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Susceptibility-weighted MRI for the evaluation of brain oxygenation and brain iron in sickle cell disease

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Susceptibility-weighted MRI for the evaluation of brain oxygenation and brain iron in sickle cell disease

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Content Susceptibility-Weighted MRI for the Evaluation of Brain Oxygenation and Brain Iron in Sickle Cell Disease by Xin Miao A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulllment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Biomedical Engineering) May 2019 Copyright 2019 Xin Miao Dedication To my mom, dad and Yan ii Acknowledgements This thesis would not have been possible without the support from many people, but there are a few to whom I would like to give my deepest acknowledgement. To John and Krishna: There is not enough to say how blessed I am to have both of you as my mentors. You held my hand and walked me step by step on the way to become a scientist. You are not just my advisors of research, you make me a better person. To John: You gave me the courage to go beyond the comfort zone and chase where the real problem leads. You taught me how to solve problems with perse- verance, patience and also an open mind. When I felt the bitterness of research, I would remember the scene of you working at your desk while still wearing the on-call scrub; you showed me the power of passion. Thank you for always nding time to save me out of the frustrations and falls. Thank you for pushing the limits and reassuring me that I could get through them. Thank you and Ruth for giving me the sense of home during holidays and celebrations. To Krishna: You brought me to the fantastic world of MRI! If it had not been your encouragement, I might just have passed by MRI as a rotation student instead of nding it as my greatest interest. From you, I learnt how to learn with intuitive understanding, expressive graphs and incisive questions. Thank you for all those one-on-ones where you enlightened me not only with research ideas but also with discussions on professional appearance. Thank you for pushing me to think big. Thank you for believing in me more than I do. iii To my defense and qualication committee: Dr. Thomas Coates, Dr. Michael Khoo, Dr. Scott Fraser and Dr. Justin Haldar, thank you for generously oering your time, support and advice throughout the preparation of my thesis. Thank you for inspiring me with your insights from dierent aspects. To the members of my research family: Ziyue and Sajan, you two are such inspirations to me. I was lucky to have your guidance when I rst started. Vanessa, thank you for sitting with me for hours to help with my writing and thank you for always being there for me. The warmth of your home helped me go through the hardest time of my PhD. Adam, thank you for all the `big-brother' advice on research and life. When I felt lost, you always helped me see the problems with a calmer mind. Wayne and Yi, thank you for being the pals with whom I can share my laughters and tears. Ahsan and Terrence, thank you for helping me with sequence programming and thank you for being such friends who always listen to me. Chau, thank you for lightening up my day with the "bonding time" during patient scans and lunch breaks. Mischal, Noel, Nathan and Bertin, thank you for helping me with administratives and schedules. Your prompt emails often saved my day. Jian, Soyoung, Silvie, Yaqiong, Botian, Yongwan, Yannick, Eamon and Hung, thank you for all the company and fun in lab. To my husband, Yan: thank you for holding me together with your love, care and support. I can not wait for our new chapter of life together. To my mom and dad: our family had the hardest time during the last year of my PhD. But you still supported me by choosing to face the challenge alone and telling me not to worry. Thank you for your precious love. This thesis is dedicated to you. iv Table of Contents Dedication ii Acknowledgements iii List Of Tables viii List Of Figures ix Abstract xvi Chapter 1: Introduction 1 1.1 Clinical motivation: Sickle cell disease . . . . . . . . . . . . . . . . 1 1.1.1 Sickle cell disease basics . . . . . . . . . . . . . . . . . . . . 1 1.1.1.1 Molecular basis and genotypes . . . . . . . . . . . 1 1.1.1.2 Prevalence . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Cerebrovascular diseases in SCD . . . . . . . . . . . . . . . . 2 1.1.3 Clinical need for brain oxygenation evaluation in SCD . . . . 5 1.1.3.1 Fick's model of CMRO 2 . . . . . . . . . . . . . . . 5 1.1.3.2 Previous studies on oxygen delivery in SCD . . . . 7 1.1.3.3 Previous studies on OEF in SCD . . . . . . . . . . 8 1.1.4 Clinical need for brain iron evaluation in SCD . . . . . . . . 9 1.1.4.1 Brain iron metabolism . . . . . . . . . . . . . . . . 9 1.1.4.2 Brain iron overload in neurovascular diseases . . . . 9 1.1.4.3 Linkage between SCD-associated cerebrovascular con- ditions and brain iron abnormality . . . . . . . . . 11 1.2 Susceptibility-weighted MRI . . . . . . . . . . . . . . . . . . . . . . 12 1.2.1 Tissue magnetism . . . . . . . . . . . . . . . . . . . . . . . . 12 1.2.2 Magnetic eld generated by tissue magnetization . . . . . . 14 1.2.3 Susceptibility eects on MRI signal . . . . . . . . . . . . . . 17 1.2.4 MRI-based tissue susceptibility quantication . . . . . . . . 21 1.2.4.1 Quantitative susceptibility mapping (QSM) . . . . 21 v 1.2.4.2 MRI-based oxygenation imaging . . . . . . . . . . 26 Chapter 2: Comparison of T2- and susceptibility-based venous oxy- gen saturation measurements under hypoxia and hypercapnia 32 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.1 Study Design . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.2.2 S v O 2 measurement using TRUST . . . . . . . . . . . . . . . 36 2.2.3 S v O 2 measurement using SBO . . . . . . . . . . . . . . . . . 37 2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.1 Comparison of S v O 2 measurements using TRUST and SBO . 39 2.3.2 Validation with jugular catheterization . . . . . . . . . . . . 41 2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4.1 Validation with jugular vein catheterization . . . . . . . . . 44 2.4.2 Comparison of T2- and susceptibility-based S v O 2 measurements 45 2.4.3 Variance in SBO measurement . . . . . . . . . . . . . . . . . 46 2.4.4 Practical considerations of TRUST and SBO . . . . . . . . . 48 2.4.5 Limitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6 Supplemental Methods . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6.1 Sources of variance in S v O 2 -TRUST measurement . . . . . . 50 2.6.1.1 Underestimation of T2 due to short TR . . . . . . 50 2.6.1.2 Underestimation of T2 due to blood ow . . . . . . 52 2.6.1.3 Bovine blood model and human HbA model . . . . 53 2.6.2 Sources of variance in S v O 2 -SBO measurement . . . . . . . . 54 2.6.2.1 Violation of long straight cylinder assumption . . . 54 2.6.2.2 Error due to background eld removal . . . . . . . 55 Chapter 3: Increased brain iron deposition in patients with sickle cell disease: an MRI quantitative susceptibility mapping study 58 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.2.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.2.2 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 60 3.2.3 Image processing . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2.4 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . 62 3.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3.1 Patient characteristics . . . . . . . . . . . . . . . . . . . . . 63 3.3.2 Age and sex eects on brain iron deposition . . . . . . . . . 64 3.3.3 Group dierence in brain iron deposition . . . . . . . . . . . 64 3.3.4 Covariates of susceptibility measurements in deep gray matter 66 3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 vi Chapter 4: Eect of low spatial resolution on quantitative suscepti- bility mapping 76 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76 4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.1 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.2 Image processing . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.3 Numerical phantom simulation . . . . . . . . . . . . . . . . 80 4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.3.1 Deep gray matter structures . . . . . . . . . . . . . . . . . . 81 4.3.2 Straight sagittal sinus . . . . . . . . . . . . . . . . . . . . . 83 4.3.3 Small vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Chapter 5: Conclusion and ongoing work 90 Reference List 94 vii List Of Tables 1.1 Summary of literature reported OEF measurement using PET- and MRI-based techniques. . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.1 Literature values of venous oxygen saturation under dierent physi- ological conditions a . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.2 Summary of CBF measurements using phase contrast MRI, S v O 2 measurements using TRUST and SBO, and calculation of normalized CMRO 2 from room air to hypercapnia (N = 8). Student t-test was used to test if the sample mean is signicantly dierent from zero. Arterial ow: ml/min, S v O 2 : %, and CMRO 2 : % . . . . . . . . . 47 3.1 Subject demographics. Group averages and standard deviations are given. Group dierences were assessed using unpaired student's t-test. 65 4.1 Simulated spatial resolution levels for susceptibility quantication of deep gray matter structures and straight sagittal sinus. Voxel size (in mm) along the three spatial dimensions is listed. A-P: anterior- posterior dimension; R-L: right-left dimension; F-H: feet-head di- mension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 viii List Of Figures 1.1 Two types of stroke in SCD. A. Overt stroke in the anterior cerebral artery and middle cerebral artery territories shown by T2-weighted MRI (left) was caused by occlusion of the internal carotid artery shown by MR angiography (right). Adapted from Switzer et al [6]. B. Silent stroke lesions shown as hyperintensities (red arrows) in uid-attenuated inversion recovery T2-weighted images. . . . . . . . 3 1.2 Prevalence of SCI in children and young adults with SCD. The cumulative prevalence of SCI increases 1-2% per age year with no plateau towards young adulthood despite appropriate TCD screen- ing. Adapted from Kassim et al [16]. . . . . . . . . . . . . . . . . . 5 1.3 Field induced by a magnetized sphere. Left: spherical coordinate system for describing the eld at a point (r,) relative to the sphere. The main B 0 eld is parallel to thez direction. Right: magnetic eld in the x-z plane. Amplitude of the eld is shown as a ratio to B 0 . 15 1.4 Field induced by a magnetized cylinder. Left: cylindrical coordinate system for describing the eld at a point (r, , ). The cylinder is at an angle to the main B 0 eld. Right: induced magnetic elds when the cylinder has dierent orientations with respect to the main B 0 eld. Amplitude of the eld is shown as a ratio to B 0 . . . . . 16 1.5 Absolute magnitude of the dipole kernel in Fourier space. Although only thek x -k z plane is shown here, it should be noted that the kernel is radially symmetric in the k x -k y plane. . . . . . . . . . . . . . . . 18 1.6 Processes in MRI signal formation. Left: equilibrium magnetiza- tion due to polarization. Middle: transverse magnetization after RF exciation. Right: signal dephasing due to magnetic eld variation, B 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 ix 1.7 3D multi-echo gradient echo (GRE) sequence. This example se- quence acquires three gradient echoes. The echo time (TE) is cal- culated as the time interval between the center of the exitation RF pulse and the formation of a gradient echo. Readout gradient is ap- plied in the x direction, and the two phase encoding gradients are applied in the y and z directions. For every repitition time (TR), the sequence is repeated with changing phase encoding gradients. . 20 1.8 Comparison of background eld removal methods including PDF, RESHARP, and LBV. The local eld is obtained by subtracting the estimated background eld from the total eld. It is plotted in the sagittal (top) and axial (bottom) views. . . . . . . . . . . . . . . . . 22 1.9 Comparison of eld-to-susceptibility inversion methods including TKD, L1-QSM and MEDI. The estimated susceptibility maps are plotted in the sagittal (top) and axial (bottom) views. . . . . . . . . . . . . 26 1.10 Comparison of three calibration models in the TRUST measurement of venous oxygen saturation. Venous oxygen saturation measure- ments in SCD patients (red diamonds) and healthy controls (gray dots) are plotted against oxygen content. Left: using the bovine blood model, there is a signicant positive correlation between ve- nous oxygen saturation and oxygen content. SCD patients demon- strate signicantly lower venous oxygen saturation than healthy con- trols. Middle: using the healthy human blood model, venous satura- tion measurements in the two populations are not signicantly dif- ferent. Right: using the sickle cell blood model, there is a signicant negative correlation between venous oxygen saturations and oxygen content. SCD patients have signicantly higher venous oxygen sat- uration than healthy controls. Adapted from Bush et al. [92]. . . . 28 2.1 Protocol of scan without catheterization. Three scan sessions in the order of hypoxia (orange block), hypercapnia (yellow block) and room air (green block) were rst performed. Pauses of 2 to 3 min were allotted (grey blocks), depending on the time needed for the subject to reach steady oxygenation state. Subsequently, two more scan sessions were conducted at room air, in which the subject was repositioned and new pre-scans were played. Order of MRI ac- quisitions under the same oxygenation state was counterbalanced to avoid bias. TRUST: T2 relaxation under spin tagging; SBO: susceptometry-based oximetry; PC: phase contrast. . . . . . . . . . 36 x 2.2 A: Localization of the TRUST imaging plane (red line) at the supe- rior sagittal sinus. B: The resulting dierence image upon subtrac- tion of the control and labeled images at four eective echo times. Red boxes highlight the isolated blood signal at the sagittal sinus. C: Mono-exponential tting of the four dierence images is then per- formed to estimate T2 of blood. . . . . . . . . . . . . . . . . . . . . 37 2.3 Background eld removal in SBO. A. The total B 0 eld in sagittal view. Segmentation of the superior sagittal sinus (SSS) is highlighted in red dashed line. Region of interest (ROI) was chosen as a cylin- drical segment of SSS with vertical length of 10 mm and minimum intra-ROI variance of B 0 values. B. Background eld was esti- mated by performing a second-order polynomial t to the B 0 eld in a tissue region (yellow dashed line) within an in-plane 40-mm range from the ROI center. The background eld was extrapolated to the ROI and subtracted from the total B 0 eld. . . . . . . . . . . . . . 38 2.4 Comparison of S v O 2 -TRUST and S v O 2 -SBO measurements at the superior sagittal sinus. (A) S v O 2 -TRUST and S v O 2 -SBO measure- ments averaged across subjects under each condition. (B) Average change of S v O 2 from room air to hypercapnia and to hypoxia. (C) Scatterplot of S v O 2 -TRUST and S v O 2 -SBO with the linear correla- tion regression line (solid) and identity line (dashed). (D) Bland- Altman plot with the average of the two measurements displayed in the horizontal axis and the dierence between the two displayed in the vertical axis. **: p< 0:01 . . . . . . . . . . . . . . . . . . . . . 40 2.5 Time-course plots of S v O 2 measurements in two subjects who un- derwent jugular catheterization. Co-oximetry measurement was re- peated approximately every 3 min (purple circles), S v O 2 -TRUST measurement at the superior sagittal sinus was repeated approxi- mately every 1.5 min (orange square), and S v O 2 -SBO measurement was only performed when steady state was achieved under each gas condition (blue triangle). . . . . . . . . . . . . . . . . . . . . . . . . 41 2.6 Comparison of TRUST and SBO measurement against the co-oximetry reference. A. 15 and 13 TRUST measurements from subject 1 (blue circle) and subject 2 (red cross) respectively are compared against time-aligned co-oximetry reference. Proportional bias of S v O 2 -TRUST was observed in subject 2. Taken all data points, the mean bias of S v O 2 -TRUST is -9.2% (p < 0:0001). B. six and seven SBO mea- surements from subject 1 and 2 respectively are compared against co-oximetry reference at steady oxygenation states. Taken all data points, the mean bias of S v O 2 -SBO is -1.0% (p = 0:45). . . . . . . . 42 xi 2.7 TRUST sequence experienced by blood spins in two consecutive TRs. The top diagram demonstrates the case of control imaging, in which the previous TR has an inversion RF pulse and T2 preparation mod- ule. The bottom shows the case of tag imaging, in which the previous TR only has the T2 preparation module. . . . . . . . . . . . . . . . 52 2.8 Relation between estimated T2 and true T2 in the case of short TR. Simulation on the underestimation of T2 caused by short TR. A. The relation between estimated T2 (ms) and true T2 (ms) under dierent TR (s) is plotted. B. Assuming Hct = 0.42, T2 underestimation is converted into saturation underestimation using the bovine blood model. Over a range of true saturation from 30% to 80%, saturation underestimation is approximately constant. . . . . . . . . . . . . . . 53 2.9 Comparison of the T2-preparation sequence without (A) and with (B) a gradient eld. