments were developed using the same fundamental principles of optics. These results are presented in the appendices. Therefore, in addition to the scientific results presented in this thesis, it should serve as a framework for developing and characterizing families of medical devices. 29 Chapter Overview Chapter 1. 1.1. Motivation Due to the decrease in size and cost of optical components driven by the communications industry, optical methods have increasingly been used to develop flexible and specific sensors [1-5]. Refractometric approaches have been used to develop systems where direct interaction of the molecule with the optical field generates a signal [2]. Alternative approaches where there is no direct interaction with the field have been developed in optical fiber based systems. One such method is photo-elastic detection, which has been used to develop accurate pressure sensors called polarimetric stress sensors [6-8]. The advantages of such optical methods include rapid, sensitive, and label- free detection. Additionally, they are flexible and the same platforms can be slightly modified to characterize diseases with distinct pathologies. In parallel, understanding the mechanical behavior of biomaterials has been proposed as an alternative method to chemical and imaging approaches for understanding how diseases develop. Physical changes in tissues have been observed in both chronic diseases such as cancer [9-12] and acute traumas such as traumatic brain injury [13-15]. Despite a growing interested in understanding the role of the mechanical behavior of normal and diseased tissues, the existing methods for measuring these properties have primarily been adapted from materials testing. These methods such as Atomic Force Microscopy (AFM) and rheology are designed for materials with regular microarchitectures [16]. However, they have been applied extensively to the study of different biomaterials and cells, which are heterogeneous and have unpredictable 30 microarchitectures [17-20]. Therefore, the limit of what these methods can elucidate about the mechanics of biomaterials has been reached. 1.2. Chapter Overview Chapter 2 provides the background for this thesis. Primarily, it focuses on sensor theory, optics, and viscoelastic material characterization. Therefore, it covers the fundamentals for developing optical instrumentation for medical applications. Details are provided regarding considerations when designing new instrumentation such as sensitivity, specificity, false positive/negative rate, response time, and signal to noise ratio. Subsequently, information is provided on a few fundamentals of optics including optical waveguides, optical polarization, optical birefringence, and optical fiber based detection. The final section outlines the properties of viscoelastic materials and considerations for mechanical testing of these complex materials. Chapter 3 outlines the development of an optical fiber polarimetric elastography (OFPE) instrument. The OFPE instrument is designed and built for the purpose of generating 2D maps of the mechanical properties of viscoelastic materials. The OFPE instrument is based on an optical sensor that detects changes in polarization as a compressive force is applied to the sample. The setup and function of the device are described in detail. Chapter 4 outlines experiments performed on animal tissue to understand the mechanical behavior of biological tissue from different organs. The device has been used to test salmon skeletal muscle and a variety of porcine organs. Salmon skeletal muscle was used as a testbed to demonstrate the ability to detect sub-mm heterogeneity within 31 biomaterials. Building upon these results, five porcine organs were tested to demonstrate that different organs exhibit different mechanical properties. This same work demonstrates that the method of OFPE does not destroy the tissues during compressive testing. Finally, porcine cartilage was tested to demonstrate that biomaterials with stiffness three to four orders of magnitude larger could be tested. This same work demonstrates that OFPE can detect the biomechanical properties of three different types of cartilage within a joint. Chapter 5 outlines the experiments performed on human tissues to understand the mechanical behavior of cancer. The focus of this chapter is how the mechanical behavior of normal tissues compares to that of cancerous tissues. Chapter 6 outlines the work performed to develop 3D printed biomimetic structures and computational models to understand specific mechanical behaviors of tissues. Results from OFPE testing of porcine tissues were used to establish physiological parameters for the physical and computational models. After designing a core structure, these systems were iteratively changed to test the impact of specific geometries on the mechanical behaviors of biomaterials. Chapter 7 outlines the future work that will be performed to develop the OFPE system. This chapter focuses on the projects that are related to this thesis and will be continued by the Armani Research Group and our collaborators. These projects include: testing alternative mechanical methods, adding a calibration step into OFPE testing, clinical testing with the multi-fiber array, and expanding the 3D printed and computational models. 32 Chapter A1 outlines additional preliminary investigations that are ongoing with the OFPE system. Results from OFPE testing of porcine tissues for eight hours after resection are presented. Results from OFPE testing of porcine tissues before and after freezing are presented. These preliminary results indicate that the time since resection and storage method have a significant impact on the mechanical behaviors of tissue samples. Chapter A2 outlines a new optical device intelligently fabricated to decrease the threshold power needed to excite the optomechanical modes in whispering gallery mode resonators. Additionally, these asymmetric whispering gallery-mode resonators have previously unobserved optomechanical modes based on their geometry. As a result, these devices have the potential to be used in future sensing and optical computing systems because of their unique and controllable optomechanical mode structure. Chapter A3 outlines the development of a malaria diagnostic device. The instrument is a modified version of the OFPE device and demonstrates that the same platform can be slightly modified to address a much different disease. The instrument works by detecting changes in polarization within a blood sample as a magnetic field is applied to the sample. The change occurs due to the presence of hemozoin, a magnetic nanoparticle generated by malaria parasites. Due to the unique signature of infected blood, it can be used to diagnose malaria very accurately. Chapter A4 outlines new methods for single cell detection. Understanding and modeling the scattering of bacteria and cancer cells has proven to be challenging in the past because of the difference in membrane number, characteristic, and size. In order to be able to develop in-process single cell detectors for batch processing commonly used in 33 biomanufacturing, we developed a platform based on an array of Vertical Cavity Surface Emitting Lasers (VCSEL) to perform these measurements. Chapter A5 contains the Matlab codes used for data analysis. The Matlab code used to calculate the ΔPol for the loading and unloading curves is included. The four Matlab codes used to fit the loading and unloading curves to a Quasi-Linear Viscoelastic Model are also included. 34 1.3. References 1. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, "Label-free, single-molecule detection with optical microcavities," Science 317, 783-787 (2007). 2. H. K. Hunt, and A. M. Armani, "Label-free biological and chemical sensors," Nanoscale 2, 1544-1559 (2010). 3. T. J. Akl, M. A. Wilson, M. N. Ericson, and G. L. Cote, "Quantifying tissue mechanical properties using photoplethysmography," Biomed. Opt. Express 5, 2362- 2375 (2014). 4. K. M. Kennedy, C. Ford, B. F. Kennedy, M. B. Bush, and D. D. Sampson, "Analysis of mechanical contrast in optical coherence elastography," J. Biomed. Opt. 18, 12 (2013). 5. S. E. McBirney, K. Trinh, A. Wong-Beringer, and A. M. Armani, "Wavelength- normalized spectroscopic analysis of Staphylococcus aureus and Pseudomonas aeruginosa growth rates," Biomed. Opt. Express 7, 4034-4042 (2016). 6. T. H. Chua, and C.-L. Chen, "Fiber polarimetric stress sensors," Appl. Opt. 28, 3158-3165 (1989). 7. M. C. Harrison, and A. M. Armani, "Portable polarimetric fiber stress sensor system for visco-elastic and biomimetic material analysis," Applied Physics Letters 106, 191105 (2015). 8. R. C. Gauthier, and J. Dhliwayo, "Birefringent fibre-optic pressure sensor," Optics & Laser Technology 24, 139-143 (1992). 9. M. V. Apte, and J. S. Wilson, "Dangerous liaisons: Pancreatic stellate cells and pancreatic cancer cells," Journal of Gastroenterology and Hepatology 27, 69-74 (2012). 10. M. Erkan, S. Hausmann, C. W. Michalski, A. A. Fingerle, M. Dobritz, J. Kleeff, and H. Friess, "The role of stroma in pancreatic cancer: diagnostic and therapeutic implications," Nat Rev Gastroenterol Hepatol 9, 454-467 (2012). 11. P. Lu, V. M. Weaver, and Z. Werb, "The extracellular matrix: A dynamic niche in cancer progression," The Journal of Cell Biology 196, 395-406 (2012). 12. D. Öhlund, A. Handly-Santana, G. Biffi, E. Elyada, A. S. Almeida, M. Ponz- Sarvise, V. Corbo, T. E. Oni, S. A. Hearn, E. J. Lee, I. I. C. Chio, C.-I. Hwang, H. Tiriac, L. A. Baker, D. D. Engle, C. Feig, A. Kultti, M. Egeblad, D. T. Fearon, J. M. Crawford, H. Clevers, Y. Park, and D. A. Tuveson, "Distinct populations of inflammatory fibroblasts and myofibroblasts in pancreatic cancer," The Journal of Experimental Medicine 214, 579-596 (2017). 13. E. Bar-Kochba, M. T. Scimone, J. B. Estrada, and C. Franck, "Strain and rate- dependent neuronal injury in a 3D in vitro compression model of traumatic brain injury," Scientific Reports 6, 30550 (2016). 14. A. Chodobski, B. J. Zink, and J. Szmydynger-Chodobska, "Blood-brain barrier pathophysiology in traumatic brain injury," Translational stroke research 2, 492-516 (2011). 15. W. Zheng, Q. ZhuGe, M. Zhong, G. Chen, B. Shao, H. Wang, X. Mao, L. Xie, and K. Jin, "Neurogenesis in Adult Human Brain after Traumatic Brain Injury," J. Neurotrauma 30, 1872-1880 (2013). 35 16. M. Badea, M. Braic, A. Kiss, M. Moga, E. Pozna, I. Pana, and A. Vladescu, "Influence of Ag content on the antibacterial properties of SiC doped hydroxyapatite coatings," Ceram. Int. 42, 1801-1811 (2016). 17. Maxim E. Dokukin, Nataliia V. Guz, and I. Sokolov, "Quantitative Study of the Elastic Modulus of Loosely Attached Cells in AFM Indentation Experiments," Biophysical Journal 104, 2123-2131 (2013). 18. N. Guz, M. Dokukin, V. Kalaparthi, and I. Sokolov, "If Cell Mechanics Can Be Described by Elastic Modulus: Study of Different Models and Probes Used in Indentation Experiments," Biophysical Journal 107, 564-575 (2014). 19. M. Ayyildiz, S. Cinoglu, and C. Basdogan, "Effect of normal compression on the shear modulus of soft tissue in rheological measurements," J. Mech. Behav. Biomed. Mater. 49, 235-243 (2015). 20. E. L. Baker, J. Lu, D. Yu, R. T. Bonnecaze, and M. H. Zaman, "Cancer Cell Stiffness: Integrated Roles of Three-Dimensional Matrix Stiffness and Transforming Potential," Biophysical Journal 99, 2048-2057 (2010). 36 Background Chapter 2. This dissertation discusses a wide variety of topics, but specifically explores the methods used for developing and characterizing an optical sensor that uses photoelastically-induced polarization changes to determine the mechanical behavior of biomaterials. This method is called Optical Fiber Polarimetric Elastography (OFPE). The following section is a brief review of the fundamental background necessary for each of the projects outlined in this dissertation and serves to tie them together. Additional information regarding the specific impact and motivation of each project is included at the beginning of each chapter. 2.1. Sensor Theory Designing new optical sensors requires the synthesis of a multitude of complex variables and the development of novel detection methods. In developing novel instruments, the sensor parameter values can be described in terms of five key sensor metrics: (1) sensitivity, (2) specificity, (3) false positive/negative rate, (4) response time, and (5) signal to noise ratio. Based on these fundamental properties, sensors can be designed, built, and validated. Depending on the use of the sensor, the five metrics have different relative importance. Within our systems, we use photodiodes as detectors to record the optical signal. Therefore, the key metrics of the sensor are primarily tied to our photodiode and associated powermeter or polarimeter. 37 2.1.1 Sensitivity Sensitivity is generally defined as the minimum signal the sensor can detect or the minimum magnitude of input signal required to produce an output signal [1]. The sensitivity of photodiodes is the lowest detectable light level. While this is a useful metric, responsivity (or radiant sensitivity) of a photodiode is generally used when discussing photodiodes. Responsivity is the ratio of generated current to incident optical power. Therefore, the responsivity of a photodiode is represented by the following relationship [2]: 𝑅= ! !" ! (2-1) where 𝐼 !" is the generated photocurrent, and 𝑃 is the power of the incident light. Otherwise stated, the responsivity can be related to the quantum efficiency ( η) of the diode material itself and the frequency ( ν) of the incident light source [2]: 𝑅= !" ℏ! (2-2) where e is the fundamental electron charge, and ℏ is the reduced Plank constant. Additionally, sensitivity is dependent on the detection confidence and environment of the sensor. Detection confidence is the probability of detecting a signal when the signal-generating element is present and is impacted by external factors that can cause false positives/negatives [1]. For example, if elements that cause vibrations are on the same surface as the optical source or detector, the detection confidence decreases. This is because elements within the system are known to cause false positives/negatives. In validating the device, we measure the sensitivity and detection confidence under different conditions to determine the efficacy of the sensor in various environments. The 38 OFPE instrument is highly sensitive to changes in force during compressive testing of viscoelastic materials. 2.1.2 Specificity The specificity of the instrument is the probability of correct detection of the desired signal-generating element [1]. More simply, specificity is how well the sensor detects the desired element and not other components of the environment. As a result, specificity is dependent on the environment and on the sensitivity of the sensor. The specificity of the sensor is determined primarily by using statistics to fit the data obtained by the sensor. Within photodiodes, the detector characteristics are often known and depend upon the semiconductor used to fabricate the photodiode. The specificity of a photodiode is correlated to its ability to detect a specific wavelength of light or range of wavelengths and tends to follow Poissonian statistics [2]. Quantum dots have been used as highly specific photodiodes, though this method can only be used to detect lasers [3]. Therefore, photodiodes generally have low specificity to enable more flexible systems to be designed and developed. The OFPE instrument acts as force sensor that can measure slight variations in force applied to the sensor when a viscoelastic material is compressively tested. The sensor is not specific to one type of viscoelastic material, and as a result has low specificity. Therefore, the OFPE sensor is sensitive, but not specific. 39 2.1.3 False Positive/Negative Rate The false positive rate of the sensor is the number of times the sensor records a signal that is not due to the presence of the signal-generating element. Depending on the signal-generating element, there are different reasons a false positive may occur, including similar signal-generating elements, noise, poor specificity, or poor sensitivity [1]. The noise-level events are distinguished from significant events by determining specific detection/intensity levels for the sensor. For photodioides, these are generally reported by the manufacturer and depend on the material used to fabricate the photodiode. For the OFPE instrument, the primary source of false positives is different environmental factors such as vibrations of the system and alternative light sources. These factors cause a signal to be recorded by our photodiode that is not due to the compressive force applied to the viscoelastic material. Through trial and error, these factors were identified and removed from the testing environment. Within systems designed as medical diagnostic or prognostic devices, false positives are an important aspect of sensor design because frequently the output of the sensor is used to make medical decisions. Therefore, having positive results that are not true can lead to unnecessary follow-ups and treatment. Despite the fact that false positives are costly, often in medical devices false positives are preferential to false negatives. As a result, medical devices are designed to minimize false negatives. This design strategy increases the number of false positives. In such a case, it is important to validate the prevalence of false positives so that the end user has a more complete 40 understanding of the sensor and the assumptions made in its design because they impact its operation. 2.1.4 Response Time The response time of the sensor is the interval between a change in the signal generating element and the sensor detecting the change [1]. The response time is variable depending on the method of sensing and is generally limited by one of the components. For the OFPE instrument, the limitation is the rate at which the optical signal from the photodiode can be converted to an electrical signal and recorded by the computer. These are both intrinsic values that are known when components are purchased. When designing a sensor, it is important to align the intended use with the inherent temporal changes of the system. Within biological systems, response time is highly dependent on the scale of change in the signal-generating element. For example, if the signal is generated by compression of a tissue for biomechanical analysis the response time will be indicated by the strain rate and may only need to be updated on the millisecond scale [4-6]. However, if a single molecule in solution generates the signal the response time may need to be in femtoseconds to ensure that the molecule is detected when it is in solution [7]. 2.1.5 Signal to Noise Ratio The signal to noise ratio (SNR or S/N) is a metric used to describe the ratio of the desired signal to the background noise detected by a sensor. The signal to noise ratio is dependent on the sensing modality and the environment. Therefore, it directly impacts the 41 utility of the sensor and can limit the environments where it practically be used [7]. To combat this challenge, the sensor can be tested in different environmental conditions. This is a controlled way to understand the relationship between the noise, clutter, and signal within the unique sensor that has been built. For the OFPE instrument discussed in the following chapters, the SNR of the instrument was characterized at length in different environments to evaluate the robustness of the sensor system [8]. In order to determine the SNR, the sensor is set up in the laboratory and the signal is recorded without a sample or compression. After the data was analyzed, the noise distribution is evaluated and plotted it as a histogram. By fitting the noise distribution to a Gaussian function the noise threshold for each environment is determined. If a system has poor SNR, alternative methods such as filters can be used to process the data after it has been taken. If the noise is high frequency, a low pass filter can be used to mitigate its impact. If the noise is low frequency, a high pass filter can be used to mitigate its impact. While these are the most commonly used methods, there are other more complex filters that can be used depending on the system and noise profile. Within optics, the standard cut-off for noise filters is 3bB. Within biological systems, the SNR is important because it directly impacts the sensitivity and working range of the sensor [9-11]. Often biological samples are heterogeneous and complex, so validating the sensor in real biological materials is the best way to determine the correct SNR. 42 2.2 Optical Sensors Optical sensors use light as their primary operating mechanism. Optical sensors have a number of advantages when compared to chemical, electronic, or mechanical sensors including manufacturability, miniaturization, and accuracy [8, 12-14]. Specifically for biosensing, optics is a robust platform because devices can be constructed with small and adjustable sensing regions [15-17]. Within the subsequent chapters, the design and use of an optical sensor that uses photoelastically-induced polarization changes to determine the mechanical behaviors of biological tissues is discussed. Therefore, in the immediate sections to follow, the focus is on the fundamental properties of optics that enable this specific sensor to function. 2.2.1 Refractive Index All materials have a refractive index. The refractive index is a dimensionless number that describes how light propagates through a material. This metric is important in all optical sensors because it will impose physical limits onto the system. The refractive index (𝑛) describes the relationship between how fast light travels within the material as compared to within a vacuum [18]: 𝑛= ! ! (2-3) where 𝑐 is the speed of light in a vacuum and 𝑣 is the phase velocity of light in the medium. Due to the fact that the speed of light within a vacuum (3x10 8 ) has been well characterized, this relationship provides a reference for understanding how the optical properties of different materials compare. At 1550nm, the refractive index of several 43 commonly used and well characterized materials are water (n=1.33), silica (n=1.45), and silicon (n=3.48) [18]. If light travels from one medium to another, we can use Snell’s Law to describe the angles of incidence and refraction. Snell’s law is described as [18]: 𝑛 ! sin𝜃 ! =𝑛 ! sin𝜃 ! (2-4) where 𝑛 ! is the refractive index of the original material, 𝑛 ! is the refractive index of the new material, 𝜃 ! is the angle of incidence, and 𝜃 ! is the angle of refraction. Figure 2-1 depicts a schematic of Snell’s Law at the interface between two materials with different refractive indices. This phenomenon helps form the basis for the guiding of optical waves through materials, thus facilitating the fabrication of optical sensors. Figure 2-1: Schematic of Snell’s Law representing how the difference in refractive index in material one (𝑛 ! ) and the refractive index of material two (𝑛 ! ) impacts the angle of incidence (𝜃 ! ) and the angle of refraction 𝜃 ! . 44 2.2.2 Optical Waveguides There are several sub-classes of optical sensors depending on the path of the light between the source and the detector. One sub-class of optical sensors utilizes free-space optics. Within free-space optical instruments the path of light travels through air or vacuum. Therefore, elements must be aligned so that they receive the light in the correct orientation to pass it along to the next element while minimizing loss. Another sub-class of optical sensors utilizes fiber-optics. Within fiber optical instruments, the path of light travels through optical waveguides. While there are still junctions between the elements, the need for alignment can be minimized because the orientation of the light is known at both ends of an optical waveguide. For the purpose of this work, we focus on fiber-optics and optical waveguides. Initially, optical technology development focused on free-space components such as lenses, mirrors, and gratings [18]. However, these systems are large, expensive, and require frequent realignment. One solution to this challenge was to develop integrated systems such as optical waveguides [18]. A schematic of an optical waveguide is shown in Figure 2-2. A cladding with refractive index 𝑛 ! surrounds a fiber core (typically made from Silica) with a refractive index of 𝑛 ! . In order to guide the light, the refractive index of the cladding must be lower than the core because light is guided from low to high refractive indices. Due to the difference in the refractive indices of the two materials, the light remains confined within the waveguide. 45 Figure 2-2: Schematic representing total internal reflection in an optical waveguide. Within an optical waveguide if the light travels at a small enough angle it will remain within the core of the waveguide and propagate. The cladding and the core of the optical waveguide have different refractive indices (n 1 and n 2 respectively). Optical fibers are a subset of non-integrated optical waveguides that can be cheaply and quickly mass-produced. Optical fibers have therefore become the foundation of several families of optical devices because the path of the light can be easily controlled and the fibers can be disposed of periodically without significantly increasing the cost of the instrument. 2.2.2.1 Power Loss within Waveguides Optical loss is the decrease in power as light travels through an optical system and encounters different elements. Therefore, as the optical loss in the system decreases, the signal to noise ratio increases and in turn the sensitivity of the sensor increases [19]. There are a multitude of power loss mechanisms within optical waveguides due to both their intrinsic and extrinsic properties. The intrinsic loss mechanisms include: absorption loss, scattering, and bending loss. The extrinsic loss mechanisms include: coupling loss. The signal level of waveguides can be measured in absolute power and is typically presented in watts (W) or decibels (dB) for optical devices. Decibels are a relative unit of measurement defined as: 𝑑𝐵=−10log ! ! ! ! (2-5) where 𝑃 ! is a reference and 𝑃 ! is the power measured. If a reference of 𝑃 ! = 1𝑚𝑊 is used within the system and 𝑃 ! remains the power measured, then units are reported in dBm. Power loss within optical systems is generally measured in dB so that it is a relative measure independent of absolute power [18]. Additionally, dB is sometimes reported as 46 dB/(unit length) to indicate the distance over which the loss occurs for loss mechanisms that are distance dependent [18]. Absorption loss is a type of material loss that is due to the absorption of light by the material as it travels along the length of the waveguide. In general, materials with high refractive indices have high absorption loss, and materials with low refractive indices have low absorption loss [19]. Additionally, the absorption loss is wavelength dependent due to the different interactions between the material and the wavelength of light. For optical fibers, the absorption loss is typically low, and as a result, they are often used to send optical signals long distances [19]. Within waveguides, scattering loss is a type of material loss that occurs due to artifacts along the optical path that cause photons to scatter as they travel. Within fiber- optic sensors, if there are artifacts along the boundary between the core and cladding of optical waveguides (Figure 2-2) there can be scattering [18, 20]. In developing instruments with reusable and disposable optical fiber sensors, increases in scattering loss can be indicative of a need to replace the optical fiber. Experimentally, scattering can be visualized with a <1.5mW 633nm laser. By using a 633nm laser and turning the lights off, scattering in the fiber can be clearly identified. If there is significant scattering loss in the fiber, there will be regions where red light can be seen at different points. Bending loss is due to bends in waveguide that cause changes in the path that the light can follow [21]. One factor that impacts the bend loss is the bend radius. As the bend radius becomes smaller, the bending loss increases [18]. This is in part due to the fact that when the waveguide is curved, the optical field distribution is pushed toward the edge. As a result, there is increased scattering loss in the bent section. This can occur 47 experimentally when the polarizer or polarization maintaining optical fiber sensor becomes bent. If this occurs, the output of the sensor read by the polarimeter will be incorrect. Coupling loss is due to power loss at different junction points within an optical instrument. In order to have light propagate in a waveguide, it must be coupled into the waveguide at some point from a source, which will give the initial power. At any junction points within the path of light, coupling loss can occur between different elements. While this type of loss is common across all optical devices due to mode mismatches, it is more pronounced in polarization based optical devices. If there is mismatch between the fast and slow axis of the polarization maintaining elements, significant coupling loss will occur at these transition points [18, 22]. This is especially pronounced in the multi-fiber array discussed in Chapter 3. 2.2.3 Optical Polarization Polarization is a property of electromagnetic waves that occurs because the waves can oscillate between multiple orientations that are transverse to the direction of propagation [23]. By tracking changes in this fundamental property of light in response to external stimuli, highly specific and sensitive polarization-based optical sensors can be created. When choosing a light source, there are a variety of different characteristics to consider such as wavelength, phase, and polarization state. Lasers represent a coherent light source at a specific wavelength (λ). Lasers are usually linearly polarized, but can have other polarization states as well. Typically, the polarization of the laser emission is a 48 result of the gain medium being an anisotopic crystal (Nd:YAG, Ti:Sapphire, etc), giving rise to emission along a certain crystal plane, effectively polarizing the light linearly. There may still be a variety of polarization states due to the oscillations between different orientations of the light. These oscillations occur in pairs related to the electric (E) and magnetic (B) fields and the direction of propagation. An optical element called a polarizer can be used to eliminate the oscillations of the light, leaving only one electric field vector (Equation 2-6) and magnetic field vector (Equation 2-7) [18]. 𝐸 𝑧,𝑡 = 𝑒 ! 𝑒 ! 0 𝑒 !(!"!!") (2-6) 𝐵 𝑧,𝑡 = 𝑏 ! 𝑏 ! 0 𝑒 !(!"!!") (2-7) where 𝐸 is the electric field vector, 𝐵 is the magnetic field vector, 𝑧 is the propagation direction and 𝑡 is time. 𝑘 is the wave number and is represented by 𝑘= 2𝜋𝑛 𝜆. 𝜔 is the angular frequency and is represented by 𝜔= 2𝜋𝑓. The 𝐸 and 𝐵 vectors are perpendicular to each other and are both perpendicular to the direction of propagation (𝑧), as shown in Figure 2-3. Due to this highly specific configuration of light, small changes in the polarization state can be recorded in response to external stimuli. As a result, highly sensitive optical sensors can be developed based on optical polarization [8, 24-26]. 49 Figure 2-3: A polarized electromagnetic wave depicting the single orientation in the E and B fields of coherent polarized light. The E and B field are perpendicular and dependent on the direction of propagation, z. The wavelength of the light is labeled by λ. 2.2.4 Optical Birefringence Optical birefringence or optical anisotropy is a property of optical materials where there are different refractive indices along different axes of an optical fiber (Figure 2-4). This means that the effective refractive index of the fiber depends on the polarization state and the propagation direction of the light. Birefingent optical materials can be uniaxial (three axes with two different refractive indices) or biaxial (three axes with three different refractive indices). Birefringence can be created either by the crystal structure of the material or by internal stresses within the material. In polarization maintaining fiber, the initial polarization state of the light as it enters the fiber is maintained along the length of the waveguide. 50 Figure 2-4: Schematic of unpolarized light passing through a birefringent material (blue). The parallel (pink and black dots) and perpendicular (blue arrows) polarizations see different refractive indices and the light is refracted at two different angles. In polarization maintaining waveguides, the optical wave will experience the refractive index along the axis aligned with the polarization. If the polarization is aligned between two axes, the different components of the optical wave will split and experience their respective refractive index. Within polarization maintaining optical fibers, the birefringence is uniaxial. The birefingent axes are referred to as the fast and slow axes of the fiber [8, 18, 22]. The fast axis has the lower refractive index and the slow axis has the higher refractive index. The relationship between these two axes is called the beat length. The beat length is the distance between instances when the phase relation between the waves returns to an integer value of the initial linearly polarized light [8, 22, 23, 27]. Similar to other waveguides, polarization waveguides have been adapted into polarization maintaining optical fibers to increase their translatability. A polarization maintaining optical fiber comes in a variety of geometries, but at its core is a fiber with a strong built-in birefringence. Because the polarization state can be controlled without time consuming and difficult alignment steps, fiber based systems are ideal for devices that will be used by individuals with a wide range of skill levels who may not be adept at free space alignment of optical components. 51 2.2.5 Photoelastically-induced Polarization Detection The photoelastic effect is an indirect change in the refractive index of a material in response to external stimuli [22, 27]. One use for this inherent property of optical waveguides is to develop systems for photoelastic detection. A variant of photoelastic detection is photoelastically-induced polarization detection. In this approach, the change in the refractive index induces a change in the polarization state of the optical field. This change can be recorded by a polarimeter and used to develop and optical sensor [4, 8, 22, 28-31]. The theory behind photoelastic-induced polarization detection is that the change in the refractive index along one axis induces a change in the polarization state of the optical field. As a result, the beat length of the fiber changes as birefringence changes, causing the polarization vector to undergo a rotation, Φ. Fundamental work to translate change in beat length within an optical fiber to stress was performed by Chua et al [22]. In order to develop a sensor based on photoelastically-induced polarization detection, we develop a method for determining the change in polarization (ΔPol). In order to measure the ΔPol during compression, the phase 𝜙 (π radians) is calculated from the Stokes parameters measured by the polarimeter. When stress is applied to the polarization maintaining fiber, the polarization state changes according to the photoelastic effect. The polarization state is defined by the Stokes parameters <s 1 , s 2 , s 3 > recorded by the polarimeter. The Stokes parameters trace a line on the Poincaré sphere as they change Figure 2-5. The trace has two relevant features: (1) the line will always be circular, and (2) it will always be centered on the equator of the Poincaré sphere due to the initial linear polarization. 52 Figure 2-5: Visual representation of the loading and unloading cycle of one compressive test by graphing the circle trace of the three Stokes parameters <s 1 , s 2 , s 3 > on a unit sphere. From the Stoke’s parameters, the ΔPol can be determined by solving for a series of intermediate variables. In order to analyze the results, two variables need to be solved for through a series of transfer matrices: 𝛽 and 𝛾. 𝛽 is the angle of offset between the polarization state as aligned and the fast and slow axis of the fiber. Thus, 𝛽 is an experimental variable that can be minimized when setting up the device. 𝛾 is the angle of offset between the alignment of the fiber coupled into the polarimeter and the fast and slow axis of the fiber. 𝛽 and 𝛾 are related to 𝜙 through the series of transfer matrices [8]: 𝐸 ! 𝐸 ! = cos𝛾 sin𝛾 −sin𝛾 cos𝛾 1 0 0 𝑒 !" cos𝜙 −sin𝜙 sin𝜙 cos𝜙 𝑒 !!"! ! ! 0 0 𝑒 !!"! ! ! cos𝜙 sin𝜙 −sin𝜙 cos𝜙 ∗ cos𝛽 sin𝛽 −sin𝛽 cos𝛽 𝐸 !! 0 (2-8) where 𝐸 !! is the initial state of polarization. 𝐸 ! and 𝐸 ! are the x and y components of the electric field at the polarimeter. The length of the section under compression is represented by l. The phase experienced within the fiber before and after the sensing region of fiber is included in δ. The modified fast and slow axes of the fiber are N f and 53 N s . The modified fast and slow axes of the fiber are related to the stressed beat length (L b ) by the relationship: N s -N f =2π/kL b . Therefore, the transfer matrices can be used to solve for 𝛽 and 𝛾. Additional details on these calculations are published in previous works on optical fiber polarimetry [8, 22, 32, 33]. Using the photoelastic effect as a detection mechanism has advantages and disadvantages over a direct refractive index approach traditionally used for optical biosensors [4, 7, 22, 27]. Because the optical field does not directly interact with the sample, the transmitted power is more stable, the optical loss is independent of the environment, and the sensor is less susceptible to degradation. Because this approach is less susceptible to noise, it offers an improvement in overall detection sensitivity. Based on these advantages, this method was originally used to develop pressure sensors for failure modeling of large mechanical components [30]. One common use for photoelastically-induced polarization detection systems is as high-resolution stress sensors [22]. These optical systems can conduct non- destructive materials characterization methods and complex material analysis on heterogeneous natural and manmade composite materials [4, 8, 22, 28, 29, 31]. Due to the lack of established methods for studying biomaterials, this optical method has the potential to provide a variety of insights to the changes in biomaterials in response to different mechanical loads. The OFPE instrument detects changes in polarization in response to compressive testing of a viscoelastic biomaterial using a polarimeter. Figure 2-6 is a schematic of the optical path of the OFPE instrument. A coherent light source with a single polarization state is used to carefully control the light input into the system. A polarizer is then used to 54 ensure only a single known polarization state enters the sensing region. Based on the angle of offset of the polarization between the initial polarization and the final polarization of the sensing region, the change in polarization as a result of applying a force can be determined. Figure 2-6: Schematic of an optical path within an optical polarimetry sensor setup as light travels through the system. 