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 2.10 Eect of intra-voxel dephasing on T2 estimation, assuming the B 0 eld variation as a gradient eld of 1500 Hz/m. A. Signal loss ratio (%) depends on both the spin velocity (cm/s) and the duration of the CPMG T2-prep module. B. Estimated T2 is shown as a function the true T2. C. Using the bovine blood model and assuming a Hct of 0.42, saturation error increases with spin velocity (cm/s) and the true saturation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.11 Time-course plots of S v O 2 measurements using co-oximeter (purple), TRUST with bovine blood model (orange) and TRUST with HbA model (blue) on two subjects who underwent jugular catheterization. 56 2.12 Large variation of S v O 2 -SBO measurement along the axis of SSS. For each subject, the slice-by-slice S v O 2 -SBO measurement is plotted as a function of slice index (vertical axis). Measurements under hypercapnia, hypoxia and room air are represented as red, yellow and blue lines. Sagittal view of SSS susceptibility map (converted to saturation values) is also shown aligning with the vertical axis of the S v O 2 plot. Both the range of variation and standard deviation along the axis of SSS are given. . . . . . . . . . . . . . . . . . . . . 57 xii 3.1 Segmentation of deep gray matter structures on quantitative sus- ceptibility map. Example axial (a to c) and coronal slices (d to f) of the susceptibility map are displayed. Locations of the slices are indicated in the sagittal view of T1-weighted image (top left). Struc- tures of the caudate nucleus (CN), putamen (PT), globus pallidus (GP), substantia nigra (SN), red nucleus (RN), and dentate nucleus (DN) are highlighted with yellow boxes in the susceptibility map and enlarged two to four times for better visualization. . . . . . . . . . . 71 3.2 Susceptibility increases with age in all deep gray matter structures. Linear regression was performed on the susceptibility measurements with respect to log-transformed age. p-values and r 2 of tting are given. The tted curves and observation bounds of 95% condence intervals are plotted as doted and dashed lines respectively. . . . . . 72 3.3 R2* measurements increase with age in all deep gray matter struc- tures except the caudate nucleus. Linear regression was performed on the R2* measurements with respect to log-transformed age. p- values and r 2 of tting are given. The tted curves and bounds of 95% condence intervals are plotted as doted and dashed lines respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.4 SCD patients exhibit higher susceptibility and R2* in multiple sub- cortical nuclei, compared with age-matched controls. (A) Average susceptibility (in parts per billion (ppb)) and R2* (in s 1 ) of deep gray matter ROIs in SCD patients and healthy controls. Values are reported as mean (standard deviation). All values were corrected for age and sex. d is Cohen's eect size, which is dened as the dierence between group means divided by the pooled standard deviation. **: p< 0:01. *: p< 0:05. (B) Examples of susceptibility and R2* maps in the regions of substantia nigra and red nucleus. Susceptibility maps (top), R2* maps (middle) and T2*-weighted images at TE = 20 ms (bottom) are shown. Blue and pink dashed boxes highlight the regions of substantia nigra and red nucleus respectively. The left two columns compare an SCD patient with a control who are both 29 years old, and the right two columns compare two subjects who are both 25 years old. . . . . . . . . . . . . . . . . . . . . . . . . . . 74 xiii 3.5 Susceptibility values of multiple subcortical nuclei increase with sever- ity of anemia and white matter damage. (A) Age corrected suscep- tibility measurements present signicant negative correlation with hemoglobin in substantia nigra (p = 0:008, r 2 = 0:14), red nucleus (p = 0:028, r 2 = 0:10), and dentate nucleus (p = 0:023, r 2 = 0:13). Dotted lines show the linear regression of the data and shaded ar- eas delimit the 95% condence interval. (B) Susceptibility of the globus pallidus and substantia nigra (after correction for age and sex) is higher in SCD patients with silent infarcts (SCI+), compared to patients with normal appearing white matter (SCI-). Mean and standard deviation of globus pallidus susceptibility are 180.529.8 ppb in the SCI+ group and 149.323.7 ppb in the SCI- group. **: p = 0:007. Mean and standard deviation of substantia nigra suscep- tibility are 151.735.5 ppb in the SCI+ group and 115.329.1 ppb in the SCI- group. **: p = 0:010. . . . . . . . . . . . . . . . . . . . 75 4.1 Segmentation of deep gray matter structures on quantitative sus- ceptibility map. Example axial (a to c) and coronal slices (d to f) of the susceptibility map are displayed. Locations of the slices are indicated in the sagittal view of T1-weighted image (top left). Struc- tures of the caudate nucleus (CN), putamen (PT), globus pallidus (GP), substantia nigra (SN), red nucleus (RN), and dentate nucleus (DN) are highlighted with yellow boxes in the susceptibility map and enlarged two to four times for better visualization. . . . . . . . . . . 79 4.2 Mean susceptibility measurement error at dierent spatial resolu- tions for gray matter ROIs. The horizontal axis represents six levels of spatial resolution detailed in Table 1. The range of acceptable error,5 ppb is denoted as gray area. When the voxel dimension along all three axes wasleq 2.0 mm, estimation error was< 5 ppb in CN, PT and GP. When the voxel size was 2:0 2:0 1:3 mm 3 , esti- mation error was< 5 ppb in SN and DN. For RN, spatial resolution of 1:5 1:5 2:0 mm 3 or higher is required. . . . . . . . . . . . . . 82 4.3 Bland-Altman plot of susceptibility measurement error at spatial resolution of 2:0 2:0 2:0 mm 3 for gray matter ROIs. Solid and dashed lines represent the mean and the 95% condence interval (i.e. mean 2.03 SD) of measurement error. Signicant measurement bias (p< 0:05, t-test) is labeled in red. . . . . . . . . . . . . . . . . 83 xiv 4.4 Eect of spatial resolution on the accuracy of susceptibility and S v O 2 measurements in the straight sinus. Bland-Altman plots of suscep- tibility and S v O 2 measurement errors at dierent spatial resolution levels are shown in (A) to (E). Solid and dashed lines represent the mean and the 95% condence interval (i.e. mean 2.03 SD) of mea- surement error. Signicant measurement bias (p < 0:05, t-test) is labeled in red. Error of saturation measurement was 2.3% (sat- uration unit), when the voxel dimension along all three axes was 1:5 1:5 2:0 mm 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.5 Numerical simulation of susceptibility underestimation at low spa- tial resolution for a cylindrical ROI with physical diameter of 2 mm and orientation perpendicular to the main magnetic eld. Estimated susceptibility of the cylinder (A) and relative estimation error (B) are plotted against the true susceptibility. Solid lines represent the mean values of the 10 measurements with complex Gaussian noise. Simulations at three levels of spatial resolution (blue: 0:50:51:0, red: 0:25 0:25 0:5, yellow: 0:125 0:125 0:25 mm 3 ) and at four echo times (TE = 5, 10, 15 and 20 ms) are shown. Simulated susceptibility underestimation depends on not only the spatial res- olution but also the echo time. Intra-voxel phase aliasing produces additional eect on susceptibility quantication (black arrows). . . . 89 5.1 (a) Susceptibility measurement of internal cerebral vein as a func- tion of hematocrit (%). (b) Compared with healthy controls, ve- nous oxygen saturation of internal cerebral vein is signicantly lower (p < 0:05) in both SCD and non-SCD anemia patients. Mean ve- nous oxygen saturation of internal cerebral vein in the three groups: CTL = 73.9%, ACTL = 73.6% and SCD = 69.3%. ACTL: non-SCD anemia controls (pink dots), CTL: healthy controls (green dots), and SCD: sickle-cell disease patients (red dots). Boxes represent 95% con- dence interval of the mean in each group. Statistical signicance is denoted as **. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 xv Abstract Sickle cell disease (SCD) is a genetic disorder characterized with abnormal hemoglobin that polymerizes upon deoxygenation, creating rigid, sickle-shaped red blood cells. Recurrent red blood cell sickling causes anemia and vasculopathy, which have the most devastating consequences in the brain. Silent cerebral infarction (SCI) is a common and progressive problem in SCD and is linked to high stroke risks and neurocognitive decits. However, the prediction and pathogenesis of SCI is still obscure. This thesis aims to develop a brain oxygenation marker to predict SCI and to investigate brain iron deposition in its correlation with SCD and SCI. Susceptibility-weighted magnetic resonance imaging (MRI) provides noninva- sive quantication of the magnetic property of brain tissue, which can be exploited for the assessment of brain oxygenation and brain iron deposition in SCD. Cerebral venous oxygen saturation measurement using susceptibility-weighted MRI has the advantages of model simplicity and calibration exemption. However, the technique has seldomly been validated in a controlled manner under a broad range of physio- logical states. In this thesis, I cross-validated susceptibility-based oximetry (SBO) with both the clinical gold standard (jugular vein catheterization) and a relaxation- based oximetry (RBO) technique widely used in SCD literature. Systematic bias between SBO and RBO was revealed and analyzed. Error bonds of SBO and RBO were placed for the rst time based on the comparison with the clinical standard. Brain iron has been shown to increase with recurrent ischemic-reperfusion in- juries, chronic hypoxia and microvasculature damage, which are common conditions in SCD. As a consequence, excessive brain iron could potentially aggravate white xvi matter damage and accelerate neurodegeneration. In the second part of this thesis, susceptibility-weighted MRI was applied to measure the brain iron in SCD patients. Increased brain iron accumulation in multiple subcortical nuclei was observed in SCD patients. Iron concentration in deep gray matter demonstrated correlation with severity of anemia and the presence of SCI. Given the potential clinical translation of susceptibility-weighted MRI, practi- cal consideration on the trade-o between scan time and spatial resolution becomes important, especially in SCD pediatric imaging. The third part of the thesis in- vestigated the eect of spatial resolution on susceptibility-based brain oxygenation and brain iron quantication. Susceptibility quantication errors due to low spa- tial resolution were bounded based on both simulation and in-vivo data. Practical guidelines on shortening scan time by lowering spatial resolution were provided. xvii Chapter 1 Introduction This chapter divides into two parts. The rst part explains the clinical motiva- tion behind this thesis - sickle cell disease (SCD). Pathological basics of SCD are introduced with a focus on SCD-associated cerebrovascular conditions. The un- met clinical needs and current research status on brain oxygenation and brain iron evaluation in SCD are reviewed. The second part covers the imaging methodol- ogy that is used to address the clinical needs - susceptibility-weighted MRI. Tissue magnetism and its eect on MRI signals are rst described because they are the physical basis of susceptibility-weighted MRI. Existing techniques in susceptibility- weighted MRI are discussed, along with their applications to brain oxygenation and brain iron evaluation. 1.1 Clinical motivation: Sickle cell disease 1.1.1 Sickle cell disease basics 1.1.1.1 Molecular basis and genotypes Sickle cell disease (SCD) is a genetic disorder characterized by an abnormal hemoglobin called hemoglobin S (HbS). When oxygen pressure is reduced, the deoxygenated 1 HbS molecules will polymerize, forming long rigid bers that force the red blood cells (RBC) to a crescent shape. This is the molecular basis of RBC \sickling" [1]. The hemoglobin molecule contains four protein subunits, two alpha-globins and two beta-globins. A single-point mutation in the beta-globin gene causes the pro- duction of HbS [2]. When both beta-globin subunits are replaced with HbS, the condition is known as sickle cell disease (HbSS). When only one beta-globin is re- placed with HbS, this generally benign condition is called sickle cell trait (HbSA). When the two beta-globins are replaced with HbS and a dierent abnormal variant, such as hemoglobin C or beta thalassemia, then the condition is described as HbSC or HbSBetaThal respectively. 1.1.1.2 Prevalence SCD is most commonly found among people whose ancestors come from Africa, India, and South America. SCD aects 250,000 births each year worldwide [3]. In the United States, there are more than 90,000 patients with SCD [4] with annual health care costs exceeding 1.1 billion in 2009 [5]. 1.1.2 Cerebrovascular diseases in SCD Cerebrovascular disease is a common and devastating complication of SCD. RBC sickling is central to the development of cerebrovascular diseases in SCD, although the mechanisms are heterogeneous [6]. Sickled RBCs can easily hemolyze, causing anemia. They also have abnormal adherence to the endothelium, causing vaso- occlusion that is most prominent in the microvasculature. The toxic compounds released from damaged sickle cells can promote hypercoaguable state and impair vasomotor tone. Moreover, recurrent episodes of vaso-occlusion and reperfusion cause additional in ammatory vascular injury. The ultimate results are large-vessel vasculopathy and small-vessel occlusion, which form the basis of a devastating com- plication in SCD { stroke. 2 In SCD, there are two forms of stroke: overt stroke and silent stroke (Figure 1.1). Overt stroke, dened by the presence of a localizing neurological symptom, is caused by either occlusion (ischemic stroke) or rupture (hemorrhage stroke) of large vessels. Overt stroke has the most severe consequences, including high rates of mortality and lifelong morbidity. In the 1990s when there was no established stroke- prevention strategies, 11% of SCD patients have overt (ischemic) stroke by age 20 years and 24% by age 45 years [7]. Without treatment, the majority experienced a recurrent stroke within 5 years [8]. Figure 1.1: Two types of stroke in SCD. A. Overt stroke in the anterior cerebral artery and middle cerebral artery territories shown by T2-weighted MRI (left) was caused by occlusion of the internal carotid artery shown by MR angiography (right). Adapted from Switzer et al [6]. B. Silent stroke lesions shown as hyperintensities (red arrows) in uid-attenuated inversion recovery T2-weighted images. Transcranial ultrasound (TCD) screening and chronic transfusion therapy has been proven in clinical trials to successfully reduce the incidence of primary and recurrent overt stroke [8, 9]. Clinically, SCD pediatric patients who have middle cerebral artery TCD > 200 cm/s are considered having high risk of stroke. They will be referred to chronic blood transfusion every 3 to 6 weeks with a goal to keep the HbS level under 30%. Although the incidence of stroke in children with 3 SCD has fallen remarkably (92% [10]) with blood transfusion [11], the treatment has serious side eects including body iron overload. Hydroxyurea is an emerging alternative to blood transfusion for secondary stroke prevention, the ecacy and safety of which are under investigation in clinical trials [12]. The other type of SCD-associated stroke, silent stroke or silent cerebral infarc- tion (SCI), refers to cerebral infarction that shows on the MRI but corresponds to no focal neurological decit. Silent stroke lesions are typically small, measuring at least 3 mm in greatest linear dimension, visible in at least 2 planes of T2-weighted images. These lesions are more likely to appear in deep supraventricular white mat- ter, corresponding to the internal border zone [13, 14]. It has been reported that the cumulative risk for silent stroke was 19.2% by age 8 years, 32.4% by age 14 years, 39.1% by age 18 years and higher than 40% in adults with SCD [15, 16]. Though devoid of neurological sign, silent stroke in children with SCD are associated with neurocognitive impairment, poor academic performance, and future overt strokes [17, 18]. In contrast to overt stroke, there is lack of established relationship between SCI presence and abnormal TCD measurements [19]. Although studies have shown strong associations of SCI with low hemoglobin [20], relative hypertension [20], acute anemia events [21], and abnormal MRA [21, 22], these risk factors alone or together still do not provide accurate prediction of SCI [10]. What is more confusing is that the incidence of new SCI in SCD patients does not attenuate in adulthood despite treatment with chronic transfusion and hydroxyurea [16]. Although the Silent Cerebral Infarct Multi-Center Clinical Trial (`SIT') has shown that the in- cidence of the recurrent silent stroke in children with SCD is signicantly reduced by regular blood transfusion [23], the mechanism is still unclear. In summary, compared to overt stroke, the pathogenesis, prevention and treat- ment of silent stroke are still obscure, despite its high prevalence and progressive 4 nature [24] (Figure 1.2). Finding more specic predictors of SCI and understanding the progressive nature of SCI is the central clinical motivation of this thesis. Figure 1.2: Prevalence of SCI in children and young adults with SCD. The cumula- tive prevalence of SCI increases 1-2% per age year with no plateau towards young adulthood despite appropriate TCD screening. Adapted from Kassim et al [16]. 1.1.3 Clinical need for brain oxygenation evaluation in SCD 1.1.3.1 Fick's model of CMRO 2 According to Fick's principle, cerebral metabolic rate of oxygen (CMRO 2 ) can be modeled as: CMRO 2 = (CaO 2 CvO 2 ) CBF CaO 2 CBF OEF (1.1) 5 where CaO 2 and CvO 2 are oxygen contents in arterial and venous blood (ml O 2 /ml blood), CBF is cerebral blood ow (ml/100g tissue/min), and OEF is oxygen ex- traction fraction ratio (%). CaO 2 is dened as: CaO 2 = 1:34 HbY a + 0:003 pO 2 (1.2) where Hb is hemoglobin level (g/dl),Y a is arterial oxygen saturation (%), and pO 2 is partial pressure of oxygen (mmHg). The product of CaO 2 and CBF represents total oxygen delivery to the brain in unit of ml O 2 /100g tissue/min. CBF and CMRO 2 are often normalized to brain weight to compensate for age and sex dierences in brain size and oxygen consumption. OEF is dened as: OEF = Y a Y v Y a (1.3) where Y a and Y v are oxygen saturations in the arteries and veins supplying the brain. The approximation in Eq. (1.1) is valid when the dierence of dissolved oxygen content in arterial and venous blood can be neglected. In healthy people, CMRO 2 remains on the order of 3 ml O 2 /100g tissue/min regardless of dierent brain activities [25]. Normal and stable CMRO 2 is guaranteed by the balance between oxygen supply and demand. For example, in a hypercapnia challenge where breathing higher content of CO 2 in room air induces vaso-dilation, OEF will decrease due to the increase of CBF. Under abnormal conditions, the brain will try to maintain its CMRO 2 through two stages of compensation [26]. Take the case of carotid occlusion for example. Cerebral arterioles will dilate in order to preserve CBF, which is the rst stage of compensatory response. If perfusion pressure continues to decrease and vasodilation alone fails to maintain CMRO 2 , OEF will start to increase as a second-stage compensatory mechanism. When limits of the two compensatory mechanisms are reached and yet the required CMRO 2 is still not maintained, stroke will occur. 6 Positron emission tomography (PET) is considered the gold standard for cal- culation of CMRO 2 . So far, there has only been two PET studies on SCD pa- tients [27, 28], and neither observed signicant dierence of resting CMRO 2 between SCD patients without neurological symptoms and healthy controls. However, both studies were limited by their low statistical power (N = 6) due to high radiation doses and invasive monitoring. With the application of noninvasive MRI scans, researchers are able to study SCD brain oxygenation with bigger sample size and higher spatial specicity. 1.1.3.2 Previous studies on oxygen delivery in SCD The previously described two stages of hemodynamic compensation may apply to the cases of large-vessel vasculopathy in SCD. However, in the absence of major stenosis, SCD can have additional or even altered physiological challenges. Resting baseline CBF is elevated secondary to anemia and increased HbS percentage in SCD patients [29]. Studies using MRI techniques for noninvasive CBF measurement, including phase-contrast [30], arterial spin labeling [31, 32, 33] and gadolinium- enhanced perfusion imaging [34], have conrmed elevated CBF in SCD patients who have SCI but no overt stroke. Combining CaO 2 and CBF, the oxygen delivery in SCD was found to be identical to healthy subjects [30]. It should be noted that the preserved oxygen delivery via elevated baseline CBF comes with a cost. The proportion of CBF that can increase under metabolic stress, known as the cerebrovascular reserve (CVR), becomes limited [35], leaving the brain vulnerable to acute stresses including hemoglobin desaturation (e.g. sleep apnea) [36], decreased hemoglobin (e.g. bleeding or acute hemolysis) [37], and increased cerebral metabolic rate (e.g. fever [37], seizure). 7 1.1.3.3 Previous studies on OEF in SCD OEF is the other factor in Fick's model of CMRO 2 besides oxygen delivery. Com- pared to CBF measurement, studies on the cerebral OEF in SCD patients are scarce and face many technical challenges (detailed in Chapter 1.2.4.2). Furthermore, con- icting conclusions are found among the very few OEF studies on SCD. Jordan et al. [33] used an MR T2 relaxation based method to measure the intravascular OEF of superior sagittal sinus, and they observed higher OEF in SCD patients unaected by overt stroke compared to age-matched healthy subjects. Using the same MRI technique but with a dierent T2-saturation calibration model, Bush et al. observed decreased OEF in SCD patients [38], supporting a functional arteriovenous shunting hypothesis [38, 39]. Guilliams et al. exploited a T2 0 -based method to measure the OEF at tissue level. They observed that chronic blood transfusion lowered OEF in deep white matter at higher risks of SCI [14], indicating reduced metabolic stress by blood transfusion in SCD patients. These studies all showed that, in SCD patients without overt stroke, abnor- mal OEF occurred even when normal CMRO 2 was maintained and CBF was far from the limit of compensation. Whether sequentially or simultaneously to CBF compensation, OEF changes in response to potential physiological challenges in- cluding microvasculature ow impairment and decreased arterial oxygen content in SCD patients, which suggests that resting OEF can be a logical predictor of fu- ture stroke risk. However, given the controversial ndings in previous OEF studies, independent evaluations of brain oxygenation in SCD are strongly needed. 8 1.1.4 Clinical need for brain iron evaluation in SCD 1.1.4.1 Brain iron metabolism There are two types of iron in the brain: heme iron and nonheme iron. While heme iron is responsible for oxygen transportation, nonheme iron is critical to normal pro- cesses including oxidative phosphorylation, myelin synthesis, and neurotransmitter metabolism. Iron is carried by transferrin in blood and crosses the blood-brain barrier via a transferrin-receptor process. Iron not immediately needed for brain activities is stored mainly in ferritin. There is a heterogeneous distribution of brain iron both cellularly and regionally. Oligodendrocytes have the highest amount of iron [40], while neurons, microglia and astrocytes also store iron. Spatially, deep gray matter structures have the highest iron concentration, two to three times greater than the cerebral cortex [41]. In normal ageing, iron accumulates selectively in several brain regions and cell types. Histology studies indicate that iron levels in substantia nigra, putamen, globus pallidus, caudate nucleus, and cortices follow an logarithmic growth pattern with age, in which the increase is rapid from birth until about 20 years of age and then plateaus in middle age. Although oligodendrocytes contain the largest amount of iron, they remain at constant iron concentration throughout life [40]. Iron in the microglia and astrocytes of the basal ganglia and cortex generally increase with age. Although it is still not clear, the mechanism of iron accumulation in nor- mal aging has been hypothesized to be increased blood{brain barrier permeability, in ammation, and changes in iron homeostasis [42, 43, 44]. 1.1.4.2 Brain iron overload in neurovascular diseases Excessive iron can induce oxidative stress and cellular damage through hydroxyl radical production. Abnormal brain iron deposition has been a characteristic nd- ing in a large range of neurodegenerative diseases. It is still unclear whether the 9 iron accumulation is a primary event or a secondary eect [42]. However, there is mounting evidence through iron chelation trials (listed below) that, although iron dysregulation may not represent the primary causal agent in these disorders, it appears to accelerate their course. Neurodegeneration with Brain Iron Accumulation (NBIA). NBIA is a group of neurodegenerative diseases, in which abnormal accumulation of iron in the brain causes progressive movement disorder and neuropsychiatric conditions. A pilot trial treating NBIA patients with deferiprone [45] observed that mitigation of the pallidal iron accumulation eectively improved motor symptoms and slowed down disease progression. Friedreich Ataxia (FA). FA is a genetic disorder characterized by progres- sive motor disorders including impaired muscle coordination and slurred speech. Abnormal iron accumulation in dentate nuclei has been suggested by MRI on pa- tients with FA. Pilot trial [46] showed that iron chelation treatment improved ma- nipulative dexterity, uency of speech and some subjective signs of neuropathy. Parkinson's Disease (PD). PD is the most common motor disorder. High iron deposition in the substantia nigra is one of the hallmarks of the disease. Several studies have found that iron concentrations in the substantia nigra increased with disease severity. Decrease of substantia nigra iron deposits by deferiprone treatment correlated with Unied Parkinson's Disease Rating Scale motor indicators of disease progression [47]. Alzheimer's Disease (AD). AD is the most frequent cause of dementia. Recent data demonstrated that the risk for developing AD-dementia was closely linked to cerebral iron in cortical and subcortical regions [48]. 10 1.1.4.3 Linkage between SCD-associated cerebrovascular conditions and brain iron abnormality Systematic iron overload as a side eect of chronic blood transfusion receives the most research attention in SCD, whereas brain iron has never been investigated in SCD patients. Brain iron is tightly regulated and does not necessarily relate to body iron. But there are other physiological factors in SCD, such as chronic hypoxia and cerebrovascular diseases, which can induce abnormal brain iron deposition. Hypoxia has been recognized to stimulate brain iron uptake. In animal models of hypoxia, disruption of iron homeostasis was observed due to increased synthesis of ferritin in oligodendrocytes [49, 50] and upregulation of transferrin receptors in brain capillary endothelial cells [51, 52]. In human subject studies, increased iron deposition was observed in basal ganglia after hypoxia exposure at high altitude [53] and in white matter of premature newborns with periventricular white matter damage [54]. Besides hypoxia, hemolysis, ischemic-reperfusion injuries and in ammation are common chronic processes in the brain of SCD patients, and these factors have also been indicated to cause imbalance of brain iron in other disease models [51, 55]. Hemosiderin from degraded red blood cells can contribute to elevated iron level in the brain [55]. In ammatory reactions involve reactive microglia, a cell type with abundant amount of iron. Accumulation of microglia has been suggested to increase the iron level in neurodegenerative diseases [51]. SCD patients have been reported to have progressive neurocognitive impair- ment. It is well accepted that overt stroke has measurable impact on neuropsy- chological functions. However, SCD patients without history of overt stroke are also found to have neurocognitive decits. Despite normal brain imaging, chil- dren with SCD have been observed with declining IQ scores (about 5-point drop in full-scale IQ [56]), learning diculties, and impairment of executive function [10]. Adult patients also showed poorer performance on neurocognitive tests when 11 compared with controls [57]. SCI has been suggested as a factor in neurocognitive dysfunction. Researchers found that 80% of the children with SCD and SCI have clinically signicant impairments in at least one neurocognitive domain, compared to 30% of the children with SCD and normal appearing white matter [58]. Despite the strongly suggested association, SCI presence does not fully explain the neu- rocognitive performance dierences observed between SCD patients and controls [57]. Furthermore, the decits of neurocognitive functions seems to progress with age in SCD patients. The Cooperative Study of Sickle Cell Disease (CSSCD) [56] found that the scores of verbal IQ, math achievement, and coding (a subscale of Performance IQ) decreased with increasing age in children with SCD and normal MRI, and the rate of change did not signicantly dier between patients with and without SCI. In summary, prior literature supports the motivation to investigate brain iron deposition in SCD patients: a) SCD patients are known to have cerebrovascular conditions that may increase brain iron deposition; b) SCD patients have progres- sive cognitive dysfunction, which could be reinforced by brain iron overload, as suggested by other research on neurodegenerative diseases. 1.2 Susceptibility-weighted MRI 1.2.1 Tissue magnetism When a material is placed in an external magnetic eld, there will be magnetiza- tion induced in the material that is associated with the orbital motion and spins of electrons. Molecules with unpaired electrons will have non-vanishing electron spin moments and produce a bulk magnetic moment parallel to the applied eld. This eect is referred to as `paramagnetism'. Paramagnetism is absent in molecules that have net cancellation of spin moments due to paired electrons. In this case, 12 the omnipresent electron orbital moments are no longer dominated by spin mo- ments, leading to the formation of a bulk magnetic moment anti-parallel to the applied eld. This eect is called `diamagnetism'. In the presence of an external eld, diamagnetism exists in all magnetic materials, while paramagnetism, when present, dominates diamagnetism. The totality of these responses is described by the susceptibility of the material. Susceptibility, , is a dimensionless parameter that quanties the degree of magnetization a material obtains in response to an external magnetic eld. Sus- ceptibility is dened as: M =H = 0 (1 +) B 0 0 B 0 (1.4) whereM is the induced magnetic moment,H is the auxiliary magnetic eld dened asH B 0 0 M, and 0 is the permeability of free space with a value of 4 10 7 . Materials with negative susceptibility are called `diamagnetic', while those with positive susceptibility are referred to as `paramagnetic'. The majority of biological tissues are weakly magnetic and havejj 1, which warrants the approximation in Eq. (1.4). Parts-per-million (ppm) and parts-per-billion (ppb) in SI unit system will be used to describe susceptibility throughout this thesis. Biological tissues typically have susceptibility values close to that of water, which is approximately -9.05 ppm. For this reason, we will follow the convention to describe tissue susceptibility relative to that of water unless stated otherwise. There is a large variation of tissue susceptibility in the human body. Hemoglobin, the protein for oxygen delivery, and ferritin, the protein for non-heme iron storage, are two main contributors to paramagnetic tissue susceptibility (if any). Hemoglobin. The hemoglobin protein consists of four globin molecules, each containing an iron ion, Fe 2+ . When combined with oxygen, the resultant oxy- hemoglobin molecule has all electrons paired up in Fe 2+ and therefore is slightly diamagnetic. With the release of oxygen, Fe 2+ in the deoxyhemoglobin molecule 13 reaches a state with four unpaired electrons, making deoxyhemoglobin paramag- netic. Given the intrinsic susceptibility of deoxyhemoglobin, oxyhemoglobin and water molecules and the volume fraction of each composition, Spees et al. [59] calculated the theoretical susceptibility value of a red blood cell. They experi- mentally veried the susceptibility dierence between fully deoxygenated and fully oxygenated red blood cells to be do = 4 0:27 ppm. Susceptibility of venous blood can thus be modeled as: blood = do (1SvO 2 ) Hct + ow Hct (1.5) where ow =40:03 ppm is the susceptibility shift of oxygenated hemoglobin [60], S v O 2 is the oxygen saturation and Hct is the volume fraction of red blood cells in blood. Assuming a Hct of 0.42 and S v O 2 of 0.6 in venous blood, then the blood should have a susceptibility of around 0.4 ppm. Ferritin. The structure of ferritin has a protein shell formed by peptide units, which houses up to 4500 Fe 3+ . The iron ion, Fe 3+ , have 5 unpaired electrons making ferritin paramagnetic. The susceptibility of ferritin at body temperature (310K) is 520 ppm [61]. The susceptibility of iron-containing tissues can thus be calculated by: (1:3 10 6 )c (1.6) where c is the iron concentration in unit of mg of iron per gram of wet tissue and is tissue density in g=cm 3 . If iron concentration in the caudate nucleus is 0.105 mg/g [62] and the density of brain tissue is 1.04 g/cm 3 in a healthy brain, then the nucleus should have a susceptibility of around 0.142 ppm. 1.2.2 Magnetic eld generated by tissue magnetization When placed in an initially uniform magnetic eld, B 0 , an object becomes magne- tized and generates its own magnetic eld that distorts the original external eld. 14 The induced magnetic eld depends on the geometry and orientation of the ob- ject. Calculating the induced eld is essentially solving partial dierential equations with boundary values, which usually requires numerical methods [63]. Fortunately, magnetic elds induced by ellipsoidal susceptibility sources can be described ana- lytically. The induced magnetic eld due to the presence of a sphere source (after Lorentz sphere correction) is (Figure 1.3): b(r) = 8 > < > : 0 ifjrj<a 3 a 3 r 3 (3 cos 2 1)B 0 ifjrja (1.7) where is the polar angle in spherical coordinates, anda is the radius of the sphere. B 0 Ѳ r x y z x z -0.25 0.25 Figure 1.3: Field induced by a magnetized sphere. Left: spherical coordinate system for describing the eld at a point (r, ) relative to the sphere. The main B 0 eld is parallel to the z direction. Right: magnetic eld in the x-z plane. Amplitude of the eld is shown as a ratio to B 0 . 