2.3 Mechanical Characterization of Viscoelastic Materials 2.3.1 Viscoelastic Materials Viscoelastic materials are characterized as having both a viscous and an elastic regime. Viscoelastic materials exhibit hysteretic behavior, time-dependent, rate- dependent, strain-dependent, and temperature-dependent mechanical behaviors. There are a variety of organic and synthetic materials that fall within the category of viscoelastic materials including biomaterials, metals at high temperatures, and amorphous polymers 55 [34-36]. Viscoelastic materials are one of the largest and most complex families of materials and have been characterized and modeled in detail [34-40]. Due to the wide variety in characteristics exhibited by this large class of materials, a multitude of methods have been developed for their characterization. Traditional methods for viscoelastic material analysis include load frames, rheometery, and atomic force microscopy [38, 40-47]. Load frames are a method of mechanical testing where both compressive and tensile tests can be performed with the same instrument [40-42]. Due to its versatility, this platform is commonly used for mechanical testing of viscoelastic materials. Rheometry is a method where the primary goal of the measurements is to capture the shear and extension responses of viscous materials [38, 43, 44]. Therefore, rheometry is often conducted as a complementary analysis to better understand the viscous regime of a material. Atomic Force Microscopy (AFM) is a method where a nanometer probe is used to compressively test materials [41, 45-47]. Therefore, AFM is the highest resolution method of mechanical testing. 2.3.2 Biomaterials Biomaterials are a sub-class of viscoelastic materials, which are notoriously complex to characterize [36]. In addition to exhibiting the traditional viscoelastic material behaviors, biomaterials are also heterogeneous, compressible, and anisotropic [4, 28, 29, 31, 36]. Furthermore, the stiffness of biomaterials spans nine orders of magnitude [48]. Bone is the stiffest biomaterial, with a Young’s Modulus of 15GPa, and brain tissue is the softest biomaterial, with a Young’s Modulus of 50Pa. One advantage of characterizing the mechanical behavior of biomaterials is that the mechanical behaviors of biomaterials 56 can be directly correlated to certain physiological properties of the organ. In fact, in many chronic and acute diseases, it has been demonstrated that the biomechanical behavior of tissues change [49-51]. Therefore, determining the mechanical characteristics of biomaterials is an underutilized mechanism for determining the severity of disease and further understanding disease development over time. Advances in medical device technologies that focus on identifying the mechanical behavior of biomaterials have applications in therapeutic, diagnostic, and prognostic medical devices. However, measuring the mechanical properties of unprocessed biomaterials is significantly more complex than characterizing synthetic polymers and composites. The four main requirements for instrumentation to characterize biomaterials are that the system (1) has sub-mm resolution, (2) is non-destructive, (3) is portable, and (4) can be modular. First, due to the heterogeneity of biomaterials, sub-mm resolution is needed to capture the changes known to occur between normal and diseased tissues [49- 51]. Second, the mechanical testing method must be non-destructive so subsequent analysis can be run on the same biomaterial sample. Third, mechanical testing of biomaterials is conducted in sterile spaces so the instrument must be portable enough to be assembled and decontaminated in operating rooms and BLS2+ environments. Fourth, because the stiffness of biomaterials falls within a range of six orders of magnitude, methods need to be modular. This gives the user flexibility in determining the experimental parameters. Traditional methods for viscoelastic material analysis are unable to accurately capture the heterogeneity of biomaterials because they are designed to capture the mechanical behavior of materials with a known and repeated microarchitecture [40, 52- 57 54]. However, biomaterials are highly variable in their structure due to their complex functions. Therefore, each existing system is limited in its ability to appropriately characterize biomaterials by its resolution. Load frames are limited by their centimeter scale sensor area and cannot fully capture the complexity of biomaterials [55-57]. Rheometers experience the same limitations as they also have centimeter scale sensors [52, 58, 59]. Atomic force microscopy has the opposite issue. The nanometer scale sensor can only capture limited regions of the material, making it too small to capture the mechanics of the biomaterial comprehensively [60-62]. Alternative methods have been developed to address the issues in characterizing biomaterials including ultrasound sonoelastography and imaging [63-72]. Ultrasound sonoelastography is a clinical method where the relative stiffness of tissues can be compared using compression paired with ultrasound [70-72]. However, this method is not quantitative and has millimeter resolution. The three most commonly used imaging methods include immunohistochemistry, second harmonic generation imaging, and confocal microscopy [63-69]. Immunohistochemistry (IHC) is a form of imaging the enables specific biomarkers indicative of stiffness to be selected and imaged [63-65]. Second harmonic generation imaging (SHG) is a method where incident light is converted to second harmonic light through the non-linearity of the material. SHG can be used to resolve ECM structure within biomaterials because of the non-linear optical properties of collagen [64, 65, 69]. For both IHC and SHG, the images can only be taken along one 2D plane. Confocal imaging has been used to capture 3D images of the structure of different biomaterials on the mm scale with µm resolution [66-68]. For all imaging methods of mechanical characterization, the biomaterial samples must undergo 58 significant processing, staining, and fixing with additional reagents, which impact the structure of the material. Additionally, for all imaging techniques the results are static, so there is no way to measure the mechanical response of the structures in real time. 2.3.3 Mechanical Testing While OFPE can measure the mechanical response to external forces, another part of the system must provide a mechanical stimuli to the sample for the sensor to record. Therefore, in order to determine the dynamic response of biomaterials, the sample must be exposed to a load. There are a variety of different methods that are used for mechanical testing of materials including compressive testing, tensile testing, and shear testing [36, 38, 40-47, 73]. The vast majority of the testing conducted with the OFPE instrument on biomaterials has been based on compressive testing. This decision was made in order to minimize the preparation needed before testing and to minimize the damage to samples [4]. The mechanical testing used during OFPE testing of the samples is conducted by compressing the sample to a specific point at a constant rate and then returning to the initial point. This type of compressive testing is sometimes referred to as triangle wave compression testing [36]. Regardless of the method used to characterize the mechanical behavior of a biomaterial, the stress is recorded in response to a given strain (Figure 2-7). Strain (ε) is the measurement of the change in height as a result of the compression, divided by the original height of the sample (Δh/h 0 ). Stress (σ) is the force that the particles within the material exert on each other in response to the strain (𝜎=𝐹 𝐴). One commonly used 59 metric for determining the mechanical behavior of a material is the Young’s Modulus, which is the relationship between the stress and the strain at a single point: E= σ(ε)/ε. Figure 2-7: Graphical representation of a loading and unloading curve generated by a representative biomaterial using a triangle method of compressive testing. The loading curve is the response of the material due to the initial load. The unloading curve is the response of the material to the load being removed. The loading and unloading curves shown demonstrate hysteresis, characteristic of viscoelastic materials. Within the OFPE instrument, the user determines the strain applied by the compressive stage. The user can control the displacement and the rate by programing a motorized microactuator. The applied strain is modified by increasing the maximum displacement (Δh) and the strain rate (Δh/time). 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However, measuring the mechanical properties of unprocessed biomaterials is significantly more complex than characterizing synthetic polymers and composites. The three main requirements for instrumentation to characterize biomaterials are that the system (1) has sub-mm resolution, (2) is non- destructive, (3) is portable, and (3) is modular [1-3, 9]. To address the shortcomings of existing methods, we developed Optical Fiber Polarimetric Elastography (OFPE). OFPE is a non-destructive optical method of determining the mechanical properties of biomaterials. Chapter 3 summarizes the work done in collaboration with Mark Harrison (group member who defended in 2015) to develop an OFPE instrument to measure the biomechanical behavior of viscoelastic materials. Details regarding the original device used for viscoelastic material testing were published in 2015 [10]. The viscoelastic materials previously tested with this method had Young’s Modulus values of approximately 5 MPa [10]. While this falls within the range of Young’s Modulus values for biomaterials, 50 Pa – 5 GPa, the majority of soft tissues fall between 50-15,000 Pa [4, 11-13]. The primary interest in developing this device is to study diseases that impact the soft tissues within the body. Thus, significant modifications were made to the instrument 66 to ensure the working range extended down to 50 Pa [9, 14]. In this chapter, we elaborate on the design and validation of the OFPE instrument for testing biomaterials. 3.2 OFPE Instrument Configurations There are two primary configurations of the OFPE instrument developed and tested. The first configuration of the OFPE instrument is comprised of a single optical fiber sensor. This configuration of the instrument is useful for taking single point measurements in biomaterials. This configuration is used for the majority of data obtained with the OFPE instrument to date. The second configuration of the OFPE instrument is comprised of multiple optical fiber sensors. This configuration of the instrument is useful for taking multiple measurements within a single biomaterial sample with significant heterogeneity due to physiological function or potential disease. 3.2.1 Single Fiber OFPE Instrument Setup The OFPE instrument is initially developed with a single optical fiber sensor for point measurements to determine the mechanical behavior of viscoelastic materials. The OFPE instrument is comprised of several elements: (1) the compressive stage, (2) the optical fiber sensor, (3) laser, (4) polarizer, and (5) polarimeter. Adapters are used to connect the different components. A rendering of the OFPE system with several key components labeled is depicted in Figure 3-1. 67 Figure 3-1: Rendering of the single fiber configuration of the OFPE instrument setup for testing including all of the components of both the compressive stage (micrometer controlled) and the optical fiber sensor. The disposable optical fiber sensing region is the portion of the optical fiber between the bare fiber adapters. 3.2.1.1 Compressive Stage The compressive stage is created from a linear stage, a linear actuator, and a custom-built plunger (Figure 3-1). The custom-built aluminum plunger is mounted on the linear stage (Newport, M-SDS25). The plunger used in the present work is 25mm x 25mm. The linear stage and plunger are then connected to motorized micrometer (Newport, TRB25CC), which can be programed by a computer. The micrometer is programed using the software provided by Newport. The viscoelastic material sample is placed on the optical fiber sensor, between the baseplate and the plunger for mechanical testing. Additional designs and materials for the plunger were also investigated as part of this work, including a glass plunger. While the glass plunger did offer the ability to 68 visualize the compression as it was occurring, monitoring the degree of sample deformation, it also was not a flat or parallel to the baseplate. Thus, the force applied was not as uniform. The mechanical testing used during OFPE testing of the samples is conducted by compressing the sample to a specific point at a constant rate and then returning to the initial point. This type of compressive testing is sometimes referred to as triangle wave compression testing [15]. The total loading interval is 15 seconds, and the unloading interval is 15 seconds, for a 30 second total interval. To determine the strain (Δh/h) and the strain rate (Δh/time), first the initial height of the sample is measured. Then, the desired strain is multiplied by the height to give Δh for the strain. By dividing Δh by 15 seconds, the strain rate can be determined. For a 5mm sample, the experimental Δh values are 0.5, 1.0 and 1.5mm, and the experimental strain rates are 0.033, 0.067, and 0.1mm/sec. By integrating a force sensor, the strain rate could be converted to a force. In the work published by Harrison an Instron Loadframe was used as a force sensor for converting the strain rate to force [10]. However, the Instron Loadframe cannot be used within a biosafety hood. Therefore, additional work integrating an alternative force sensor either to the surface of the plunger or to the baseplate was explored. Example force sensors studied were Interlink Electronics 30-49649 and Interlink Electronics 34- 00004. However, these sensors were unable to accurately capture the force applied. The primary challenge with these flexible sensors was that when placed in contact with tissues the components of the sensor would delaminate. In turn, this caused the electronic elements of the sensor to corrode and no longer record accurate force measurements. A 69 secondary issue was maintaining uniform contact on the tissues during the unloading measurement. Often, the force sensor would stick to the tissue sample, resulting in jumps in the force measurements. As a result, these sensors rarely recorded smooth unloading curves. 3.2.1.2 Optical Fiber Sensor The optical fiber sensor is comprised of a laser, a polarizer, a disposable optical fiber, and a polarimeter (Figure 3-1). The light source of the optical sensing region is a 2mW 1550nm laser (Thor Labs, MCLS1) connected to an inline polarizer (Thor Labs, ILP1550PM-APC). To detect the polarization state after the compression, the output of the optical fiber sensing region is connected to a polarimeter (Thor Labs, PAX5710IR3- T). A polarization maintaining optical fiber (Newport, F-SPS) is located under the sample to create the sensing region. The mode field of the fiber is 6.6 µm. Thus, the diameter of the sensing element is on the micron scale. An image of the instrument, specifically the sensing region, taken during compressive testing of a porcine cartilage sample is depicted in Figure 3-2. While only the length of the fiber that is directly interacting with the sample will impact the signal generated, the residual length on either side can influence the signal in other ways, namely increasing the noise due to movement. As a result, the sensitivity of detection which is related to the SNR will change. There are two ways to combat this: use the minimum length of fiber needed and fix the fiber to the sample stage. As can be seen in the figure, the adaptors are taped to the stage. 70 Figure 3-2: Image of the single fiber configuration of the OFPE instrument during compressive testing of a porcine cartilage sample. The polarimeter is selected as the detector for the single fiber OFPE instrument configuration because it’s integrated polarizer, photodiode, and powermeter decrease the knowledge of optics that an operator must have in order to use the device. The polarimeter records the three Stokes parameters and a time stamp. The Stokes parameters are subsequently converted to phase angle (𝜙) in Matlab as described in Chapter 2. Based on the intrinsic sampling rate of the polarimeter, data is taken every 30 milliseconds. For our measurements, data is recorded over a 30 second interval for a total of 1024 data points per loading and unloading curve. An image of the instrument during testing is depicted in Figure 3-2. The light source selected for the single fiber OFPE instrument configuration is a 2mW 1550nm. We tested the system with several lasers in our lab with powers ranging from 0.5mW to 10mW. The 2mW laser is chosen because it is inexpensive, portable, and 71 provides sufficient optical power to have a good SNR and limit false negatives/positives. This is in part due to the fact that the polarimeter can detect changes in polarization between -60dBm and 10dBm. 3.2.1.3 Example Data Set An example loading and unloading curve generated from compressive testing of a sample of porcine kidney with the single fiber configuration is shown in Figure 3-3. Subsequent data analysis can be performed on the loading and unloading curves to correlate the results from our compressive testing to the mechanical behaviors of the sample. Further details on the data analysis methods are provided later in this chapter. Further data analysis and more results from the single fiber OFPE configuration are presented in Chapters 4, 5, 6, and A1. Figure 3-3: Example loading and unloading curve generated with the single fiber configuration of the OFPE instrument. Data set from compression testing of a porcine kidney sample at 30% strain. 3.2.2 Multi-Fiber OFPE Instrument Setup The OFPE instrument is modified to include multiple optical fiber sensors to generate 2D maps that better characterize the mechanical behavior of heterogeneous 72 viscoelastic materials. The multi-fiber configuration of the OFPE instrument is shown in Figure 3-4. It is similar to the single fiber system with the exceptions that the single fiber is replaced with a splitter, fiber array, and MEMs switch and that the polarimeter is replaced with a polarizer and powermeter for detection. In the initial tests, the fiber array was comprised of four fibers. The goal of this configuration is to determine the mechanical behavior of a section of a material at multiple points within close proximity. By taking multiple measurements within a sample, eventually a 2D map of the mechanical behavior of a sample will be able to be generated. Additionally, by replacing the polarimeter with an alternative detection method (polarizer/photodiode/powermeter), we increase our sampling rate by an order of magnitude. This change enables greater flexibility in the type of compressive testing that can be performed with the OFPE instrument. Figure 3-4: Rendering of the multi fiber configuration of the OFPE instrument setup for testing including all of the components of both the compressive stage and the optical fiber sensor. The disposable optical sensing region is the portion of the optical fiber between the splitter and the MEMS switch. 73 3.2.2.1 Compressive Stage All elements of the compressive stage component of the multi-fiber system are identical to the single fiber system. The reader is referred to the previous section for details on the design and components of the compressive stage. 3.2.2.2 Optical Fiber Sensor Array The optical fiber sensor array is comprised of a laser, a polarizer, a disposable optical fiber, a second polarizer, a MEMs switch, a photodetector, and a power meter (Figure 3-4). Polarization maintaining optical fibers (Newport, F-SPS) are located under the sample to create the sensing region. The light source of the optical sensing region is a 15mW 1550nm laser (Agilent, 81940A) connected to an inline polarizer (Thor Labs, ILP1550PM-APC). The output from the polarizer is split into four channels using a polarization maintaining splitter (OZ Optics, PLCS-14-8/125-P-1550-25-50-3S-1-1). Four optical fiber sensing regions are created with sections of polarization maintaining optical fiber (Newport, F-SPS). The channels are recombined after the sensing region using a MEMS switch (DiCON, MLC-1X4-TTL-15-PMS-2B-FC/PC-1), which is programed by a DAQ (NI, DAQ USB 6008). To detect the polarization state after the compression, the output of the optical fiber sensing region is connected to a second inline polarizer (Thor Labs, ILP1550PM-APC) and a photodetector (Thor Labs, S154C). The power is measured by the powermeter (Thor Labs, PM100USB) and recorded on a laptop. An image of the instrument, specifically the sensing region, taking during compressive testing of a porcine cartilage sample is depicted in Figure 3-5. 74 Figure 3-5: Image of the multi-fiber configuration of the OFPE instrument during compressive testing of a human pancreatic cancer sample. The diameter of the optical fibers is 375µm. A 3D printed fiber array holder (similar to a guitar nut) is used to control the spacing between the fibers (Figure 3-6). Because there are more notches in the array holder than fibers, the user can adjust the spacing according to the sample being tested. Several methods were tested to fabricate the array of optical fibers. The original method for fabricating the array was to encapsulate the fibers in thermoresponsive polymer sheets (i.e. FEP, Acetal, and PEEK films) or a curable liquid polymer (i.e. PDMS). For this method of array fabrication, the fibers were aligned before they were encapsulated in the polymer. During fabrication, at least one optical fiber would become misaligned. As a result, the arrays fabricated with this method were often fabricated with six to eight optical fibers even though only four would be used during testing. This method was abandoned because in the fiber arrays fabricated with this method the optical fibers recorded the same force, rather than four distinct forces. This was due to the fact 75 that the polymer acted to distribute the force along the optical fibers. To address this issue, we developed the 3D printed fiber array holder. This method prevents the optical fibers from moving while ensuring they have the ability to sense independently (Figure 3- 6). Additionally, this method enables the alignment to be modified during testing, which is a significant advantage over past methods. Figure 3-6: (a) Rendering of the 3D printed fiber array holder. The entire part is 15mm x 25mm x 10mm (w x l x h). The notches for holding the fibers are 500µm wide. The spacing between the notches is 1mm. (b) Image of the 3D printed fiber array holder. The light source is a 15mW 1550nm laser. The power is increased from the single fiber configuration because the multi-fiber configuration has higher optical loss and splits the power between four fibers. The increase in loss is due to the addition of several polarization maintaining optical components (splitter, MEMS switch, and polarizer). We tested the system with several lasers in our lab with variable powers. This is the only laser with sufficient input power to generate a sufficient signal with the modified detection system. A polarization maintaining power splitter is incorporated between the polarizer and the input of the optical fiber sensing region. This method is used because it is a more cost effective solution than incorporating a single mode splitter and four polarizers. The polarimeter from the single fiber configuration of the instrument is replaced with a second polarizer, photodiode, and a powermeter in this configuration. This change 76 is necessary because the sampling rate of the polarizer is not high enough to reconstruct the loading and unloading curves of multiple fibers. The powermeter records the change in power recorded by the photodiode every 3 miliseconds over a variable time interval. This represents an order of magnitude improvement in the sampling rate. Additionally, this changes the output of the OFPE sensor from the Stokes parameters to power. With the introduction of the MEMS switch the data recorded by the powermeter represents the output of all four optical fibers. Therefore, the data must be parsed. In order to parse the data a “dip” is added by turning off the MEMS switch every time the MEMS switch changes input fiber. This enables the data to be parsed into a data set for each optical fiber in python. After parsing the data, a low pass filter is applied to remove data points that were taken when the MEMS switch was between optical fibers. The resulting data points are used to generate a loading and unloading curve for each fiber over the time interval of interest. An example of the raw data (Figure 3-6a) and the parsed data (Figure 3-6b) are included. There are several limitations to the multi-fiber OFPE configuration. First, the mode field of the fiber (6.6 µm) determines the size of the sensor. However, the fiber itself has a 125µm cladding and a 245µm coating. Therefore, the total thickness of the fiber is 375µm. The thickness of the fiber limits the spacing of the optical fibers within the array. If closer spacing of the optical fibers is needed, alternative optical fibers or fabrication methods for the array will have to be used. Second, this configuration is currently limited to four optical fibers due to limitations in manufacturing of the optical MEMS switch component. Alternative fabrications methods to address the current limitations are actively under investigation. 77 3.2.2.3 Example Data Set In the multi-fiber configuration of the OFPE instrument, the powermeter records the power every 3 milliseconds as the MEMS switch cycles between fibers. As a result, the raw data of the sensor is difficult to interpret (Figure 3-6a). Using a parsing code, written in python, the data is parsed by identifying the artificial dips programed into the MEMS switch. To remove data points between optical fibers or the off configuration a low pass filter is applied. The parsed data is then plotted and separated into unique .csv files (Figure 3-6b). Figure 3-7: Example of the (a) raw data and (b) parsed data recorded by the polarizer/photodiode/powermeter system implemented to replace the polarizer. This data was recorded during compression testing of a salmon skeletal muscle at 30% strain. An example loading and unloading curve generated from compressive testing of a sample of salmon skeletal muscle with the multi-fiber configuration is shown in Figure 3- 8. Subsequent data analysis can be performed on the loading and unloading curves to correlate the results from our compressive testing to the mechanical behaviors of the sample. Further details on the data analysis methods are provided later in this chapter. 78 Figure 3-8: Example loading and unloading curve generated with the multi-fiber configuration of the OFPE instrument. Loading and unloading curves from: (a) fiber one, (b) fiber two, (c) fiber three, and (d) fiber four. Data set from compression testing of a salmon skeletal muscle sample at 30% strain. 3.3 Data Analysis Throughout the design, validation, and testing of different biomaterials with the OFPE instrument, several methods of data analysis are used to determine the mechanical behavior of biomaterials. 3.3.1 Loading-Unloading Curves Once the relationship between the Stokes parameters and the phase has been established for a given instrument configuration, as described in Chapter 2, the ΔPol can be determined. The ΔPol is simply the difference between the initial polarization state and the polarization at that point in time. Based on the photoelastically-induced 79 polarization effect, the ΔPol is directly proportional to the stress. Therefore, the ΔPol is plotted vs. strain to generate loading and unloading curves that represent the mechanical behavior of the sample. 3.3.2 Normalizing Loading-Unloading Curves One feature of the loading and unloading curves generated using the OFPE method is that the initial polarization state of the light is not always the same. This difference can make it difficult to compare multiple runs of the same experimental conditions. Therefore, the loading and unloading curves are all normalized to begin at (0,0). Because ΔPol is not an absolute value, and the same shift is applied to all data points in the curve, the normalization does not change the data. The normalization simply serves to align the data so it can be more easily compared. 3.3.3 Maximum Phase Difference One approach used to quantify the stiffness of different biomaterials based on the loading and unloading curves is to determine the maximum phase difference (Figure 3-9). The maximum phase difference was calculated by determining difference between the initial polarization and the final polarization of the loading or unloading curve. Thus, the total change in the polarization upon compression of the sample can be evaluated. The biomaterials community commonly uses this strategy for analyzing an absolute signal change [16]. However, for viscoelastic materials the error in the maximum phase difference can be large because it simply compares two points in the loading or unloading curve. Viscoelastic materials exhibit hysteresis, strain dependence, and rate dependence 80 at different points within the loading and unloading curves. This information becomes lost when maximum phase difference is used as a comparative metric. Figure 3-9: Graphical representation of a loading and unloading curve with the maximum phase difference highlighted. The y-axis is labeled as both stress and ΔPol because the stress is proportional to the ΔPol due to the photoelastic effect. 3.3.4 Energy Loss One approach used to quantify the stiffness of different biomaterials based on the loading and unloading curves is to determine the energy loss of the material due to the compression. The energy loss is determined by finding the area between the loading and unloading curves. This value is typically calculated using the following expression where U is energy, σ is stress, and ε is strain [15]: (3-1) Hysteresis between the loading and unloading curve is indicative of the energy loss to or absorbed by the sample during the entire loading and unloading interval (Figure 3-10). To determine the relative energy loss to the sample, the fact that phase is proportional to stress (σ) is used. 00 loading unloading Ud d εε σε σ ε = − ∫∫ 81 Figure 3-10: Graphical representation of a loading and unloading curve with the energy loss shaded in blue. A value proportional to the energy loss can be calculated by taking the area between the two curves because the stress is proportional to the ΔPol photoelastic effect. 3.4 Sample Preparation Different biomaterials have different stiffness and thicknesses depending on their function within the organism. For OFPE, the only requirement is that the samples must be flat on both the top and bottom to ensure the compression is evenly distributed throughout the sample. If this condition is not met, the sensor will convolve multiple values and give a single output, and the measurement will not be accurate. Examples of tissue section parameters used for testing of several different biomaterials are depicted in Figure 3-11. These small sections are generally cut from larger regions of tissue resected from organs. In animal models the sections are usually around 10mm x 10mm x 10mm. These larger tissues are stored in cell culture media (RPMI) on ice until testing. Tissues are all tested within two hours of resection before the onset of rigor mortis [17]. This timeframe and storage method were determined based on a systematic study. The details of this study are presented in Chapter A1. 82 Depending on the region of the tissue it can be difficult to get a piece of tissue with two flat sides. Through training of multiple new users, it has become clear that sample preparation is one of the hardest skills for new users of the OFPE instrument. Figure 3-11: Rendering of the different types of tissue samples cut from multiple biomaterial types for OFPE testing: (a) salmon skeletal muscle – 9 mm × 9 mm × 5 mm (l×w×h), (b) porcine pancreatic tissue – 7 mm × 7 mm × 4 mm (l×w×h), and (c) porcine cartilage tissue – 7 mm × 7 mm × 4 mm (l×w×h) The interaction length (l) between the sample and the optical fiber sensor impacts the signal that can be recorded by the OFPE instrument. This is due to the fact that the interaction length directly impacts the force transferred from the fiber to the sample. Therefore, the ΔPol recorded by the polarimeter changes as a result of l. For this reason, when testing using the OFPE instrument, the l for samples that will be directly compared is held constant. Figure 3-12 summarizes the results from changing the l in salmon skeletal muscle testing. The dependence of the signal on l is determined by compressive loading of 10%, 20%, and 30% strain within a uniform sample of salmon skeletal muscle. Three different values of l were investigated: 20mm, 10mm, and 5mm. The expected linear relationship as a function of sample length is observed. 83 Figure 3-12: Analysis of the impact of the interaction length on the loading and unloading curves for a sample of uniform salmon skeletal muscle. (a) Loading and unloading curves for a uniform salmon sample of salmon with an interaction length of 5mm, 10mm and 20mm. (b) Analysis of the phase difference for three different interaction lengths at the three different strain rates. (c) Analysis of the energy loss for the three different interaction lengths at the three different strain rates. Another consideration when preparing the viscoelastic material samples is that some materials have directionality. For example, it is well established that the microarchitecture of cartilage has directionality due to its collagen fiber alignment [18]. Therefore, to ensure reproducibility in our results, samples are always cut and aligned in the same direction. Ideally, the samples should be cut to mimic the natural alignment of the tissue, while ensuring the sample can lie flat on the testing surface. 3.5 Conclusion A polarimetry-based optical elastography instrument has been developed for characterizing viscoelastic materials. By using a disposable optical fiber sensor several of the limitations of current material characterization platforms are addressed. The OFPE instrument has sub-mm resolution, is non-destructive, portable, and modular. These key features make it ideal for biomaterial testing. There are two primary configurations of the OFPE instrument that can be used depending on the type of heterogeneous viscoelastic material being tested. Several methods for performing data analysis on the output of the OFPE instrument are presented. One advantage of the system is data can be plotted as 84 loading and unloading curves. Using the loading and unloading curves the maximum phase difference and energy loss of the material can be determined. Each of these methods provides interesting insight into the mechanical characteristics of the biomaterials. They can be used independently or together according to the type of research being performed. 85 3.6 References 1. M. Erkan, S. Hausmann, C. W. Michalski, A. A. Fingerle, M. Dobritz, J. Kleeff, and H. Friess, "The role of stroma in pancreatic cancer: diagnostic and therapeutic implications," Nat Rev Gastroenterol Hepatol 9, 454-467 (2012). 2. C. Feig, A. Gopinathan, A. Neesse, D. S. Chan, N. Cook, and D. A. Tuveson, "The pancreas cancer microenvironment," Clinical cancer research : an official journal of the American Association for Cancer Research 18, 4266-4276 (2012). 3. M. Cecelja, and P. Chowienczyk, "Role of arterial stiffness in cardiovascular disease," JRSM Cardiovascular Disease 1, cvd.2012.012016 (2012). 4. D. T. Butcher, T. Alliston, and V. M. Weaver, "A tense situation: forcing tumour progression," Nat Rev Cancer 9, 108-122 (2009). 5. A. Chodobski, B. J. Zink, and J. Szmydynger-Chodobska, "Blood-brain barrier pathophysiology in traumatic brain injury," Translational stroke research 2, 492-516 (2011). 6. X. Fan, I. M. White, S. I. Shopova, H. Zhu, J. D. Suter, and Y. Sun, "Sensitive optical biosensors for unlabeled targets: A review," Analytica Chimica Acta 620, 8-26 (2008). 7. M. Kjaer, "Role of extracellular matrix in adaptation of tendon and skeletal muscle to mechanical loading," Physiol. Rev. 84, 649-698 (2004). 8. C. K. Kuo, W.-J. Li, R. L. Mauck, and R. S. Tuan, "Cartilage tissue engineering: its potential and uses," Current Opinion in Rheumatology 18, 64-73 (2006). 9. A. W. Hudnut, B. Babaei, S. Liu, B. K. Larson, S. M. Mumenthaler, and A. M. Armani, "Characterization of the mechanical properties of resected porcine organ tissue using optical fiber photoelastic polarimetry," Biomed. Opt. Express 8, 4663-4670 (2017). 10. M. C. Harrison, and A. M. Armani, "Portable polarimetric fiber stress sensor system for visco-elastic and biomimetic material analysis," Applied Physics Letters 106, 191105 (2015). 11. T. Boulet, M. L. Kelso, and S. F. Othman, "Microscopic magnetic resonance elastography of traumatic brain injury model," J. Neurosci. Methods 201, 296-306 (2011). 12. C. Simmons, A. Rubiano, D. Stewart, and B. Andersen, "Custom Indentation System for Mechanical Characterization of Soft Matter," in Mechanics of Biological Systems and Materials, Volume 6: Proceedings of the 2016 Annual Conference on Experimental and Applied Mechanics, C. S. Korach, S. A. Tekalur, and P. Zavattieri, eds. (Springer International Publishing, 2017), pp. 95-99. 