15 For an innitely long cylinder at an angle to the applied magnetic eld (Figure 1.4), the induced magnetic eld is: b(r) = 8 > < > : 6 (3 cos 2 1)B 0 if inside the cylinder 2 a 2 r 2 sin 2 cos 2B 0 if outside the cylinder (1.8) where cylindrical coordinates (r, , ) are used to describe the position relative to the magnetized cylinder (Figure 1.4 left). For an arbitrary distribution of magneti- Ѳ = 0 o Ѳ = 30 o Ѳ = 60 o Ѳ = 90 o B 0 Φ Ѳ r x y z x z x y -0.25 0.25 Figure 1.4: Field induced by a magnetized cylinder. Left: cylindrical coordinate system for describing the eld at a point (r,,). The cylinder is at an angle to the main B 0 eld. Right: induced magnetic elds when the cylinder has dierent orientations with respect to the main B 0 eld. Amplitude of the eld is shown as a ratio to B 0 . zation, there is a general framework to numerically determine the induced magnetic eld. The magnetic eld observed at positionr can be considered as a summation of the dipole elds generated by each element in the magnetization distribution, M(r 0 ): b(r) = 0 4 Z 3(e r 0e rr 0)e rr 0e r 0) jrr 0 j 3 M(r 0 )d 3 r 0 (1.9) Assuming that the main B 0 eld is in the z-direction, of paramount interest in MRI is the z-direction component of b(r), because that is what aects the precession 16 frequency of nuclear spins (detailed in the next section). Using the derivation from Eq. (1.4), M(r 0 ) = (r 0 )B 0 0 , the induced magnetic eld can be written as a convolution of a kernel function, d(r), with the susceptibility distribution, (r): b z (r) = b(r)^ z = 0 4 Z 3 cos 2 1 jrr 0 j 3 M(r 0 )d 3 r 0 =d(r)(r)B 0 (1.10) where the kernel function (often called "dipole kernel")is d(r) = 1 4 3 cos 2 1 r 3 (1.11) The complex and non-local relation between b z (r) and(r) in Eq. (1.10) can be reformulated to a simple and local relation in the Fourier domain [64, 65]: B z (k) =D(k)X(k) (1.12) And D(k) = 1 3 k 2 z k 2 x +k 2 y +k 2 z (1.13) where k x , k y , and k z are coordinates in the Fourier domain (k-space). It should be noted that D(k) has zeros along the angle at 54:7 (Figure 1.5). For notational convenience, we will continue using lower case forr-space variables and upper case fork-space variables (except for the main eld B 0 ) in the rest of this thesis. 1.2.3 Susceptibility eects on MRI signal In the presence of an external eld, magnetic moments from nuclear spins form a non-zero equilibrium magnetization that's parallel to the external magnetic eld. This process called polarization is the basis of MRI signal. It should be claried that nuclear magnetization is much weaker than the electron magnetization discussed 17 B 0 kx kz 0 1 |D(k)| Figure 1.5: Absolute magnitude of the dipole kernel in Fourier space. Although only the k x -k z plane is shown here, it should be noted that the kernel is radially symmetric in the k x -k y plane. in Chapter 1.2.1. After the application of an RF pulse, the net nuclear magneti- zation, M, will rotate about the main magnetic eld at the Larmor frequency, a process called precession. Since M observes not only the external magnetic eld but also any internal eld caused by susceptibility variation, the Larmor frequency is proportional to the summation of the two: w = (B 0 + B 0 ) (1.14) where is the gyromagnetic ratio. At the same time with precession,M also tends to go back to its equilibrium state with the logitudial component increasing at a time constant of T1 and the transverse component decaying at a rate of T2. This process is called relaxation. The magnetization in the transverse plane is picked up by the coils and forms the MRI signal. To enable the encoding of spatial information, additional external elds, called gradient elds,G, are applied. The gradient elds vary linearly along each spatial axis. The idea is to encode the information of spatial position into 18 Figure 1.6: Processes in MRI signal formation. Left: equilibrium magnetization due to polarization. Middle: transverse magnetization after RF exciation. Right: signal dephasing due to magnetic eld variation, B 0 . the frequency and phase of the magnetization. With eld inhomogeneity B 0 , the demodulated MRI signal from a 3D gradient echo sequence (Figure 1.7)is: S(t) = Z (r)e t T 2 e j B 0 t e j2(kxx+kyy+kzz) dxdydz (1.15) where (r) is the apparent proton density, k x = 2 R G x ()d, k y = 2 R G y ()d, and k z = 2 R G z ()d. One important observation of Eq. 1.15 is that MRI signal is actually the Fourier transform of the imaged object. Therefore, a simple inverse Fourier transform of the signal should reconstruct the image. The eects of susceptibility-induced eld inhomogeneity on MRI signals can be considered at three levels: microscopic, mesoscopic and macroscopic. At the mi- croscopic scale, eld variation over distances comparable to atomic and molecular lengths will lead to irreversible signal dephasing (Figure 1.6), which can be charac- terized by the T2 decay. The mesoscopic scale refers to distances smaller than the imaging voxel but much larger than the molecular scales. For example, the capil- lary network in brain parenchyma or the ferritin clusters in basal ganglia nuclei can produce mesoscopic eld variation and also cause intra-voxel dephasing. This type of signal decay is usually partially reversible by the refocusing RF pulses in spin echo sequences and is characterized with T2* decay in gradient echo sequences. At 19 Figure 1.7: 3D multi-echo gradient echo (GRE) sequence. This example sequence acquires three gradient echoes. The echo time (TE) is calculated as the time interval between the center of the exitation RF pulse and the formation of a gradient echo. Readout gradient is applied in thex direction, and the two phase encoding gradients are applied in the y andz directions. For every repitition time (TR), the sequence is repeated with changing phase encoding gradients. macroscopic level, eld variation over distances larger than the imaging voxels is re ected on both the magnitude and phase signals. For the magnitude part: jM xy j =M 0 e TE T2 (1.16) where TE is the echo time, and 1/T2* = 1/T2 + 1/T2 0 . T2 0 describes the reversible part of the signal decay that originates solely from mesoscopic and macroscopic eld variation. For the phase part: = B 0 TE (1.17) Eq. (1.16) and Eq. (1.17) indicate that it is plausible to quantify the susceptibility eects using MRI. It can be seen that T2* and B 0 can be probed with multi-echo acquisition. 20 1.2.4 MRI-based tissue susceptibility quantication 1.2.4.1 Quantitative susceptibility mapping (QSM) QSM derives a pixel-wise distribution of susceptibility from its induced magnetic eld based on the 3D dipole convolution model (Eq. (1.10)) [66, 67, 68, 69, 70, 71, 72, 73, 74, 75]. Through a 3D B 0 eld mapping sequence and multiple image processing steps, QSM allows susceptibility to be quantied for tissues with arbi- trary geometry and orientation. 3D GRE with high spatial resolution and multi echo acquisition is commonly used for B 0 eld mapping. B 0 can be obtained by tting the multi-echo phase in a linear (Eq. (1.17)) or nonlinear manner [76]. Phase unwrapping is typically needed and can be performed eciently with FSL PRELUDE [77], Laplacian based algorithm [78] or region growing algorithm [79]. The complexity of QSM processing originates from two fundamental challenges: 1) background eld removal and 2) eld-to-susceptibility inversion. 1) Background eld removal. The total eld variation, b t , can be considered as a summation of a) the \background eld" caused by the global geometry, air-tissue interfaces, and system imperfection and b) the \local eld" caused solely by tissue susceptibility variation. In QSM, only the local eld, b loc , is of interest. To remove the background eld, three commonly used methods are projection onto dipole elds (PDF) [71], so- phisticated harmonic artifact removal for phase data (SHARP) [80]/regularization enabled SHARP (RESHARP) [81] and Laplacian boundary value (LBV) [82]. b t =d ( b + l ) =d b +d l = b b + b l (1.18) where the subscript "b" denotes the background eld or the susceptibility distribu- tion giving rise to the background eld, and the subscript "l" denotes what is related 21 to the local eld. Background eld removal methods including PDF, RESHARP and LBV are demonstrated in Figure 1.8. PDF LBV RESHARP Sagittal Axial -10 10 Hz Figure 1.8: Comparison of background eld removal methods including PDF, RE- SHARP, and LBV. The local eld is obtained by subtracting the estimated back- ground eld from the total eld. It is plotted in the sagittal (top) and axial (bottom) views. PDF. The magnetic elds induced by dipoles located outside the brain is approximately orthogonal to the elds induced by dipoles inside [71]. Based on this assumption, PDF calculates the background eld as a projection of the total eld to a subspace that is spanned by dipole elds originating from outside sources. ^ b = arg min b kW (b t F 1 DF ( b ))k 2 (1.19) where W is an signal to noise ratio (SNR) based weighting matrix and ^ b is the estimation of background susceptibility distribution. Subsequently, the local eld can be estimated as (b t F 1 DF (^ b )). It should be noted that the orthogonality assumption in PDF no longer holds near the boundary of brain tissue. Therefore, 22 PDF fails to accurately split the background eld and local eld at the brain tissue boundary. SHARP and RESHARP. According to the Maxwell's equations, the eld observed far from its dipole source is harmonic and hence satisfying the mean value property: b b = b b s (1.20) where s is a normalized spherical kernel. Then b t b t s = b b + b l b b s b l s = b l b l s (1.21) Eq. (1.21) can be reformulated as a Fourier domain multiplication: MF 1 CF b l =MF 1 CF b t (1.22) where M is a binary mask dening the region of brain tissue, and C = F (s). SHARP and RESHARP both essentially solve b l from b t using Eq. (1.22), while RESHARP incorporated a Tikhonov regularization that helps condition the inversion. As a nal step, an eroded brain mask is applied to remove the unreliable results close to the edges of the brain. Necessary degree of erosion depends on the size of the spherical kernel, s. LBV. Similar to SHARP, LBV also exploits the fact that the background eld is a harmonic function, i.e. the solution to Laplace's equation: r 2 b b = 0 (1.23) , wherer 2 =@ 2 x +@ 2 y +@ 2 z is the 3D Laplacian operator. Eq. (1.23) indicates that the background eld can be determined by solving this elliptic partial dierential equation with boundary conditions. Boundary values of the background eld are not be available in realistic brain imaging. However, since the local eld is usually 23 much smaller than the background eld, it can be assumed that the background eld equals to the measured total eld at the ROI boundary. With such assumption on boundary conditions, a unique solution to Eq. (1.23) can be obtained using numerical solvers such as the nite dierence methods [82]. 2) Field-to-susceptibility inversion. After the step of background eld removal, the local eld b l can be used to derive the susceptibility map. From Eq. (1.10) it can be seen that the inversion from B 0 to susceptibility is ill-posed due to the zero values of D(k) along the magic angle. Direct inversion will cause severe streak artifact. To solve this ill-posed inverse problem, multi-orientation acquisition and various regularization algorithms for single-orientation acquisition were proposed. Calculation of susceptibility through multiple orientation sampling (COSMOS) [68, 70]. The singularities of the dipole kernel in Eq. (1.13) can be eliminated by acquiring multiple B 0 eld maps with at least three dierent head orientations. At each orientation, D(k) is rotated a dierent angle relative to the main B 0 eld. Then the combined dipole matrix will have no zeros except at the origin. Although it almost completely suppresses the streak artifact, COSMOS is clinically impractical because of the prolonged scan time and the limited space for head rotation in the head coil. 2 6 6 6 4 D 1 (k) ::: D n (k) 3 7 7 7 5 X(k) = 2 6 6 6 4 B 1 (k) ::: B n (k) 3 7 7 7 5 (1.24) where 1 , ..., n are the angles w.r.t. the main B 0 eld. 24 Truncated k-space division (TKD) [66, 69]. For single-orientation acqui- sition, the simplest way to deal with the ill-posed inversion is thresholding on the function, 1 D(k) , a technique called truncated k-space division (TKD). X(k) = 1 ^ D(k) B(k); where ^ D(k) = 8 > < > : a jD(k)j<a D(k) jD(k)ja (1.25) where a is the threshold usually in the range of 0.0010.01. Although TKD is computationally ecient, it is very challenging to choose the optimal threshold. The larger the threshold, the less streak artifact in the reconstruction susceptibility map but more underestimation of susceptibility values [83]. L1-QSM [73] and morphology-enabled dipole inversion (MEDI) [67]. Priori knowledge of the susceptibility map can be utilized to better condition the inverse problem. For example, sparsity of the susceptibility distribution in the spatial total variation domain can be used to regularize the inverse problem, a technique referred to as L1-QSM. ^ (r) = arg min kW (b(r)F 1 DF ((r))k 2 +kr(r)k 2 (1.26) wherer(r) is the total variation of (r) and is the regularization weighting. The inverse problem can also be regularized by exploiting the edge information extracted from the magnitude image. This technique is referred to as MEDI. ^ (r) = arg min kW (b(r)F 1 DF ((r))k 2 +kMr(r)k 2 (1.27) whereM is a binary matrix that denes the appearance of edges in the magnitude image. Susceptibility maps obtained using dierent eld-to-susceptibility inversion methods including TKD, L1-QSM and MEDI are compared in Figure 1.9. 25 TKD L1-QSM MEDI Sagittal Axial -0.25 0.25 ppm Figure 1.9: Comparison of eld-to-susceptibility inversion methods including TKD, L1-QSM and MEDI. The estimated susceptibility maps are plotted in the sagittal (top) and axial (bottom) views. 1.2.4.2 MRI-based oxygenation imaging There are mainly four MRI techniques for oxygenation imaging: T2-based in- travascular oxygenation imaging, T2 0 (and T2*)-based tissue oxygenation imaging, susceptometry-based oximetry and quantitative susceptibility mapping. This sec- tion will review the current status of these existing techniques, their limitations and potential improvement. T2-Relaxation-Under-Spin-Tagging (TRUST). Theoretical models [84, 85] and empirical calibration models [86, 87, 88, 89, 90, 91, 92] have been proposed to relate the T2 relaxation of blood to the intravascular oxygenation level. TRUST is the most widely reported technique in the category of T2-based intravascular oxygenation imaging [91, 93]. Specically, venous blood signal is isolated using a spin labeling technique to avoid signal contamination from surrounding tissue and CSF. T2-weighting is achieved by a series of non-selective T2 preparation pulses 26 prior to image acquisition [90]. Then the T2 relaxation of blood can be calculated and converted to oxygen saturation using an in-vitro calibration model. TRUST has presented high reproducibility (intersession variation of 3.1% [94]) and equivalent results across multiple sites [95]. TRUST has been applied to in- vestigate experimentally manipulated physiological states [96, 97] and pathologic conditions, including vascular aging, drug addiction, multiple sclerosis [98], and sickle cell disease [33]. However, the biggest limitation of TRUST is potential changes in the T2-saturation calibration with physiological or hematological de- rangements. T2 not only depends on the concentration of deoxyhemoglobin in blood but also the cellularity and permeability of red blood cells [86]. Without accounting for disease-specic changes in calibration models, one can achieve con- tradictory conclusion in the comparison of brain oxygenation in SCD patients and healthy controls. Figure 1.10 highlights the problem. It demonstrates predicted sagittal sinus oxygen saturation as a function of oxygen content, using three dif- ferent T2-saturation models. The most commonly used calibration, derived from bovine blood [91, 93], demonstrates lower venous oxygen saturation in SCD than control subjects (left panel). If one uses a calibration model derived from healthy human blood (HbA T2b model [38]), venous oxygen saturation is similar in patients and controls (middle panel). However, if one uses the T2b calibration derived from sickle-cell blood (HbS T2b model [92]), SCD patients appear to have higher venous oxygen saturation than controls (right panel). To solve this problem, it is critical to develop an MRI oximetry method that is robust to changes in red blood cell shape and permeability. Quantitative blood-oxygen-level-dependence (qBOLD). Besides T2, T2 0 (and T2*) of brain tissue have also been modeled to quantify brain oxygenation. Assuming the static dephasing regime [99], MR signal acquired with an asymmetric spin echo sequence at certain imaging conditions demonstrates a single exponential decay, in which the decay rate, T2 0 , attributes to oxygenation at the tissue level 27 Figure 1.10: Comparison of three calibration models in the TRUST measurement of venous oxygen saturation. Venous oxygen saturation measurements in SCD pa- tients (red diamonds) and healthy controls (gray dots) are plotted against oxygen content. Left: using the bovine blood model, there is a signicant positive correla- tion between venous oxygen saturation and oxygen content. SCD patients demon- strate signicantly lower venous oxygen saturation than healthy controls. Middle: using the healthy human blood model, venous saturation measurements in the two populations are not signicantly dierent. Right: using the sickle cell blood model, there is a signicant negative correlation between venous oxygen saturations and oxygen content. SCD patients have signicantly higher venous oxygen saturation than healthy controls. Adapted from Bush et al. [92]. [100]. T2 0 -based quantication considered the brain having only one single com- ponent. In comparison, He et al. [101] proposed a more complete model called \qBOLD", which incorporated prior knowledge of brain tissue composition and in- cluded signal contributions from tissue, extracellular space and intravascular blood. Signal decay in the gradient-echo sampling of spin-echo (GESSE) acquisition was tted using the qBOLD model, and the resultant tting parameters were converted to oxygen extraction fraction. Although T2 0 and T2* based methods have been applied to examine tissue oxygenation changes in healthy subjects [100], stroke [102] and tumor hypoxia [103, 104], oxygenation-dependent T2 0 and T2* changes are often confounded by other factors. For example, the presence of high water content corresponding to high T2 will increase the measured T2*, which is independent of blood oxygenation. Furthermore, T2 0 and T2* are also in uenced by magnetic eld inhomogeneities that are caused by air-tissue interfaces, metal implants, and system imperfections. 28 Both TRUST and qBOLD share the limitations including complexity of signal model and dependence of measurement accuracy on imaging parameters. These limitations originate from the fact that relaxation parameters are indirect indica- tors of blood susceptibility. In comparison, there is another group of oxygenation imaging techniques that directly measure the susceptibility of blood and calculate the oxygen saturation using a simple linear model in Eq. (1.5). Susceptometry-based oximetry (SBO). SBO [105, 106] models the vessel as an innitely long cylinder with uniform susceptibility. By measuring the mag- netic eld shift of blood relative to the surrounding tissue, blood susceptibility can be calculated using Eq. (1.8) and then converted to oxygen saturation, S v O 2 , using Eq. (1.5). The straight cylinder assumption might be violated when the vein has curvature, branching, and non-circular cross-section. Numerical simulations based on realistic 3D models of superior sagittal sinus showed that the error was within 5% for vessel tilt angles<30 [107, 108]. Phantom experiments by Langham et al. [108] revealed a<2% error resulting from non-circular vessel cross section. These data supported the validity of the long cylinder model. In the conventional 2D implementation, SBO has short scan time (20 sec) and thus enables quantication of S v O 2 at high temporal resolution [106]. Interleaved with phase-contrast CBF measurement, SBO has been applied to fast measurement of global CMRO 2 at baseline [106] and during hypercapnia challenge and volitional apnea [109, 110, 111]. The arguably biggest challenge in SBO is to remove the large-scale eld that's induced by air-tissue interface (often called \background eld"). Because the back- ground eld generally has low spatial frequency, high-pass ltering has been pro- posed to remove the background eld, but the measurement demonstrated sensi- tivity to the lter size [112]. An alternative is to t the background eld inhomo- geneity to a second-order polynomial, which has been shown to produce reasonable measurement of S v O 2 in the femoral vein [112]. In contrast to the femoral vein, 29 the background eld has more complex pattern near the superior sagittal sinus lo- cated at the tissue boundary. So far, only 2D SBO has been performed, in which the dependence of accurate background eld removal on slice location has seldom been validated. Another limitation of SBO is that it is only applicable to the su- perior sagittal sinus and some small pial vessels whose tilt angles are within 30 [105, 106, 109, 110, 111, 113]. Quantitative susceptibility mapping (QSM). As described in Chapter 1.2.4.1, QSM derives a pixel-wise susceptibility map and theoretically enables oxy- gen saturation measurement without assumptions on vessel geometry or orienta- tion. Haacke et al. [83] used TKD-based QSM to measure the oxygen saturation in large veins (e.g. vein of Galen) and obtained baseline S v O 2 in the range of 66.1% to 79.4%. Using L1-QSM, Fan et al. generated 3D venography that aligned with oxygen saturation measurements [114]. Using the same QSM approach, regional ve- nous oxygen saturation in pial veins presented expected increase under hypercapnia challenge [115]. Although these data suggested the potential of QSM in measuring either global or regional venous oxygen saturation, large variation in saturation values were ob- served (from 47% [114] to 73% [116]). There are three main sources of variance in QSM-based oxygenation imaging: 1) Partial voluming can cause underestimation of intravenous susceptibility and thus overestimation of S v O 2 [83], which limits the application of QSM in small veins (e.g. pial veins); 2) Existing background eld removal methods produce inaccurate measurement at the brain tissue boundary due to the violation of their assumptions, which is the reason why S v O 2 measure- ment at the superior sagittal sinus is usually avoided in QSM applications; 3) The variation can also result from usage of dierent background eld removal and eld- to-susceptibility inversion methods. Currently, there is hardly consensus on the venous oxygen saturation measured by dierent methods (Table 1.1). Although almost all the measurements are in a 30 Table 1.1: Summary of literature reported OEF measurement using PET- and MRI-based techniques. Technique Location OEF mean Intersubject variance Reference PET tissue 35 7 Carpenter et al., 1991 42.6 5.1 Yamauchi et al., 1999 41 6 Diringer et al., 2000 T2 superior sagittal sinus 35.2 6.3 Lu and Ge, 2012 39.5 5.8 Liu et al., 2013 T2' tissue 46.5 An et al., 2003 qBOLD tissue 38.8 5.3 He et al., 2007 SBO superior sagittal sinus 36 4 Jain et al., 2010 QSM large veins 32.6 to 52.3 Fan et al., 2014 pial veins 27.8 4 Xu et al., 2014 reasonable range, none of them are validated in vivo against the gold standards, i.e. PET or direct jugular sampling via catheterization. In order for MRI-based oxygenation measurement to be used in clinical settings, systematic validation is needed. 31 Chapter 2 Comparison of T2- and susceptibility-based venous oxygen saturation measurements under hypoxia and hypercapnia 2.1 Introduction Cerebral oxygen extraction fraction (OEF), dened as the relative dierence be- tween arterial and venous oxygen saturations (S a O 2 and S v O 2 ), is an important parameter for the assessment of brain oxygen consumption and tissue viability. Accurate OEF measurement is required to model the pathophysiology and opti- mize the treatment of neurological disorders with altered cerebral hemodynamics, including stroke [117], chronic anemia [33, 92] and neurodegenerative disorders like multiple sclerosis [98]. While measurement of S a O 2 can be easily performed with pulse oximetry, standard measurement of cerebral S v O 2 is challenging due to risks associated with the invasive procedures. The clinical gold standard for global cere- bral S v O 2 measurement is using co-oximeter to measure the oxygen saturation of in- ternal jugular or superior vena cava blood sampled through central venous catheters [118]. Although commonly used in the intensive care unit, the catheterization pro- cedure is highly invasive, making it unsuitable for broad research use. Positron Emission Tomography (PET) with 15 O radiotracer is also considered gold standard 32 for OEF measurement [119], but its applicability is limited by radiation exposure, requirements of high-expense facility and invasive arterial access procedure. There- fore, there is an unmet clinical need for noninvasive and reliable measurement of cerebral OEF. MRI is a promising imaging surrogate for OEF assessment because it is noninva- sive and easy to acquire [91, 93, 105, 106, 108, 121, 111, 120, 113, 122]. There exist two types of MRI techniques for global cerebral S v O 2 measurement: MR relaxome- try and MR susceptometry. In the rst category, T2-relaxation-under-spin-tagging (TRUST) [91, 93] is the most widely applied technique. TRUST measures the T2 relaxation of venous blood and converts blood T2 to S v O 2 based on an in- vitro calibration model. Specically, the TRUST sequence applied spin-tagging to separate the signal of pure venous blood from background tissue, followed by a T2-preparation module to modulate the blood signal with T2 weightings. Mono- exponential tting of the decay of isolated venous blood signal produces the T2 relaxation of blood. The other type of MRI S v O 2 measurement is based on the magnetic susceptibility of venous blood. Susceptometry-based oximetry (SBO) [105, 106, 108, 113, 122] is the representative of this category. There is a simple linear relation between the concentration of deoxyhemoglobin and the magnetic susceptibility shift of blood, which is derived from physics with parameter con- stants readily known [59, 60]. Therefore, no external calibration experiments are needed. SBO measures the susceptibility of venous blood by modeling the vein as an innitely long cylinder [61]. For a large and straight vein that is almost parallel to the main B 0 eld, the B 0 eld shift inside the vein relative to surrounding tissue is uniform and linearly depends on the susceptibility of blood. Despite the increasing application of TRUST [33, 92, 96, 98, 123] and SBO [106, 122], in-vivo validation of these two techniques for global cerebral S v O 2 mea- surement is still lacking. Existing validations of TRUST and SBO are all based on cross-correlation with other physiological measurement [96, 106, 122, 123] rather 33 than against the clinical gold standards. In addition, the mutual agreement of TRUST and SBO in the same cohort and experimental setting has seldomly been examined. Barhoum et al [111] compared TRUST and SBO at resting condition and reported a slightly lower values provided by TRUST. Rodgers et al [110] performed interleaved TRUST and SBO acquisition in one sequence and observed higher S v O 2 response to hypercapnia indicated by TRUST than SBO. To our knowledge, there has been no comparison of these two methods under low saturation levels such as hypoxia. In order for these methods to be used clinically, their reliability needs to be tested more rigorously using an in-vivo gold standard, and their mutual agreement needs to be tested under a broader range of oxygenation levels. The purpose of this study was to investigate the reliability and mutual agree- ment of TRUST and SBO for the quantication of global S v O 2 at three dierent oxygenation levels. We performed TRUST and SBO measurements at the superior sagittal sinus (SSS) in young, healthy subjects during hypoxia, room air and hy- percapnia. On two of the subjects, validation of S v O 2 measurements with internal jugular vein catheterization was performed. Repeatability of TRUST and SBO at resting condition was also evaluated. 2.2 Methods 2.2.1 Study Design The study was approved by local Institutional Review Board (CCI-12-00338). Thir- teen healthy subjects (7 males, 24{35 years) were studied. All subjects gave written informed consent before participation. Blood hematocrit (Hct) was measured in each subject on the same day of their MRI scans. MRI was performed on a Philips 3T Achieva scanner with a 32-channel head receive coil. Subjects were placed on a 2-liter reservoir rebreathing circuit and imaged under three dierent oxygenation conditions: 1) hypoxia (12% O 2 and 88% N 2 ), 2) hypercapnia (5% CO 2 and room 34 air), 3) room air. Oxygenation state was veried by near-infrared spectroscopy (NIRS) measurement with the probe placed on the skin of the right forehead. Eleven subjects were scanned without catheterization. The experiment con- sisted of two parts (Figure 1): a) S v O 2 measurements using TRUST and SBO under three dierent oxygenation conditions, and b) inter-session repeatability evaluation of the two techniques at resting baseline. Pauses of 2 to 3 min were allotted af- ter gas switching. When the subject reached steady oxygenation state (indicated by NIRS), TRUST and SBO were performed. In addition, phase-contrast CBF measurement was performed under room air and hypercapnia. Order of the MRI acquisitions under the same oxygenation state was counterbalanced to avoid bias. After the rst room-air scan session, two more scan sessions were performed, in which the subject was repositioned and new localization and pre-scans were per- formed. In this way, there were three room-air scan sessions in total, which were used for the analysis of inter-session variance. Two subjects were scanned after internal jugular vein catheterization with a three French tracker catheter. Subjects were put under dierent brain oxygenation conditions in the following chronological order: room air, hypoxia, hypercapnia, room air, hypoxia, and hypercapnia. TRUST was continuously performed during transient physiological states, while SBO was performed only when the subject reached steady state of each oxygenation condition (indicated by NIRS). During the entire imaging session, 10 ml of blood was drawn from the catheter every 3 min by a cardiologist standing beside the patient table. The nal milliliter was used for blood oxygen sampling and the rest of the blood returned to the patient or discarded. The blood sample was delivered out of the scanner room through the waveguide. Oxygen saturation of the blood sample was measured using a portable co-oximeter (Avoximeter 4000, Accriva Diagnostics, CA). The co-oximeter measure- ment was used as ground truth, against which the TRUST and SBO measurement were evaluated. 35 Figure 2.1: Protocol of scan without catheterization. Three scan sessions in the order of hypoxia (orange block), hypercapnia (yellow block) and room air (green block) were rst performed. Pauses of 2 to 3 min were allotted (grey blocks), depending on the time needed for the subject to reach steady oxygenation state. Subsequently, two more scan sessions were conducted at room air, in which the subject was repositioned and new pre-scans were played. Order of MRI acquisitions under the same oxygenation state was counterbalanced to avoid bias. TRUST: T2 relaxation under spin tagging; SBO: susceptometry-based oximetry; PC: phase contrast. 2.2.2 S v O 2 measurement using TRUST The TRUST sequence used in this study was analogous to that described by Lu et al [93]. Scan parameters are: Four eective echo times (eTE) at 0, 40, 80, and 160 ms; CPMG= 10 m; voxel size = 3.44 3.44 mm 2 ; FOV = 220 220 mm 2 ; matrix size = 64 64 with SENSE rate of 3; slice thickness = 5 mm; labeling thickness = 100 mm; gap between imaging slice and labeling slab = 75 mm; inversion time (TI) = 1022 ms; repetition time (TR) = 3000 ms; EPI echo time = 3.77 ms. We acquired three pairs of control and label images at each eective TE. Total scan time was 1.2 minutes. Magnitude dierence between the control and labeled images was obtained at each eTE (Figure 2.2A). A region of interest (ROI) of four voxels with the largest dierence signal at the location of superior sagittal sinus (SSS) was manually se- lected. T2 of blood was obtained by tting the dierence signal to an exponential decay (Figure 2.2B) and then correcting the T1 of blood. Following a recent sys- tem upgrade, the nonselective post-saturation module in the TRUST sequence was inadvertently deactivated, forcing us to retrospectively correct the resultant T2 un- derestimation via Bloch simulation [124]. Both the bovine blood model [91] and the human HbA model [38] were used to calculate S v O 2 from the T2 of blood. 36 eTE = 0 ms 40 ms 80 ms 160 ms Control Tag SSS SSS 0 eTE/ms 0 0.2 0.4 0.6 0.8 1 Magnitude signal SSS T2 = 53.0 ms A B C 40 60 80 100 Figure 2.2: A: Localization of the TRUST imaging plane (red line) at the superior sagittal sinus. B: The resulting dierence image upon subtraction of the control and labeled images at four eective echo times. Red boxes highlight the isolated blood signal at the sagittal sinus. C: Mono-exponential tting of the four dierence images is then performed to estimate T2 of blood. 