13. E. K. Danso, J. T. J. Honkanen, S. Saarakkala, and R. K. Korhonen, "Comparison of nonlinear mechanical properties of bovine articular cartilage and meniscus," J. Biomech. 47, 200-206 (2014). 14. A. W. Hudnut, and A. M. Armani, "High-resolution analysis of the mechanical behavior of tissue," Applied Physics Letters 110, 243701 (2017). 15. Y. C. Fung, Biomechanics: mechanical properties of living tissues (Springer Science & Business Media, 1981). 16. B. Rashid, M. Destrade, and M. D. Gilchrist, "Mechanical characterization of brain tissue in compression at dynamic strain rates," J. Mech. Behav. Biomed. Mater. 10, 23-38 (2012). 86 17. E. C. Bate-Smith, and J. R. Bendall, "Factors determining the time course of rigor mortis," The Journal of Physiology 110, 47-65 (1949). 18. R. Shirazi, A. Shirazi-Adl, and M. Hurtig, "Role of cartilage collagen fibrils networks in knee joint biomechanics under compression," J. Biomech. 41, 3340-3348 (2008). 87 OFPE - Animal Results Chapter 4. 4.1 Introduction Optical Fiber Polarimetric Elastography (OFPE) is uniquely suited to measuring the biomechanical behavior of biological tissues, because it is a high-resolution, non- destructive, and portable method. The results from OFPE testing of eight tissues within two different animal models are presented in Chapter 4 [1-3]. Figure 4-1 depicts the relative stiffness of the tissues tested in Chapter 4 using the OFPE method. The variation of the stiffness and biomechanical profiles derives from the intricate function and physiology of organs [1-5]. For this reason, even within the same tissue, the biomechanical properties can change on the sub-micron scale. Figure 4-1: Summary of the Young’s Modulus of the biomaterials profiled with the OFPE instrument in animal models (liver, colon, kidney, pancreas, heart, muscle, and cartilage tissue). The values of the biomaterials tested vary by six orders of magnitude [6- 18]. The results presented in Chapter 4 demonstrate that OFPE can be used to characterize a variety of biomaterials. First, we study skeletal muscle from salmon to determine the resolution of the OFPE system [1]. We study three different regions of the skeletal muscle with different numbers of collagen membranes. Collagen membranes are 88 500µm thick and have a lower Young’s Modulus than bulk skeletal muscle tissue [19- 21]. Therefore, using salmon skeletal muscle as a model system enables us control the heterogeneity to determine the resolution of the OFPE system. By controlling the heterogeneity of the sample, we determine the OFPE system can resolve sub-mm structures within tissues. Once the system is validated in this well-defined system, we move forward with less understood systems, namely living tissue. Specifically, seven tissues from pigs were analyzed (kidney, pancreas, cartilage, colon, liver, lungs, and heart) [2, 3]. While OFPE is not suitable for all of these, we verify that OFPE is non-destructive with pathology images of liver, pancreas and kidney tissues before and after compression. Using OFPE, we explore the unique biomechanical profile of the tissue [3]. This enables us to establish a preliminary baseline for each organ from the N>30 samples that we tested for each tissue type. 4.2 Salmon Skeletal Muscle Testing with OFPE Initial testing with the OFPE instrument is conducted using salmon skeletal muscle [1]. The primary goal of the study is to assess the reproducibly of characterizing biomaterials with the OFPE instrument. The secondary goal of the study is to assess if heterogeneity can be resolved within tissue. We hypothesize that the first biomaterial tested with the OFPE instrument should be a complete tissue with a relatively high Young’s Modulus. Such a tissue would enable us to rapidly iterate our experimental procedures. Salmon skeletal muscle is chosen due to its ready availability and low cost as 89 well as its well-defined structure. Further, it provides the necessary parameters to successfully characterize the tissue. Salmon skeletal muscle has a visible muscle grain and well-defined collagen membranes. The collagen membranes are approximately 500µm thick. Samples of fresh raw salmon muscle are used, each with a different number of collagen membranes. Based on measurements taken with alternative methods and published in the literature, the collagen membranes are known to be more elastic than the surrounding bulk muscle tissue [19-21]. Therefore, the mechanical properties of the salmon skeletal muscle samples differ on the micron length scales in a way that can be controlled experimentally [1]. To achieve this variation in the heterogeneity of the tissue, three samples are cut from different region of the muscle within the same fish. Samples have zero membranes, one membrane, or two membranes. As a result, there is a clear difference in the loading and unloading curves, maximum phase difference, and energy loss from the three samples. Based on our results, the OFPE instrument can resolve microstructures that are as small as 500µm thick. This resolution is unprecedented in undigested samples. The ultimate limit of the system has yet to be determined, but it is dependent on the sensor surface area and the mechanical behavior contrast between the surrounding tissue and the item of interest. 4.2.1 Salmon Sample Preparation The samples are cut into 9mm x 9mm x 5mm (l x w x h) rectangles with zero, one, or two parallel collagen membranes dividing the sample (Figure 4-2). The salmon samples are cut such that the muscle fiber sections are 3-5mm wide and the white 90 collagen membranes are oriented perpendicularly to the baseplate. The samples with no collagen membranes are considered uniform and used to determine the influence of the muscle grain on the signal. N>30 samples are prepared and tested to enable rigorous validation of the method. The results from three samples from different regions of the same fish are presented [1]. Figure 4-2: Diagram of a section of salmon skeletal muscle used for OFPE testing. Dimensions of the tissue sample are 9mm x 9mm x 5mm (l x w x h). 4.2.2 Salmon Testing Protocol To determine the biomechanical properties of salmon skeletal muscle, the single optical fiber OFPE instrument is used. This configuration enables the user to take a point measurement within a sample and determine the loading and unloading curves for compressive testing of the sample. The salmon skeletal muscle is tested at 10%, 20%, and 30% strain because the mechanical behavior of skeletal muscle is strain dependent. 4.2.3 Salmon Data Analysis Several methods are used to analyze the data obtained with the OFPE instrument. Using the ΔPol calculated at each 30msec interval, we generate a loading and unloading 91 curve. The ΔPol is directly proportional to stress, due to the photoelastic effect. Therefore, our loading and unloading curves are effectively stress vs. strain curves. The loading and unloading curves are able to provide information into the biomechanical properties of the tissue. These include relative stiffness, compressibility, and viscoelasticity. Additionally, they can be used to generate more quantitative metrics that can be used to compare different samples and tissues. The loading and unloading curves obtained from the OFPE measurements of salmon skeletal muscle is analyzed in two complementary ways. The first method is a measurement of the maximum phase change during compression. The second method is a measurement of the total energy loss of the system during compression. 4.2.4 Salmon Results and Discussion 4.2.4.1 Uniform Sample The uniform salmon skeletal muscle sample is a piece of muscle without any collagen membranes. It is used as a baseline measurement for comparison with samples that have collagen membranes. This enables the heterogeneity of the tissue to be controlled experimentally. Figure 4-3 shows the loading and unloading curves for a uniform sample of salmon skeletal muscle. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. At low strain, the response is similar in both the loading and unloading cycles, and the slope of the response is linear. This response indicates that the material is relatively isotropic and elastic in this strain regime, as would be expected of skeletal muscle fiber [19-21]. 92 Figure 4-3: Loading and unloading curves for a uniform salmon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is 2.3E-3, 1.5E-2 and 4.1E-2 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a uniform sample of salmon skeletal muscle. As the strain increases, the maximum phase change increases. Despite multiple loading and unloading cycles, the phase consistently returns to its initial value, showing minimal residual stress in the sample. However, as the strain increases, the residual stress in the sample increases. This indicates that there is a small amount of irreversible compression occurring in the sample over time. Within a measurement, the primary source of error is fiber movement. Across multiple measurements, sample degradation plays a role, particularly at high strain values. The energy loss of the sample (Figure 4-3b) is relatively consistent at all strains. Repeated tests at 30% strain changes over time, indicating damage to the tissue nanoarchitecture. The damage in the salmon muscle sample would most likely arise from the destruction of the nanoarchitecture of the connective fibers of the muscle. Damage to these fibers impacts the sample elasticity. 93 The irreversible compression observed in the energy loss data at 30% strain for the uniform sample indicates 30% strain is at the far end of the linear elastic region for muscle. Muscle is one of the most isotropic and stiffest tissues within the body. Therefore, compression testing of other soft tissues at 30% strain is also likely to damage the nanoarchitecture of the tissue and result in residual stress, indicative of irreversible compression. 4.2.4.2 Sample with a Single Collagen Membrane The salmon skeletal muscle sample with a single membrane is a piece of muscle with one collagen membrane bisecting the tissue sample. By adjusting the number of collagen membranes in the sample, the heterogeneity of the tissue can be controlled experimentally. Therefore, the impact of collagen membranes on the biomechanics of the skeletal muscle can be determined by comparing the OFPE results of the samples with and without collagen membranes. Figure 4-4 shows the loading and unloading curves for a sample of salmon skeletal muscle with one collagen membrane. In the loading and unloading curves, the first measurement (Run 1) is an outlier in the 10% strain measurements (Figure 4-4a). This deviation is due to a change in the contact between the fiber and the tissue sample. When a sample is initially placed upon the fiber sensor, there can be air gaps. These air pockets are removed with the first compression. This type of error is commonly observed in compression measurements. With that exception, these results are highly reproducible in consecutive 30-second compression tests. 94 Figure 4-4: Loading and unloading curves for a salmon sample divided in half by a single collagen membrane, where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is 1.1E-2, 2.2E-2 and 2.1E- 2 for 10%, 20%, and 30% strain, respectively. (c) Image of OFPE testing of a salmon skeletal muscle sample divided in half by a collagen membrane. Similar to the findings with the uniform samples, the energy loss increased as the strain increased (Figure 4-4b). This behavior is due to the strain dependence of energy loss. This behavior is expected in viscoelastic materials [6]. Repeated compression tests at 30% strain demonstrate a decrease in the energy loss with consecutive compressions. This behavior indicates that there may be damage to the nanoarchitecture of the sample. The damage in the salmon muscle sample would most likely arise from the destruction of the nanoarchitecture of the connective fibers, which would result in a decrease in the sample elasticity. The collagen membranes are more sensitive to these compressions than the bulk skeletal muscle. This difference in physiology is attributed to the increase in energy loss between the uniform sample and the sample with one collagen membrane. When the energy loss of the sample with a single collagen membrane is compared to the energy loss of the uniform sample, there are two primary differences. First, 95 significantly more energy loss is observed in the sample with a single collagen membrane than in the uniform sample, even at low strain. This is attributed to the fact that the ECM of collagen is more susceptible to damage. Second, there is significantly more residual stress in the muscle and it appears at much lower strain. This is also attributed to the collagen membrane. Therefore, being able to observe these properties indicates that there is an averaging between the mechanical behaviors of the skeletal muscle and the collagen in the sample with a single collagen membrane. These results indicate the OFPE instrument can measure the biomechanical behaviors of heterogeneous tissues. 4.2.4.3 Sample with Two Collagen Membranes The third sample of interest, in this study, is a piece of salmon skeletal muscle with two collagen membranes dividing the tissue sample into three even regions. By determining the number of collagen membranes in the sample, the heterogeneity of the tissue can be controlled experimentally. Therefore, the impact of collagen membranes on the biomechanics of the skeletal muscle can be determined by comparing the OFPE results of the samples with and without collagen membranes. Figure 4-5 shows the loading and unloading curves for a sample of salmon skeletal muscle with two collagen membranes. These results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. 96 Figure 4-5: Loading and unloading curves for a salmon sample divided in thirds by two collagen membranes, where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is 1.4 E-3, 2.4 E-2 and 1.6 E-2 for 10%, 20%, and 30% strain, respectively. (c) Image of OFPE testing of a salmon skeletal muscle sample divided by two collagen membranes. The energy loss of the sample (Figure 4-5b) increases as the strain increases. This behavior occurs because the energy loss is strain dependent. This behavior is expected in viscoelastic materials [6]. Additionally, the energy loss decreases with each consecutive compression at 30% strain. This trend is similar, yet more pronounced than the sample with one collagen membrane. This behavior is indicative of irreversible damage to the nanoarchitecture of the sample. The damage in the salmon muscle sample would most likely arise from the destruction of the nanoarchitecture of the connective fibers, which would result in a decrease in the sample elasticity. The collagen membranes are more sensitive to destruction from compressive testing than the bulk skeletal muscle. This difference in physiology is attributed to the increase in energy loss between the uniform sample, the sample with one collagen membrane, and the sample with two collagen membranes. 97 When the energy loss of the sample with two collagen membranes is compared to the energy loss of the uniform sample, there are two primary differences. First, significantly more energy loss is observed in the sample with a single collagen membrane than in the uniform sample, even at low strain. This is attributed to the fact that the ECM of collagen is more susceptible to damage. Second, there is significantly more residual stress in the muscle, and it appears at much lower strain. This is also attributed to the collagen membrane. Therefore, being able to observe these properties indicates that there is an averaging between the mechanical behaviors of the skeletal muscle and the collagen in the sample with a single collagen membrane. These results indicate the OFPE instrument can measure the biomechanical behaviors of heterogeneous tissues. 4.3 Porcine Tissue Testing with OFPE Additional testing with the OFPE instrument is conducted using soft tissue from porcine samples [2]. The primary goal of the study is to assess the reproducibly of characterizing a multitude of biomaterials with the OFPE instrument. The secondary goal of the study is to assess if the physiology of the different tissues could be correlated with their mechanical behavior. Initially, seven porcine organs (kidney, pancreas, cartilage, colon, liver, lungs, and heart) were tested to establish which organs have the most interesting viscoelastic properties for future study with OFPE. The results from liver, kidney, pancreas, heart, and cartilage are presented in this chapter. The lung and colon were not pursued because of issues that prevented the tissues from being well suited for compressive testing. The lung is comprised of millions of alveoli, which are sacks that look like clusters of grapes 98 and increase the surface area for gas exchange in the lung [22]. Due to their complex microarchitecture, cutting a flat sample of lung tissue extraordinarily complex. Therefore, it was difficult to demonstrate reproducibility in the OFPE results. The colon is the last part of the gastrointestinal track and is key to digestion [22]. Due to its role in digestion, the colon resected from porcine tissues often was in use when the tissues were resected. Therefore, the tissues were stretched and it was challenging to cut a portion of tissue thick enough to characterize with OFPE. Based on these results, extensive studies are conducted on liver, kidney, pancreas, heart, and cartilage tissue. We characterize the mechanical behavior of different soft tissues from within the same organism and correlate the changes in behavior to the physiological function. We also modify the instrument to work for all organs despite the fact that the Young’s modulus varied by three orders of magnitude [2, 3, 23]. Tissues are collected using fresh porcine organs obtained from the Health Sciences Campus at USC. Research is conducted in collaboration with Dr. David Agus and Professor Shannon Mumenthaler in the Lawrence J. Ellison Institute for Transformative Medicine of USC and Dr. Nicholas Trasolini and Dr. Rick Hatch in the Orthopedic Surgery Department of USC. To obtain tissue samples, surgical fellows resect sections of tissue from animals under anesthesia (University of Southern California IACUC Approval-10843). Tissues are placed in RPMI cell culture media (Gibco) on ice until testing. Testing occurs within two hours of resection to ensure that the biomechanical properties of the tissue have not changed due to the onset of rigor mortis [24]. 99 4.3.1 Porcine Sample Preparation Studies are conducted on porcine liver, kidney, pancreas, heart, and cartilage tissue. These organs are chosen because of their wide range in Young’s Modulus values, their relative similarity to human organs, and their compatibility with the system. Liver provides a very soft organ with a relatively homogenous and spongy structure. Kidney provides a relatively soft organ with heterogeneous structure that is less complex than most other organs. Pancreas provides a relatively stiff organ with a heterogeneous structure and high internal organ pressure. Heart provides a relatively stiff, yet homogenous tissue with well-defined microarchitecture similar to skeletal muscle. Cartilage provides a completely different system to truly test the limitations of the OFPE system for biomechanical characterization. Cartilage tissue has a Young’s Modulus three orders of magnitude greater than the tissues previously tested with OFPE. Additionally, cartilage has a physiology suited to load bearing and therefore varies within joints. The samples are cut into 7 mm x 7 mm x 4mm (l x w x h) rectangles (Figure 4-6). N>30 samples are prepared and measured using OFPE from each organ. Testing each organ sub-type extensively enables rigorous validation of the method. The results from a single sample from each of the organs are presented. The biomechanical behaviors of the tissues are correlated to their unique function and physiology. 100 Figure 4-6: Diagram of a section of porcine pancreatic tissue used for OFPE testing. Dimensions of the tissue sample are 7mm x 7mm x 4mm (l x w x h). These dimensions are used for testing of all porcine tissue sub-types. 4.3.2 Porcine Testing Protocol To determine the biomechanical properties of porcine tissue, the single optical fiber OFPE instrument is used. This configuration enables the user to take point measurements within a sample and determine the loading and unloading curves for compressive testing of the sample. Because tissue is a viscoelastic material, the mechanical behavior of the tissue is strain-dependent. Therefore, the seven porcine tissue sub-types are each tested at 10%, 20%, and 30% strain. 4.3.3 Porcine Data Analysis Several methods are used to analyze the data obtained with the OFPE instrument. Using the ΔPol calculated at each 30msec interval, we generate a loading and unloading curve. The ΔPol is directly proportional to stress, due to the photoelastic effect. Therefore, our loading and unloading curves are effectively stress vs. strain curves. The loading and unloading curves are able to provide information into the biomechanical 101 properties of the tissue. These include relative stiffness, compressibility, and viscoelasticity. Additionally, they can be used to generate more quantitative metrics that can be used to compare different samples and tissues. The data from the loading and unloading curves obtained from the porcine measurements is analyzed in three complementary ways. The first method is a measurement of the total energy loss of the system during the OFPE measurement. The second method is a fit of the loading and unloading curves to a Quasi-Linear Viscoelasticity (QLV), which uses an equation known to have coefficients directly linked to biomechanical behaviors of tissues. The third method is identifying the mechanical deformations by pairing the local maxima and local minima of the loading and unloading curves to known physiological properties. This method enables us to track the dependence of the biomechanical behavior of the tissue on strain. 4.3.3.1 Quasi-Linear Viscoelastic Fit One alternative approach used to quantify the stiffness of different materials based on the loading and unloading curves is to fit the curves and use the coefficients to compare different materials. The predominant method for fitting loading and unloading curves within the biomaterials community is the Quasi-Linear Viscoelasticity (QLV) method [6, 25-27]. The QLV fit provides several material constants that can directly be compared between samples and measurements [15, 25, 28]. The QLV fit can be applied directly to the loading and unloading curves. One example of a loading and unloading curve obtained with OFPE and subsequently fit using the QLV method is presented in Figure 4-7. 102 Figure 4-7: Graphical representation of a QLV fit of the loading and unloading curves of a pancreatic tissue sample compressively tested to 20% strain. The goal of this step is to increase the ability to directly compare data from different tissues and with different instrument configurations of the setup. Using the fit to correlate data sets with variable device configuration is necessary because tissue samples are tested on different days, and the optical fiber alignment is slightly changed every time the disposable fiber sensor is replaced. When the alignment of the optical components changes, the device sensitivity can also change. Because ΔPol is proportional to stress, we can directly fit our experimental data in Matlab to the QLV model [2]. The associated Matlab codes written by Behzad Babaei (Postdoc collaborator from NeuRA, Neuroscience Research Australia) are include in Chapter A5. The QLV model then gives quantitative solutions to several key elasticity metrics. These metrics can then be compared across tissue types or across samples. The QLV uses the relaxation function (G(u)) and the elastic stress response ( !! ! !" ) to determine the stress and strain at a specific point in time [6]. By solving the QLV 103 model for C, 𝜏 ! , 𝜏 ! , A, and B, the material characteristics of the different organ types can be directly compared. The relationship takes the following form: 𝜎 𝜀,𝑡 = 𝐺 𝑡−𝑢 !! ! !" !" !" 𝑑𝑢 ! !! (4-1) where σ is the stress measured by the polarimeter (ΔPol), !! ! !" is the elastic stress response, G(u), is the relaxation function, and !" !" is the strain rate. The elastic stress response, 𝜎 ! 𝜀 , is represented by the equation: 𝜎 ! 𝜀 =𝐴 𝑒 !" −1 (4-2) where A represents the elasticity parameter and B represents the non-linearity parameter. Specifically, B describes the exponential increase in stiffness with increasing strain, which is due in part to the collagen makeup and cellular plasticity [29, 30]. The relaxation function, G(u), is represented by the equation: 𝐺 𝑢 = !! ! ! ! ! ! ! !" ! ! ! ! !! ! ! !" ! ! ! ! (3) where C is the damping coefficient, and 𝜏 ! and 𝜏 ! represent the upper and lower boundary of the time constants of relaxation. 104 4.3.3.2 Mechanical Deformations One approach used to compare the biomechanical properties of different biomaterials based on the loading and unloading curves is to identify points along the curve that demonstrate the location where mechanical deformations occur. There are several types of mechanical deformation that are known to occur in soft polymers, composites, and biomaterials including buckling, delamination, and bridging [31-35]. The mechanical deformations are caused by changes in the different structural elements as a result of compression. Therefore, in biomaterials, the mechanical deformations are caused by changes in the extracellular matrix (ECM) and can be directly correlated to specific physiological phenomenon. To quantify the mechanical deformations within the material, the loading and unloading curves are determined and tracked in subsequent runs and across all three strains. By tracking the maximum and minimum points on the curve, the physiological changes that cause them can be determined [3]. Based on how the mechanical behaviors within the tissue change with time, additional information regarding the biomechanical characteristics of the tissue can be inferred [3]. Three common types of mechanical deformation are buckling (Figure 4-8a), delamination (Figure 4-8b), and bridging (Figure 4-8c). Buckling is the response of the material to a compressive load where the load bearing elements deflect sideways. It has been demonstrated that in viscoelastic materials there can be multiple buckling points at high strain [34]. Delamination is the response of the material to a compressive load where either one or two parallel load bearing elements deflect sideways creating a reversible gap within the biomaterial. Bridging is the response of a composite material to a 105 compressive load where permanent damage occurs to the matrix, but not the reinforcements. As a result, the reinforcements form bridges across the damaged matrix. Figure 4-8:Cartoons of three common forms of mechanical deformation within viscoelastic materials: (a) buckling, (b) delamination, and (c) bridging. The red lines represent the individual load bearing elements. The blue line denotes the difference between the material before compression and during compression. 4.3.4 Porcine Results and Discussion 4.3.4.1 Pathology Imaging Analysis of Soft Tissues Soft tissues within the body are highly responsive to compression. Even slight compressions can change their nanoarchitecture and impact their biomechanical behaviors. Therefore, if systems for biomechanical analysis are developed with the hope of subsequent analysis of the tissue, they need to be non-destructive. The OFPE system was designed with this in mind, and imaging is used to validate the impact of OFPE on the microarchitecture of the different tissues. To ensure the OFPE instrument is non-destructive, we conducted imaging analysis before and after testing with the OFPE instrument. The imaging results demonstrate our device is non-destructive, despite applying multiple compression tests at different strains. Figure 4-9 shows Hematoxylin and Eosin (H&E) images used to analyze the tissue microstructures [2]. The Hematoxylin (blue/purple) stains acidic components of the tissues such as DNA. The eosin (pink) stains basic components of the tissues such as 106 the extracellular matrix (ECM). Therefore, the H&E stain can be used to identify if the compressive testing of the tissue damages the microstructures within the tissues. Inspection of the images presented in Figure 4-9 clearly demonstrates that there is no damage to the microstructure of the organs due to the compressive OFPE tests. Figure 4-9: H&E images from tissues before and after compressive testing with OFEP: (a) uncompressed liver sample, (b) compressed liver sample, (c) uncompressed kidney sample, (d) compressed kidney sample, (e) uncompressed pancreas sample, (e) compressed pancreas sample. The arrows indicate the microstructures from each organ that would be most likely to be destroyed due to compression. These structures remain intact across all three tissue types, indicating OFPE is non-destructive. Within the liver, hepatocytes are used to identify if damage occurred to the tissues (Figure 4-9a/b). Hepatocytes make up more than 70% of cells within the liver. They synthesize proteins and filter exogenous and endogenous compounds [22]. It is clear from the H&E images of compressed and uncompressed tissue that the hepatocytes remain intact. Therefore, the OFPE instrument does not impact the structure of the liver tissue. Within the kidney, the glomeruli are used to identify if damage occurred to the tissues (Figure 4-9c/d). The glomeruli are functional units within the kidney, which are comprised of a network of capillaries where the blood is filtered [22]. It is clear from the 107 H&E images of compressed and uncompressed tissue that the glomeruli remain intact. Therefore, the OFPE instrument does not impact the structure of the kidney tissue. Within the pancreas, the acinar cells are used to identify if damage occurred to the tissues (Figure 4-9e/f). The acinar cells are exocrine cells within the pancreas, which produce enzymes [22]. It is clear from the H&E images of compressed and uncompressed tissue that the acinar cells remain intact. Therefore, the OFPE instrument does not impact the structure of the pancreatic tissue. 4.3.4.2 Porcine Liver Results and Discussion Liver tissue is spongy and has a relatively homogenous microarchitecture due to its physiological function as a filter [22]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical properties of normal liver tissue. Testing liver tissue with OFPE enables the biomechanical properties of different tissue to be experimentally determined and compared. N>30 samples of liver tissue are characterized using the OFPE instrument. Figure 4-10 shows the loading and unloading curves for a representative sample of porcine liver. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. At low strain, the response is similar in both the loading and unloading cycles. At low strain, the slope of the response is relatively linear, indicating that the tissue is primarily elastic in this regime. As the strain increases, the hysteresis in the sample increases, indicating that the tissue is less elastic. This is characteristic of viscoelastic materials. The liver is one of the softest and most 108 homogenous tissues within the body. The OFPE instrument is able to resolve both of these characteristics. Figure 4-10: (a) Loading and unloading curves for a porcine liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 2.8E-8, 1.2E-8, and 5.0E-8 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine liver. There are three key features observed within the loading and unloading curves for the liver tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress within each sample after each run. This signifies that with each loading and unloading interval there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that as the rate of compression and maximum strain increases, the maximum stress increases. Third, the non-linearity of the mechanical behavior of the liver increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. 109 One feature that is unique to the liver is that it is relatively elastic at low strain. This behavior is a result of its relatively homogenous microarchitecture. As the strain increases, this behavior becomes less pronounced. Given that the strain values tested in this work span the entire physiological compression range, this variability in behavior is expected. Similar to the findings within the other biomaterial samples, the energy loss increased as the strain increased (Figure 4-10b). At high strain rates, the energy loss decreases in subsequent runs. This behavior is caused by damage incurred during sample collection. The damage in the liver sample most likely arises from the destruction of the nanoarchitecture of the connective fibers of the tissue. Damage to these fibers impacts the sample elasticity, but is not visible on H&E images due to the small scale. This indicates that the OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is currently under investigation. Further results may indicate that the OFPE method can be used in parallel with currently accepted characterization techniques. 4.3.4.3 Porcine Kidney Results and Discussion Kidney tissue has a very heterogeneous microarchitecture comprised of complex sub-units due to its physiological function as a reclamation point [22]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical properties of normal kidney tissue. Testing kidney tissue with OFPE enables the biomechanical properties of different tissue to be experimentally determined 110 and compared. N>30 samples of kidney tissue are characterized using the OFPE instrument. Figure 4-11 shows the loading and unloading curves for a sample of porcine kidney. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. At low strains, the system is near the noise limit for the fiber optic sensor. Therefore, there is more visible variability in the loading and unloading curves and noise in the measurements at low strain. Similar to the other materials tested, as the strain increases the hysteresis in the sample increases. This is characteristic of viscoelastic materials. The kidney is one of the softest and most heterogeneous tissues within the body. The OFPE instrument is able to resolve both of these characteristics. Figure 4-11: (a) Loading and unloading curves for a porcine kidney sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 2.8E-8, 1.2E-8, and 5.0E-8 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine kidney. There are three key features observed within the loading and unloading curves for 111 the kidney tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress within each sample after each run. This signifies that with each loading and unloading interval, irreversible compression is occurring. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that the rate of compression, maximum strain, and the maximum stress are directly proportional. Third, the non-linearity of the mechanical behavior of the kidney increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increase. All three of these behaviors are expected for viscoelastic materials. Similar to the findings within the other biomaterial samples, the energy loss increases as the strain increases (Figure 4-11b). At low strains, the energy loss is consistent between the five runs. With increasing strain, the data followed a very traditional loading and unloading pattern. At high strain rates, the energy loss decreases in subsequent runs. This behavior is because the sample is being damaged. The damage in the kidney sample most likely arises from the destruction of the nanoarchitecture of the connective fibers of the tissue. Damage to these fibers impacts the sample elasticity, but is not visible on H&E images due to the small scale. This indicates that the OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is also currently under investigation. 4.3.4.4 Porcine Pancreas Results and Discussion Pancreatic tissue is extremely heterogeneous, and due to its physiological function of hormone regulation, it has a complex microarchitecture and exhibits high enzymatic 112 activity [22]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical properties of normal pancreatic tissue. Testing pancreatic tissue with OFPE enables the biomechanical properties of different tissue to be experimentally determined and compared. N>30 samples of pancreatic tissue are characterized using the OFPE instrument. Figure 4-12 shows the loading and unloading curves for a sample of porcine pancreas. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. As the strain increases, the hysteresis in the sample increases. This is characteristic of viscoelastic materials. The pancreas is one of the most homogenous tissues. The OFPE instrument is able to resolve this characteristic. Figure 4-12: (a) Loading and unloading curves for a porcine pancreas sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.1E-8, 2.8E-8, and 4.5E-8 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine pancreas. 113 There are three key features observed within the loading and unloading curves for the pancreatic tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress within each sample after each run. This signifies that with each loading and unloading interval, irreversible compression is occurring. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that the rate of compression, maximum strain, and the maximum stress are directly proportional. Third, the non-linearity of the mechanical behavior of the pancreas increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increase. All three of these behaviors are expected for viscoelastic materials. One feature that is unique to the pancreas is that at high strains there is a distinct buckling point, after which the stress decreases and plateaus. This behavior is a result of the collagen IV matrix within the pancreas that acts as a support to the acinar cells [45]. Given that the strain values tested in this work span the entire physiological compression range, this behavior is expected. Similar to the findings within the other biomaterial samples, the energy loss increased as the strain increased (Figure 4-12b). At both 20% and 30% strain the energy loss decreases in subsequent runs. This is because the sample is being damaged. The damage in the pancreas sample most likely arises from the destruction of the nanoarchitecture of the connective fibers of the tissue. Damage to these fibers impacts the sample elasticity, but is not visible on H&E images due to the small scale. This indicates that the OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is under further investigation to determine 114 the resolution of OFPE and the best methods to use in parallel to characterize tissue mechanics and destruction in response to compression. 4.3.4.5 Porcine Heart Results and Discussion Heart tissue has relatively homogenous microarchitecture of repeated sub-units due to its physiological function as a pump for blood throughout the body [22]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical properties of normal heart tissue. Testing heart tissue with OFPE enables the biomechanical properties of different tissues to be experimentally determined and compared. N>30 samples of heart tissues are characterized using the OFPE instrument. Figure 4-13 shows the loading and unloading curves for a sample of porcine heart. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. Even for lower strain values, the loading and unloading curves seemed to reach a maximum point before the end of the compression. As the strain increases, the hysteresis in the sample increases. This is characteristic of viscoelastic materials. The heart is one of the stiffest and most homogenous tissues within the body. The OFPE instrument is able to resolve both of these characteristics. 115 Figure 4-13: (a) Loading and unloading curves for a porcine heart sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 5.6E-9, 8.8E-8, and 2.9E-8 for 10%, 20% and 30% strain respectively. (c) Image of OFPE testing of a sample of porcine heart. There are three key features observed within the loading and unloading curves for the heart tissues. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress within each sample after each consecutive run. This signifies that, with each loading and unloading interval, there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. In turn, the rate of compression, maximum strain, and the maximum stress are directly proportional. Third, the non-linearity of the mechanical behavior of the heart increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. Similar to the findings within the other biomaterial samples, the energy loss increased as the strain increased (Figure 4-13b). At high strain rates, the energy loss 116 decreases in subsequent runs. This is because the sample is being damaged. The damage in the heart sample most likely arises from the destruction of the nanoarchitecture of the connective fibers of the tissue. The OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is under further investigation to determine the resolution of OFPE and the best methods to use in parallel to characterize tissue mechanics and destruction in response to compression. One feature that is unique to heart tissue is that the loading and unloading curves cross after the buckling point. This finding from compressive testing of the heart is confounding due to the lack of previous work on biomechanical tissue characterization. These complex results are being actively investigated by 3D modeling of the tissue. This behavior may be due to the fact that the individual cells within the heart have viscoelastic properties due to their physiology as a muscle tissue. Figure 4-14 depicts the H&E images before and after compressive testing of the heart tissue. The H&E images demonstrate the repeated units within the muscle. There is also a change in the spacing between the muscle cells after compression. Additional experiments have been conducted to further elucidate the role that orientation of the tissue has on the biomechanical behaviors. Because these results are not understood, they have not been published. 117 Figure 4-14: H&E images from heart tissues before and after compressive testing with OFEP: (a) uncompressed heart sample and (b) compressed heart sample. The H&E images demonstrate the repeated units within the muscle. The elasticity of the individual heart cells is hypothesized to be the reason for the unique behavior of the heart at high strain. 4.3.4.6 Porcine Cartilage Results and Discussion The porcine cartilage sample is a piece of cartilage tissue cut from one of the three primary regions of the knee joint to the appropriate dimensions for OFPE testing. It is used to characterize the biomechanical properties of normal cartilage tissue. The cartilage has a striated microarchitecture that varies depending on its location in the joint due to its physiological function of load bearing [22, 46-49]. Testing cartilage tissue with OFPE enables the biomechanical properties of different tissue to be experimentally determined and compared. Cartilage is unique when compared to the other tissues tested with OFEP for two reasons. First, the cartilage is a load bearing tissue. Second, there are multiple types of cartilage that comprise a single joint. Therefore, based on the physiology of the joint, we tested the cartilage from three regions of the porcine knee [3]. Unlike the other organs, there are many different sub-types of cartilage. Within the joints, the cartilage types have different mechanical behaviors depending on their physiology and function. Within the knee, there are three types of cartilage, and their congruence is integral to proper joint function [46]. The anatomy of the knee with the locations of the three cartilage types highlighted is depicted in Figure 4-15. The primary types of cartilage in the knee are articular cartilage from the femoral condyles (ACFC), articular cartilage from the patella (ACP), and fibrocartilage from the meniscus (MC) [47-50]. In the future, the subfailure biomechanical characteristics of the cartilage types can be used to determine the potential efficacy of materials engineered to act as cartilage 118 replacements. Figure 4-15: Gross anatomy of the porcine knee: (a) Schematic of the knee demonstrating the three locations of the cartilage resected for OFPE testing. (b) Photo of the articular cartilage of the femoral condyles with a box marking the location where the cartilage is harvested. (c) Photo of the articular cartilage of the patella with a box marking the location where the cartilage is harvested. (d) Photo of the fibrocartilage of the meniscus with a box marking the location where the cartilage is harvested. 4.3.4.6.1.1 Porcine ACFC Results and Discussion ACFC tissue is the cartilage tissue from the articular cartilage of the femoral condyles (Figure 4-15b). ACFC tissue has a striated microarchitecture due to its physiological function of weight bearing and gliding during tibiofemoral articulation [48, 49]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical properties of normal ACFC tissue. Testing ACFC tissue 119 with OFPE enables the biomechanical properties of different tissue to be experimentally determined and compared. N>30 samples of ACFC tissue are characterized using the OFPE instrument. Figure 4-16 shows the loading and unloading curves for a sample of ACFC. The results are reproducible in five consecutive 30-second compression tests repeated at three different strains. At low strain, the loading and unloading curves from the first and second run deviate slightly from subsequent runs. This deviation is due to a change in the contact between the fiber and the tissue sample. When a sample is initially placed upon the fiber sensor, there can be air gaps. These air pockets are removed with the first compression. This type of error is commonly observed in compression measurements. As the strain increases, the hysteresis in the sample increases. Figure 4-16: (a) Loading and unloading results for a sample of porcine Articular Cartilage from the Femoral Condyles where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 4.0E-8, 9.2E-8, and 1.0E-7 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of Articular Cartilage from the Femoral Condyles. There are three key features observed within the loading and unloading curves for 120 the ACFC tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress within each sample after each run. This signifies that with each loading and unloading interval, there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that the rate of compression, maximum strain, and maximum stress are directly proportional. Third, the non-linearity of the mechanical behavior of the cartilage increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. One feature that is unique to ACFC is that the loading and unloading curves cross. For each cartilage type, the curves cross at a single point, which is unique to cartilage. Previous compressive studies of cartilage have observed similar behavior [32]. These are a result of collapse within the superficial zone of the cartilage and a subsequent reduction in fluid imbibition. Given the strain values tested in this work, which span the entire physiological compression range, this behavior is expected. Another feature that is unique to ACFC is that the secondary buckling point does not appear until high strains are applied to the tissue. This behavior is a result of the loads that are typically applied to the ACFC tissue within the joint. Given the strain values tested in this work, which span the entire physiological compression range, this behavior is expected. Similar to the findings within the other biomaterial samples, the energy loss increases as the strain increases (Figure 4-16b). At high strain rates the energy loss decreases in subsequent runs. This behavior is because the sample is being damaged. The 121 damage in the ACFC sample most likely arises from the destruction of the collagen nanoarchitecture of the connective fibers of the tissue. This indicates that the OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is under further investigation to determine the resolution of OFPE and the best methods to use in parallel to characterize tissue mechanics and destruction in response to compression. 4.3.4.6.1.2 Porcine ACP Results and Discussion ACP tissue is the cartilage tissue from the articular cartilage of the patella (Figure 4-15c). The ACP has a striated microarchitecture due to its physiological function of absorption of forces during quadriceps activation [48, 49]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical properties of normal ACP tissue. Testing ACP tissue with OFPE enables the biomechanical properties of different tissue to be experimentally determined and compared. N>30 samples of ACP tissue are characterized using the OFPE instrument. Figure 4- 17 shows the loading and unloading curves for a sample of ACP. The results are reproducible in five consecutive 30-second compression tests repeated at three different strains. For all strains tested, the loading and unloading curves from the first run deviates slightly from subsequent runs. This deviation is due to a change in the contact between the fiber and the tissue sample. When a sample is initially placed upon the fiber sensor, there can be air gaps. These air pockets are removed with the first compression. This type of error is commonly observed in compression measurements. As the strain increases, the hysteresis in the sample increases. 122 Figure 4- 17: Loading and unloading results for a sample of porcine Articular Cartilage from the Patella where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 3.8E-8, 1.4E-7, and 1.0E-7 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of Articular Cartilage from the Patella. There are three key features observed within the loading and unloading curves for the ACP tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress within each sample after each run. This signifies that with each loading and unloading interval there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that the rate of compression, maximum strain, and the maximum stress are directly proportional. Third, the non-linearity of the mechanical behavior of the cartilage increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. One feature that is unique to ACP is that the loading and unloading curves cross. For each cartilage type, the curves cross at a single point, which is unique to cartilage. 123 Previous compressive studies of cartilage have observed similar behavior [32]. These are a result of collapse within the superficial zone of the cartilage and a subsequent reduction in fluid imbibition. Given the strain values tested in this work, which span the entire physiological compression range, this behavior is expected. Another feature that is unique to heart is that the ACP experiences less delamination and buckling than the other articular cartilage subtype. This behavior is a result of the physiological function of the ACP tissue. The ACP bears less load than the ACFC tissue and therefore has a less complex biomechanical signature. Similar to the findings within the other biomaterial samples, the energy loss increased as the strain increased (Figure 4- 17b). At high strain rates, the energy loss decreases in subsequent runs. This behavior is because the sample is being damaged. The damage in the ACP sample most likely arises from the destruction of the collagen nanoarchitecture of the connective fibers of the tissue. This indicates that the OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is under further investigation to determine the resolution of OFPE and the best methods to use in parallel to characterize tissue mechanics and destruction in response to compression. 4.3.4.6.1.3 Porcine MC Results and Discussion MC tissue is the cartilage tissue from the meniscus of the knee (Figure 4-15d). The MC has a striated microarchitecture due to its physiological function of a shock absorber that enables the joint to distribute large loads [47]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the biomechanical 124 properties of normal MC tissue. Testing MC tissue with OFPE enables the biomechanical properties of different tissue to be experimentally determined and compared. N>30 samples of MC tissue are characterized using the OFPE instrument. Figure 4-18 shows the loading and unloading curves for a sample of MC. The results are reproducible in five consecutive 30-second compression tests repeated at three different strains. At low strain, the loading and unloading curves from the first and second runs deviate slightly from the subsequent runs. This deviation is due to a change in the contact between the fiber and the tissue sample. When a sample is initially placed upon the fiber sensor, there can be air gaps. These air pockets are removed with the first compression. This type of error is commonly observed in compression measurements. This artifact is most pronounced in MC because the collagen fibers run parallel to the optical fiber making complete contact more difficult in fibrocartilage than any of the other tissues tested with OFPE. As the strain increases, the hysteresis in the sample increases. 125 Figure 4-18: Loading and unloading results for a sample of porcine Fibrocartilage from the Meniscus where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 6.2E-8, 1.2E-7, and 2.3E- 7 for 10%, 20%, and 30% strain respectively. (c) Image of OFPE testing of a sample of Fibrocartilage from the Meniscus. There are three key features observed within the loading and unloading curves for the MC tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual stress after each run. This signifies that with each loading and unloading interval there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that the rate of compression, maximum strain, and the maximum stress are directly proportional. Third, the non-linearity of the mechanical behavior of the MC increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. One feature that is unique to MC is that the loading and unloading curves cross. 126 For each cartilage type, the curves cross at a single point, which is unique to cartilage. Previous compressive studies of cartilage have observed similar behavior [32]. These are a result of collapse within the superficial zone of the cartilage and a subsequent reduction in fluid imbibition. Given the strain values tested in this work, which span the entire physiological compression range, this behavior is expected. Similar to the findings within the other biomaterial samples, the energy loss increased as the strain increased (Figure 4-18b). At high strain rates, the energy loss decreases in subsequent runs. This behavior is because the sample is being damaged. The damage in the MC sample most likely arises from the destruction of the collagen nanoarchitecture of the connective fibers of the tissue. This indicates that the OFPE method has higher resolution than traditional imaging methods [36-44]. This difference in OFPE and imaging results is under further investigation to determine the resolution of OFPE and the best methods to use in parallel to characterize tissue mechanics and destruction in response to compression. 4.4 Comparison of Data Analysis Methods Four methods of data analysis are used to study the biomechanical behavior of tissue: (1) maximum phase change, (2) energy loss, (3) QLV fit, and (4) mechanical deformation. Each method has positive and negative aspects. Therefore, depending on the tissue type, or experimental goals, different data analysis methods are used. In order to assist with the design of future experiments we outline specific use cases for each of the methods in this section. 127 4.4.1 Maximum Phase Difference Analysis To quantify the maximum phase difference the final point of the loading or unloading curve is subtracted from the initial point of the curve. Therefore, the maximum phase difference is a point measurement calculated from the loading and unloading curves. Calculating the maximum phase difference is the convention within the biological community for determining the biomechanical properties of a sample [51]. As an example of how the maximum phase change differs for samples with increasing heterogeneity, Figure 4-19 summarizes all of the maximum phase difference results from compressive testing of one sample of salmon skeletal muscle tested with OFPE [1]. The maximum phase difference is calculated for both the loading and unloading curves for all five runs at all three strains. Figure 4-19a depicts the results from compressive testing of the uniform sample. Figure 4-19b depicts the results from compressive testing of the sample with one collagen membrane. Figure 4-19c depicts the results from compressive testing of the sample with two collagen membranes. Figure 4-19: (a) Maximum phase change for a uniform sample for the five consecutive runs at three different strain rates where the maximum error is 1.7 E-2, 4.9 E-2 and 8.4 E- 2 for 10%, 20% and 30% strain respectively. (c) Maximum phase change for the five consecutive runs at three different strain rates where the maximum error is 1.1 E-1, 9.4 E- 2 and 8.0 E-2 for 10%, 20% and 30% strain respectively. (e) Maximum phase change for the five consecutive runs at three different strain rates where the maximum error is 2.0 E- 2, 2.6 E-2 and 4.2 E-2 for 10%, 20% and 30% strain respectively. In comparing the maximum phase change, several trends are apparent. Across sample types, the maximum phase change increases with increased strain. There is little 128 difference between the maximum phase change of the loading and unloading curves. The total phase change decreases as the number of membranes increased. These trends are sufficient to provide a baseline understanding of the relative biomechanics of the different tissues. However, tissues are viscoelastic materials and much of their mechanical behavior is tied into complex behaviors such as hysteresis, buckling, and delamination. These behaviors cannot be captured with point measurements. 4.4.2 Energy Loss Analysis To quantify the energy loss, the area between the loading and unloading curves is calculated [2]. Because this value is determined by integrating the area under the curve, all of the points in the loading and unloading curve are used in its calculation. Quantifying the mechanical behavior of a material using the energy loss is the convention within the material science and mechanical engineering community [52]. As an example of how the energy loss changed with an increase in the heterogeneity of the sample, the energy loss from OFPE testing of salmon skeletal muscle with increasing heterogeneity is shown. Figure 4-20 summarizes all of the energy loss results from compressive testing of the salmon skeletal muscle [1]. The energy loss is calculated for both the loading and unloading curves for all five runs at all three strains. Figure 4-20a depicts the results from compressive testing of the uniform sample. Figure 4-20b depicts the results from compressive testing of the sample with one collagen membrane. Figure 4-20c depicts the results from compressive testing of the sample with two collagen membranes. 129 Figure 4-20: (a) Energy loss for the five consecutive runs at three different strain rates where the maximum error is 2.3 E-3, 1.5 E-2 and 4.1 E-2 for 10%, 20% and 30% strain respectively. (b) Energy loss for the five consecutive runs at three different strain rates the maximum error is 1.1 E-2, 2.2 E-2 and 2.1 E-2 for 10%, 20% and 30% strain respectively. (c) Energy loss for the five consecutive runs at three different strain rates where the maximum error is 1.4 E-3, 2.4 E-2 and 1.6 E-2 for 10%, 20% and 30% strain respectively. In comparing the differential energy loss, several trends are apparent. Across sample types, the energy loss increases with increased strain. When energy loss is used to analyze the data, it is possible to detect the presence of the 500µm collagen membranes. Within a biomaterial sample energy loss is a result of irreversible compression and destruction of nanoarchitecture of the material. The general trend observed in biomaterial testing with the OFPE instrument is that the energy loss decreases with consecutive compressions at high strain. The energy loss at 30% strain for most tissues decreases with subsequent compressions. This indicates that there is damage to the nanoarchitecture as a result of the compression. This finding raises concerns regarding the accuracy of using 30% strain in analyzing biomaterials. 30% strain has been the assumed optimum applied strain for determining the mechanical properties in past theoretical and experimental work [53-55]. Based on the results with OFPE, 20% strain is outside the linear elastic range for soft tissues. Therefore, it is likely that current methods are changing the biomechanical behavior during testing. In turn, this will add experimental error into the measurements that currently cannot be tracked. 130 There is one limitation to using the energy loss as a method of data analysis when calculating the biomechanical properties of tissues. If the loading and unloading curves cross, then the energy loss metric no longer can be correlated with tissue biomechanics. This trend has been observed in OFPE testing of cartilage tissue and heart tissue, as shown previously. Therefore, when using energy loss to analyze OFPE results, the loading and unloading curves should be generated and checked for intersections between the loading and unloading curves before determining the energy loss. 4.4.3 Quasi-Linear Viscoelasticity Analysis To quantify the coefficients of the material elasticity, the loading and unloading curves are fit to the QLV model [2]. The QLV model is chosen for the fit because the coefficients of the equation have been directly linked to unique physiological behaviors of the tissues [25, 29, 56]. Example data sets for the liver, kidney, and pancreas and their associated QLV fits are presented in Figure 4-21. The QLV model is able to accurately fit the loading and unloading curves for the porcine organs with a mean squared error less than 0.09. The result is a numerical solution for each of the five coefficients: A, B, C, 𝜏 1 , and 𝜏 2 . Figure 4-21: Representative QLV fit for one the loading and unloading curve for liver, kidney, and pancreatic tissue. 131 The coefficients determined from the QLV fit of the experimental data, and energy loss are plotted in Figure 4-22. These five coefficients each have a physiological basis and can be used to directly compare data sets across different days of testing and different organs. Figure 4-22: Coefficients of the QLV fit of the loading and unloading curves for liver, kidney, and pancreatic tissue. Coefficient A represents the elastic modulus of the material (Figure 4-22a). The elastic modulus has several contributing factors, including the ECM composition and microarchitecture of the tissue. The general trend in coefficient A is that the elastic modulus increases as the strain increases. This behavior is commonly observed in viscoelastic materials [8, 57]. The experimentally determined range of elastic modulus values using the OFPE method and QLV fit is 0.1-0.5 KPa for liver, 0.15-0.9 KPa for kidney, and 0.2-8.0 KPa for pancreas. Therefore, our results are within the range of previously published elastic modulus values for these organs [7, 8, 57-61]. This confirms the QLV fit is a good metric for measuring and quantifying the viscoelastic behavior of different tissues for direct comparison. 132 Coefficient B represents the non-linearity within the system (Figure 4-22b). The non-linearity of the system has several contributing factors, including the ECM composition and cellular plasticity. The general trend in the measurements is that as the strain increases, the non-linearity decreases. This response is due to the fact that as the rate of compression increases, the impact of the different non-linear components decreases. This behavior is commonly observed in viscoelastic materials [6, 62]. Coefficient C represents the damping coefficient of the material (Figure 4-22c). The damping coefficient is an intrinsic material property that indicates whether a material will return energy to a system. It is primarily due to the tissue microarchitecture, and previously has been used to determine the amount of mechanical energy dissipated in biomaterials [63]. The general trend in the measurements is that the damping coefficient decreases as strain increase. However, the accuracy of the damping coefficient calculated decreases as strain increases. This is in part due to the poor fit of the model at the extremes of the data. Limitations of the QLV fit include the fact that it does not accurately model the flattening at the end of the high strain curves for more heterogeneous tissues, like the kidney and pancreas. The poor fit of the model at the extremes of the data leads to less accurate coefficients being calculated. Therefore, it can lead to improper analysis and comparison. The error of the fit can be a good metric for ensuring this does not occur. Additionally, there are few issues if the QLV fit is used on 10% and 20% strain data regardless of the tissue. 133 4.4.4 Mechanical Deformation Analysis To quantify the mechanical deformations within the material, the loading and unloading curves are analyzed to determine the maximum and minimum points along the curves [3]. Using these results, the number of points where mechanical deformations generate a change in the loading and unloading curves can be identified. Based on how the mechanical deformations change with time, they can be linked to specific mechanical behaviors within the tissue [3, 45]. This method is used to compare the different cartilage types. There are three main mechanical deformations that we analyze within the cartilage: (1) buckling, (2) delamination, and (3) bridging. The results from mechanical deformation analysis from cartilage tissue are depicted in Figure 4-23 and Figure 4-24. There is always at least one loading buckling point and one unloading buckling point within all cartilage types at all strains. The strain where each buckling point occurs for each cartilage type is summarized in Figure 4-23. The general trend is that strain where the loading buckling point and unloading buckling point occurs increases as the strain increases. This is due to the low coefficient of friction and fluid-dependent mechanisms characteristic of cartilage. Such behavior is necessary for the joint to function in a variety of different physiological pressures of different movement types. A secondary loading buckling point is observed at high strain. This mechanical is observed because the different layers of cartilage buckle response to compressive loads with different mechanisms. The secondary loading buckling point appears outside the normal physiological loading experienced by the joint. Therefore, strain values of this magnitude are unlikely to normally occur within the joint. By comparing the physiology of the tissue to these mechanical deformations, we can better understand the biomechanical behavior 134 of the tissue and why certain behaviors occur within similar tissues. Figure 4-23: Mechanical Buckling Location: (a) Primary loading buckling point indicated by an absolute maximum in our loading curves. (b) Secondary loading buckling point indicated by a local maximum in our loading curves. (c) Unloading buckling point indicated by an absolute maximum in our unloading curves. In addition to the buckling points, delamination and bridging are observed in the cartilage tissue. The strains where the mechanical deformations occur in the three cartilage samples tested are summarized in Figure 4-24. The strain where the delamination and bridging point occurs remains relatively constant as the strain increases. This is due to the fact that these mechanical deformations are due to interactions between different cellular components in the ECM, rather than the interaction between the interstitial fluid and the ECM. The strain where the delamination occurs is higher in the ACP than the ACFC. This is due to the fact that this delamination may enable the ACFC to more effectively dissipate excess energy when high loads are applied. Delamination is present at all three strains in the MC due to the more complex ECM structure of the fibrocartilage, which makes delamination between the collagen fibers more likely. Bridging is the response of the material to a compressive load where permanent damage occurs to the material the load bearing elements run through, and the load bearing elements form bridges across the damage. Bridging only occurs with the MC. This response is indicative of irreversible damage to the cartilage. Within the meniscus, 135 the collagen fibers run perpendicular to the other components of the ECM, making this type of mechanical deformation probable. Figure 4-24: Mechanical Deformation: (a) Delamination point indicated as a local minimum in the unloading curves. (b) Bridging point indicated as a local minimum in the unloading curves. Based on the results from the mechanical deformation analysis, it is clear that articular cartilage and fibrocartilage have different responses to the compressive mechanical load. This is expected due to the well-established difference in structure. The mechanical deformation analysis is limited to tissues where an extensive amount of characterization has been conducted on the physiology of the tissue. While this is sufficient when establishing baseline measurements for different tissue types, it will not be able to be translated to results from individual patients or poorly characterized diseases. 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This is due to the unique structure of the extracellular matrix (ECM) that gives tissues both their function and biomechanical characteristics. Within certain forms of cancer, the biomechanical behavior of the tissue changes as the disease develops due to restructuring of the ECM [1-6]. Therefore, the biomechanics of tissues has the potential for use as a diagnostic and prognostic marker for cancer. However, the lack of existing instrumentation has prevented the biomechanical behavior of tissues from being incorporated into the standard of care [1]. Optical Fiber Polarimetric Elastography (OFPE) has been demonstrated as a novel method for characterizing the biomechanics of tissues with higher resolution than previous methods [7-9]. This improvement in resolution could lead to a more comprehensive understanding of how biomechanics impact cancer development. In order to explore this possibility, we used OFPE within patient samples to determine the biomechanical profile of different regions of tissue removed during surgical tumor resection. Though these results are incomplete, they demonstrate that OFPE can resolve the difference between different regions of tumors. In turn, these results lay the foundation for future studies into the role of biomechanics in tumor progression. Figure 5-1 depicts the relative stiffness of the normal and cancerous tissues tested in Chapter 5 using the OFPE instrument. The majority of variation of the stiffness and biomechanical profiles of the tissues tested derives from the unique ECM of each tissue type [1-6]. For this reason, the tissue stiffness does not necessarily directly correlate 143 between the normal tissue and the cancerous tissue. For example, colon tissue has a lower Young’s modulus than pancreatic tissue, but colon cancer has a higher Young’s modulus than pancreatic cancer. Additionally, the Young’s modulus values for normal and healthy tissue are subsets of a range, and have not been well characterized in patient tissue. Figure 5-1: Summary of the Young’s Modulus of patient tissues profiled with the OFPE instrument: liver, liver cancer, colon, colon cancer, pancreas, and pancreatic cancer. The values of the biomaterials tested vary by three orders of magnitude [1, 10-15]. The results from OFPE testing of matched normal and cancerous tissue from cancer patients are presented in this chapter. They demonstrate that OFPE can be used to characterize normal and diseased tissues within the same patients. OFPE is uniquely suited to measuring the biomechanical behavior of normal and cancerous tissues because it is a high resolution, non-destructive, and portable system. Eventually the goal is to use OFPE in parallel with existing methods to determine if tissues are healthy or diseased without knowing their pathology before testing. Such testing could serve as a therapeutic biomarker and supplement current prognostic indicators. Using pathology images of tissues before and after compression, we demonstrate that OFPE is non-destructive. We demonstrate that normal and diseased tissues have unique biomechanical profiles depending on their physiology. 144 5.2 Patient Clinical Testing Methods with OFPE Patient clinical tissue testing with the OFPE instrument is conducted using tissue removed by a surgeon, during tumor resection surgery. The main goal of the study is to assess the reproducibility of characterizing normal and diseased tissue samples from the same patient. The secondary goal of the study is to assess which downstream markers are the best for correlating the OFPE measurement to clinical pathologies. The results from one liver cancer and one colon cancer patient are presented in this chapter. Pathologists collect tissue samples after resection by surgeons on USC Health Sciences Campus. Research is conducted in collaboration with Dr. David Agus and Professor Shannon Mumenthaler in the Lawrence J. Ellison Institute for Transformative Medicine of USC. To obtain tissue samples, surgeons remove sections of primary solid tumor during resection surgeries from patients with pancreatic, colon, or liver cancer. The tissues are transferred from the surgeon to a pathologist who performs the required clinical tests. Excess tissue is transferred from the pathologist to us through an IRB approved protocol (University of Southern California IRB Approval 0S-16-1). Tissues are placed in RPMI cell culture media (Gibco) on ice until testing. Testing occurs within two hours of resection to ensure that the biomechanical properties of the tissue have not changed due to the onset of rigor mortis [16]. One issue with our protocol is that the time for testing is limiting due to the complexity of obtaining tissue within the clinical setting. Often we are notified of a sample when the time since resection is greater than two hours. Therefore, we cannot test even though we have prepared to receive tissue. In the eighteen months since we have 145 been enrolling patients, we have had twenty-three opportunities to test. However, in nine of these cases we did not received the tissue in time to perform the OFPE measurements before the onset of rigor mortis. 5.3 OFPE Testing Protocol 5.3.1 Tissue Preparation The samples are cut into 7mm x 7mm x 5mm (l x w x h) rectangles (Figure 5-2). N>4 samples are prepared for each patient and tested to enable rigorous validation of the method. Currently, two samples are cut from normal tissue and two samples are cut from distinct regions of the tumor. The number of samples is limited by the time required for testing. With the single fiber system one sample takes 15 minutes to test at 10%, 20% and 30% strain. The arrayed configuration of the OPFE device can be used to increase the number of points within a sample. Therefore, the array enables a more comprehensive understanding of the tumor by expanding the number of replicates within a patient’s tissue. Figure 5-2: Diagram of a section of patient tissue used for OFPE testing. Dimensions of the tissue sample are 7mm x 7mm x 4mm (l x w x h). These dimensions are used for testing of all human tissue sub-types. 146 5.3.2 OFPE Experimental Parameters In order to determine the biomechanical properties of patient tissue, OFPE is used to characterize healthy and diseased tissue samples (Figure 5-3). Tissue is a viscoelastic material, so the mechanical behavior of the tissue is strain-dependent. In order to determine the biomechanical behaviors of the tissue the normal and diseased tissues are each tested at 10%, 20%, and 30% strain. By testing at multiple strains we determine the mechanical behaviors at different physiological loads. Figure 5-3: Schematic of the OFPE instrument used for testing. Either the single fiber or arrayed system can be used for patient testing, depending on the experimental parameters of interest. The total loading interval is 15 seconds and the unloading interval is 15 seconds for a 30 second total interval. To determine the strain (Δh/h) and the strain rate (Δh/time), first the initial height of the sample is measured. Then, the desired strain is multiplied by the height to give Δh for the strain. The Δh is then divided by 15 seconds to determine the strain rate. The Δh values are 0.4, 0.8 and 1.2mm. The strain rates are 0.027, 0.053, and 0.08mm/sec. 147 The single fiber configuration is used for proof of concept experiments to demonstrate that human samples can be tested with OFPE. This configuration enables the user to take point measurements within a sample and determine the loading and unloading curves for compressive testing of the sample. However, with the single fiber system, only four measurements can be conducted in the time between when the samples are obtained and the onset of rigor mortis. Therefore, we have set up the array configuration in anticipation of tissue testing for twelve patients. However, for a variety of reasons we have not been able to obtain tissue from any of these patients. 