2.2.3 S v O 2 measurement using SBO In SBO, the magnetic eld shift, B 0 , induced inside the vessel has a linear rela- tionship with the S v O 2 : B 0 = 1 6 Hct (1 SvO 2 ) (3cos 2 1) do B 0 (2.1) , where Hct is the hematocrit determined from the blood sample, do =4(0.27) ppm is the susceptibility dierence (in SI units) between fully deoxygenated and fully oxygenated blood, and is the tilt angle of the vessel with respect to the main B 0 eld. In this study, SBO was performed in a 3D manner (Figure 2.3). The sequence used for SBO is a 3D multi-echo GRE with full ow compensation [116]. Scan parameters are: TR=31 ms; four echoes (TE) at 4.2, 11.2, 18.2, 25.2 ms; voxel size = 1 1 1:3 mm 3 ; FOV = 210 189 109 mm 3 ; FA = 17; BW = 293 Hz/pixel; SENSE rate of 2 in the right-left direction and 1.29 in the head-feet direction. Images were zero-padded to have reconstruction voxel size of 0:460:461:3 mm 3 . Flow was compensated for all echoes along all spatial axes. Total scan time was 3.5 min. 37 B 0 eld map was generated from the multi-echo phase images using a nonlinear least square tting algorithm [76]. SSS was manually segmented based on the B 0 eld map. Vessel tilt angle was computed from the central line of the vessel. ROI for blood susceptibility measurement was chosen as a cylindrical segment of SSS with a vertical length of 10 mm. Vessel tilt angle was computed from the central line of the segment. To estimate the background eld due to air-tissue interface, a 3D tissue region within 100-pixel distance from the ROI axis was dened (Figure 2.3). The background eld was calculated by rst performing a second-order polynomial t to the B 0 eld in the tissue region and then extrapolating the polynomial functions to the location of ROI. B 0 eld shift of venous blood was obtained by subtracting the background eld from the total eld and then converted to venous oxygen saturation using Eq. (2.1). Each viable segment of the SSS (vessel tilt < 30 ) was processed in the above approach. Then the segment that had the minimum intra-ROI variance was selected for the nal computation of S v O 2 . Figure 2.3: Background eld removal in SBO. A. The total B 0 eld in sagittal view. Segmentation of the superior sagittal sinus (SSS) is highlighted in red dashed line. Region of interest (ROI) was chosen as a cylindrical segment of SSS with vertical length of 10 mm and minimum intra-ROI variance of B 0 values. B. Background eld was estimated by performing a second-order polynomial t to the B 0 eld in a tissue region (yellow dashed line) within an in-plane 40-mm range from the ROI center. The background eld was extrapolated to the ROI and subtracted from the total B 0 eld. 38 2.3 Results Among the eleven volunteers scanned without catheterization, nine of them com- pleted both the hypercapnia and hypoxia challenges, two of them only completed the hypercapnia challenge. The two subjects scanned under jugular catheterization completed both the hypercapnia and hypoxia challenges. The intersession variance of S v O 2 measurement were 1.7% and 2.2% using TRUST and SBO respectively, which suggested high repeatability. 2.3.1 Comparison of S v O 2 measurements using TRUST and SBO The S v O 2 measurements using TRUST (noted as `S v O 2 -TRUST') and using SBO (`S v O 2 -SBO') are compared in Figure 2.4. S v O 2 -TRUST averaged across the 13 subjects were 75.55.1%, 61.95.0%, 50.05.0% under hypercapnia, room air and hypoxia, and averaged S v O 2 -SBO were 77.55.3%, 68.05.5%, 59.43.6%. One- way analysis of variance showed the absolute S v O 2 -TRUST and S v O 2 -SBO measure- ments were signicantly dierent under room air and hypoxia but comparable under hypercapnia (Figure 2.4A). TRUST increased S v O 2 by 13.73.2% from room air to hypercapnia and a decreased S v O 2 by 11.64.3% from room air to hypoxia. In com- parison, the corresponding changes were considerably smaller with SBO: 9.53.7% (p = 0:003) and 8.53.8% (p = 0:06) (Figure 2.4B). A strong linear correlation was observed between S v O 2 -TRUST and S v O 2 -SBO (Pearson r = 0:91;R 2 = 0:84, Figure 2.4C), and Bland-Altman analysis revealed a signicant proportional bias (p< 0:01, Figure 2.4D). 39 Hypercapnia Baseline Hypoxia 40 50 60 70 80 90 100 Venous Oxygen Saturation (%) A Hypercapnia Hypoxia -20 -10 0 10 20 Venous Oxygen Saturation Change (%) B 40 50 60 70 80 90 TRUST (%) 40 50 60 70 80 90 SBO (%) C 40 50 60 70 80 90 (TRUST + SBO)/2 (%) -20 -10 0 10 20 SBO - TRUST (%) D Identity line Correlation, R 2 = 0.84 Linear fit (p < 0.001) SBO TRUST ** ** ** Hypercapnia Room air Hypoxia Figure 2.4: Comparison of S v O 2 -TRUST and S v O 2 -SBO measurements at the su- perior sagittal sinus. (A) S v O 2 -TRUST and S v O 2 -SBO measurements averaged across subjects under each condition. (B) Average change of S v O 2 from room air to hypercapnia and to hypoxia. (C) Scatterplot of S v O 2 -TRUST and S v O 2 -SBO with the linear correlation regression line (solid) and identity line (dashed). (D) Bland- Altman plot with the average of the two measurements displayed in the horizontal axis and the dierence between the two displayed in the vertical axis. **: p< 0:01 40 2.3.2 Validation with jugular catheterization Figure 2.5 displays the time-course plots of S v O 2 measurements under jugular catheterization. In both two subjects, S v O 2 -TRUST closely matched the jugular reference under hypercapnia but lower than reference under hypoxia and room air. In comparison, the dierence between S v O 2 -SBO and the reference was independent on the physiological state. All S v O 2 -TRUST measurements (28 in total) were compared with time-aligned co-oximetry reference, and all SBO measurements (13 in total) were compared with co-oximetry reference during steady oxygenation states (Figure 2.6). On average, the bias between S v O 2 -TRUST (bovine blood model) and the co-oximetry reference was -9.2% in saturation unit (p < 0:0001), while the bias between S v O 2 -SBO and reference was -1.0% (p = 0:45). Both bovine blood [91] and human HbA model [38] were used to convert the intravascular T2 into S v O 2 . The bias between TRUST and co-oximeter reference did not vary signicantly with the choice of T2 calibration model (supplemental material Figure 2.11). 0 600 1200 1800 2400 3000 Time (s) 40 46 52 58 64 70 76 82 Venous Oxygen Saturation (%) Hypoxia Hypercapnia Room Air Hypoxia Hypercapnia 0 600 1200 1800 2400 3000 3600 4200 Time (s) 40 46 52 58 64 70 76 82 Venous Oxygen Saturation (%) Hypoxia Hypercapnia Hypoxia Hypercapnia Co-oximetry TRUST SBO Room Air A B Subject 1 Subject 2 Figure 2.5: Time-course plots of S v O 2 measurements in two subjects who underwent jugular catheterization. Co-oximetry measurement was repeated approximately every 3 min (purple circles), S v O 2 -TRUST measurement at the superior sagittal sinus was repeated approximately every 1.5 min (orange square), and S v O 2 -SBO measurement was only performed when steady state was achieved under each gas condition (blue triangle). 41 55 60 65 70 75 80 85 90 -25 -20 -15 -10 -5 0 5 10 55 60 65 70 75 80 85 90 -25 -20 -15 -10 -5 0 5 10 TRUST - Co-oximetry(%) Co-oximetry (%) SBO - Co-oximetry(%) A B Co-oximetry (%) Subject 1 Subject 2 Figure 2.6: Comparison of TRUST and SBO measurement against the co-oximetry reference. A. 15 and 13 TRUST measurements from subject 1 (blue circle) and subject 2 (red cross) respectively are compared against time-aligned co-oximetry reference. Proportional bias of S v O 2 -TRUST was observed in subject 2. Taken all data points, the mean bias of S v O 2 -TRUST is -9.2% (p < 0:0001). B. six and seven SBO measurements from subject 1 and 2 respectively are compared against co-oximetry reference at steady oxygenation states. Taken all data points, the mean bias of S v O 2 -SBO is -1.0% (p = 0:45). 2.4 Discussion Although previous studies have demonstrated the accuracy and repeatability of T2- based [96, 123, 94] and susceptibility-based S v O 2 quantication [106, 111], this is the rst validation of MRI-based S v O 2 measurements with internal jugular catheteriza- tion. Furthermore, this study performed the rst comparison of the two categories of techniques under a broad range of physiological states in healthy volunteers. The mean S v O 2 values obtained at room air, hypoxia and hypercapnia conditions are comparable to those reported in previous TRUST and SBO studies (Table 2.1). The inter-subject and inter-session variances of S v O 2 measurement are also in line with literature values, supporting the validity of our results. 42 Table 2.1: Literature values of venous oxygen saturation under dierent physiolog- ical conditions a Physiological State Methods S v O 2 (%) S v O 2 Change b Reference Hypercapnia TRUST 78.21.4 (N=14) 15.8 Xu et al., 2011 TRUST 78.43.5 (N=10) 16.1 Rodgers et al., 2015 TRUST 75.55.1 13.7 This study SBO 77.24.8 (N=10) 10.5 Rodgers et al., 2015 SBO 785 (N=10) 13 Jain et al., 2011 SBO 77.55.3 9.5 This study Hypoxia TRUST 54.61.1 c (N=16) 10.5 Xu et al., 2012 TRUST 50.05.0 11.6 This study SBO 59.43.6 8.5 This study Room air TRUST 61 to 65 Xu et al, 2011; Xu et al., 2012; Liu et al., 2013 TRUST 644 d (N=10) De Vis et al., 2017 TRUST 624 e (N=10) De Vis et al., 2017 TRUST 61.95.0 This study SBO 64.0 to 68.6 Jain et al, 2009, 2011; Barhoum et al., 2015; Rodgers et al., 2015; SBO 68.05.5 This study a : S v O 2 measurements were made at the superior sagittal sinus unless noted other- wise. b : S v O 2 change from room air, in saturation unit (%), calculated from reference paper. c : Hypoxia challenge induced by breathing gas of 14% O 2 and 86% N 2 d : Measurement at the straight sinus e : Measurement at the internal jugular vein 43 2.4.1 Validation with jugular vein catheterization In both of the two subjects scanned with jugular catheterization, S v O 2 -TRUST measurements were close to the reference under hypercapnia. However, TRUST yielded lower S v O 2 values under hypoxia and room air than the reference. Com- pared to TRUST, SBO provided closer agreement with the jugular reference (Figure 2.5). The internal jugular vein drains both brain and face, while the superior sagittal sinus only drains the brain. One could logically question whether the internal jugular vein is an adequate reference. In fact, the saturation dierence between the two veins has been well characterized (2-3% under resting conditions [120]), which is much smaller than the discrepancy we observed between the jugular reference and the TRUST measurement. We found the ratio of external/internal carotid ow derived from phase contrast images to be independent of the inhaled gas mixtures (not shown). This indicates that the ow distribution in face and brain remained the same regardless of oxygenation conditions. Thus, the large discrepancy between TRUST and the jugular reference is unlikely to relate to physiological distinction of the two veins, when such discrepancy is only observed under room air and hypoxia conditions. Furthermore, S v O 2 changes in jugular vein should match the changes in the superior sagittal sinus because of consistent ow distribution; in our observation, S v O 2 changes measured by TRUST were much larger than those measured by co- oximetry. Flow through an inhomogeneous magnetic eld can cause intravoxel dephasing [125, 126], which has not been counted in the conventional TRUST quantication. If the B 0 eld variation is approximated as a gradient eld of 1500 Hz/m con- currently playing with the T2-prep module, intravoxel dephasing caused by spins owing at 20 cm/s can induce signal loss of 2%, 9% and 34% at eective echo time of 40 ms, 80 ms and 160 ms respectively. Such signal loss can cause T2 underesti- mation and further translate to saturation underestimation. At true saturation of 44 55% (representative of hypoxia saturation) and 85% (representative of hypercapnia saturation), saturation can be underestimated by 2% and 7% respectively assuming normal Hct of 0.4. The pattern of estimation error (small during hypoxia, large dur- ing hypercapnia) is opposite to our observation. Therefore, although ow-induced intravoxel dephasing might exist, the factor alone can hardly explain the observed discrepancy between TRUST and the reference. Related simulation is detailed in supplemental material. We suspect that the discrepancy between TRUST and the jugular reference under hypoxia and room air may originate from the calibration models used in TRUST. Experiment by Lu et al. showed that the arterial saturation measurement by TRUST matched closely with pulse-oximeter measurement under hypoxia [91], where the pH and pCO 2 of arterial blood were relatively tightly controlled. Previous in-vitro TRUST calibrations (both bovine and human blood) have been performed under controlled gas conditions, all approximating those found in arterial blood (pH 7.4 and pCO 2 40 torr). Hypoxia can stimulate increased minute ventilation, leading to hypocapnia and respiratory alkalosis. In the present study, co-oximeter measurement under baseline reported pH of 7.37 and pCO 2 of 50 torr in jugular blood sample. Under hypoxia, pH and pCO 2 were measured 7.40 and 35 torr respectively. In contrast, hypercapnia produced pCO 2 's of 55 torr and a mild acidosis (pH = 7.32). Conceivable uctuations in pCO 2 and pH might modulate red blood cell membrane properties, which in turn can alter the T2-saturation relationship. However, this hypothesis requires further investigation. 2.4.2 Comparison of T2- and susceptibility-based S v O 2 measurements The proportional bias between TRUST and SBO has been suggested by several prior studies [111, 110], but we demonstrate it more convincingly because of the broad range of oxygenation produced. Compared to SBO, TRUST presented signicantly 45 lower S v O 2 values under room air and hypoxia conditions (-6.0% and -10.0%) but comparable S v O 2 values under hypercapnia. As a result, TRUST indicated a signif- icantly bigger increase of S v O 2 induced by hypercapnia challenge than SBO, which agrees with the previous ndings by Rodgers et al [110]. The comparison of TRUST and SBO based on datasets acquired without jugular catheterization were in line with the observation we had in the jugular validation experiments. Therefore, we believe the dierence between TRUST and SBO measurements could essentially be a state-dependent S v O 2 underestimation by TRUST. According to Fick's principle, relative change of cerebral metabolic rate of oxy- gen (CMRO 2 ) can be predicted using the measurements of CBF and S v O 2 under two conditions. We also performed phase-contrast measurements of whole-brain CBF during hypercapnia and room air in eight subjects. As shown in Table 2.2, TRUST indicated a signicant decrease of CMRO 2 induced by hypercapnia, which matches Ref. 23 and 27 [111, 110]. In contrast, SBO presented non-signicant change of CMRO 2 , in accordance with Ref. 27 [110]. The con icting interpretation of CMRO 2 based on TRUST and SBO measurements indicated a strong need to further validate these two techniques. 2.4.3 Variance in SBO measurement Although SBO had smaller bias than TRUST, this technique has major challenges for use in the sagittal sinus. In its conventional 2D implementation, SBO selects the slice location by visual inspection on a survey scan or a venography scan [106]. In this study, we acquired 3D whole-brain multi-echo GRE dataset. The purpose was to investigate the contribution of slice location to the variance of SBO mea- surement, an issue overlooked in previous SBO studies. In this study, 2D SBO processing was performed for all \plausible" axial slices (vessel tilt < 20 degree), and the predicted S v O 2 values varied by an average range of 22% (saturation unit) (supplemental Figure 2.12). Such high variance along the slice direction will lessen 46 Table 2.2: Summary of CBF measurements using phase contrast MRI, S v O 2 mea- surements using TRUST and SBO, and calculation of normalized CMRO 2 from room air to hypercapnia (N = 8). Student t-test was used to test if the sample mean is signicantly dierent from zero. Arterial ow: ml/min, S v O 2 : %, and CMRO 2 : % Sub Hypercapnia Room air CMRO 2 by TRUST CMRO 2 by SBO Arterial ow S v O 2 -TRUST S v O 2 -SBO Arterial ow S v O 2 -TRUST S v O 2 -SBO 1 921.7 74.4 75.4 611.3 57.5 59.6 -9.2 -8.2 2 801.8 68.2 76.7 627.0 58.0 70.1 -3.2 -0.3 3 521.3 72.4 65.1 389.3 54.7 59.2 -18.4 14.5 4 898.7 80.8 84.3 596.7 60.6 70.3 -26.6 -20.4 5 828.0 79.1 83 705.8 62.3 70 -35.1 -33.5 6 852.3 67.4 77.2 679.1 58.3 66.8 -1.9 -13.8 7 914.4 80.4 81.4 667.1 69.7 76.4 -11.5 8.0 8 617.7 80.3 82.8 504.9 67.0 73.2 -27.0 -21.5 Mean -16.6 p = 0.006 -9.4 p = 0.14 the condence of using 2D SBO processing for absolute S v O 2 quantication and inter-subject comparison. To investigate the impact of vessel orientation and geometry, we created digital phantoms based on the 3D segmented SSS geometry from each subject. B 0 eld variation was simulated by assigning a constant susceptibility value to the vessel and applying 3D dipole convolution [65]. SBO processing was then performed slice-by- slice and compared with the truth. Based on our simulation, variation of saturation measurement is about 3.6% across plausible slices. Therefore, vessel orientation and geometry does not explain such large variation of saturation measurement along the slice direction. We hypothesized that the error from incomplete background eld removal could contribute to such variation. Background eld is typically estimated by tting the eld variation to a second-order polynomial, but accuracy of this approach has only been veried in the femoral vein [108]. The superior sagittal sinus is near an air- tissue boundary, where the background eld has higher order of spatial variation. 47 In this study, we performed SBO processing slice-by-slice on the 3D B 0 eld map and chose a 10-mm ROI that has the lowest intra-ROI standard deviation. For SBO measurements, spins owing through an inhomogeneous magnetic eld can cause quadratic phase evolution in gradient echo acquisition. Xu et al [116] demonstrated that using linear phase tting to obtain the B 0 eld shift inside veins can cause estimation error depending on both the blood velocity and the gradient eld. However, hypoxia and hypercapnia produced similar increases in ow, which should result in similar S v O 2 bias due to this type of ow eect if present. 