5.3.3 Downstream Molecular Analysis After OFPE testing, subsequent molecular analysis is performed on the tissue samples to study the correlation between biomechanical properties and phenotype (Figure 5-4). Because the OFPE method is non-destructive, a variety of downstream analyses can be performed [8]. Based on the literature, we select four methods with which to investigate the underlying biology: (1) Hematoxylin and Eosin (H&E) imaging, (2) Immunohistochemistry (IHC) and Second Harmonic Generation (SHG) imaging, (3) qPCR and targeted genomic sequencing, and (4) generating organoids and cancer- associated fibroblasts. After OFPE testing, the sample that was compressively tested is split into two sections. The first is formalin fixed and made into slides for imaging. The second is used for qPCR analysis of the molecular phenotype, and frozen for future sequencing once a larger patient cohort has been enrolled. Any tumor tissue remaining after the sections for OFPE are cut from the tumor sample is combined, digested, and used to grow organoids. The primary goal of our downstream studies in humans is to 148 understand the causality of ECM structure and cellular plasticity in tissue biomechanics. With these methods, we aim to better understand this relationship in order to identify prognostic factors. Figure 5-4: Flow chart of planned future downstream molecular analysis of patient samples after they have been characterized with OFPE. The biological assessment is performed by collaborators or in core facilities. Using a subset of slides, a Hematoxylin and Eosin (H&E) stain is used to analyze the tissue microstructure. The Hematoxylin (blue/purple) stains acidic components of the tissues such as DNA. The eosin (pink) stains basic components of the tissues such as the extracellular matrix (ECM). Therefore, the H&E stain can be used to identify the physiology of different regions of the tissue. H&E is also currently the standard of care for diagnosis and staging cancer. We work with pathologists at USC Keck Hospital and Cedars-Sinai Hospital to identify the characteristics of the samples characterized with OFPE. Using a subset of slides, several imaging methods including immunohistochemistry and multiphoton microscopy are used to characterize the tissues [17-23]. For all imaging and chemical characterization measurements, the tissue samples must undergo significant processing, including staining and fixing with additional 149 reagents. Immunohistochemistry (IHC) is a form of imaging that enables specific biomarkers indicative of stiffness to be selected and imaged [17-19]. This method is limited by the fact that the biomarkers must be known before conducting experiments. IHC images vary depending on the tumor type and include the following targets: liver cancer- BRAF, CDKN2A, CTNNB1, NRAS, STK11 [24-26]; pancreatic cancer - KRAS, SMAD4, and p16 [27-29]; colon cancer- BRAF, KRAS, PIK3CA, PTEN [30-32]. Multiphoton microscopy is an alternative method of imaging that can be used to resolve ECM structure within the tissue. Specifically, second harmonic generation imaging (SHG) has been used extensively to visualize collagen within different tissues [18-20]. For the molecular analysis of collagen fiber, SHG has high sensitivity across diverse tissue samples [33-35]. In addition to imaging, we use quantitative polymerase chain reaction (qPCR) to study the genetic makeup of the tissue. qPCR is a method of monitoring specific genes with PCR. This method is primarily used to study RNA expression, and is a well- established method for understanding the genetic profile of a tumor [36-38]. The qPCR measurements serve as a baseline for the patient tumor. When tumor cells are subsequently cultured and subjected to different environments, additional qPCR studies are used to determine how the tumor changed in response to external factors. In the future, targeted sequencing will be done to understand the mutational profile of each patient. RNA-seq will be used to obtain a comprehensive picture of the RNA expression profile. In addition to studying the properties of the tissue samples themselves through imaging and qPCR, cell lines are derived from the patient tissue. Once the tissue is 150 digested to the cellular level, it is split into two; half is seeded into a soft gel matrix for growing organoids, and the other half is seeded onto a plastic dish. The difference in mechanical properties of the environment promotes growth of different cell types. The soft gel allows epithelial cells to grow into organoids, and stiff plastic allows the cancer- associated fibroblasts (CAFs) to proliferate. Organoids are 3D systems derived from primary cell lines that retain many features of the originating tissue, and which have not been immortalized. These cultures can be used as a more realistic in vitro method to study the impact of different environmental factors on cancer progression [39-46]. This component of the project is being led by researchers under Dr. David Agus and Professor Shannon Mumenthaler. They have developed methods for growing organoids and CAFs from our patient tissue. We can modify the mechanical properties of the ECM scaffolding to monitor if there are phenotypic changes, as well as do any range of genetic and environmental perturbation studies (i.e. gene knockouts and drug response). These experiments are ongoing, but have the potential for future applications in personalized medicine. Clinical tests are still in progress because it is difficult to establish correlation from single patient data. The eventual goal is to accrue enough patients to use these established methods to determine the relationship between the Young’s Modulus of tissue, ECM composition, and cellular plasticity in the three cancer sub-types covered by the IRB protocol. 151 5.4 Data Analysis Several methods are used to analyze the data obtained with the OFPE instrument. Using the ΔPol calculated at each 30msec interval, we generate a loading and unloading curve. The ΔPol is directly proportional to stress, due to the photoelastic effect. Therefore, our loading and unloading curves are effectively Stress vs. Strain curves. The loading and unloading curves provide information into the biomechanical properties of the tissue, including relative stiffness, compressibility, and viscoelasticity. They can also be used to generate more quantitative metrics that can subsequently be used to compare different samples and tissues. The data from the loading and unloading curves, obtained from the patient tissue, is analyzed in two complementary ways. The first method is a measurement of the total energy loss of the system during the OFPE measurement. The second method is a pairing of local maximum and local minima of the loading and unloading curves to known physiological properties. These points can be used to identify the biomechanical deformations to characterize the tissue or to track the dependence of the biomechanical behaviors on strain. To quantify the energy loss, the area between the loading and unloading curves is calculated [8]. The energy loss is determined by taking the integral of the unloading curve and subtracting it from the integral of the loading curve. As such, all of the points in the loading and unloading curve are used in its calculation. Quantifying the mechanical behavior of a material using the energy loss is the convention within the material science and mechanical engineering community [47]. This method has also been demonstrated to 152 be useful for characterizing the tissue biomechanics of tissue testing with OFPE in Chapter 4 and the associated texts [7, 8, 48]. To quantify the mechanical defects within the material, the local maxima and minima are identified on the loading and unloading curves. By identifying the maximum and minimum points on the curve the physiological changes that cause them can be determined. Based on how the mechanical behaviors within the tissue change with time, additional information regarding the biomechanical characteristics of the tissue can be inferred [48]. 5.5 Patient Clinical Samples Results and Discussion 5.5.1 Liver Cancer Patient (CCTU-12935) Liver tissue is spongy and has a relatively homogenous microarchitecture due to its physiological function as a filter [49]. Liver cancer is common, with 40,000 new diagnoses each year in the United States [50]. Liver cancer is more likely to develop in patients with a history of fibrosis, cirrhosis, Hepatitis B, and Hepatitis C [51-54]. These diseases all impact the ECM structure of the liver, and there is believed to be a correlation between these changes and increased risk of cancer [55-57]. Based on these characteristics, it was selected for testing with the OFPE instrument. Figure 5-5 shows the loading and unloading curves for a representative sample of normal liver. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. The liver is one of the softest and most homogenous tissues within the body. The OFPE instrument is able to resolve both of these characteristics. 153 Figure 5-5: (a) Loading and unloading curves for a normal liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.66E-7, 1.43E-8, and 1.86E-8 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the normal liver. Figure 5-6 shows the loading and unloading curves for a representative sample of one region of the patient’s liver cancer. Macroscopically, this section appeared to be a dark red color; the H&E staining shows that there was extensive infiltration of blood cells. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. The OFPE instrument is able to resolve the difference in the biomechanical behavior of the cancer when compared to the normal tissue. This is especially pronounced at 20% and 30% strain by the unique shape of the loading and unloading curve. 154 Figure 5-6: (a) Loading and unloading curves for one region of the cancerous liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 2.46E-7, 1.46E-7, and 1.95E-8 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the one region of the cancerous liver. Figure 5-7 shows the loading and unloading curves for another representative sample of one region of the patient’s liver cancer. Macroscopically, this section appeared to be white and more fatty, which is confirmed by the H&E imaging. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. The OFPE instrument is able to resolve the difference in the biomechanical behavior of the cancer when compared to the normal tissue and other region of the cancer. This is especially pronounced at 20% and 30% strain by the unique shape of the loading and unloading curve. 155 Figure 5-7: (a) Loading and unloading curves for one region of the cancerous liver sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.33E-7, and 3.12E-7, for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the one region of the cancerous liver. There are three key features observed within the loading and unloading curves for both the normal and cancerous liver tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual strain within each sample after each run. This signifies that with each loading and unloading interval, there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that as the rate of compression and maximum strain increases, the maximum stress increases. Third, the non-linearity of the mechanical behavior of the liver increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. One feature that is unique to the normal liver tissue in this patient is that the tissue exhibits steatosis. Steatosis is abnormal retention of lipids, which can impair the normal 156 processeing of triglyeride fats within the body [49]. This behavior is consistent with the theory that the liver tissue frequently exhibits abnormal ECM matrix characterisitics before cancer forms [55-57]. The OFPE instrument can resolve this difference between the normal tissue and cancer tissue, as evidenced by the plateau in the strain after the buckling point. One feature that is unique to the the first cancerous region of the liver is that there is almost no fat, and there is significant infiltration of red blood cells in the tissue. This behavior is a result of increased vascularization of this region of the tumor. This difference in the tumor structure most likely leads to the unique behavior observed after the buckling point within the sample. One feature that is unique to the second cancerous region of the liver is that there is an extrodinary amount of steatosis. In fact, the H&E image looks more similar to adipose tissue than to liver tissue, which is normally defined by hepatocytes [49]. At 20% strain, this characteristic accounts for the decrease in the maximum strain with each consective run. At 30% strain, this characteristic results in a plateau after the first buckling point before the secondary buckling point. The energy loss increases as the strain increases for both normal and cancerous regions of the tissue (Figure 5-5b, Figure 5-6b, and Figure 5-7b). At high strain rates, the energy loss decreases in subsequent runs. This behavior is because the samples are damaged by the compression used during OFPE testing. The damage in the liver sample most likely arises from the destruction of the nanoarchitecture of the connective fibers of the tissue. Damage to these fibers impacts the sample elasticity, but is not visible on H&E images due to the small scale. 157 One feature that is unique to the energy loss observed in the normal liver is that it changes very little even with an increase in strain. This behavior has not been observed in tissues previously and is a result of the high fat content of the tissue. Given that the tissue has such a high fat content, this behavior is expected, if atypical. One feature that is unique to the the first cancerous region of the liver is that at 20% strain there seems to be no pattern in the energy loss. This pattern is not repeated at 30% strain. This behavior indicates that this tissue has viscoelastic properties that have not been oberved in previous samples. Work is currently being conducted by the Armani Research group to try and model this behavior and determine which ECM elements generate this unique behavior. The energy loss of the second cancerous region of the liver is similar to the normal liver tissue. This behavior is a result of the fact that both tissues are primarily characterized by the high fat content of the samples. This is an interesting finding because few of the tissues previously tested with OFPE have had high fat content. The ability of OFPE to detect differences despite similar energy loss highlights a strength of using this method. Additionally, these results indicate that even the normal regions of tissues in these patients may be more similar to cancer than tissue from a truly healthy individual. 5.5.2 Colon Cancer Patient (CCTU-12982) Colon is an organ involved in reabsorption of nutrients and passage of stool through the digestive tract. There are four unique regions of the colon: (1) ascending colon, (2) transverse colon, (3) descending colon, and (4) sigmoid colon. The colon also 158 has several layers, the mucosa, sub-mucosa, muscularis proparia, and serosa [49]. Depending on the region, the microarchitecture differs due to its physiological function, but all colon tissue is intrinsically highly heterogeneous [49]. Colon cancer is common with over 140,000 new diagnoses each year in the United States [50]. Additionally, recent research has highlighted that the location of colon cancer tumors can be correlated with prognosis, but it has not been explained [58-61]. Based on these characteristics it was selected for testing with the OFPE instrument. Figure 5-8 shows the loading and unloading curves for a representative sample of one region of the patient’s normal colon tissue. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. The colon is one of the most heterogeneous tissues within the body. The OFPE instrument is able determine the biomechanical behavior of colon tissue despite its complex structure. 159 Figure 5-8: (a) Loading and unloading curves for a normal colon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 7.05E-9, 6.28E-9, and 6.97E-9 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the normal colon. Figure 5-9 shows the loading and unloading curves for a representative sample of one region of the patient’s colon cancer. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. The OFPE instrument is able to resolve the difference in the biomechanical behavior of the cancer when compared to the normal tissue. This is especially pronounced at 20% and 30% strain by the unique shape of the loading and unloading curve. 160 Figure 5-9: (a) Loading and unloading curves for one region of the cancerous colon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.05E-8, 1.81E-8, and 1.79E-8 for 10%, 20%, and 30% strain respectively. (c) H&E Image of the one region of the cancerous colon. Figure 5-10 shows the loading and unloading curves for a representative sample of a second region of the patient’s colon cancer. The results are highly reproducible in five consecutive 30-second compression tests repeated at three different strains. The OFPE instrument is able to resolve the difference in the biomechanical behavior of the cancer when compared to the normal tissue. This is especially pronounced at 20% and 30% strain, indicated by the unique shape of the loading and unloading curve. 161 Figure 5-10: (a) Loading and unloading curves for one region of the cancerous colon sample where each set of parameters for the compression test is run five times. (b) Energy loss for each run where the maximum error is less than 1.71E-8, 1.86E-8, and 1.79E-8 for 10%, 20%, and 30% strain, respectively. (c) H&E Image of the one region of the cancerous colon. There are three key features observed within the loading and unloading curves for both the normal and cancerous cancer tissue. First, there is a difference in the initial polarization and the final polarization due to the accumulation of residual strain within each sample after each run. This signifies that with each loading and unloading interval there is irreversible compression that occurs. Second, the change in polarization (ΔPol) increases linearly with strain. This signifies that as the rate of compression and maximum strain increases, the maximum stress increases. Third, the non-linearity of the mechanical behavior of the liver increases with strain. This signifies that the viscoelastic behavior of the tissue becomes more pronounced as the rate of compression and maximum strain increases. All three of these behaviors are expected for viscoelastic materials. 162 The normal colon is relatively consistent with past results on healthy colon. It is slightly less reproducible at high strains, indicating the sample may be quite heterogenous. In comparison, the first cancerous region of the colon is primarily characterized by an atypical unloading curve. There is high stress mismatch between the loading and unloading curves, which indicates the tissue is highly compressible. The H&E images of the colon cancer region one is like a seed pod from a lotus plant, representing abnormal villi structures. This demonstrates an ECM structure unlike any tissue previously characterized using OFPE. The second cancerous region of the colon is much more similar to the normal colon tissue musculature. However, the curves are less reproducible, indicating the second tumor region is more heterogenous than the normal region. The energy loss increases as the strain increases for both normal and cancerous regions of the tissue (Figure 5-8b, Figure 5-9b, and Figure 5-10b). At high strain rates, the energy loss decreases in subsequent runs. This behavior is because the nanoarchitecture of the samples are damaged by the compression used during OFPE testing. The damage in the colon sample most likely arises from the destruction of the nanoarchitecture of the connective fibers of the tissue. Damage to these fibers impacts the sample elasticity, but is not visible on H&E images due to the small scale. The energy loss profiles of both the normal colon and the second colon cancer region are similar. At high strains, the first two runs have much higher energy loss, and subsequent runs experience a lower energy loss. This behavior is likely due to the destruction of the nanoarchitecture of the samples. 163 One feature that is unique to the energy loss of the first cancerous region is that there seems to be little to no pattern in the energy loss at high strains. This behavior is a result of the complexity of the structure as seen on the H&E images. Additionally, the loading and unloading curves appear to cross. The same behavior of the curves crossing was observed in OFPE testing of cartilage tissues. Based on past results, if the loading and unloading curves cross, then the energy loss no longer remains a good predictor of the biomechanical characteristics of the tissue. Therefore, while the results from this tumor region are confusing, they are most likely incomplete and should not be used to compare to the other regions of the tissue. 5.6 Downstream Molecular Analysis Results In accordance with the downstream molecular analysis methods, slides have been created from the samples tested with OFPE. However, to date, imaging of the human samples has been limited to H&E stains. The targets for IHC have been selected, and are as follows: liver cancer- BRAF, CDKN2A, CTNNB1, NRAS, STK11 [24-26]; pancreatic cancer - KRAS, SMAD4, and p16 [27-29]; colon cancer- BRAF, KRAS, PIK3CA, PTEN [30-32]. They are currently being optimized with the slides generated from OFPE. Initial viability analysis was done with a TUNEL assay on the slides. However, due to the inconsistency of results, this method will not be used in molecular analysis for future patients. Using another sample of the cancer tissue, qPCRs were performed on the tissue to look at stiffness and cancer markers. However, due to the fact the protocol is not yet well- established, characterizing tissue proved to be inconclusive due to the heterogeneity. 164 Work is actively being conducted to determine a good control gene and protocols for studying the primary cancer tissue via qPCR. A cancer-associated fibroblast (CAF) line is derived from colon cancer patient 12982. From this culture, qPCRs were performed to characterize the cultured cells as CAFs. First, the qPCR is used to confirm that the cells grown from the patient tissue express common CAF markers like alpha-SMA, Vimentin, and Fibronectin, but not common epithelial markers like EpCam and E-Cadherin. Second, qPCR is used to assess any changes in response to passaging and drug treatment. Additionally, co-culture experiments are preformed with the 12982 CAF line and HCT116 (an established colon cancer epithelial cell line). The relative growth rates of HCT116 are assessed, and we determine whether the presence of CAFs has a drug protective effect. These experiments are ongoing, and no conclusions have been drawn. It is clear from these results that downstream molecular analysis is still in progress. Molecular methods are complex, so we are actively optimizing the protocols in collaboration with the Lawrence J. Ellison Institute for Transformative Medicine of USC. Additionally, it is difficult to establish correlation from single patient data, so this work remains in the preliminary stages and currently incomplete. The goal is to continue studying patients using these methods to determine the relationship between the Young’s Modulus of tissue, ECM composition, and cellular plasticity in the three cancer sub-types covered by the IRB protocol. 165 5.7 Conclusion The OFPE instrument has been used to characterize the biomechanical behavior of healthy and cancerous tissue resected from patients at the Keck Hospital of USC. These preliminary results demonstrate that the data is highly reproducible within the first two hours of resection, and that the OFPE method can distinguish heterogeneity within the tumor. We have developed methods for downstream imaging and molecular analysis to correlate the tissue biomechanics determined with OFPE to cancer phenotype. Due to the complexity of this proposition, this work is ongoing in collaboration between the Armani Research Group and the Lawrence J. Ellison Institute for Transformative Medicine of USC. 166 5.8 References 1. D. T. Butcher, T. Alliston, and V. M. 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Optical Fiber Polarimetric Elastography (OFPE) has emerged as a method for high-resolution mechanical testing of biomaterials that can detect dynamic mechanical behaviors such as buckling, hysteresis, and bridging [4-7]. While this innovative method provides interesting insight into the biomechanical behavior of specific tissues, existing models are unable to support the OFPE results. This is in part due to the fact that, in order to reduce computational load, current models assume that tissues are isotropic, incompressible, and viscohyperelastic [8-15]. The OFPE results in previous chapters clearly indicate that these assumptions do not describe our experimental data. Therefore, there are no existing modeling techniques that we can use to further explore our OFPE results. One solution to the lack of reliable models is to design and fabricate flexible biomimetic structures, to computationally and experientially establish the impact of geometry on the mechanical behaviors. Methods for fabricating flexible structures have emerged to address limitations in developing absorbents, soft robotics, stretchable electronics, and tissue scaffolds [16-22]. The most common methods of fabricating flexible materials are directly writing with elastomeric and hydrogel inks, casting hydrogels, and lithographic etching of silicone elastomer [23-25]. However, due to the complexity of the ECM structures, these current methods are unable to recreate the 172 scaffold geometries. Therefore, we use an alternative method to create an inverse mold of the desired biomimetic structure. Within our method, we 3D print a shell that is then filled with a silicone elastomer to form the final structure [26]. This method enables the creation of flexible biomimetic structures with nearly arbitrary geometries to better understand the implications of our OFPE results [7]. This chapter outlines the creation and validation of a novel method for modeling the impact of the ECM geometry on biomechanical behaviors. Biomimetic structures are designed, fabricated, and computationally modeled using the Finite Element Method (FEM). This method enables alterations in the ECM geometry to be correlated to specific mechanical behaviors. In turn, this enables the scope of experimental parameters to be expanded. As a proof of concept, a model of pancreatic tissue is developed based on past imaging results in the literature [27-33]. Specifically, the buckling point of the pancreatic tissue and 3D printed structures are used to correlate the ECM geometry to the OFPE results. By combining our model and experimental systems, we are able to address gaps in the understanding of tissue biomechanics [7]. 6.2 Methods 6.2.1 Pancreatic Tissue Sample Preparation To obtain pancreatic tissue samples, surgical fellows resect sections of pig pancreatic tissue from animals under anesthesia (University of Southern California IACUC Approval-10843). The organ samples are placed in RPMI media and stored on ice until testing. Individual sections with dimensions of 7mm x 7mm x 4mm (l x w x h) 173 are cut for OFPE testing. All mechanical testing is completed on unprocessed tissue samples within the delay period before the onset of rigor mortis, which starts to occur two hours after resection [34]. To confirm that the structure of the pancreas samples tested with OPFE correlates with past results in the literature, pathology imaging is conducted on the sample. The pancreatic tissues are fixed in 10% neutral buffered formalin for 24-30 hours, paraffin- embedded, and sectioned at 5µm thickness. A hematoxylin and eosin (H&E) stain is performed according the manufacturer's instructions (Leica Biosystems). The stained sections are then imaged using a light microscope. An example of the images obtained after H&E staining is shown in Figure 6-1. Figure 6-1: (a) Sections of pancreatic tissue are stained with hematoxylin and eosin (H&E) and imaged using a light microscope to inform the design of a model of the ECM structure within the pancreas. (b) Simplified structures are drawn in SolidWorks based on the H&E images and past results from the literature. This geometry is subsequently used for FEM modeling and fabricating biomimetic structures. 6.2.2 Biomimetic Structure Design The results from H&E imaging (Figure 6-1a) and past characterization of pancreatic tissue in the literature, are used to develop a simplified model of the ECM structure in SolidWorks (Figure 6-1b) [27-33, 35]. The structure is an orthorhombic crystal structure with an interconnecting support lattice. To study the impact of the ECM 174 geometry on the mechanical characteristics, two experiments are designed. In the first experiment, five variants on the base structure are created by changing the diameter (D) of the beams while holding the length (L) constant, providing a range of D/L values spanning from 0.11 to 0.25. In the second experiment, six variants on the base structure are created by systematically removing different support beams from one face of the structure. The arrows in Figure 6-1b indicate which support beams are removed. In this set of structures, the D/L ratio is fixed at 0.25. This D/L ratio is chosen because it most closely matches the physiological parameters of our system. 6.2.3 FEM Modeling In collaboration with Professor Qiming Wang and An Xin of the USC Viterbi Sonny Astani Department of Civil and Environmental Engineering, we use SolidWorks to build a FEM model of the pancreatic ECM that can be solved computationally. This provides additional insight into the role of the different geometries designed to mimic the ECM structure. Within the FEM model, a series of analytical functions are used to describe the materials that comprise the structures. The biomimetic structures are fabricated from a hyperelastic material. Thus, the following equation can be used to describe the elastic behavior of the materials in terms of a strain energy function [36]: 𝑊= 𝐶 !" 𝐼 ! −3 ! ∙ 𝐼 ! −3 ! ! !!!!! (6-1) To fit the results to a neo-Hookean model, the strain energy function is derived from the reduced polynomial model. Equation 6-2 is modified to reflect this change [37]: 𝑊= 𝐶 !! 𝐼 ! −3 ! + ! ! ! 𝐽 !" −1 !! ! !!! ! !!! (6-2) 175 where j = 0, J el is the elastic volume ratio, 𝐼 ! is the first invariant of the deviatoric strain, and N is the number of terms in the strain energy function. The material constants C i0 and D i describe the shear behavior and the compressibility of the material, respectively. For the purposes of this work, the structures are created from silicone, which is a neo- Hookean material and with the material coefficients of 0.5 (C 10 ) and 0.1 (D 1 ), respectively. A displacement load of 0.5mm is applied to the top surface of the structure to simulate a compressive load. A mesh of 0.09mm is applied to the structure. Leveraging the structural symmetry, boundary conditions are built along the five planes of symmetry to decrease the computational cost. The strength of the FEM model is that, in addition to looking at different geometries, different loading conditions can be applied to study the strain-dependence of the ECM. Therefore, the flexibility of the FEM model gives us the ability to interrogate research questions that would be impossible using OFPE alone. 6.2.4 Biomimetic Structure Fabrication In order to fabricate the biomimetic structures, we collaborated with Professor Qiming Wang and used his facilities to conduct projection microstereolithography of the biomimetic structures designed in SolidWorks. Lian Lash-Rosenberg (group member who defended her Masters thesis in 2017) designed and fabricated the structures based on pancreatic tissue. Projection microstereolithography is used to 3D print the biomimetic structures. The models created in SolidWorks replicate the ECM structure of the pancreas. These models are used to 3D print hollow scaffolds using projection microstereolithography. The scaffolds are printed from a photoresin comprised of N,N- 176 Dimethylacrylamide (40%wt), Methacrylic Acid (40% wt), Methacrylic Anhydride (7% wt), Polyvinylpyrrolidone (11% wt), 2,4,6-Trimethylbenzoyl, and Phosphine Oxide (2% wt) [26, 38]. In this method of projection microstereolithography, the system prints a single 2D slice of the structure, using UV light to cure each layer before printing the subsequent layers. This process is performed iteratively to create the scaffold [26]. Once printed, the scaffold sits in ambient lab conditions for 2hrs to ensure it is dry (Figure 6-2a). If additional drying is desired the scaffolds can be rinsed thoroughly with ethanol (squirting ethanol in the channels until the liquid runs clear) and then placed in the UV curing box for 30 minutes. Subsequently, the scaffold is filled with a tin- catalyzed silicone elastomer (Mold Max NV14) using a syringe pump (Figure 6-2b). A mixture with a 10:1 ratio of base to crosslinker is used for the silicone elastomer. The silicone elastomer is then cured for 12hrs at 25°C. After the silicone elastomer cures, the scaffold is dissolved away by placing the structure in 1mol/L NaOH for 6hrs. The elastomers are cleaned and rinsed in deionized (DI) water before mechanical testing (Figure 6-2c). Figure 6-2: Fabricating the biomimetic structures has three primary steps. (a) Step 1: a scaffold is 3D printed using projection microstereolithography, (b) Step 2: the scaffold is filled with a silicone elastomer and cured for 12 hours, and (c) Step 3: the scaffold is dissolved using an NaOH bath for 6 hours, freeing the silicone elastomer. 177 6.2.5 Compressive Testing Methods Compressive testing is used to characterize the mechanical behavior of the samples. Different methods of compressive testing are performed based on the sample. The biomimetic structures are tested using an Instron Loadframe (Figure 6-3a) because the posts of the 3D printed structure have the potential to move, which would result in a non-uniform force on the OFPE sensor during compressive testing. Additionally, the 3D printed system is a “scaled-up” version of the biological system. Therefore, the size or scale of the printed system is several orders of magnitude larger than the fibers. The pancreatic tissues are tested using OFPE (Figure 6-3b) because the Instron Loadframe cannot be transported to the BSL2+ environment required for porcine testing. Though they are tested using two different methods, the experimental parameters of compression are the same. Strains of 10%, 20%, and 30% are applied to each sample over a 30 second loading-unloading interval. The strain is varied experimentally by increasing the rate of compression. The loading curve is recorded and used to determine the buckling point. Figure 6-3: Schematics of the two different compressive testing methods used: (a) the Instron system used for mechanical testing of the biomimetic structures and (b) the OFPE system used for mechanical testing of the pancreatic tissue samples. 178 Compressive testing of the biomimetic structures is conducted using an Instron Loadframe (model 5942, Instron). A schematic of the testing setup is shown in Figure 6- 3a. The biomimetic structures are tested at 10%, 20%, and 30% strain. The strain is varied experimentally by increasing the rate of compression. Compression rates of 0.067, 0.13, and 0.2 mm/sec are used. Compressive testing of the pancreatic tissue samples is conducted using OFPE. A schematic of the instrument is shown in Figure 6-3b. The OFPE method is based on the same principle as the Instron Loadframe with an optical fiber acting as the force sensor. The fiber sensor offers a significant improvement in spatial resolution over the loadframe’s dashpot sensor because it is tracking the load on a specific section rather than on the whole sample. The pancreas samples are tested at 10%, 20%, and 30% strain. The strain is varied experimentally by increasing the rate of compression. Compression rates of 0.033, 0.067, 0.1 mm/sec are used. 6.3 Results and Discussion 6.3.1 Results from Compressive Testing of Pancreatic Tissue The loading and unloading curves generated from OFPE testing of pancreatic tissue are shown in Figure 6-4. This testing protocol was previously demonstrated to be below the threshold of tissue damage [6]. In the pancreatic tissue sample previously published, the buckling point of the pancreatic tissue occurs between 22-25% strain. In order to understand how the ECM composition impacts the biomechanical behavior of the tissue, we compare these results to those of the biomimetic structures. We focus on 179 reproducing the observed buckling characteristics through physical and computational modeling. Figure 6-4: OFPE testing results from compressive testing of pancreatic tissue at 10%, 20%, and 30% strain. 6.3.2 Modeling Results The results from the FEM model of the structures conducted by An Xin are presented in this section. In order to understand the impact of changing the geometry of the biomimetic structures on the buckling behavior, FEM models are developed. Two different sets of geometric changes are modeled to understand the relative impact of structural elements and expand the scope of the experimental 3D printed work. The first set of geometric changes investigates the dependence of the mechanical behavior on the ratio between the diameter and length (D/L) of the pillars. The second set of geometric changes investigates the impact of removing support pillars. The second set of models matches the experimental structures and provides a way to validate the modeling wok. 180 The buckling point can be quantified using the FEM models. Example images from FEM modeling of the biomimetic structures are presented in Figure 6-5. Figure 6-5: Images from FEM simulation of the buckling of the biomimetic structure with a D/L ratio of 0.21. As the strain increases, buckling begins to occur. The structure undergoes several unique regimes during the mechanical testing (a) before compression occurs, (b) during compression but before buckling, (c) during compression when buckling occurs, and (d) during compression after buckling has occurred. Using the results from the FEM model, the stress vs. strain within a suite of five structures with different D/L ratios is plotted in Figure 6-6a. The D/L ratios modeled vary between 0.11 and 0.25. These values are selected because they are expected to be within the working range of the ECM of the pancreas based on previous studies [27-29]. The model stops at 0.45 strain for the structure with D/L=0.25 because the model can no longer reach convergence at that point. As came be observed in Figure 6-6a, in response to changes in the geometry, the buckling points change. Over the D/L range studied, the dependence of the buckling point on D/L is linear. This linear relationship is plotted in Figure 6-6b. 181 Figure 6-6: Simulation results for buckling characteristics of five biomimetic structures with variable D/L ratios. (a) Loading curves for five simulated structures. (b) Linear fit of the buckling strain for the five simulated structures vs. the D/L ratio. Based on the results from modeling of the D/L ratio, a suite of six geometries where the D/L is fixed at 0.25, and the lattice structure is modified are designed. The geometries of the six structures are shown in Figure 6-7a-f, where the purple beams represent the beams that have been removed. These geometries also match the geometries that were 3D printed. Figure 6-7: A suite of six silicone elastomer structures with known defects are modeled and subsequently fabricated. The structures are modified by removing the support beams of one of the faces of the lattice structure. The removed support beams are indicated in purple. (a) Structure where all the support beams remain intact. (b) Structure where all the support beams are removed. (c) Structure where the middle support beam is removed. 182 (d) Structure where one outer support beam is removed. (e) Structure where both the middle support beam and one outer support beam are removed. (f) Structure where both the outer support beams are removed. Using the results from the FEM modeling of these six biomimetic structures we plot the loading curves (Figure 6-8). Despite the geometric changes, the buckling point remains fairly constant, varying from 0.23 to 0.24. The maximum stress varies from 0.39 MPa to 0.51 MPa and is directly related to the number of pillars that are removed. As expected, the structure with all of the support pillars removed has the lowest maximum stress when it buckles and the structure without any modification to the support pillars has the highest maximum stress when it buckles. Based on these results and the OFPE results, structure (e) represents the buckling characteristics most similar to the pancreatic tissue. However, clearly, changing the D/L value has a larger effect than removing support posts. Figure 6-8: Loading curves generated from simulation results for all six biomimetic structures. The structure names correspond to Figure 6-7. The D/L ratio is held constant at 0.25. 183 6.3.3 Results from Compressive Testing of the Biomimetic Structures The six structures with load bearing elements removed are subsequently fabricated and compressively tested. The results from the compressive testing with the Instron Loadframe of structure (e) are plotted in Figure 6-9. There is good reproducibility between subsequent runs of the same sample at the each strain. Because the individual components of the structure can bend and return to their original configuration, the buckling occurs at the same point within consecutive runs. Deviations are attributed to movement of the sample on the platform between runs. The experimental buckling points are consistent with the simulated buckling points for all six structures. None of the structures exhibit damage in response to repeated compressive loading, as can be seen in the repeatability of the curves. Therefore, the difference in buckling point for each structure is attributed primarily to the geometry of the structures. The geometry in both the biomimetic structures and the pancreatic tissue systems have regions where the structure can bend without breaking. Figure 6-9: Instron Loadframe testing results from compressive testing of the biomimetic structure (e) tissue at 10%, 20%, and 30% strain. 184 6.3.4 Comparison of Pancreatic Tissue and Biomimetic Structure Results While the biomimetic structures are an order of magnitude larger than the microstructures in the pancreatic tissue, the observed buckling behavior and general mechanical response is extremely similar. To understand the parallels between our tissue and the biomimetic structures, the buckling points of five different pancreatic tissue samples are plotted on the linear fit of D/L ratio to buckling point determined with our FEM model (Figure 6-10). Using the FEM results as a calibration curve, we are able to approximate the D/L ratio of the pancreatic tissue samples. Based on our experimental results, buckling within the pancreatic tissue occurs between 22-25% strain. Therefore, our D/L ratio values fall between 0.16 and 0.18. Figure 6-10: Linear fit of the buckling strain for the five simulated structures vs. the D/L ratio. The buckling point for five pancreatic tissue samples, determined with OFPE, plotted alongside the theoretical results. This method provides us with a system for quantifying what components of the ECM of the tissue cause specific mechanical behaviors. Using the results from the fit, we can determine the ECM structure primarily responsible for the mechanical behavior of the pancreatic tissue. Based on the geometry and D/L value, the ECM structure modeled with the biomimetic structures is the collagen 185 IV that comprises the basement membrane of pancreatic tissue. These structures have been well characterized, and are generally described as a chicken wire or honeycomb structure that provides a framework for cells to connect to each other [35]. Each acinar cell is an ellipse that connects to the intercalated duct [39]. Therefore, the acinar lie adjacent to each other, but are only connected by the ECM at one point. This directly corresponds to the biomimetic structure (e), where a single support beam at one end of the structure supports the load applied. Additionally, these structures are roughly 100µm in size and the relative D/L ratio corresponds to the best fit of the model [35]. The relative scale and geometry fits within our imaging, modeling, and biomimetic structural results. Therefore, our model provides an unprecedented way to understand impact of the geometry of the ECM on the mechanical behavior of the tissues. 6.4 Conclusion In conclusion, we have demonstrated a novel method for modeling how geometric changes in the ECM impact biomechanics. This method provides the ability to correlate biomimetic structures to the microstructure of biological tissues analyzed using non- destructive OFPE. In the future, this approach will enable researchers to perform studies focusing on the role that the ECM structure plays on the biomechanical characteristics of the tissue. The biomimetic structures also allow researchers to test these characteristics without being limited to studying resected tissue samples in a short window of time, thus expanding the scope of the experiments they can conduct. In turn, this approach will facilitate a deeper understanding of the mechanical properties of tissues. 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While each chapter contributes to knowledge within the field, there is still work to be conducted in each aspect of the research presented. The following chapter outlines possible future work and applications, based upon the results presented in preceding sections. 7.1 OFPE Instrument Design With regards to the OFPE instrument design, there are several areas that can be explored with future work. The first one is the development and testing of other mechanical methods based on the OFPE instrument. The second one is the incorporation of a calibration step into the measurements, such that stress is reported as the output of the sensor instead of ΔPol. Another is the fabrication of an on-chip fiber array, to increase the portability and decrease the need for optical fiber alignment. Currently, the majority of mechanical testing using the OFPE instrument is conducted with triangle wave of symmetric loading and unloading to 10%, 20%, and 30% strain. This method is able to provide interesting information regarding the mechanical behavior of the samples. However, by only using a single loading and unloading profile, the OFPE methods are limited. These limitations are artificial and were imposed to decrease the initial scope of work. A multitude of alternative mechanical testing methods can be adapted for use on the OPFE system. For example, within mechanical testing of biomaterials stress relaxation curves are common alternatives to loading and unloading curves. In order to change the profile of compressive testing, the 191 automated micrometer would need to be re-programmed to match the desired experimental loads. The second possible modification is to add a calibration step to the data analysis and experimental procedure. In the experiments conducted to date, the ΔPol is plotted vs. strain because ΔPol is proportional to Stress. However, this point can easily be overlooked. As such, it has come up as a point of contention in peer review and conference presentations. To avoid confusion in the future, a method for calibrating the sensor could be developed. In turn, a calibration method may increase the possibility of other research groups adopting this system because the output of the OFPE instrument would be parallel to that of existing systems. One possible calibration method would be to use a weight to apply a known force to the fiber and record the result. In this case, the calibration must be performed after the sensor is set up, and the weight cannot be placed directly on the fiber. Therefore, a method that incorporates the automated micrometer and a sample with known viscoelastic properties is being developed by the Armani Research Group to automate the calibration. The primary area of future research within the OFPE instrument design will be fabrication of a miniature array of polarization maintaining waveguides to improve the portability of the instrument and decrease user training. Currently, the disposable optical fiber sensor alignment limits the scope of the experiments the OPFE instrument can be used to perform. This is especially true for the arrayed system, where there are ten non- keyed junctions where polarization-maintaining elements need to be aligned. The extensive alignment limits the portability and increases the training needed for new users. In order to combat these challenges, one future area of research is to fabricate an on-chip 192 fiber array. By creating a series of polarization maintaining waveguides, the system could be integrated into existing systems. For example, the OFPE instrument could eventually be used as a platform to provide haptic feedback on surgical tools. 7.2 Animal Testing with OFPE The studies on the biomechanical behaviors of animal tissues presented in this dissertation have proven extremely useful in establishing and validating the OFPE instrument. Animal testing provides interesting baseline data and is also informative in developing workflow and initial hypotheses. Due to the established relationships within the USC Keck School of Medicine and USC Viterbi School of Engineering, testing of animal tissues before euthanasia has proven straightforward. Therefore, in exploring future applications of the OFPE instrument, initial studies will continue to be conducted on animal tissues. Due to the frequency of available tissues, the Armani Research Group is conducting several larger experiments. The goal of these studies is to use animal tissue to answer some fundamental questions within the biomaterials community. For example, it is established that the mechanical behavior of tissues changes after the onset of rigor mortis. However, within the literature, there is little to no consistency in the time from resection and storage method before mechanical testing across research groups. OFPE provides a novel way to study how time and freezing impact the biomechanical behavior of tissues. Therefore, the Armani Research Group is actively investigating how storage method and time impact the biomechanical behavior of samples taken from the same 193 primary tissue sample in an attempt to understand existing experimental results and establish consistency within the field. 7.3 Clinical Testing with OFPE The methods for clinical testing with the OFPE instrument and initial results from liver, pancreatic, and colon cancer are presented in this dissertation. However, clinical testing with the OFPE instrument remains one of the largest areas for future work. In ongoing clinical testing, the arrayed OFPE system has been implemented in lieu of the single fiber system. By replacing the single fiber system with an arrayed system, the number of data points within a patient sample is increased and used to generate 2D maps of the stiffness. Moving forward, the goal is to expand the results from individual patients to a larger cohort. Based on these results, statistics will be used to determine the relationship between the Young’s Modulus of tissue, ECM composition, and cellular plasticity in the three cancer sub-types covered by the IRB protocol. 7.4 Modeling of Tissue Biomechanics with 3D Printed Structures Details regarding novel methods for modeling the extracellular matrix geometry to different biomechanical behaviors in pancreatic tissue are presented in this dissertation. Based on these results, additional studies are being conducted in the Armani Research Group to elucidate the role of the ECM in heart and cartilage biomechanics. The goal is that with time, these methods and infrastructure will develop. Thus, future research will always include complementary computational and physical models to support the interpretation of experimental results. 194 Chapter A1. Additional Preliminary Investigations A1.1 Introduction Optical Fiber Polarimetric Elastography (OFPE) is uniquely suited to measuring the biomechanical behavior of biological tissues because it is a high-resolution, non- destructive, and portable method. Due to these advantages, OPFE can be used to answer questions that have persisted within the biomechanics community due to limitations of the instrumentation. One such question is the time-dependence of the mechanical characteristics of biomaterials. Rigor mortis is the third stage of death where the tissues begin to stiffen as a result of chemical changes in the body [1-3]. It is well established that rigor mortis impacts the chemical characteristics and temperature of tissues as soon as they are resected from the body [1-3]. While it has been hypothesized that rigor mortis changes the mechanical characteristics of tissues, no existing methods have been able to demonstrate this theory experimentally. Therefore, research groups either choose to test within two hours of resection to avoid possible effects of rigor mortis, or assume there will be no effects and test within the first forty-eight hours after resection. As a result, there is little consistency in how samples are stored and when they are tested in the literature. This chapter summarizes the preliminary investigations conducted with OFPE to try and understand the impact of experimental parameters such as time and storage method on the mechanical characteristics of several biomaterials. First, we look at liver and cartilage tissue over an 8 hr interval to determine how the mechanical characteristics change. Second, we look at cartilage before and after it is frozen to determine how the mechanical characteristics change. Preliminary results are promising, and indicate that 195 OFPE can be used as a method to begin answering these questions and help establish standards across the biomaterials community. A1.2 Time Course Testing with OFPE The primary goal of the study is to assess the changes in the mechanical behavior of tissues during the first eight hours after they are resected and when they are frozen. Preliminary studies are conducted on porcine liver and cartilage tissue. A subset of these experiments represented the first set of experiments conducted with OFPE on porcine tissue. We tested one sample of tissue for eight hours and compared the loading and unloading curves. Based on our results, we determined that the first four hours of testing the mechanical behaviors remained fairly consistent. To maximize our signal, and avoid any issues with rigor mortis we determined that we would conduct all of our testing within the first two hours after resection. The subsequent experiments in Chapter 4, 5, and 6 are all conducted within this two-hour time frame. After conducting extensive experiments on different tissues, we returned to this question. The results in this chapter are from the experiments we conducted to quantify the changes in the mechanical behaviors of the tissues that we observe with time and sample preparation. Tissues are collected using fresh porcine organs obtained from the Health Sciences Campus at USC. Research is conducted in collaboration with Professor David Agus and Professor Shannon Mumenthaler in the Lawrence J. Ellison Institute for Transformative Medicine of USC and Dr. Nicholas Trasolini and Dr. Rick Hatch in the Orthopedic Surgery Department of USC. To obtain tissue samples, surgical fellows resect 196 sections of tissue from animals under anesthesia (University of Southern California IACUC Approval-10843). Tissues are placed in RPMI cell culture media (Gibco) on ice until testing. For the first set of experiments, testing occurs every hour beginning fifteen minutes after resection to determine if the biomechanical properties of the tissue change due to the onset of rigor mortis. For the second set of experiments, testing occurs once thirty minutes after resection and once after the tissue has been frozen at -80°C for 72 hrs to determine if the biomechanical properties of the tissue change due to freezing. A1.2.1 Time Course Sample Preparation Studies are conducted on porcine liver and cartilage tissue. These organs are chosen because of their wide range in Young’s Modulus values and their relative similarity to human organs. Liver provides a very soft organ with a relatively homogenous and spongy structure. Liver is also currently used in forensics to determine the time since death since it correlates well to the core body temperature [1-3]. Cartilage tissue has a Young’s Modulus three orders of magnitude greater than liver. Additionally, the majority of research on the mechanical behaviors of cartilage is conducted on frozen tissue [4-6]. Tissue samples are cut into 7 mm x 7 mm x 4mm (l x w x h) rectangles (Figure A1-1). N>3 samples are prepared and measured using OFPE from each organ. Testing each organ sub-type extensively enables rigorous validation of the method. The results from a single sample from each of the organs are presented. The changes in biomechanical behaviors of the tissues over time are determined by comparing the loading and unloading curves. 197 Figure A1-1: Diagram of a section of porcine pancreatic tissue used for OFPE testing. Dimensions of the tissue sample are 7mm x 7mm x 4mm (l x w x h). These dimensions are used for testing of all porcine tissue sub-types. A1.2.2 Time Course Testing Protocol In order to determine the biomechanical properties of porcine tissue, the single optical fiber OFPE instrument is used. This configuration enables the user to take point measurements within a sample and determine the loading and unloading curves for compressive testing of the sample. Because tissue is a viscoelastic material, the mechanical behavior of the tissue is strain-dependent. Therefore, the tissues are each tested at 10%, 20%, and 30% strain. A1.2.3 Time Course Data Analysis Using the ΔPol calculated at each 30msec interval, we generate loading and unloading curves for the sample at each time point. From these curves, we determine the biomechanical properties of the tissue. These include relative stiffness, compressibility, and viscoelasticity. For now, our measurements are limited to loading and unloading 198 curves at single. In the future, these curves can be used to generate more quantitative metrics that can be used to compare the time points. A1.3 Time Course Results and Discussion A1.3.1 Liver Results and Discussion Liver tissue is spongy and has a relatively homogenous microarchitecture due to its physiological function as a filter [7]. Additional information about OFPE measurements of normal liver tissue tested before the onset of rigor mortis can be found in Chapter 4 and the associated manuscript [8]. For this experiment, a sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the mechanical properties of liver tissue over a five-hour testing period. N>2 samples of liver tissue are characterized using this protocol on the OFPE instrument. Figure A1-2 shows the loading and unloading curves for a representative sample of porcine liver that is tested seven times over a 5 hr interval. The results are from 30- second triangle wave compression tests repeated at three different strains. At low strain, the response is similar in both the loading and unloading cycles. At low strain, the slope of the response is relatively linear, indicating that the tissue is primarily elastic in this regime. As the strain increases, the hysteresis in the sample increases, indicating that the tissue is less elastic. The liver is one of the softest and most homogenous tissues within the body, which is why its behavior is primarily elastic. 199 Figure A1-2: Loading and unloading curves for a porcine liver sample that has been tested for five hours and is stored at RT between tests. There are two key features observed within the loading and unloading curves for the liver tissue during the first five hours after resection. The first feature is that the maximum change in polarization decreases for every loading and unloading curve for the first four hours. However, in the fifth hour the maximum change in polarization spikes to more than twice that recorded in the previous hour. Based on the characteristics of rigor mortis, this is approximately what is to be expected in the mechanical behavior of a soft tissue such as the liver. The second feature is that the energy loss seems relatively consistent over the entire 5 hr interval. This potentially indicates that the ECM structure remains intact, and the change observed is due to other elements within the tissue. Based on these results, there are three experimental parameters that we will change for subsequent testing. First, the 5 hr interval tested with the liver sample is insufficient to differentiate the changes in the mechanical behavior before and after rigor mortis. Moving forward, we intend to expand the time course over which the measurements are taken. Second, we intend to change how the samples are stored between runs. The sample shown in Figure A1-2 is stored at room temperature (20°C) 200 between measurements. Moving forward, we plan to test three conditions for storage between testing: 4°C, 20°C, and 37°C. This will enable us to study if the storage method impacts how the tissue experiences rigor mortis. Third, we plan to freeze several samples at -80°C for 72 hr and thaw them for subsequent mechanical testing. This will enable us to understand how cold storage impacts the mechanical behavior of tissue samples. A1.3.2 Articular Cartilage Results and Discussion Articular cartilage is a sub-type of cartilage within the knee. Additional information about OFPE measurements of normal articular cartilage tested before the onset of rigor mortis can be found in Chapter 4 and the associated manuscript [9]. For our time course measurements, we use articular cartilage from the femoral condyles (ACFC). ACFC tissue has a striated microarchitecture due to its physiological function of weight bearing and gliding during tibiofemoral articulation [10, 11]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the mechanical properties of ACFC tissue over an 8 hr interval. N>4 samples of ACFC tissue are characterized on this protocol using the OFPE instrument. Figure A1-3 shows the loading and unloading curves for a sample of ACFC. The results before the onset of rigor mortis (0hr to 4hr) are presented in Figure A1-3a. The results after the onset of rigor mortis (5hr to 8hr) are presented in Figure A1-3b. As observed in all of our biomaterials, as the strain increases, the hysteresis in the sample increases. 201 Figure A1-3: (a) Loading and unloading results for a sample of porcine Articular Cartilage from the Femoral Condyles from the first four hours of compression testing. (b) Loading and unloading results for a sample of porcine Articular Cartilage from the Femoral Condyles from hours five through eight of compression testing. There are two key features observed within the loading and unloading curves for the ACFC tissue before the onset of rigor mortis. The first feature is that the maximum change in polarization increases for every loading and unloading curve for the first four hours. Based on the characteristics of rigor mortis, this not what would be expected. However, this is potentially because cartilage is a hard tissue, rather than a soft tissue such as the liver. Therefore, the mechanical behaviors may change differently within cartilage tissues. The second feature is that the energy loss seems relatively consistent over the first three hours of the interval before the onset of rigor mortis. This potentially indicates that the ECM structure remains intact and that the change observed is due to other elements within the tissue. However, at hour four, we see the energy loss drop drastically, and this trend persists after the onset of rigor mortis. This potentially indicates that as rigor mortis sets in the ECM begins to degrade. There is one key feature observed within the loading and unloading curves for the ACFC tissue after the onset of rigor mortis. This feature is that the curves for hour five through seven look almost identical in terms of the maximum change in polarization and the energy loss. This result was unexpected and is under significant investigation. This 202 may be the reason that past research has indicated no change in tissues tested within 24 hr or after freezing. Based on these results, there is one experimental parameter that we will change for subsequent testing. We intend to change how the samples are stored between runs. The sample shown in Figure A1-3 is stored at room temperature (20°C) between measurements. Moving forward, we plan to test three conditions for storage between testing: 4°C, 20°C, and 37°C. This will enable us to study if the storage method impacts how the tissue experiences rigor mortis. This is the final variable to understand this complex system. The focus for ACFC moving forward will simply be to repeat the experiment sufficiently to ensure our conclusions are correct and reproducible. A1.3.3 Fibrocartilage Results and Discussion Fibrocartilage is a sub-type of cartilage within the knee. Additional information about OFPE measurements of normal fibrocartilage tested before the onset of rigor mortis can be found in Chapter 4 and the associated manuscript [9]. For our time course measurements, we use fibrocartilage from the meniscus (MC). MC has a striated microarchitecture due to its physiological function as a shock absorber that enables the joint to distribute large loads [12]. A sample is cut to the appropriate dimensions for OFPE testing and is used to characterize the mechanical properties of MC tissue over an 8 hr interval. N>4 samples of MC tissue are characterized on this protocol using the OFPE instrument. Figure A1-4 shows the loading and unloading curves for a sample of MC. The results before the onset of rigor mortis (0hr to 4hr) are presented in Figure A1-4a. The 203 results after the onset of rigor mortis (5hr to 8hr) are presented in Figure A1-4b. As observed in all of our biomaterials, as the strain increases, the hysteresis in the sample increases. Figure A1-4: (a) Loading and unloading results for a sample of porcine fibrocartilage from the meniscus from the first four hours of compression testing. (b) Loading and unloading results for a sample of fibrocartilage from the meniscus from hours five through eight of compression testing. There are two key features observed within the loading and unloading curves for the MC tissue before the onset of rigor mortis. The first feature is that the maximum change in polarization increases for every loading and unloading curve for the first four hours. Based on the characteristics of rigor mortis, this not what would be expected. However, this result is potentially because cartilage is a hard tissue comprised primarily of high density collagen, rather than a soft tissue such as the liver. Therefore, the mechanical behaviors may change differently within cartilage tissues. This same trend is observed in the ACFC results. The second feature is that the energy loss seems relatively consistent over the first three hours of the interval before the onset of rigor mortis. This potentially indicates that the ECM structure remains intact and the change observed is due to other elements within the tissue. However, at hour four, we see the energy loss drop drastically, and this trend persists after the onset of rigor mortis. This potentially indicates that as rigor mortis sets in the ECM begins to degrade. 204 There are two key features observed within the loading and unloading curves for the MC tissue after the onset of rigor mortis. The first feature is that the maximum change in polarization increases for every loading and unloading curve for the first four hours. This is the same as the trend that was observed before the onset of rigor mortis. This is interesting because it differs from the ACFC results. The second feature is that the energy loss seems relatively consistent, but it is much lower than the energy loss before the onset of rigor mortis. This potentially indicates that as rigor mortis sets in the ECM begins to degrade. Based on these results, there is one experimental parameter we will change for subsequent testing. We intend to change how the samples are stored between runs. The sample shown in Figure A1-4 is stored at room temperature (20°C) between measurements. Moving forward, we plan to test three conditions for storage between testing: 4°C, 20°C, and 37°C. This will enable us to study if the storage method impacts how the tissue experiences rigor mortis. This is the final variable to understand this complex system. The focus for MC moving forward will simply be to repeat the experiment sufficiently to ensure our conclusions are correct and reproducible. A1.3.4 Frozen Cartilage Results and Discussion In addition to studying the impact of rigor mortis on the mechanical behaviors of cartilage, we ran preliminary experiments to study the impact of freezing on the mechanical behaviors of cartilage. These experiments are conducted because many research groups will freeze samples before conducting mechanical testing. For these measurements, we use ACFC and MC cartilage. A sample is cut to the appropriate 205 dimensions for OFPE testing and is used to characterize the mechanical properties of cartilage before and after freezing. We test the samples with the OFPE instrument within 30 minutes of resection. Then, we place the samples in eppendorf tubes with 1.5mL RPMI and 5% DMSO. The eppendorf tubes are stored at -80°C for 72 hr. To thaw the samples, the eppendorf tubes are placed in a 37°C water bath for 30 minutes. Then the samples are tested with the OFPE instrument to characterize the mechanical behaviors after freezing. N>4 samples of ACFC and MC tissue are characterized on this protocol using the OFPE instrument. Figure A1-5 shows the loading and unloading curves for the cartilage samples before and after freezing. The results before and after freezing of the ACFC are presented in Figure A1-5a. The results from before and after freezing of the MC are presented in Figure A1-5b. The results are from 30-second triangle wave compression tests repeated at three different strains. As observed in all of our biomaterials, as the strain increases, the hysteresis in the sample increases. Figure A1-5: (a) Loading and unloading results for a sample of porcine fibrocartilage from the meniscus from the first four hours of compression testing. (b) Loading and unloading results for a sample of fibrocartilage from the meniscus from hours five through eight of compression testing. There are two key features observed within the loading and unloading curves for cartilage tissue before and after freezing. The first feature is that the maximum change in 206 polarization decreases after freezing. This is approximately what is to intuitively be expected in the mechanical behavior of a tissue that has been frozen and then thawed. The second feature is that the energy loss drops dramatically after freezing. This potentially indicates that the ECM structure is severely damaged during the freeze/thaw cycle. A1.3 Conclusion Preliminary studies have been conducted with the OFPE instrument to characterize how the mechanical behavior of three different tissue types change with time. These results demonstrate that there are differences in the mechanical behavior of the three tissues that occur both before and after the onset of rigor mortis. Further investigations are under way to better understand these results and repeat them across multiple samples. Preliminary studies have been conducted with the OFPE instrument to characterize how the mechanical behavior of two different cartilage tissue types change before and after freezing. These results demonstrate that there is a significant change in the mechanical behavior of the tissues after they are frozen. Further investigations are under way to better understand these results and repeat them across multiple samples and additional organs. For now, the results are simply compared by inspection of the loading and unloading curves. In the future, alternative methods of data analysis such as maximum phase difference, energy loss, quasi-linear viscoelastic fitting, and mechanical deformation identification can be used to better understand the result. These results are 207 important to the field of biomechanics because currently the methods of storing biomaterials are different between research groups. This work has the potential to provide the foundation for discussion of standards across the field in order to facilitate collaboration and comparison of results. 208 A1.4 References 1. E. C. Bate-Smith, and J. R. Bendall, "Factors determining the time course of rigor mortis," The Journal of Physiology 110, 47-65 (1949). 2. J. Simonsen, J. Voigt, and N. Jeppesen, "Determination of the Time of Death by Continuous Post-Mortem Temperature Measurements," Medicine, Science and the Law 17, 112-122 (1977). 3. G. De Saram, G. Webster, and N. Kathirgamatamby, "Post-mortem temperature and the time of death," J. Crim. L. Criminology & Police Sci. 46, 562 (1955). 4. B. L. Wong, W. C. Bae, J. Chun, K. R. Gratz, M. Lotz, and R. L. Sah, "Biomechanics of cartilage articulation: Effects of lubrication and degeneration on shear deformation," Arthritis & Rheumatism 58, 2065-2074 (2008). 5. L. A. Setton, V. C. Mow, and D. S. Howell, "Mechanical behavior of articular cartilage in shear is altered by transection of the anterior cruciate ligament," Journal of Orthopaedic Research 13, 473-482 (1995). 6. M. Szarko, K. Muldrew, and J. E. A. Bertram, "Freeze-thaw treatment effects on the dynamic mechanical properties of articular cartilage," BMC Musculoskeletal Disorders 11, 231-231 (2010). 7. D. Kasper, A. Fauci, S. Hauser, D. Longo, and J. Jameson, Harrison's Principles of Internal Medicine (McGraw-Hill Education, 2015). 8. A. W. Hudnut, B. Babaei, S. Liu, B. K. Larson, S. M. Mumenthaler, and A. M. Armani, "Characterization of the mechanical properties of resected porcine organ tissue using optical fiber photoelastic polarimetry," Biomed. Opt. Express 8, 4663-4670 (2017). 9. A. W. Hudnut, N. A. Trasolini, G. F. R. Hatch, and A. M. Armani, "Biomechanical Analysis of Porcine Cartilage Elasticity " Under Reveiw (2018). 10. L. A. Setton, D. M. Elliott, and V. C. Mow, "Altered mechanics of cartilage with osteoarthritis: human osteoarthritis and an experimental model of joint degeneration," Osteoarthritis and Cartilage 7, 2-14 (1999). 11. V. C. Mow, A. Ratcliffe, and A. Robin Poole, "Cartilage and diarthrodial joints as paradigms for hierarchical materials and structures," Biomaterials 13, 67-97 (1992). 12. Q. Li, F. Qu, B. Han, C. Wang, H. Li, R. L. Mauck, and L. Han, "Micromechanical anisotropy and heterogeneity of the meniscus extracellular matrix," Acta Biomater. 54, 356-366 (2017). 209 Chapter A2. Asymmetric Toroid Optomechanics A2.1 Introduction Integrated optical devices are devices comprised of optical components that have been fabricated directly onto a silicon wafer. The primary advantage of these systems is the ability to fabricate many components together in complex configurations onto a single, compact system on a wafer [1]. One such system is a whispering gallery mode resonator, which can be directly fabricated onto silicon wafers (Figure A2-1). Based on their geometry and optical properties, including the interaction with the environment, whispering gallery mode resonators are ideally suited for detection applications [2-4]. The quality factor is a measure of the device efficiency. Their unique optical behavior can be modeled and monitored through a variety of different measurements. Specifically within the field of biology, these optical cavities have been demonstrated to be highly efficient devices for label-free biosensing applications [5-8]. Label-free biosensing is a significant advancement within biodetection because it can be used to identify a variety of different biomarkers rather than a single chemically-amplified signal. 