2.4.4 Practical considerations of TRUST and SBO TRUST has been used to measure changes in brain oxygenation in response to hypercapnia [96], hyperoxia [97], hypoxia [97], and caeine[121] challenges and in disease states such as multiple sclerosis [98] and sickle cell anemia [92]. The wide application of TRUST is motivated by its high reproducibility and ease of use. TRUST has been shown with test-retest probability < 2% (saturation points) [94] and comparable variability across ve major imaging centers [95]. The blood iso- lation feature also exempts the operator dependence on ROI selection. However, before potential biases are conrmed and corrected, caution should be placed when TRUST is used or compared in alternative physiological conditions. For diseases that provide drastically dierent blood property from the existing in-vitro calibra- tion material, like sickle cell anemia, calibration models should also be reconsidered [92]. Previous studies have demonstrated the utility of SBO for quantifying S v O 2 in the internal jugular [107], superior sagittal sinus (SSS) [106], and femoral veins [108]. The biggest advantage of SBO is its simple linear model and no requirement of calibration, making it robust to derangements of red cell shape and permeabil- ity. SBO with single axial slice acquisition, combined with phase-contrast CBF measurement, has been applied to study the change of CMRO 2 at high temporal 48 resolution. However, SBO is better suited for deep veins where background eld removal is less challenging. Absolute S v O 2 measurement in boundary veins such as the sagittal sinus require caution because of inadequately compensated local eld variations. Despite uncertainly in absolute saturation, S v O 2 changes by SBO are likely to be robust to background eld errors and can serve to track response to physiological perturbations. 2.4.5 Limitation There are several limitations to this study. First, we only had internal jugular vein data in two subjects because it was challenging to recruit subjects to this study arm. Another limitation lies in the long data acquisition time (3.5 minutes) for SBO. The scan time was long mainly due to the 3D whole-brain spatial coverage and long echo time. While long echo time is required to achieve optimal SNR for blood susceptibility measurement, whole-brain spatial coverage might be unnecessary to perform accurate SBO measurements. Scan time can be shortened by limiting the FOV, which should be investigated in the future. Lastly, we discovered that the current implementation of the TRUST sequence was not engaging the post-saturation module to reset the longitudinal magneti- zation after each TR. Therefore, spin history from previous TRs could cause TR- dependent T2 underestimation. This T2 underestimation is relatively constant (3.5 { 4.5 saturation %) across the range of observed saturations (supplemental Figure 2.11). When we corrected T2 using Bloch simulations, we obtained predicted sat- urations similar to previous studies (Table 2.1). Furthermore, dierences in S v O 2 in response to our challenges should be robust to residual spin history. 49 2.5 Conclusion In conclusion, we performed the rst systematic comparison of T2- and susceptibility- based S v O 2 quantication under a broad range of physiological states; validation with internal jugular catheterization was also performed in two subjects. TRUST yielded systematic lower saturations than SBO and jugular catheterization under hypoxia and room air conditions. While TRUST and SBO responded concordantly with gas challenges, the magnitude of S v O 2 change was higher for TRUST than SBO and jugular catherization. Taken together, these data suggest that the T2- hematocrit-saturation relationship may have an additional confounder such as blood pCO 2 or pH. While S v O 2 by SBO was unbiased with respect to jugular catheter- ization across physiological states, we found absolute S v O 2 measurements highly vulnerable to slice position and background correction. The results suggested that caution should be taken for comparison of absolute S v O 2 measurements using dif- ferent quantication methods. 2.6 Supplemental Methods 2.6.1 Sources of variance in S v O 2 -TRUST measurement 2.6.1.1 Underestimation of T2 due to short TR If the longitudinal magnetization of blood spins does not fully recover every TR, the spin history can cause T2 underestimation. Fortunately, such bias can be modeled using Bloch equation. The TRUST sequence used in this study had interleaved control and tag imaging order, which means, if the current TR is for control imaging, blood spins should experience an inversion RF pulse and a non-selective T2-prep 50 composition pulse in the previous TR (Figure 2.7 top). Therefore, signal in the current control image is: M z;control =M 0 [(1 2e (TIeTE)R 1b )e eTER 2b e (TReTE)R 1b +::: 1e (TReTE)R 1b ]e eTER 2b (2.2) where R1 b and R2 b are the R1 (1/T1) and R2 (1/T2) of blood, eTE is the duration of the T2-prep module. If the current TR is for tag imaging, then blood spins should only experience a T2-prep in the previous TR (Figure 2.7 bottom). Therefore, signal in the current tag image is: M z;tag =M 0 [e eTER 2b e (TReTE)R 1b +e (TReTE)R 1b +12e (TIeTE)R 1b ]e eTER 2b (2.3) The subtracted signal is: M z =M z;control M z;tag = 2M 0 e eTE(R 2b R 1b ) [e eTER 2b e TRR 1b e eTER 2b e (TR+TIeTE)R 1b +::: e TIR 1b e TRR 1b ] (2.4) In contrast to the situation where longitudinal magnetization fully recovers every TR, the nal signal is: M z = 2M 0 e eTE(R 2b R 1b ) e TIR 1b (2.5) Based on Eq. 2.4, a one-to-one relation between estimated T2 and true T2 can be generated (Figure 2.8A). In this study, TR = 3000 ms, TI = 1020 ms and T1 = 1620 ms. Correspondingly, the linearly regressed relation between true T2 and estimated T2 is: T 2 cor = T 2 est 1:2 0:86 (2.6) 51 Eq. 2.6 was used to correct the underestimation of T2 due to short TR. At TR = 3 s, the resultant saturation underestimation is approximately constant over a typical range of true saturation, 30% to 80% (Figure 2.8B). Figure 2.7: TRUST sequence experienced by blood spins in two consecutive TRs. The top diagram demonstrates the case of control imaging, in which the previous TR has an inversion RF pulse and T2 preparation module. The bottom shows the case of tag imaging, in which the previous TR only has the T2 preparation module. 2.6.1.2 Underestimation of T2 due to blood ow Ideally, the T2-prep module in TRUST sequence induces signal decay that solely depends on T2 (Figure 2.3A). However, B 0 eld variation can cause additional signal decay for owing spins (Figure 2.3B). Spins moving in a gradient eld accumulate phase shifts that depend on the velocity and the rst gradient moment. In a laminar ow model, signal loss will occur due to intravoxel dephasing. Haacke et al. presented a mathematical description of the signal loss induced by ow and accompanying gradient. Assuming linear velocity distribution in one voxel, the relative signal loss is 1- sinc(), where is the phase dispersion within the voxel. Assuming spins velocity at 20 cm/s and approximating the B 0 eld variation as a gradient eld of 1500 Hz/m, intra-voxel phase dispersion will be 0.12, 0.24 and 0.48 at eTE of 40 ms, 80 ms and 160 ms, which correspond to signal loss ratio of 2.3%, 9.2%, and 33.8% respectively. Such signal loss is added on top of the 52 20 40 60 80 100 120 140 True T2 (ms) 20 40 60 80 100 120 140 Estimated T2 (ms) TR = 2 TR = 3 TR = 4 TR = 5 TR = 7 Identity 20 40 60 80 100 True Sat (%) -15 -10 -5 0 Sat estimation error (%) A B Figure 2.8: Relation between estimated T2 and true T2 in the case of short TR. Simulation on the underestimation of T2 caused by short TR. A. The relation be- tween estimated T2 (ms) and true T2 (ms) under dierent TR (s) is plotted. B. Assuming Hct = 0.42, T2 underestimation is converted into saturation underesti- mation using the bovine blood model. Over a range of true saturation from 30% to 80%, saturation underestimation is approximately constant. T2 eect, causing T2 underestimation. We simulated the signal loss ratio due to intra-voxel dephasing as a function of eTE and spin velocity (Figure 2.4). It can be seen that higher the velocity induces more underestimation of T2. Using the bovine blood model and assuming true saturation of 60% and a Hct of 0.42, the resultant saturation underestimation is 2% with spin velocity of 20 cm/s and ignorable with spin velocity of 5 cm/s. 2.6.1.3 Bovine blood model and human HbA model Critical to TRUST is the use of empirically derived calibration curves that covert T2 of blood into oxygen saturation. The most widely used T2 calibration model at 3 Tesla was proposed by Lu et al in experiments using bovine blood. Recently, Bush 53 Figure 2.9: Comparison of the T2-preparation sequence without (A) and with (B) a gradient eld. et al proposed another T2 calibration model based on healthy human blood (hu- man HbA model). To investigate whether the choice of T2 calibration model con- tributes to the systematic bias we observed between S v O 2 -TRUST and co-oximeter measurements, we used both bovine blood and human HbA model to convert the intravascular T2 into S v O 2 . Figure S5A demonstrates the dierence between two models under dierent oxygenation levels. From Figure S5B, it can be seen that the bias between TRUST and co-oximeter reference did not vary signicantly with the choice of T2 calibration model. 2.6.2 Sources of variance in S v O 2 -SBO measurement Along the axis of SSS, S v O 2 measurement with 2D SBO processing presented a large range of values (Figure 2.12). The average range of variation was 22% across subjects. In order to investigate the sources of variance, we conduct two simulation experiments. 2.6.2.1 Violation of long straight cylinder assumption Equation 2.1 is based on the assumption that the vein can be approximated as an innitely long cylinder. In reality, SSS has curvature, branching and tapering that violate that assumption. In order to investigate error of S v O 2 measurement 54 0 100 200 Duration of CPMG module (ms) 0 10 20 30 40 Signal loss (%) v = 5 v = 10 v = 15 v = 20 40 60 80 100 120 True T2 (ms) 40 60 80 100 120 Estimated T2 (ms) 40 60 80 100 True Sat (%) -8 -6 -4 -2 0 Sat estimation error (%) A B C Figure 2.10: Eect of intra-voxel dephasing on T2 estimation, assuming the B 0 eld variation as a gradient eld of 1500 Hz/m. A. Signal loss ratio (%) depends on both the spin velocity (cm/s) and the duration of the CPMG T2-prep module. B. Estimated T2 is shown as a function the true T2. C. Using the bovine blood model and assuming a Hct of 0.42, saturation error increases with spin velocity (cm/s) and the true saturation. due to the curvature of SSS, we created a digital phantom of a curved tube by using the central line of SSS extracted from each in vivo dataset. The tube had a xed radius of 6 mm. A single susceptibility value of 0.4 ppm representing blood Hct of 0.4 and S v O 2 of 0.6 was assigned to the SSS phantom, and the background susceptibility was 0. Induced magnetic eld shift was simulated using the forward model. Slice-by-slice SBO processing was then applied, and the S v O 2 measurement was compared against the truth, i.e. 60%. Measurement error was largest at the two ends of the SSS, indicating these regions should be avoided. The average variation along the slice direction was 3.61.0%, and the average error of S v O 2 measurement was 5.21.6%. 2.6.2.2 Error due to background eld removal SBO calculates the background magnetic eld due to air-tissue interface by per- forming low-order polynomial tting to the total B 0 eld. However, SSS is close 55 0 600 1200 1800 2400 3000 Time (s) 40 46 52 58 64 70 76 82 Venous Oxygen Saturation (%) Hypoxia Hypercapnia Room Air Hypoxia Hypercapnia 0 600 1200 1800 2400 3000 3600 4200 Time (s) 40 46 52 58 64 70 76 82 Venous Oxygen Saturation (%) Hypoxia Hypercapnia Hypoxia Hypercapnia Co-oximeter Bovine HbA Room Air Figure 2.11: Time-course plots of S v O 2 measurements using co-oximeter (purple), TRUST with bovine blood model (orange) and TRUST with HbA model (blue) on two subjects who underwent jugular catheterization. to the brain tissue boundary, and the background eld has higher order of vari- ation. In the order to investigate error of S v O 2 measurement due to background eld removal, a digital phantom, in which the aforementioned tube was embedded in a tissue region dened by the brain mask extracted from each in-vivo dataset. A single susceptibility value of -9.5 ppm was assigned to brain tissue, 0.4 ppm was assigned to the tube, and the background susceptibility was 0. Using the same processing described in 2.6.2.1, the S v O 2 measurement was compared against the truth. The average variation along the slice direction was 11.64.4%, and the average error of S v O 2 measurement was 15.86.4%. 56 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 40 60 80 Hypercapnia Room air Hypoxia 0 100% Slice index Saturation Figure 2.12: Large variation of S v O 2 -SBO measurement along the axis of SSS. For each subject, the slice-by-slice S v O 2 -SBO measurement is plotted as a function of slice index (vertical axis). Measurements under hypercapnia, hypoxia and room air are represented as red, yellow and blue lines. Sagittal view of SSS susceptibility map (converted to saturation values) is also shown aligning with the vertical axis of the S v O 2 plot. Both the range of variation and standard deviation along the axis of SSS are given. 57 Chapter 3 Increased brain iron deposition in patients with sickle cell disease: an MRI quantitative susceptibility mapping study 3.1 Introduction Sickle cell disease (SCD) is a genetic blood disorder aecting more than 100,000 peo- ple in the United States [4]. Red blood cell sickling from the abnormal hemoglobin, HbS, causes vascular endothelial damage, premature red blood cell demise, and vaso-occlusion. This ultimately produces vasculopathy in many organs [127, 128], with the most devastating consequences in the brain. Progressive white matter disease, especially silent cerebral infarcts (SCI), is a major problem in SCD [129]. While the risk of symptomatic ischemic stroke has been reduced by chronic trans- fusion therapy and hydroxyurea, the prevalence of SCI in SCD patients continues to be 1-2% per age year with no plateau [16]. Many studies have focused on the structural and hemodynamic aspects of SCI in SCD [130, 131, 132], but few have examined brain iron accumulation [133, 134] and its possible role in reinforcing white matter injury. 58 Iron is essential for normal brain metabolism, including oxygen transport, myelin production, and neurotransmitter synthesis [135]. However, excessive iron deposi- tion can promote the generation of highly reactive radical species and exacerbate oxidative stress [136], causing lipid perioxidation and neuronal injury. Both his- tology [137] and in-vivo imaging studies [138] have shown that large quantities of non-heme iron (in the form of ferritin) accumulate in the basal ganglia during the normal process of aging. Furthermore, excessive brain iron has been shown to ag- gravate white matter damage [139, 140, 141] and accelerate neurodegeneration in Parkinson's and Alzheimer's disease [42, 142, 143]. Unfortunately, most iron stud- ies on SCD have focused on iron deposition in the liver, heart, and pancreas after chronic blood transfusion [144, 145] with only a few abstracts on iron deposition in the brain [133, 134]. Although iron is tightly regulated in the central nervous system, iron home- ostasis can be disrupted by brain tissue injury and microvasculature damage [142]. Hypoxic-ischemic injuries, which are common in SCD patients [15, 146, 147, 148], have been shown to cause iron accumulation at vulnerable locations in animals [52, 49, 50] and humans [149, 53]. Additionally, microvasculature damage, which is also common in SCD patients [147, 150, 151], could potentially raise brain iron levels by disrupting the blood brain barrier. To test the hypothesis that brain iron deposition is increased in SCD patients, we compared quantitative susceptibility mapping (QSM) and R2*-based brain iron quantication in SCD patients and age and race matched controls. We also inves- tigated the factors of age, hematological markers, and SCI presence on brain iron deposition. 59 3.2 Methods 3.2.1 Participants The study was approved by the Institutional Review Board at Children's Hospital Los Angeles (CCI#11-00083). Thirty-nine clinically asymptomatic SCD patients and thirty-three healthy controls were recruited with informed consent or assent. Exclusion criteria for SCD patients included pregnancy, previous overt stroke, acute chest or pain crisis hospitalization within one month. Twenty-four control subjects were recruited from rst degree relatives of the patients. Eleven SCD patients and eight healthy controls were excluded due to motion during the scan. Two SCD patients were excluded due to image artifacts caused by a failing radiofrequency amplier. Twenty-six SCD patients and twenty-ve controls remained in our anal- ysis group. 3.2.2 Data acquisition MRI images were acquired on a 3T Philips Achieva scanner with 32-channel head coil. Sequences included: 1) T1-weighted, 3D magnetization prepared rapid ac- quisition gradient echo (MPRAGE) sequence (TE/TR = 3.7/8.1 ms, TI = 944 ms, ip angle = 8 , spatial resolution = 111 mm 3 ) for anatomical referenc- ing and tissue segmentation; 2) T2-weighted uid-attenuated inversion recovery (FLAIR) sequence (TE/TR = 280/4800 ms, TI = 1650 ms, spatial resolution = 111.3 mm 3 ) for the identication of white matter hyperintensities [130]; 3) 3D time-of- ight MR angiography sequence for the assessment of vasculopathy; 4) 3D multi-echo gradient echo (GRE) sequence (rst TE = 5.0 ms, echo spacing = 5.2 ms, number of echoes = 4, TR = 31 ms, ip angle = 18 , spatial resolution = 0.60.61.3 mm 3 ) for quantitative susceptibility mapping (QSM) and R2* map- ping. Blood samples were obtained on the same day of MRI scans for each subject. 