210 Figure A2-1: Integrated optical devices can be fabricated on a silicon wafer. One example is a microtoroid where silica toroids are fabricated onto a silicon wafer. This figure depicts a scanning electron microscope (SEM) image of one such microtoroid. High Quality Factor (Q) whispering gallery mode resonators exhibit optomechanical vibrations at low input optical powers higher due to a build up of the radiation pressure within the device [9-16]. The deformation pattern of excitable optomechanical modes that can be excited is inherently limited by the cavity geometry and power coupled into the device [17]. In radially symmetric cavities, there are two categories of optomechanical modes that are excited, the cantilever mode and the crown mode. If the fundamental symmetry of the device is changed through novel fabrication methods, the properties of the radiation pressure within the device are modified. Thus, the optomechanical modes excited at the lowest input powers shift. By developing a novel fabrication method for creating asymmetric whispering gallery mode resonators, we were able to modify the optomechanical energy transfer process and excited two new modes, the asymmetric crown mode and the asymmetric cantilever mode. The new modes exhibit a change in both the frequency and behavior of the optomechanical oscillations. The following chapter summarizes the work done as part of a collaboration with Soheil Soltani (group member who defended in 2017) to develop a repeatable and precise 211 method of fabricating asymmetric, high optical Q devices. Initial modeling work was performed by Maxwell Reynolds (an undergraduate researcher). By characterizing the optomechanical vibrations of the devices, we show that the asymmetric resonators demonstrate previously unobserved self-exciting optomechanical modes at sub-mW threshold powers. A2.2 Methods Asymmetric microtoroids were a previously unrealized system within the field of optical microresonator research. Asymmetric microtoroids were fabricated in order to study the impact of device symmetry on the optomechanical modes that occur within whispering gallery mode resonators [17]. Their unique geometry is characterized primarily by a non-uniform torus (Figure A2-1). Figure A2-2: (a) Rendering of an asymmetric microtoroid device. (b) Schematic of an asymmetric microtoroid device with parameters labeled including: minimum minor radius (r min ), maximum minor radius (r max ), maximum major radius (R max ), minimum major radius (R min ), and total diameter (D). (c) SEM cross section of an asymmetric microtoroid device. A2.2.1 Modeling Based on the geometry of the device a FEM model for predicting the properties of the optical mechanical oscillations was developed in COMSOL. To solve for the optomechanical modes numerically, Soheil Soltani developed a theoretical model which 212 is briefly explained in this section. More detailed information is contained in the associated paper [17]. Asymmetric whispering gallery mode resonators exhibit the same fundamental properties as symmetric whispering gallery mode resonators. The damped harmonic oscillator equation can be used to describe the mass of the torus in motion [17]: !! x(t)+ γ 0 2 ! x(t)+Ω 2 x(t)= f (t) m eff + F L m eff (A2-1) where x is the radial displacement, γ 0 is the damping coefficient, Ω is the mechanical frequency, m eff is the effective vibrating mass of the cavity, and f(t) is the optical force. The damping coefficient γ 0 is defined as γ 0 =Ω/(Q m ) , where Q m is the quality factor [10, 17, 18]. The optical force within a circular whispering gallery mode resonator can be described by [17]: f(t)=(2πn|a| 2 )/(cT r ) (A2-2) where n is the refractive index, a is the optical energy amplitude, c is the speed of light and T r is the cavity round trip time. The term (F L ) is added to equation 1 to represent the solution to the equation if there is no optical force, and it represents the force due to thermal noise. 0 (), ( ') ( ') LL B eff Ft Ft kTm t t γδ = − (A2-3) Equations A2-1 thru A2-3 describe the dynamics of motion in the mass. On the other hand, the eigenfrequencies of an asymmetric whispering gallery mode resonator can be calculated in COMSOL using the spatial equation of Hooke's law [17, 19, 20]: (λ+µ) ! ∇.( ! ∇. ! Φ n ( ! r))+µ ! ∇ 2 ! Φ n ( ! r)=−ρω n 2 ! Φ n ( ! r) (A2-4) 213 where (1 )(1 2 ) E σ λ σσ = + − and 2(1 ) E µ σ = + represent the Lamé constants, σ is the Possion’s ratio, E is the Young's Modulus, ρ is the density of the material, and Φ n (r) is the position dependent mode profile function. Therefore, the system is described as a set of damped harmonic oscillators, and the eigenfrequencies of the structure can be solved numerically in COMSOL Multiphysics. In order to model these devices, it is critical to model the precise asymmetric nature or geometric structure which requires a perfectly designed initial structure. This challenge was solved by Max Reynolds, an undergraduate researcher in the group. He developed a way to precisely draw each structure in SolidWorks and import the structure into COMSOL Multiphysics. The SolidWorks drawings were based on measurements of the largest and smallest parts of the torus performed using light microscopy (multiple individuals preformed this task and the values were averaged). Then, within SolidWorks, we created a torus that matched these two extreme radii. To create our devices we created one circle with the smallest radii and one with the largest radii and revolved the two. We created a separate SolidWorks file for the pillar to study how the asymmetric offset changed the frequency by changing the orientation of the two parts within COMSL. The two components of our device were imported into COMSOL using the import wizard from the structural mechanics module. Using this method, we were able to create the exact geometry of the devices that were fabricated experimentally for our simulations. Additional details on the modeling is in Soheil Soltani’s thesis. 214 A2.2.2 Fabrication Symmetric microtoroid devices were fabricated through a well-characterized procedure comprised of photolithography, buffered oxide etching, XeF 2 etching, and CO 2 reflow [21, 22]. Figure A2-3 outlines the steps of microtoroid fabrication. In an attempt to fabricate asymmetric devices, the fabrication process was modified at each step to determine if parameters could be determined to induce asymmetry. The two most effective methods were (1) creating asymmetry during CO 2 reflow and (2) creating asymmetry through a pillar offset during XeF 2 etching. The method of asymmetric device fabrication using CO 2 reflow to create asymmetry proved more reproducible and controllable in terms of tuning the degree of asymmetry (Figure A2-3d). Figure A2-3: Rendering of the microtoroid device fabrication process. (a) Silica pads with a diameter of 150µm were fabricated using photolithography. (b) XeF 2 etching was used to create microdisks, which were silica pad on a silicon pillar created by etching away the silicon under the silica pad. (c) Symmetric CO 2 reflow was used to create a symmetric microtoroid with a uniform torus. (d) Asymmetric CO 2 reflow was used to create an asymmetric microtoroid with a non-uniform torus by offsetting the laser during reflow. During the fabrication process asymmetry was introduced by modifying the alignment of the CO 2 laser, so the CO 2 laser beam was no longer aligned to the silicon pillar. This misalignment creates a non-uniform thermal gradient and results in a torus with a variable thickness. Therefore, the minor and major radii of the device vary with respect to the azimuthal angle. The laser-pillar offset ranged from 60-80 µm, and the laser 215 intensity was increased at a constant rate of 5 W/s to 25 W [17]. The resulting devices had major diameters of 44-48 µm, AR of 0.67-0.9, and pillar offsets (Δz) of 1-3.5 µm. A2.2.3 Device Characterization Optical testing was performed using a Resonator Setup within the Armani Lab [17]. A schematic of the testing setup is shown in Figure A2-4. A tapered optical fiber waveguide couples light from a 1550 nm tunable laser source into the asymmetric optical cavities. The laser was scanned across the resonant frequency of the device, and the transmission spectrum was recorded. The transmission spectrum was later fit to a Lorentzian to calculate the optical quality factor [21, 23, 24]. Despite the asymmetry of the asymmetric devices, they maintain high quality factors that range from 1x10 6 to 3x10 7 . The primary loss mechanism within the asymmetric toroids was radiation loss due to the variation within the optical mode profile [25-27]. An Electrical Signal Analyzer (ESA) was used to measure the mechanical frequency spectrum and the threshold power for the onset of mechanical oscillations [28]. 216 Figure A2-4: Rendering of the testing setup used to measure the mechanical properties of the asymmetric toroids. A 1550nm tunable laser was used as a light source. A tapered optical fiber was used to couple light into the cavity. An oscilloscope was used to track the peaks of the laser. An ESA was used to measure the frequency and threshold power of the optomechanical modes of the toroid. A2.3 Results A2.3.1 Finite Element Method Modeling Results Using the structure import method described previously, COMSOL Multiphysics, a Finite Element Method (FEM) software, was used to numerically calculate the eigen frequencies of the asymmetric structures. Figure A2-5 depicts a subset of the optomechanical frequencies from a single asymmetric device with an aspect ratio of 0.68 and a pillar offset of 2.1 µm. The behavior of the asymmetric device is completely unique. The symmetric crown mode and cantilever mode still exist within the asymmetric device. However, the threshold power to excite them increases. Therefore, the asymmetric crown and asymmetric cantilever mode become the two lowest threshold 217 modes. This is because the optical force is no longer uniformly distributed along the device periphery. As a result, the symmetric mechanical modes require more power to be excited. Figure A2-5: Subset of the FEM simulation results of the optomechanical modes of an asymmetric cavity. The lowest threshold modes for the asymmetric devices were the asymmetric crown mode and the asymmetric cantilever mode. The crown mode and cantilever mode still exist within the fourteen mechanical mode profile of the asymmetric device; however, the input power needed to excite them increases. A2.3.2 Asymmetric Crown and Cantilever Mode To further characterize the optomechanical behavior of the asymmetric toroids the frequency spectrum and power thresholds were determined for the two most easily excited optomechanical modes. Figure A2-6 shows an example of the spectra of the two lowest threshold mechanical modes of an asymmetric device. Two modes were readily excited, the asymmetric crown and the asymmetric cantilever mode. The first optomechanical mode occurs at a frequency of 15.96 MHz and has a 38µW threshold (Figure A2-6b and Figure A2-6d). Based on the FEM results, this mode corresponds to the asymmetric crown mode. The second optomechanical occurs at a frequency of 47.3 MHz has a 148µW threshold (Figure A2-6c and Figure A2-6e). Based on the FEM results, this mode corresponds to the asymmetric cantilever mode. 218 Figure A2-6: (a) Bright field microscope image of an asymmetric device. (b) ESA spectra data for the asymmetric crown mode. (c) ESA spectra data for the asymmetric cantilever mode. (d) Threshold curve for the asymmetric crown mode. (e) Threshold curve for the asymmetric cantilever mode. Modified from Soltani et al [17]. The power was increased by an order of magnitude to determine if the symmetric modes can still be excited. The first and third cantilever modes were excited at 9.58 MHz and 72.8 MHZ. In a symmetric device, these modes would be excited with threshold powers on the order of 20-40 µW [29]. However, in the asymmetric devices they were excited closer to 1.4 mW. While the mechanical modes with the lowest thresholds differ in asymmetric and symmetric toroids, the threshold values for the two most easily excited optomechanical modes were of the same order of magnitude [17, 30, 31]. Therefore, we conclude that the energy conversion process in asymmetric and symmetric devices has the same efficiency. A2.3.3 Dependence of Threshold on Asymmetry In order to better understand the relationship between the onset of the optomechanical modes and the asymmetry of the devices, the threshold powers were 219 measured and plotted as a function of the normalized threshold (Figure A2-7). Based on these measurements, there is a clear dependence of the threshold power on asymmetry. Specifically, the threshold power drops drastically in response to asymmetry in both asymmetric modes. This finding agrees with our other experimental results and predictions of energy transfer within asymmetric devices. Figure A2-7: (a) Plot of the normalized threshold vs. pillar offset for graph for an asymmetric crown mode. (b) Plot of normalized threshold vs. pillar offset for an asymmetric cantilever mode. Modified from Soltani et al [17]. A2.4 Conclusion In conclusion, a variety of asymmetric whispering gallery mode optical microcavities were fabricated and characterized. Despite their asymmetry, their quality factors ranged from 1x10 6 to 3x10 7 . Because of the device asymmetry and high-Q, previously unobserved optomechanical modes were excited with sub-mW threshold powers. Future applications of these devices include quantum optics [18, 32-34], chaos studies and directional coupling [35-39]. 220 A2.5 References 1. C. Kopp, S. Bernabé, B. B. Bakir, J. M. Fedeli, R. Orobtchouk, F. Schrank, H. Porte, L. Zimmermann, and T. Tekin, "Silicon Photonic Circuits: On-CMOS Integration, Fiber Optical Coupling, and Packaging," IEEE Journal of Selected Topics in Quantum Electronics 17, 498-509 (2011). 2. A. Armani, D. Armani, B. Min, K. Vahala, and S. Spillane, "Ultra-high-Q microcavity operation in H2O and D2O," Applied Physics Letters 87, 151118 (2005). 3. A. M. Armani, R. P. Kulkarni, S. E. Fraser, R. C. Flagan, and K. J. Vahala, "Label-free, single-molecule detection with optical microcavities," Science 317, 783-787 (2007). 4. D. Armani, B. Min, A. Martin, and K. J. Vahala, "Electrical thermo-optic tuning of ultrahigh-Q microtoroid resonators," Applied physics letters 85, 5439-5441 (2004). 5. H. S. Choi, S. Ismail, and A. M. Armani, "Studying polymer thin films with hybrid optical microcavities," Optics Letters 36, 2152-2154 (2011). 6. C. Soteropulos, H. Hunt, and A. M. Armani, "Determination of binding kinetics using whispering gallery mode microcavities," Applied Physics Letters 99, 103703 (2011). 7. M. I. Cheema, S. Mehrabani, Y.-A. Peter, A. M. Armani, and A. G. Kirk, "Simultaneous measurement of quality factor and wavelength shift by phase shift microcavity ring down spectroscopy," Opt. Express 20, 9090-9098 (2012). 8. A. B. Matsko, and V. S. Ilchenko, "Optical resonators with whispering-gallery modes-part I: basics," IEEE Journal of Selected Topics in Quantum Electronics 12, 3-14 (2006). 9. R. Dahan, L. L. Martin, and T. Carmon, "Droplet optomechanics," Optica 3, 175- 178 (2016). 10. T. J. Kippenberg, and K. J. Vahala, "Cavity Opto-Mechanics," Opt. Express 15, 17172-17205 (2007). 11. X. Jiang, Q. Lin, J. Rosenberg, K. Vahala, and O. Painter, "High-Q double-disk microcavities for cavity optomechanics," Opt. Express 17, 20911-20919 (2009). 12. J. D. Teufel, J. W. Harlow, C. A. Regal, and K. W. Lehnert, "Dynamical Backaction of Microwave Fields on a Nanomechanical Oscillator," Physical Review Letters 101, 197203 (2008). 13. S. Groblacher, K. Hammerer, M. R. Vanner, and M. Aspelmeyer, "Observation of strong coupling between a micromechanical resonator and an optical cavity field," Nature 460, 724-727 (2009). 14. D. J. Wilson, C. A. Regal, S. B. Papp, and H. J. Kimble, "Cavity Optomechanics with Stoichiometric SiN Films," Physical Review Letters 103, 207204 (2009). 15. B. S. Sheard, M. B. Gray, C. M. Mow-Lowry, D. E. McClelland, and S. E. Whitcomb, "Observation and characterization of an optical spring," Physical Review A 69, 051801 (2004). 16. M. Tomes, and T. Carmon, "Photonic Micro-Electromechanical Systems Vibrating at X-band (11-GHz) Rates," Physical Review Letters 102, 113601 (2009). 17. S. Soltani, A. W. Hudnut, and A. M. Armani, "On-chip asymmetric microcavity optomechanics," Opt. Express 24, 29613-29623 (2016). 221 18. A. A. Clerk, and F. Marquardt, "Basic Theory of Cavity Optomechanics," in Cavity Optomechanics: Nano- and Micromechanical Resonators Interacting with Light, M. Aspelmeyer, J. T. Kippenberg, and F. Marquardt, eds. (Springer Berlin Heidelberg, 2014), pp. 5-23. 19. S. Forstner, J. Knittel, E. Sheridan, J. D. Swaim, H. Rubinsztein-Dunlop, and W. P. Bowen, "Sensitivity and performance of cavity optomechanical field sensors," Photonic Sensors 2, 259-270 (2012). 20. K. D. Hjelmstad, Fundamentals of Structural Mechanics (Springer US, 2004). 21. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, "Ultra-high-Q toroid microcavity on a chip," Nature 421, 925-928 (2003). 22. S. Soltani, and A. M. Armani, "Optothermal transport behavior in whispering gallery mode optical cavities," Applied Physics Letters 105 (2014). 23. S. M. Spillane, T. J. Kippenberg, O. J. Painter, and K. J. Vahala, "Ideality in a Fiber-Taper-Coupled Microresonator System for Application to Cavity Quantum Electrodynamics," Physical Review Letters 91, 043902 (2003). 24. A. R. Nelson, "Coupling optical waveguides by tapers," Appl. Opt. 14, 3012-3015 (1975). 25. X. Zhang, H. S. Choi, and A. M. Armani, "Ultimate quality factor of silica microtoroid resonant cavities," Applied Physics Letters 96, 153304 (2010). 26. M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, "Ultimate Q of optical microsphere resonators," Optics Letters 21, 453-455 (1996). 27. D. W. Vernooy, V. S. Ilchenko, H. Mabuchi, E. W. Streed, and H. J. Kimble, "High-Q measurements of fused-silica microspheres in the near infrared," Optics Letters 23, 247-249 (1998). 28. A. Yariv, "Universal relations for coupling of optical power between microresonators and dielectric waveguides," Electronics Letters 36, 321-322 (2000). 29. H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities," IEEE Journal of Selected Topics in Quantum Electronics 12, 96-107 (2006). 30. M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, "Cavity optomechanics," Reviews of Modern Physics 86, 1391-1452 (2014). 31. H. Rokhsari, T. J. Kippenberg, T. Carmon, and K. J. Vahala, "Theoretical and experimental study of radiation pressure-induced mechanical oscillations (parametric instability) in optical microcavities," Selected Topics in Quantum Electronics, IEEE Journal of 12, 96-107 (2006). 32. A. Schliesser, and T. J. Kippenberg, "Cavity Optomechanics with Whispering- Gallery-Mode Microresonators," in Cavity Optomechanics: Nano- and Micromechanical Resonators Interacting with Light, M. Aspelmeyer, J. T. Kippenberg, and F. Marquardt, eds. (Springer Berlin Heidelberg, 2014), pp. 121-148. 33. C. H. Metzger, and K. Karrai, "Cavity cooling of a microlever," Nature 432, 1002-1005 (2004). 34. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, "Analysis of Radiation-Pressure Induced Mechanical Oscillation of an Optical Microcavity," Physical Review Letters 95, 033901 (2005). 222 35. J. U. Nockel, and A. D. Stone, "Ray and wave chaos in asymmetric resonant optical cavities," Nature 385, 45-47 (1997). 36. Y.-S. Park, and H. Wang, "Radiation pressure driven mechanical oscillation in deformed silica microspheres via free-space evanescent excitation," Opt. Express 15, 16471-16477 (2007). 37. J. Wiersig, and M. Hentschel, "Unidirectional light emission from high-$Q$ modes in optical microcavities," Physical Review A 73, 031802 (2006). 38. S.-B. Lee, J. Yang, S. Moon, J.-H. Lee, K. An, J.-B. Shim, H.-W. Lee, and S. W. Kim, "Chaos-assisted nonresonant optical pumping of quadrupole-deformed microlasers," Applied Physics Letters 90, 041106 (2007). 39. Y.-F. Xiao, C.-L. Zou, Y. Li, C.-H. Dong, Z.-F. Han, and Q. Gong, "Asymmetric resonant cavities and their applications in optics and photonics: a review," Frontiers of Optoelectronics in China 3, 109-124 (2010). 223 Chapter A3. Malaria Diagnostic A3.1 Introduction Malaria infects over 250 million people each year and kills over 500,000 [1-6]. Malaria is an infection caused by parasites that are transmitted from their primary host, mosquitos, into humans. Malaria is characterized by a series of nonspecific symptoms including: fevers, fatigue, vomiting, diarrhea, and body aches [7]. While in the human body, malaria parasites metabolize blood, and as a byproduct they create a rod-shaped crystal called hemozoin [8, 9]. Hemozoin exhibits paramagnetic behavior, and is found in concentrations between 1 to 5 µg/mL in an infected patient’s blood [10-14]. The majority of deaths from malaria could be prevented if there was sufficient access to early diagnosis and treatment of infection [7]. As a result, there is much international interest in developing more specific and robust diagnostic tools to identify and treat both symptomatic and asymptomatic malaria infections. The goal is to eradicate the disease worldwide through better diagnoses and treatment [7]. Currently, there are several methods for diagnosing malaria. The two most common methods are light microscopy and antibody-based diagnostics [15-22]. Light microscopy is the standard of care and was developed a century ago [15-19]. Blood from patients is placed on a glass slide and imaged to determine if parasites or their characteristic physiological markers are present. While this method is reliable and sensitive, it requires significant facilities and expertise to diagnose malaria. These factors make it difficult to deploy to the rural communities disproportionately affected by malaria. In an attempt to address these limitations, antibody-based diagnostics, or rapid diagnostic test (RDT), were developed in the 1990’s [19-22]. While there are over twenty 224 different RDT’s for the detection of malaria, the reliability of all of these methods is governed by stability of the antibodies within the diagnostic. This is a major issue that researchers have tried to address over the past twenty years to no avail [23-25]. Currently, throwing away thousands of damaged RDTs is still more cost effective than light microscopy for low resource communities. In addition to these challenges, the current light microscopy and RDT methods have high false-negative rates. Therefore, additional tests are frequently run to confirm each case [26, 27]. This leads to a leaky treatment pipeline, causing many people with malaria never to be accurately diagnosed or treated. Recently, alternative methods have tried to leverage the presence of hemozoin in blood to diagnose malaria [28-31]. However, in their current configuration, these methods remain time consuming and expensive. If a portable and robust hemozoin based malaria diagnostic could be developed, it would fill a huge unmet need worldwide. The following chapter summarizes the work done as part of a collaboration with Samantha McBirney (group member who defended in 2018) and Dongyu Chen (current group member) to develop a portable and highly-specific diagnostic device for detecting malaria in blood samples [32]. This portable optical diagnostic system (PODS) for malaria detection is based primarily on the unique paramagnetic properties of hemozoin. We take a sample of blood, apply a magnetic field, and record if the optical signal of the sample changes. If a change in the optical signal is detected, it is a highly specific indication that there is malaria within the blood sample. Due to the unique paramagnetic properties of the hemozoin, we can control the location of this magnetic nanoparticle within a sample using low-power magnets. When a magnetic field is applied to a sample of blood that is infected, the hemozoin within the sample will move out of the path of 225 light. In turn, this changes the optical signal of the blood samples positive for malaria in a way that is distinct from that of an uninfected blood sample. Additionally, based on the change in optical power, we can determine the concentration of nanoparticles in the solution. A3.2 Sensor Design There are four primary configurations of the PODS developed and tested. The first configuration is comprised of a single magnet and optical transmission based detection. This configuration of the instrument is used as a demonstration for the PODS system and the manuscript is currently under review [32]. In order to improve the limit of detection (LOD) of the PODS system, we added two modifications to the original PODS system: (1) a magnetic guide, and (2) a polarization based optical detection method. As a result, we built and validated three additional configurations. The second configuration is comprised of two magnets and optical transmission based detection. This configuration of the instrument utilizes a simpler optical system, but should have a greater sensitivity and specificity due to the improved magnetic system. The third configuration is comprised of a single magnet and optical polarization based detection. This configuration of the instrument utilizes a more complex optical system for more sensitive detection while maintaining the original magnetic system. The fourth configuration is comprised of two magnets and an optical polarization based detection. This configuration of the instrument utilizes both modifications to improve both the sensitivity and the throughput of the PODS. 226 A3.2.1 Magnetic Manipulation To determine if there are magnetic nanoparticles present in the samples, we monitor the optical power before, during, and after a magnetic force is applied to the sample. Because the magnets control the location of the hemozoin in the cuvette they represent a significant part of the PODS sensor design. The magnetic field in the PODS is designed to have two states: on and off. This enables us to measure the response of the magnetic nanoparticles as they move out of solution and onto the side of the cuvette where the magnet is present. For any magnetic system within the PODS, the system is configured so that initially there is no magnetic field experienced by the sample (B=0). In the PODS system the magnet is attached to a motorized stage so that the speed and distance can be controlled automatically, reducing potential variability. Bringing the magnet closer to the sample increases the magnetic field. In the design and validation of the initial PODS system, several different magnetic strengths and distances between the sample and magnet are tested. While stronger magnets increase the time-to-signal, they also need to initially be placed further from the sample. Therefore, they increase the throughput, but also the footprint of the instrument. The magnetic setup is design so that it can be modified easily to incorporate magnets of different strengths depending on the needs of the end user. We configure the PODS system in two ways: (1) with one magnet or (2) a magnetic guide with two magnets. In the configuration with one magnet, the magnet serves to pull the nanoparticles from the path of the light source. In turn, this changes the transmission of the sample if hemozoin are present. In the magnetic guide configuration, 227 two magnets are used to concentrate the hemozoin along the beam path to increase the measurement efficiency. The current magnetic guide includes two magnets that are rotated by a microservo to a position aligned with the sides of the cuvette, at the top of the cuvette. Then a linear actuator moves the pair of magnets down the cuvette to concentrate the magnetic particles at the bottom, of the cuvette. Subsequently, the magnets are moved upwards to position the concentrated magnetic particles into a wide enough region in the cuvette for the beam of light to pass through without scattering from the sides and bottom of the cuvette. A3.2.2 Optical Scattering Optical scattering is a fundamental concept of optics that explains the interaction between electromagnetic waves and their environment. Due to the unique relationship between light of a specific wavelength and a material, information regarding the structure and dynamics of the material can be determined with high accuracy by measuring the pattern of the light as it scatters [33-35]. Recent advances in fabrication methods of optical sources and detectors have enabled the miniaturization of highly accurate optical systems. This can be used for scattering measurements. Therefore, complex and dynamic biological systems can be understood by using this method of optical characterization [33-35]. There are three primary forms of optical scattering that occur, and each depends on the size of the particle relative to the wavelength of light. If the particle is much larger than the wavelength of light, Snell’s Law relates the angle of incidence and the angle of reflection. For small particles, like hemozoin, the interaction of the particle and light is 228 directly related to the size parameter (x=2πr/λ). If x~1 then the interaction is described by Mie scattering. If x<<1 then the interaction is described by Rayleigh scattering. For our systems Mie scattering primarily describes the interaction between the hemozoin and our light source within the PODS [34, 35]. Scattering is primarily comprised of transmission and reflection caused by the particles in the sample. Specifically, within the PODS system, we look at the transmission of a single wavelength of light as it passes through a plastic cuvette that contains our sample. As light passes through the sample, the transmission is recorded. The normal transmission through a complex media, such as human blood, is consistent under a magnetic field. If there is a magnetic nanoparticle present, the transmission will change as the particles move from the path of the light in response to the magnetic field [36-38]. Therefore, within the PODS system, we are able to detect hemozoin by measuring the change in transmission when a magnetic field is applied to our sample. A3.2.3 Optical Polarization The PODS system was initially based on optical scattering [32]. While this method enabled us to create specific and sensitive sensors, the same system could be improved by introducing optical polarizers to enhance the signal. We introduce a linear polarizer before the cuvette to polarize the source, and a second linear polarizer after the cuvette as an analyzer. By modifying the optical path in this way, we decrease the variability of the optical input and improve the sensitivity of the PODS system. Polarization based detection as a detection mechanism has several advantages over a simple scattering approach traditionally used for optical biosensors [39-41]. It has 229 been demonstrated that by using linearly polarized light within a turbid medium that the signal from optical systems can be amplified [42-46]. By adding a polarization detector after the sample, the same change in power can be recorded that was used in other configurations of the PODS system. Therefore, a simple change in the optics of the system can improve the sensitivity of an optical system for hemozoin detection. A3.2.4 Theory To better understand the signal generated by the PODS system, Dongyu Chen developed a theoretical model and detailed information is contained in the associated paper [32]. Given the size of the particles and the laser wavelength used, the optical signal in the PODS system is primarily due to Mie scattering [32, 34-38, 47, 48]. Using the fundamentals of optical spectroscopy, a time-dependent model of the magnetic nanoparticles in solution is developed to better understand the experimental results. Depending on the optical pathlength, the theory is slightly different. If the PODS system uses the original optical scattering system, the power of the light recorded by the photodetector is inversely proportional to the concentration of nanoparticles in the path of the laser. If the PODS system uses the dual polarizer optical system the power of the light recorded by the photodetector is proportional to the concentration of nanoparticles in the path of the laser. A3.3 Instrument Configurations The PODS system is comprised of free space optical components for detection and a moveable magnet to control the nanoparticle distribution within the sample. 230 Therefore, when we apply a magnetic field, we can monitor the changes in the optical signal generated. In turn, we can use this information determine if hemozoin is present in the sample. There are four primary configurations of the PODS system that have been developed to optimize the instrument. In each configuration, a 633nm laser is used as the light source (Thor Labs – CPS635). A photodiode (Thor Labs – S120C) is used to measure the transmitted light and a powermeter interface (Thor Labs – PM100USB) is used to send the information to a laptop where the data is recorded. The magnets (K&J Magnetics) are connected to an actuator (Firgelli) via custom-made 3D printed parts. The PODS system is based on differential optical spectroscopy. Therefore, to determine the concentration of magnetic nanoparticles in a sample, we monitor the optical power. This strategy eliminates the need for a separate normalization step and reduces the effect of sample-to-sample variation. The optical power is recorded every second. The power is then plotted vs. time to generate a detection curve. Using the detection curves from each of the points in the serial dilution, we plot a calibration curve for the PODS system. The sensitivity of the instrument can be determined using this information. The first instrument configuration is comprised of a single magnet and optical transmission based detection (Figure A3-1). This configuration of the instrument is used as a demonstration for the PODS system and these findings are currently under review [32]. 231 Figure A3-1: Optical path for the first configuration of the malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the first configuration of the PODS depicting the same configuration as the rendering. The second instrument configuration is comprised of two magnets and optical transmission based detection (Figure A3-2). This configuration of the instrument potentially could have greater sensitivity and specificity due to the dual magnetic system. Figure A3-2: Optical path for the second configuration of the malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the second configuration of the PODS depicting the same configuration as the rendering. The third instrument configuration is comprised of a single magnet and optical polarization based detection (Figure A3-3). This configuration of the instrument utilizes a more complex optical system that could potentially improve the sensitivity of detection while maintaining the single magnet system. 232 Figure A3-3: Optical path for the third configuration of the optical malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the third configuration of the PODS depicting the same configuration as the rendering. The fourth instrument configuration is comprised of two magnets and optical polarization based detection (Figure A3-4). This configuration utilizes both modifications to potentially improve the sensitivity and the throughput of the PODS. Figure A3-4: Optical path for the fourth configuration of the malaria diagnostic. (a) Rendering of the device depicting the magnet on the linear actuator, cuvette, laser source, and detector. (b) Photo of the optical path of the fourth configuration of the PODS depicting the same configuration as the rendering. A3.4 Sample Characterization Samantha McBirney validated the first configuration of the PODS with several different sample types. More detailed information is contained in the associated manuscript and her thesis [32]. In order to validate the PODS, the behavior of two different magnetic nanoparticles in four solutions with different viscosities is determined. Initially, Fe 3 O 4 nanoparticles are synthesized to demonstrate the magnetic system worked 233 in heterogeneous solutions. After preliminary experiments with Fe 3 O 4 indicated our system worked as expected, she synthesized a hemozoin mimic, β-hematin. β-hematin and hemozoin share the same unit crystal structure and the same magnetic and optical properties, making β-hematin the standard hemozoin mimic used in the field [49, 50]. The same experiments are conducted with both types of magnetic nanoparticle. Using serial dilutions, the concentration of nanoparticles is varied in several solutions with different viscosities to understand the limit of detection of our device. The particles were suspended in one of three solutions: water, 10% PEG, or 15% PEG. After demonstrating the PODS is able to detect magnetic nanoparticles in solution with different viscosities, she tested on blood removed from Dutch Belted rabbits on the USC Health Sciences Campus (IACUC Approval 20693). More detailed information is contained in the associated paper [32]. The second, third, and fourth generation system configurations shown in Figures A3-2 through A3-4 have yet to be tested. A3.5 Conclusion In collaboration with Samantha McBirney and Dongyu Chen, we develop an optical malaria diagnostic that can be used to reproducibly measure the change in transmission when a magnetic field is applied to a sample containing magnetic nanoparticles. Using a variety of magnetic nanoparticles and solutions, Samantha McBirney was able to validate the first configuration of the PODS [32]. These experiments demonstrate that the PODS system is a robust and highly specific new diagnostic tool for diagnosing malaria in low resource settings. 234 A3.6 References 1. J. G. 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Mezzenga, "Lipidic Cubic Phases as a Versatile Platform for the Rapid Detection of Biomarkers, Viruses, Bacteria, and Parasites," Advanced Functional Materials 26, 181- 190 (2016). 47. W. L. Peticolas, B. Fanconi, B. Tomlinson, L. A. Nafie, and W. Small, "Inelastic light scattering from biological and synthetic polymers," Ann N Y Acad Sci 168, 564-588 (1969). 48. R. G. Smith, "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and brillouin scattering," Appl Opt 11, 2489-2494 (1972). 49. M. Jaramillo, M. J. Bellemare, C. Martel, M. T. Shio, A. P. Contreras, M. Godbout, M. Roger, E. Gaudreault, J. Gosselin, D. S. Bohle, and M. Olivier, "Synthetic Plasmodium-like hemozoin activates the immune response: a morphology - function study," PLoS One 4, e6957 (2009). 50. G. S. Noland, N. Briones, and D. J. Sullivan, Jr., "The shape and size of hemozoin crystals distinguishes diverse Plasmodium species," Mol Biochem Parasitol 130, 91-99 (2003). 238 Chapter A4. VCSEL and Cell Scattering A4.1 Introduction Scattering is a fundamental concept within optics that explains the interaction between electromagnetic waves and their environment. Due to the unique relationship between light of a specific wavelength and material, information regarding the structure and dynamics of the material can be determined with high accuracy by measuring the pattern of the light as it scatters. Recent advances in fabrication methods of optical sources and detectors have enabled the miniaturization of highly accurate optical systems, which can be used for scattering measurements. Therefore, complex and dynamic biological systems can be understood using these methods. Current applications of this technology include pathogen detection and water monitoring [1-3]. There are three primary forms of optical scattering that occur, and each depends on the size of the particle relative to the wavelength of light. If the particle is much larger than the wavelength of light Snell’s Law relates the angle of incidence and the angle of reflection. For small particles, like individual cells, the interaction of the particle and light is directly related to the size parameter (x=2πr/λ). If x~1, then the interaction is described by Mie scattering. If x<<1, then the interaction is described by Rayleigh scattering. For our systems Mie scattering primarily describes the interaction between the cells and the light. Previous work has used Mie scattering for a variety of biomedical applications, including method for identify cancer cells and parasitemia [4, 5]. One area where this research could be expanded is batch processing within bio- manufacturing facilities. There is currently no way to monitor the structure of cells in real time. The current gold standard for monitoring bio-manufacturing facilities remains 239 hemocytometry [6]. Alternative methods such as flow cytometry are used in research facilities, but due to cost and time they have not been integrated into batch processing [7- 9]. Therefore, there is a demonstrated need to develop a miniature flow cytometer that could be integrated into bio-manufacturing facilities. One method for developing a miniature flow cytometer would be to fabricate a device that measures optical scattering using an integrated laser with an on-chip photodetector. By measuring the change in current as a solution flows through a chamber, cell morphology could be determined. In such a system, the current will vary as a direct result of the distance between the source and the particle, as well as the particle size and morphological characteristics (Figure A4-1). In collaboration with Professor Jongseung Yoon and Dr. Dongseok Kang, we tested an existing integrated system and demonstrated that cells could be detected at different concentrations [10]. Figure A4-1: Cartoon outlining how the change in current can be used as a detection signal to measure optical scattering. By comparing the change in current over time, the dwell time, and the relative number and position of particles can be detected within a heterogeneous sample. Difference in the current indicated by A, B, and C can be a result of multiple factors such as the number of cells in the chamber or the distance between the cell and the laser. 240 By leveraging recent advances in the field of flexible optoelectronics, a label-free flow cytometer was developed. The system acts as a real-time flow cytometer with single particle and single cell detection and profiling capabilities. The VCSEL was integrated with an on-chip photodetector and a microfluidic sample delivery system [11-13]. A4.2 Methods A4.2.1 Device Setup We tested two different device platforms to determine if optical scattering could be used to detect different cells. The initial platform we used was a small desktop UV- VIS spectrometer (Biochrom WPA S1200 Spectrawave Visible Spectrophotometer) connected to computer for real time analysis. Using this method, data from five strains of MRSA and two cancer cell lines were taken and parameters for computational modeling were developed. We used serial dilutions following experiments previously conducted in the Armani Lab to determine the change in scattering as the concentration approached zero [14]. In parallel to developing our model, we tested serial dilutions of cancer cells using a Vertical Cavity Surface Emitting Lasers (VCSEL) platform. The device was comprised of a VCSEL and integrated Si-photodetector (Figure A4-2a). The VCSEL in the device was 276 µm x 276 µm, and the photodetector was a U shaped SiPD which was 2mm x 2mm x 2mm (Figure A4-2b). The integrated device platform was combined with microfluidics to control liquid sample delivery to mimic the ideal process for monitoring of biomanufacturing reactors. The microfluidics system was a simple 2mm x 2mm x 241 2mm chamber fabricated from PDMS that sits directly above the integrated VCSEL-PD system. Figure A4-2: Schematic of the integrated VCSEL and photodetector systems proposed. (a) SiPD system with integrated VCSEL used for preliminary testing. (b) GaAs photodetector system built, but not tested. A4.2.2 Experimental Methods In order to test for the presence of cells within our microfluidic chamber we monitored the change in current recorded by the photodetector over time. The liquid was pumped into the chamber at a rate of 13.3mL/hr (=0.00369 mL/sec). There was one syringe full of colorless media and one syringe full of cancer cells suspended in colorless media at a variable concentration of cells. These two syringes were connected with a T valve into the microfluidic chamber. For reference, given a concentration of 10,000 cells/mL there was ~1.5 cells within the chamber during each interval. Every one minute the syringe pump was manually switched between the media and the media+cells. The current in amps was recorded every 0.02 seconds over a 900 second interval. 242 A4.3 Results A4.3.1 VCSEL Detection Results We preformed preliminary tests with an existing flexible VCSEL sensor, designed and fabricated in Professor Yoon’s group at USC. The performance was characterized, and the discretization of the signal was observed, proving single cell detection occurs. The VCSEL tested was designed to emit at 850nm, and the detection platform was combined with microfluidics to control sample delivery to the VCSEL array. The performance was characterized with cancer cells that are approximately 20µm in diameter. As individual cells flow in between the VCSEL and the detector, the signal was scattered, resulting in a quantized decrease in the signal. As expected for single cell measurements, the frequency of events was proportional to the cell concentration while the maximum signal change measured was constant. As individual cells flowed between the VCSEL and the detector, the signal was scattered, resulting in an easily detectable signal change. In the results presented in Figure A4-3, there was a change in the current (ΔI) that indicates a particle was within the microfluidic chamber. There was a clear difference between the signal recorded when the flow within the chamber was media or the cells+media. When the cells+media were pumped through the chamber the relative difference in the ΔI was due to the location of the cell within the chamber. There is a 2mm area in the z direction, and therefore the cells can have relative heights within the chamber up to 10x the size of the particle. Also the cells can be clumped together, which would lead to a larger ΔI. There are several spikes in the current even when the cells were not flowing through the 243 chamber. This was because the cells can get stuck in the tubing or within the microfluidic channel. Therefore, they can be dislodged and flow through the chamber at a later point. Figure A4-3: Example data from the SiPD-VCSEL system. (a) Differential normalized current plotted over time (sec). The flow was switched between cells (red) and media (black). The concentration was too high (~15 cells) in the sensing region of the chamber to definitively claim single cell detection. (b) Plot of each minute interval of either media or cells+media plotted on top of each other in terms of frequency. These plots can be used to statistically show if single cell detection occurs. Additionally, as expected for single particle measurements, the change was quantized. Using statistical methods we are able to confirm single cell detection by discretization of the signal and fitting to a Poisson distribution (Figure A4-4). However, based on these results it appears that there were multiple cells within the chamber at the concentration tested in these results. Therefore, this experiment was repeated with a variety of cell concentrations to determine the detection limit and resolution of the device. 244 Figure A4-4: Statistical analysis of the relative current to determine if single cell detection occurs. (a) Histogram of counts from only cell events. (b) Reorganization of counts and fit to a Poisson distribution. The fit is shifted to the right, indicating that there were multiple cells within the well during each measurement. The same experiment was repeated with a decrease in the initial cell count to improve the detection. Additionally, the GaAs PD was built in the hope that by modify the design of the VCSELs it would improve the sensing capabilities. The results are summarized in Figure A4-5. There are clearly fewer events with the lower concentration of the cells. The signal generated with the GaAs PD also seems to have generated higher signal in the magnitude of the change in current in Figure A4-5. Figure A4-5: Example data from the GaAsPD-VCSEL system. (a) Differential normalized current plotted over time (sec). The flow was switched between cells (red) and media (black). (b) Plot of each minute interval of either media or cells+media plotted on top of each other in terms of frequency. 245 A4.4 Conclusion Easy to use and rapid particle profiling and counting methods have numerous applications, including biomanufacturing, atmospheric measurements and environmental monitoring [15]. Significant advances have been made within the fields of integrated laser and detector fabrication and modeling which have enabled us to study and design new systems in ways that will improve the capabilities of current diagnostic methods. We have developed a model where the scattering of different concentrations of cells can be modeled in COMSOL. We have demonstrated that single cell measurements of human cells can be performed using a VCSEL platform. These preliminary experimental results provide the foundation for future development of miniature flow-cytometers. 246 A4.5 References 1. P. P. Banada, K. Huff, E. Bae, B. Rajwa, A. Aroonnual, B. Bayraktar, A. Adil, J. P. Robinson, E. D. Hirleman, and A. K. Bhunia, "Label-free detection of multiple bacterial pathogens using light-scattering sensor," Biosensors and Bioelectronics 24, 1685-1692 (2009). 2. B. Rajwa, M. M. Dundar, F. Akova, A. Bettasso, V. Patsekin, E. D. Hirleman, A. K. Bhunia, and J. P. Robinson, "Discovering the unknown: detection of emerging pathogens using a label-free light-scattering system," Cytometry. Part A : the journal of the International Society for Analytical Cytology 77, 1103-1112 (2010). 3. S. Zhou, C. Burger, B. Chu, M. Sawamura, N. Nagahama, M. Toganoh, U. E. Hackler, H. Isobe, and E. Nakamura, "Spherical Bilayer Vesicles of Fullerene-Based Surfactants in Water: A Laser Light Scattering Study," Science 291, 1944-1947 (2001). 4. A. Wax, C. Yang, V. Backman, K. Badizadegan, C. W. Boone, R. R. Dasari, and M. S. Feld, "Cellular Organization and Substructure Measured Using Angle-Resolved Low-Coherence Interferometry," Biophysical Journal 82, 2256-2264 (2002). 5. Y. M. Serebrennikova, J. Patel, and L. H. Garcia-Rubio, "Interpretation of the ultraviolet-visible spectra of malaria parasite Plasmodium falciparum," Appl. Opt. 49, 180-188 (2010). 6. K. W. Ng, D. Leong, and D. Hutmacher, "The challenge to measure cell proliferation in two and three dimensions," Tissue Engineering Part A: Tissue Engineering 11, 182-191 (2005). 7. D. A. A. Vignali, "Multiplexed particle-based flow cytometric assays," Journal of Immunological Methods 243, 243-255 (2000). 8. D. Marie, F. Partensky, S. Jacquet, and D. Vaulot, "Enumeration and Cell Cycle Analysis of Natural Populations of Marine Picoplankton by Flow Cytometry Using the Nucleic Acid Stain SYBR Green I," Applied and Environmental Microbiology 63, 186- 193 (1997). 9. P. O. Krutzik, and G. P. Nolan, "Intracellular phospho-protein staining techniques for flow cytometry: Monitoring single cell signaling events," Cytometry Part A 55A, 61- 70 (2003). 10. D. Kang, B. Gai, B. Thompson, S.-M. Lee, N. Malmstadt, and J. Yoon, "Flexible Opto-Fluidic Fluorescence Sensors Based on Heterogeneously Integrated Micro-VCSELs and Silicon Photodiodes," ACS Photonics 3, 912-918 (2016). 11. D. Kang, S.-M. Lee, Z. Li, A. Seyedi, J. O'Brien, J. Xiao, and J. Yoon, "Compliant, Heterogeneously Integrated GaAs Micro-VCSELs towards Wearable and Implantable Integrated Optoelectronics Platforms," Advanced Optical Materials 2, 373- 381 (2014). 12. D. Kang, S.-M. Lee, A. Kwong, and J. Yoon, "Dramatically Enhanced Performance of Flexible Micro-VCSELs via Thermally Engineered Heterogeneous Composite Assemblies," Advanced Optical Materials 3, 1072-1078 (2015). 13. F. Koyama, "Recent Advances of VCSEL Photonics," Journal of Lightwave Technology 24, 4502-4513 (2006). 14. S. E. McBirney, K. Trinh, A. Wong-Beringer, and A. M. Armani, "Wavelength- normalized spectroscopic analysis of Staphylococcus aureus and Pseudomonas aeruginosa growth rates," Biomed. Opt. Express 7, 4034-4042 (2016). 247 15. H. K. Hunt, and A. M. Armani, "Label-free biological and chemical sensors," Nanoscale 2, 1544-1559 (2010). 248 Chapter A5. Associated Matlab Codes A5.1 Calculating ΔPol A5.1.1 LoadingUnloading.m %%%%%%%%%%%%%%%%%%%%%%%%%% %% Loading Unloading %% Written by Mark Harrison (Armani Research Group – USC) %% Modified for OFPE by Alexa Hudnut %this script reads in the stokes parameters as measured by our thorlabs %polarimeter from a data file and converts them to the angle of the circle traced out on the %surface of the sphere when performing strain measurements. It then plots %stress vs. strain using the angle as a parameter of stress. Strain can be %read from the motorized micrometer, as it is simply the amount of %deformation. This version has thickness and micrometer rate hardcoded in %to the program (assuming that for analyzing a batch of data these values %won't change). It also fixes issues with the phase angle cycling over. %This version can handle forward and reverse directions in the same trace, %and the direction does not need to be specified. %This version can handle arbitrary gamma. It solves for the rotation, then %uses an x-y view to find the phase. clear; clc; %Find the current path to revert back to it when done currentPath = pwd; % Look for m files in current folder and count them. d = dir([currentPath, '/*.csv']); n2=length(d); k=0; %loop over all the files. for q = 1:n2 display('in loop') %read the data from the csv file (only the time stamp and stokes vectors) data = csvread(d(q).name,23,0,[23,0,1046,3]); 249 %put the data into appropriate vectors time = data(:,1); s1 = data(:,2); s2 = data(:,3); s3 = data(:,4); %convert stokes vector to polar coordinates (radius = 1) sx = sqrt(s1.*s1+s2.*s2); theta = atan2(s2,s1); psi = atan2(s3,sx); wrapCount = 0; thetaCounter = zeros(length(theta),1); %theta can have sign issues based on where it is on the sphere. This code %fixes those problems by making sure there isn't a sudden sign-change jump. for i = 1:(length(theta)-1) if sign(s1(i))==-1 if (sign(s2(i))==1)&&(sign(s2(i+1))==-1) wrapCount = wrapCount + (2*pi); elseif (sign(s2(i))==-1)&&(sign(s2(i+1))==1) wrapCount = wrapCount - (2*pi); end end thetaCounter(i+1)= wrapCount; end theta = theta + thetaCounter; %CIRCFIT Fits a circle in x,y plane % % [XC, YC, R, A] = CIRCFIT(X,Y) % Result is center point (yc,xc) and radius R. A is an optional % output describing the circle's equation: % % x^2+y^2+a(1)*x+a(2)*y+a(3)=0 % by Bucher Izhak 25/oct/1991 n=length(theta); xx=theta.*theta; yy=psi.*psi; xy=theta.*psi; A=[sum(theta) sum(psi) n;sum(xy) sum(yy) sum(psi);sum(xx) sum(xy) sum(theta)]; B=[-sum(xx+yy) ; -sum(xx.*psi+yy.*psi) ; -sum(xx.*theta+xy.*psi)]; a=A\B; xc = -.5*a(1); yc = -.5*a(2); R = sqrt((a(1)^2+a(2)^2)/4-a(3)); %create x and y coordinates so that the center of the circle is at the %origin, and we are rotated correctly according to variable gamma. x = s1.*sin(-xc)+s2.*cos(-xc); 250 y = s3; %find the angle of the circle (phase). Use atan2 to get an answer from %[-pi,pi] and so we can normalize on any rotation. phase = atan2(y,x)./pi; % figure(1) % plot(time,phase) % title('phase vs. time') % xlabel('time (s)') % ylabel('phase (*/pi radians)') %normalize the phase so it starts at zero and is always increasing or decreasing, not %bound between -pi/2 and pi/2 or -pi and pi k = length(phase); phaseCounter = zeros(k,1); %this variable counts how many times the phase wraps around wrapCount = 0; %check to see if the sign has changed, but it should be different based on %rotation. When sign changes, mark location and add to phase counter. %Check based on what quadrant of the plane you are in for i = 1:(k-1) if sign(x(i))==-1 if (sign(y(i))==1)&&(sign(y(i+1))==-1) wrapCount = wrapCount + 2; elseif (sign(y(i))==-1)&&(sign(y(i+1))==1) wrapCount = wrapCount - 2; end end phaseCounter(i+1)= wrapCount; end phase = (phase + phaseCounter - phase(1)); %this code normalizes phase to start at 0 and be always positive and increasing %convert time to strain based on rate of micrometer motion thick = 4; %thickness of the samples in mm rate = 0.08; %rate of the micrometer (compression rate in mm/s) strain = ((time .* rate)./thick); %write the analyzed data into your .csv file for further analysis data = [time';strain';phase']; %[filename,pathname,filterindex] = uiputfile('*.csv'); %[filename,pathname,filterindex] = %if filterindex ~= 0 s = strcat('new',d(q).name); fid = fopen(s,'w'); fprintf(fid,'time (s),strain (mm/mm),phase (pi radians)\n'); fprintf(fid,'%f,%f,%f\n',data); fclose(fid); 251 %Plotting j=j+2; %plot phase vs. strain %trying to figure out naming %figure('name','figure number','numbertitle','off'); %Figure 2 is run 1 in folder figure(j) plot(strain,phase) title('phase vs. strain') xlabel('strain (mm/mm)') ylabel('phase (\pi radians)') %set(gca,'XDir','reverse'); % This flips the x axis % plot circle trace on sphere (for reference) %trying to figure out naming, ignore this for now %figure('Name','Sphere','NumberTitle','off') figure(j+1) scatter3(s1,s2,s3) hold sphere axis square % figure(3) % scatter(x,y) end %change the current working directory to the directory of the script cd(currentPath); A5.2 Quasi-Linear Viscoelastic Fitting A5.2.1 Run_QLV_viscoelastic_model_triangle_loading.m %%%%%%%%%%%%%%%%%%%%%%%%%% %% Run QLV Viscoelastic Model Triangle Loading %% Written by Behzad Babei (Neuroscience Research Australia) %% Modified for OFPE by Alexa Hudnut clc clear all; clear parameters; format long g; warning off; close all; data = xlsread('book1',1); U_Lb = [0,0,0,0,0]; U0 = [1, 1, 1,1,1000]; 252 U_Hb = [1e5,1e3,1e1,1e1,1e8]; [U] = solver_sawtooth_quasilinear_viscoelastic(U0,U_Lb, U_Hb, data,10,1e5,1e5); global stress yfit U strain1 strain2 %%%%%%%%%%%%%%%%%%%%%%%%%% figure(3) plot([strain1 strain2]*100,stress,'r.',[strain1 strain2]*100,yfit,'b- ','linewidth',1.5,'MarkerSize',7);hold all; xlabel('\epsilon (%)','fontsize',24,'FontName','Times New Roman'); ylabel('\sigma ','fontsize',24,'FontName','Times New Roman'); set(gcf,'PaperUnits','inches','color', 'white'); set(findobj('type','axes'),'fontsize',20); set(gca,'LineWidth', 2); axis square; % set(gca,'xtick',[0 1 2 3 4]); % set(gca,'ytick',[0 1 2 3 4 5]); h1=legend('Experiment','quasi-linear viscoelastic fit'); set(h1,'FontSize',20); grid on; axis([0 max(strain1)*100 0 1.3*max(stress)]) strFilePath1 = 'models_quasi_linear viscoelastic'; iResolution = 300; print('-dtiff', sprintf('-r%d', iResolution), strcat(strFilePath1,'.png')); A = U(1) B = U(2) C = U(3) tau1 = U(4) tau2 = U(5) A5.2.2 fminsearchbnd.m %%%%%%%%%%%%%%%%%%%%%%%%%% %% fminsearchbnd %% Written by Behzad Babei (Neuroscience Research Australia) %% Modified for OFPE by Alexa Hudnut function [x,fval,exitflag,output] = fminsearchbnd(fun,x0,LB,UB,options,varargin) % FMINSEARCHBND: FMINSEARCH, but with bound constraints by transformation % usage: x=FMINSEARCHBND(fun,x0) % usage: x=FMINSEARCHBND(fun,x0,LB) % usage: x=FMINSEARCHBND(fun,x0,LB,UB) % usage: x=FMINSEARCHBND(fun,x0,LB,UB,options) % usage: x=FMINSEARCHBND(fun,x0,LB,UB,options,p1,p2,...) % usage: [x,fval,exitflag,output]=FMINSEARCHBND(fun,x0,...) % % arguments: % fun, x0, options - see the help for FMINSEARCH % % LB - lower bound vector or array, must be the same size as x0 % 253 % If no lower bounds exist for one of the variables, then % supply -inf for that variable. % % If no lower bounds at all, then LB may be left empty. % % Variables may be fixed in value by setting the corresponding % lower and upper bounds to exactly the same value. % % UB - upper bound vector or array, must be the same size as x0 % % If no upper bounds exist for one of the variables, then % supply +inf for that variable. % % If no upper bounds at all, then UB may be left empty. % % Variables may be fixed in value by setting the corresponding % lower and upper bounds to exactly the same value. % % Notes: % % If options is supplied, then TolX will apply to the transformed % variables. All other FMINSEARCH parameters should be unaffected. % % Variables which are constrained by both a lower and an upper % bound will use a sin transformation. Those constrained by % only a lower or an upper bound will use a quadratic % transformation, and unconstrained variables will be left alone. % % Variables may be fixed by setting their respective bounds equal. % In this case, the problem will be reduced in size for FMINSEARCH. % % The bounds are inclusive inequalities, which admit the % boundary values themselves, but will not permit ANY function % evaluations outside the bounds. These constraints are strictly % followed. % % If your problem has an EXCLUSIVE (strict) constraint which will % not admit evaluation at the bound itself, then you must provide % a slightly offset bound. An example of this is a function which % contains the log of one of its parameters. If you constrain the % variable to have a lower bound of zero, then FMINSEARCHBND may % try to evaluate the function exactly at zero. % % % Example usage: % rosen = @(x) (1-x(1)).^2 + 105*(x(2)-x(1).^2).^2; % % fminsearch(rosen,[3 3]) % unconstrained % ans = % 1.0000 1.0000 % % fminsearchbnd(rosen,[3 3],[2 2],[]) % constrained % ans = % 2.0000 4.0000 % % See test_main.m for other examples of use. % 254 % % See also: fminsearch, fminspleas % % % Author: John D'Errico % E-mail: woodchips@rochester.rr.com % Release: 4 % Release date: 7/23/06 % size checks xsize = size(x0); x0 = x0(:); n=length(x0); if (nargin<3) || isempty(LB) LB = repmat(-inf,n,1); else LB = LB(:); end if (nargin<4) || isempty(UB) UB = repmat(inf,n,1); else UB = UB(:); end if (n~=length(LB)) || (n~=length(UB)) error 'x0 is incompatible in size with either LB or UB.' end % set default options if necessary if (nargin<5) || isempty(options) options = optimset('fminsearch'); end % stuff into a struct to pass around params.args = varargin; params.LB = LB; params.UB = UB; params.fun = fun; params.n = n; % note that the number of parameters may actually vary if % a user has chosen to fix one or more parameters params.xsize = xsize; params.OutputFcn = []; % 0 --> unconstrained variable % 1 --> lower bound only % 2 --> upper bound only % 3 --> dual finite bounds % 4 --> fixed variable params.BoundClass = zeros(n,1); for i=1:n k = isfinite(LB(i)) + 2*isfinite(UB(i)); params.BoundClass(i) = k; if (k==3) && (LB(i)==UB(i)) params.BoundClass(i) = 4; 255 end end % transform starting values into their unconstrained % surrogates. Check for infeasible starting guesses. x0u = x0; k=1; for i = 1:n switch params.BoundClass(i) case 1 % lower bound only if x0(i)<=LB(i) % infeasible starting value. Use bound. x0u(k) = 0; else x0u(k) = sqrt(x0(i) - LB(i)); end % increment k k=k+1; case 2 % upper bound only if x0(i)>=UB(i) % infeasible starting value. use bound. x0u(k) = 0; else x0u(k) = sqrt(UB(i) - x0(i)); end % increment k k=k+1; case 3 % lower and upper bounds if x0(i)<=LB(i) % infeasible starting value x0u(k) = -pi/2; elseif x0(i)>=UB(i) % infeasible starting value x0u(k) = pi/2; else x0u(k) = 2*(x0(i) - LB(i))/(UB(i)-LB(i)) - 1; % shift by 2*pi to avoid problems at zero in fminsearch % otherwise, the initial simplex is vanishingly small x0u(k) = 2*pi+asin(max(-1,min(1,x0u(k)))); end % increment k k=k+1; case 0 % unconstrained variable. x0u(i) is set. x0u(k) = x0(i); % increment k k=k+1; case 4 % fixed variable. drop it before fminsearch sees it. 256 % k is not incremented for this variable. end end % if any of the unknowns were fixed, then we need to shorten % x0u now. if k<=n x0u(k:n) = []; end % were all the variables fixed? if isempty(x0u) % All variables were fixed. quit immediately, setting the % appropriate parameters, then return. % undo the variable transformations into the original space x = xtransform(x0u,params); % final reshape x = reshape(x,xsize); % stuff fval with the final value fval = feval(params.fun,x,params.args{:}); % fminsearchbnd was not called exitflag = 0; output.iterations = 0; output.funcCount = 1; output.algorithm = 'fminsearch'; output.message = 'All variables were held fixed by the applied bounds'; % return with no call at all to fminsearch return end % Check for an outputfcn. If there is any, then substitute my % own wrapper function. if ~isempty(options.OutputFcn) params.OutputFcn = options.OutputFcn; options.OutputFcn = @outfun_wrapper; end % now we can call fminsearch, but with our own % intra-objective function. [xu,fval,exitflag,output] = fminsearch(@intrafun,x0u,options,params); % undo the variable transformations into the original space x = xtransform(xu,params); % final reshape to make sure the result has the proper shape x = reshape(x,xsize); 257 % Use a nested function as the OutputFcn wrapper function stop = outfun_wrapper(x,varargin); % we need to transform x first xtrans = xtransform(x,params); % then call the user supplied OutputFcn stop = params.OutputFcn(xtrans,varargin{1:(end-1)}); end end % mainline end % ====================================== % ========= begin subfunctions ========= % ====================================== function fval = intrafun(x,params) % transform variables, then call original function % transform xtrans = xtransform(x,params); % and call fun fval = feval(params.fun,reshape(xtrans,params.xsize),params.args{:}); end % sub function intrafun end % ====================================== function xtrans = xtransform(x,params) % converts unconstrained variables into their original domains xtrans = zeros(params.xsize); % k allows some variables to be fixed, thus dropped from the % optimization. k=1; for i = 1:params.n switch params.BoundClass(i) case 1 % lower bound only xtrans(i) = params.LB(i) + x(k).^2; k=k+1; case 2 % upper bound only xtrans(i) = params.UB(i) - x(k).^2; k=k+1; case 3 % lower and upper bounds xtrans(i) = (sin(x(k))+1)/2; xtrans(i) = xtrans(i)*(params.UB(i) - params.LB(i)) + params.LB(i); % just in case of any floating point problems xtrans(i) = max(params.LB(i),min(params.UB(i),xtrans(i))); 258 k=k+1; case 4 % fixed variable, bounds are equal, set it at either bound xtrans(i) = params.LB(i); case 0 % unconstrained variable. xtrans(i) = x(k); k=k+1; end end end % sub function xtransform end A5.2.3 solver_sawtooth_quasilinear_viscoelastic.m %%%%%%%%%%%%%%%%%%%%%%%%%% %% Solver Sawtooth Quasilinear Viscoelastic %% Written by Behzad Babei (Neuroscience Research Australia) %% Modified for OFPE by Alexa Hudnut function [U] = solver_sawtooth_quasilinear_viscoelastic(U0,U_Lb, U_Hb,data,maxsearch,MaxFunEvals,MaxIter) % function [U] = solver_sawtooth_quasilinear_viscoelastic(U0,U_Lb, U_Hb, data,10,1e5,1e5); % The Fung quasi-linear viscoelastic solver % % Input: % U0 - Initial guess, 5 component vector containing A, B, C, tau1 and tau2 % U_Lb - Lower boundary of A, B, C, tau1 and tau2 % U_Hb - Upper boundary of A, B, C, tau1 and tau2 % strain1,strain2 - are strain in loading part and unloading part respectively. % maxsearch - is number of iteration is the fminsearchbnd % MaxFunEvals,MaxIter - are number of function evaluation and maximum % iteration - is inside fminsearchbnd function % % Please cite: % https://doi.org/10.1016/j.jmbbm.2016.12.013 % http://rsif.royalsocietypublishing.org/content/12/113/20150707 % Last updated: May 2017 % Author: Behzad Babaei global stress strain1 strain2 t = data(:,1); strain = data(:,2); stress = -data(:,3); dt = t(2)-t(1); m = find(strain==max(strain)); stress1 = stress(1:m); stress2 = stress(m+1:end); tt1 = (1:length(stress1))*dt; tt2 = (length(stress1)+1:length(stress1)+length(stress2))*dt; tt = [tt1,tt2]; T = tt(end); 259 strain_rate = max(strain)/tt1(end); strain1 = strain_rate*tt1; strain2 = strain_rate*(T-tt2); Lt = length(tt); % stress - Stress data % strain1,strain2 - are strain in loading and unloading, respectively. % t - is time % dt - is small increment of time % Lt - is length of time vector % strain_rate - is strain rate %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% [a,b]=size(U0); if b > a U0 = U0'; end [a,b]=size(U_Lb); if b > a U_Lb = U_Lb'; end [a,b]=size(U_Hb); if b > a U_Hb = U_Hb'; end [a,b]=size(stress); if b > a stress = stress'; end strain = [strain1,strain2]; [a,b] = size(strain); if b < a strain = strain'; end options = optimset('MaxFunEvals',MaxFunEvals,'MaxIter',MaxIter); ly = length(stress); for kk = 1:maxsearch, [U] = fminsearchbnd(@(U)GQLV(U,tt,strain,stress,dt,strain_rate,Lt), U0 ,U_Lb, U_Hb,options); U0 = U(:); % Input of the next step global squared_error squared_error end save U % ### SUBS ##################################################### % function [out] = fun(U,stress,t1,t2,strain_rate) function squared_error = GQLV(U,tt,strain,stress,dt,strain_rate,Lt) global yfit F G squared_error 260 A = U(1); B = U(2); C = U(3); tau1 = U(4); tau2 = U(5); strain_dot = [strain_rate*ones(1,length(strain)/2) - strain_rate*ones(1,length(strain)/2)]; F = A * B* exp(B*strain).*strain_dot; %A * B* exp(B*strain)*strain_rate; G = ( 1+ C * ( expint(tt/tau2) - expint(tt/tau1) ) )./(1+C * log(tau2/tau1)); con = dt*conv(F(:),G(:)); yfit = stress(1) + con(1:Lt); squared_error = sum((stress(:)-yfit(:)).^2); A5.2.4 nnls.m %%%%%%%%%%%%%%%%%%%%%%%%%% %% nnls %% Written by Behzad Babei (Neuroscience Research Australia) %% Modified for OFPE by Alexa Hudnut function [x,w,info]=nnls(C,d,opts) % nnls Non negative least squares Cx=d x>=0 w=C'(d-Cx)<=0 % 2012-08-21 Matlab8 W.Whiten % 2013-02-17 Line 52 added % Copyright (C) 2012, W.Whiten (personal W.Whiten@uq.edu.au) BSD license % (http://opensource.org/licenses/BSD-3-Clause) % % [x,w,info]=nnls(C,d,opts) % C Coefficient matrix % d Rhs vector % opts Struct containing options: (optional) % .Accy 0 fast version, 1 refines final value (default), % 2 uses accurate steps but very slow on large cases, % faster on small cases, result usually identical to 1 % .Order True or [], or order to initially include positive terms % if included will supply info.Order, if x0 available use % find(x0>0), but best saved from previous run of nnls % .Tol Tolerance test value, default zero, use multiple of eps % .Iter Maximum number of iterations, should not be needed. % % x Positive solution vector x>=0 % w Lagrange multiplier vector w(x==0)<= approx zero % info Struct with extra information: % .iter Number of iterations used % .wsc0 Estimated size of errors in w % .wsc Maximum of test values for w % .Order Order variables used, use to restart nnls with opts.Order % % Exits with x>=0 and w<= zero or slightly above 0 due to % rounding and to ensure for convergence % Using faster matrix operations then refines answer as default (Accy 1). % Accy 0 is more robust in singular cases. 261 % % Follows Lawson & Hanson, Solving Least Squares Problems, Ch 23. [~,n]=size(C); maxiter=4*n; % inital values P=false(n,1); x=zeros(n,1); z=x; w=C'*d; % wsc_ are scales for errors wsc0=sqrt(sum(w.^2)); wsc=zeros(n,1); tol=3*eps; accy=1; pn1=0; pn2=0; pn=zeros(1,n); % see if option values have been given ind=true; if(nargin>2) if(isfield(opts,'Tol')) tol=opts.Tol; wsc(:)=wsc0*tol; end if(isfield(opts,'Accy')) accy=opts.Accy; end if(isfield(opts,'Iter')) maxiter=opts.Iter; end end % test if to use normal matrix for speed if(accy<2) A=C'*C; b=C'*d; %L=zeros(n,n); LL=zeros(0,0); lowtri=struct('LT',true); uptri=struct('UT',true); end % test if initial information given if(nargin>2) if(isfield(opts,'Order') && ~islogical(opts.Order)) pn1=length(opts.Order); pn(1:pn1)=opts.Order; P(pn(1:pn1))=true; ind=false; end 262 if(~ind && accy<2) %L(1:pn1,1:pn1)=chol(A(pn(1:pn1),pn(1:pn1)),'lower'); UU(1:pn1,1:pn1)=chol(A(pn(1:pn1),pn(1:pn1))); LL=UU'; end pn2=pn1; end % loop until all positive variables added iter=0; while(true) % Check if no more terms to be added if(ind && (all(P==true) || all(w(~P)<=wsc(~P)))) if(accy~=1) break end accy=2; ind=false; end % skip if first time and initial Order given if(ind) % select best term to add ind1=find(~P); [~,ind2]=max(w(ind1)-wsc(ind1)); ind1=ind1(ind2); P(ind1)=true; pn2=pn1+1; pn(pn2)=ind1; end % loop until all negative terms are removed while(true) % check for divergence iter=iter+1; if(iter>=2*n) if(iter>maxiter) error(['nnls Failed to converge in ' num2str(iter) ... ' iterations']) %warning(['nnls Failed to converge in ' num2str(iter) ... % ' iterations']) %return elseif(mod(iter,n)==0) wsc=(wsc+wsc0*tol)*2; end end % solve using suspected positive terms z(:)=0; if(accy>=2) z(P)=C(:,P)\d; else % add row to the lower triangular factor 263 for i=pn1+1:pn2 i1=i-1; %LL=L(1:i1,1:i1); %LL=LL(1:i1,1:i1); t=linsolve(LL,A(pn(1:i1),pn(i)),lowtri); %t=LL\A(pn(1:i1),pn(i)); %L(i,1:i1)=t; %LL(i,1:i1)=t; AA=A(pn(i),pn(i)); tt=AA-t'*t; if(tt<=AA*tol) tt=1e300; else tt=sqrt(tt); end %L(i,i)=sqrt(tt); %LL(i,i)=sqrt(tt); LL(i,1:i)=[t',tt]; UU(1:i,i)=[t;tt]; end % solve using lower triangular factor %LL=L(1:pn2,1:pn2); t=linsolve(LL,b(pn(1:pn2)),lowtri); %t=LL\b(pn(1:pn2)); %UU=LL'; %z(pn(1:pn2))=linsolve(UU,t,uptri); z(pn(1:pn2))=linsolve(UU,t,uptri); %z(pn(1:pn2))=LL'\t; % or could use this to solve without updating factors %z(pn(1:pn2))=A(pn(1:pn2),pn(1:pn2))\b(pn(1:pn2)); end pn1=pn2; % check terms are positive if(all(z(P)>=0)) x=z; if(accy<2) w=b-A*x; else w=C'*(d-C*x); end wsc(P)=max(wsc(P),2*abs(w(P))); ind=true; break end % select and remove worst negative term ind1=find(z<0); [alpha,ind2]=min(x(ind1)./(x(ind1)-z(ind1)+realmin)); ind1=ind1(ind2); % test if removing last added, increase wsc to avoid loop if(x(ind1)==0 && ind) w=C'*(d-C*z); wsc(ind1)=(abs(w(ind1))+wsc(ind1))*2; 264 end P(ind1)=false; x=x-alpha*(x-z); pn1=find(pn==ind1); pn(pn1:end)=[pn(pn1+1:end),0]; pn1=pn1-1; pn2=pn2-1; if(accy<2) LL=LL(1:pn1,1:pn1); UU=UU(1:pn1,1:pn1); end ind=true; end end % info result required if(nargout>2) info.iter=iter; info.wsc0=wsc0*eps; info.wsc=max(wsc); if(nargin>2 && isfield(opts,'Order')) info.Order=pn(1:pn1); end end return end
Abstract (if available)
Abstract
One fundamental challenge in developing medical devices is that the same platform can rarely be used to diagnose or characterize multiple diseases. This is because highly specific chemical sensing methods are introduced to increase the signal, which has been necessary in the majority of traditional medical devices and diagnostics. By leveraging the fundamental properties of optics, I have overcome this limitation and developed a suite of medical device and diagnostic technologies based on optical polarization. The main platform discussed in this dissertation is an optical fiber polarimetric elastography (OFPE) instrument for determining the biomechanical properties of tissues. To demonstrate the flexibility of this platform, it is used to characterize a variety of biomaterials that range in Young’s modulus by three orders of magnitude. The following work details the experiments and results for how the instrument was designed, fabricated, and validated. Additional instruments were developed using the same fundamental principles of optics. These results are presented in the appendices. Therefore, in addition to the scientific results presented in this thesis, it should serve as a framework for developing and characterizing families of medical devices.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Hudnut, Alexa Watkins
(author)
Core Title
High-resolution optical instrumentation for biosensing and biomechanical characterization
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
07/25/2018
Defense Date
05/07/2018
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
biosensors,integrated optics,medical optics instrumentation,nondestructive testing,OAI-PMH Harvest,optical fiber polarimetric elastography,optics,polarimetry,viscoelastic material analysis
Format
application/pdf
(imt)
Language
English
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Electronically uploaded by the author
(provenance)
Advisor
Armani, Andrea (
committee chair
), Agus, David (
committee member
), Chung, Eun Ji (
committee member
), Kassner, Mike (
committee member
)
Creator Email
alexahudnut@gmail.com,awhudnut@gmail.com
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-c89-30726
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UC11672283
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etd-HudnutAlex-6466.pdf (filename),usctheses-c89-30726 (legacy record id)
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etd-HudnutAlex-6466.pdf
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30726
Document Type
Dissertation
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Hudnut, Alexa Watkins
Type
texts
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University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
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The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...
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Tags
biosensors
integrated optics
medical optics instrumentation
nondestructive testing
optical fiber polarimetric elastography
optics
polarimetry
viscoelastic material analysis