60 All T1, T2, and angiographic images were interpreted by a board certied neuro- radiologist (B.T.). Silent cerebral infarcts were dened as hyperintensities greater than 3 mm in diameter in the absence of documented neurological decits. As iso- lated decits are common in children [152] and increase with age [153, 154], more than one lesion per decade was required to be considered abnormal. 3.2.3 Image processing Multiple steps were performed to calculate the susceptibility map from multi-echo GRE phase images. [66, 67, 62, 80] The phase images were rst corrected for eddy- current error using a linear tting algorithm. [155] A binary brain tissue mask was obtained using the FSL Brain Extraction Tool (FMRIB, Oxford, UK). [156] B 0 eld map was generated from the multi-echo phase images using a nonlinear least square tting algorithm. [76] Frequency aliasing in the B 0 map was unwrapped using the FSL Prelude software. [77] Background eld was removed from the total B 0 eld using projection onto dipole elds (PDF). [71] After removal of background eld, the resulting local eld was used to derive tissue susceptibility by performing morphology enabled dipole inversion (MEDI). [67] Since QSM computes suscepti- bility in relation to a reference value rather than in absolute terms, we selected splenium as the reference tissue [62, 73] and reported ROI measurements relative to the reference susceptibility. Splenium was chosen over cerebrospinal uid for reference because the former presented lower variation of susceptibility across sub- jects. R2* maps were generated by performing standard mono-exponential tting to the multi-echo GRE magnitude images. Image reconstruction was carried out in MATLAB (The Mathworks Inc, MA, US). It should be noted that QSM directly measures the magnetic susceptibility shift of brain tissue. In comparison, R2* is in uenced by not only the magnetic property but also the water content and cel- lularity of tissue. Thus, QSM is typically more sensitive and specic than R2* for 61 brain iron measurements; this was re ected in the present study by the larger eect sizes observed by QSM in the patient population. The regions of interest (ROI) included bilateral caudate nucleus, putamen, globus pallidus, substantia nigra, red nucleus, and dentate nucleus (Figure 3.1). T1-weighted images were automatically segmented using the BCI-DNI brain atlas to produce ROI masks of caudate nucleus, putamen, globus pallidus and splenium (http://brainsuite.org). T1-weighted images were rigidly registered to QSM images to obtain ane transformation matrices. ROI masks were then converted to the coordinates of QSM images by applying ane transformation. All regis- tration was performed using BrainSuite (brainsuite.org, v15a). As a nal step, transformed ROI masks were manually corrected by an expert in neuroanatomy (S.Y.C.). Substantia nigra, red nucleus and dentate nucleus, which were not easily identied on T1-weighted images, were manually segmented on the reconstructed susceptibility maps where their boundaries were distinct. 3.2.4 Statistical analysis In advance of group comparisons, susceptibility and R2* measurements were con- trolled for age and sex by linearly regressing out log-transformed age and sex then adding the residuals to the population mean. Logarithmic transformation of age was used in the regression analysis because it better predicted susceptibility than age. Eect size of disease in each measurement was estimated using Cohen's d, which is dened as the dierence between group means divided by the pooled standard deviation [157]. Multivariate regression analysis was performed on the total population. Independent variables included age (log-transformed), sex, pe- ripheral oxygen saturation, hemoglobin (g/dL), the product of oxygen saturation and hemoglobin, hematocrit (%), HbS-containing cells (%), fetal hemoglobin (HbF) (%), cell-free hemoglobin (mg/dL), mean corpuscular volume (fL), white blood cell count (10 3 ), reticulocytes (%), and lactate dehydrogenase (U/L). HbS-containing 62 cells were dened as red blood cells containing over 70% HbS. We chose to examine HbS-containing cells rather than HbS (%) because we were including control sub- jects with sickle cell trait. Sickle cell trait subjects have approximately 40% HbS in their blood but no cells containing exclusively HbS; these subjects do not have increased neurovascular risk [158]. All variables having a univariate p< 0:10 were included as candidates for the stepwise multivariate regression. Variables were only retained in the nal model forp< 0:05. Statistical analyses were carried out using JMP v13.0.0 (Cary, NC). 3.3 Result 3.3.1 Patient characteristics A total of 51 subjects remained in the nal study. Subject demographics are shown in Table 3.1. The SCD patient group consisted of 26 subjects (mean age = 24.07.6; age range = 14.3 { 41.8). At the time of the study, the ve SCD patients on chronic transfusions had systematic iron overload, indicated by an average liver iron concentration (LIC) of 24.412.0 mg/g. Two SCD patients with history of chronic transfusion had an average LIC of 4.84.3 mg/g. Ten out of the nineteen remaining non-transfused patients had documented normal iron burdens: eight patients underwent LIC measurement (LIC = 1.20.7 mg/g) and two had ferritin measurement (ferritin = 10652 ng/mL). Patients on chronic transfusions had their MRI and blood draw performed on the morning of routine transfusion visit. Susceptibility was found independent of transfusion status, so transfused and non- transfused patients were pooled together into a single SCD group. The control group consisted of 25 age-matched healthy subjects (mean age = 26.39.2; age range = 14.1 { 45.4). Sixteen control subjects had hemoglobin AA genotype, and nine had hemoglobin AS genotype (SCD trait). No dierence in 63 susceptibility measurement was observed with respect to AA or AS genotype, so these data were pooled for the control group. MR angiography, including extracranial vessels, was normal in all control and SCD subjects. Silent cerebral infarctions (SCI) were observed in 13/26 SCD pa- tients and 2/25 control subjects. Since there was no apriori reason to exclude the two control subjects with SCI and since their susceptibility values did not represent outliers with respect to the other control subjects, we did not exclude them from analysis. Five SCD patients and six healthy controls were excluded from the anal- ysis of dentate nucleus because of image artifacts caused by the boundary issues in QSM processing. Two SCD patients and two controls were excluded from the analysis of red nucleus, and one SCD patient was excluded from the analysis of substantia nigra, because the nuclei were indistinguishable from the background. 3.3.2 Age and sex eects on brain iron deposition Susceptibility values increased signicantly with age in all deep gray matter ROIs, with adjusted r 2 ranging from 0.20 to 0.45 (Figure 3.2). R2* measurements also showed signicant growth with age in all ROIs except the caudate nucleus (Figure 3.3). No eect of sex was observed on the susceptibility or R2* measurement of any ROI. 3.3.3 Group dierence in brain iron deposition Susceptibility measurements were found to be signicantly higher in the SCD pa- tient group in the regions of putamen, substantia nigra, and red nucleus after controlling for age and sex (Figure 3.4A). Eect sizes of the disease on susceptibil- ity measurements, represented by Cohen's d value, ranged from 0.70 to 0.86. R2* values were signicantly higher in the substantia nigra and the dentate nucleus. No group dierence was observed in the other nuclei. Qualitative comparison of susceptibility and R2* maps is illustrated in Figure 3.4B. 64 Table 3.1: Subject demographics. Group averages and standard deviations are given. Group dierences were assessed using unpaired student's t-test. Healthy controls SCD patients P N 25 26 Age (years) 26.39.2 24.07.6 0.21 Male : Female 10:15 15:11 0.15 Peripheral Oxygen Saturation 99.31.1 97.62.3 0.002** Hematocrit (%) 41.13.2 26.44.7 <0.0001** Hemoglobin (g/dL) 13.81.2 9.41.8 <0.0001** HbS containing cells (%) a 0 66.526.7 <0.0001** HbF (%) 0.040.11 10.59.8 <0.0001** Cell-free hemoglobin (mg/dL) 7.86.1 22.022.5 0.006** Mean corpuscular volume (fL) 84.46.7 93.415.0 0.009** White blood cell count (x103) 6.51.6 9.04.3 0.008** Reticulocytes (%) 1.40.6 9.04.4 <0.0001** Lactate dehydrogenase (U/L) 539.864.8 1046.5527.4 <0.0001** Transfused: Non-transfused 0:25 5:21 0.01* SCI+ : SCI- b 2:23 13:13 0.001** ** p< 0:01 * p< 0:05 a HbS-containing cells are dened as red blood cells containing exclusively HbS. b SCI+: subjects with silent cerebral infarcts shown on T2 FLAIR images; SCI-: subjects with normal T2 images. 65 3.3.4 Covariates of susceptibility measurements in deep gray matter In the multivariate analysis, log-transformed age was the strongest predictor for the susceptibility and R2* measurements. Besides age, signicant negative correlation with hemoglobin was found in the susceptibility measurements of substantia nigra, red nucleus and dentate nucleus (Figure 3.5A). The product of hemoglobin and pe- ripheral oxygen saturation (as a surrogate for oxygen content) did not strengthen the association of susceptibility with hemoglobin. Susceptibility and R2* values of the substantia nigra and red nucleus also showed negative correlation with hema- tocrit and positive correlation with HbS-containing cells, but they are not shown since these variables were highly correlated with hemoglobin. Susceptibility of the caudate nucleus, putamen or globus pallidus did not correlate with any labora- tory measurement. R2* measurements in the substantia nigra and dentate nucleus showed signicant dependence on HbS-containing cells. In contrast to susceptibil- ity measurement, the R2* measurement in the red nucleus did not depend on any hematological biomarker. Compared to patients with normal appearing white matter (SCI-), patients with silent infarcts (SCI+) exhibited higher susceptibility in all gray matter nuclei but only the globus pallidus and substantia nigra reached statistical signicance (Figure 3.5B). R2* measurement of the substantia nigra also had higher values in the SCI+ group (SCI+: 37.55.5 s 1 ; SCI-: 32.55.0 s 1 ; p = 0:022, not shown). There was no signicant dierence of R2* between the two patient subgroups in the other gray matter structures. 66 3.4 Discussion This study is the rst systematic assessment of brain iron deposition in patients with SCD across a broad range of ages. We found signicantly higher magnetic susceptibility of the putamen, substantia nigra, and red nucleus in SCD patients. Susceptibility values of the substantia nigra, red nucleus and dentate nucleus were negatively correlated with hemoglobin, which is a surrogate for hemolytic severity in SCD [20]. Patients with SCI exhibited higher substantia nigra susceptibility. The sensitivity of QSM measurements to the concentrations of paramagnetic iron complexes in subcortical nuclei has been validated in various histological stud- ies [62, 159]. QSM has been successfully applied to iron quantication in normal aging [73] and neurodegenerative diseases [160, 48]. In this study, both SCD pa- tients and healthy controls demonstrated nonlinear growth of susceptibility with age in deep gray matter structures. Predicted iron concentrations were in excellent agreement with previous autopsy and QSM analyses [137, 73, 161], supporting the validity and generalizability of our results. Susceptibility estimates in the putamen are lower than what Hallgren and Sourander reported in a histological brain iron study [137]. However, the putamen measurements in this study are comparable with prior in-vivo QSM ndings [161]. The dierence in reported susceptibility values may arise from the changes of putamen water content between in-vivo and post-mortem measurements. There has not been a consensus in the literature re- garding the eect of sex on subcortical iron concentrations [161, 162, 163, 164]. Although no eect of sex was observed, we might be underpowered to detect sex dierences because of the small sample size. Signicantly higher susceptibility was observed in the putamen, substantia ni- gra, and red nucleus of SCD patients. One possible explanation is that chronic hypoxia leads to the excessive brain iron deposition. Anemia, upper airway ob- struction, repeated episodes of vaso-occlusion or acute chest syndrome [15, 165, 67 166, 167, 168, 169, 170] can all cause chronic hypoxia in SCD patients. Under hy- poxic conditions, decreased anity of iron to storage proteins, increased synthesis of ferritin [49], and abnormal axonal transport of iron [139] can raise the iron level in the brain. This has been demonstrated in both animal [52, 49, 50] and clinical studies [149, 53]. We showed that the increased susceptibility of substantia nigra, red nucleus and dentate nucleus correlated with classic markers of anemia and SCD hemolytic severity, which suggests that brain iron may be a biomarker of cerebral hypoxic exposure. However, we could not completely exclude the possibility that the relationship between susceptibility measurements and hemoglobin levels repre- sented a group eect. In the present study, anemia and sickle cell disease severity were inexorably linked; future studies using non-SCD anemia patients are needed to determine whether anemia, itself, is associated with elevated brain iron. Substantia nigra susceptibility increased in SCD patients with white matter silent infarcts (SCI+), compared to patients with normal appearing white matter (SCI-). Silent infarction is a manifestation of small-vessel ischemic injury and oc- curs in brain regions with decreased vascular reserve [171] and increased metabolic stress [14]. Hypoxic-ischemic injuries are known to stimulate brain iron uptake [52, 49, 50, 149, 53]. Thus, the increased iron in the SCI+ patients could po- tentially be explained by the small vessel disease that commonly occurs in SCD patients. In such an early stage of investigation, it is impossible to know whether the increased brain iron deposition represents an incidental biomarker of sickle cell disease severity or reinforces cerebral damage or neurocognitive dysfunction. To place our observations in context, the amounts of increased substantia nigra sus- ceptibility and R2* in the SCI+ patient group are comparable to those observed in patients with Parkison's disease [172, 173]. In Parkinson's disease and other brain iron disorders, iron accelerates neurological degeneration by exacerbating ischemia- reperfusion injury and neural in ammation, even though iron dysregulation is not the primary disease process. Iron-chelation therapy using deferiprone has been 68 shown to improve neurological function in Parkinson's disease, [174] Friedreich's ataxia, [46] and pantothenate kinase deciency. [45] Thus, we believe it is critical to determine the functional role of brain iron in SCD and other anemia syndromes, because it is potentially treatable if it contributes to the progressive neurological complications observed in these patients. This study showed no dierence in the susceptibility of the caudate or globus pallidus between SCD patients and healthy controls, which is consistent with the abstracts reported by Shmueli et al [133] and Qiu et al [134]. Qiu et al [134] also reported signicantly higher susceptibility in the red nucleus and dentate nucleus of SCD patients, but they did not observe increased iron deposition in the substantia nigra. Their null nding in the substantia nigra could be explained by the younger age of the patient population (average age of 13.32.8 y/o versus 24.07.6 y/o in our study). In fact, we observed similar substantia nigra susceptibility between patients and controls when the comparison was limited to subjects younger than 22 years old. However, we should note that we had limited power for this comparison. A major limitation of all SCD QSM studies to date lies in the limited age ranges of patient cohorts. Although we didn't observe signicant group dierences in the caudate or globus pallidus, it is still possible that iron content in these nuclei might be abnormal once patients reach their third or fourth decade of life. Future investigation is needed on the progression of brain iron overload in SCD patients. 3.5 Conclusion In summary, SCD patients demonstrated increased brain iron accumulation in mul- tiple subcortical nuclei compared to age and ethnicity matched control subjects. Iron concentrations in the substantia nigra, red nucleus and dentate nucleus neg- atively correlated with hemoglobin, suggesting potential interaction between iron metabolism and chronic hypoxia in the brain. Substantia nigra and globus pallidus 69 iron was elevated in patients with SCI, consistent with an ischemic etiology. Future studies will focus on the functional correlates of brain iron in SCD patients as well as additional clinical predictors. 70 (a) (b) (c) (d) (e) (f) a b c d e f 200 ppb -200 CN SN PT RN GP DN Figure 3.1: Segmentation of deep gray matter structures on quantitative suscepti- bility map. Example axial (a to c) and coronal slices (d to f) of the susceptibility map are displayed. Locations of the slices are indicated in the sagittal view of T1- weighted image (top left). Structures of the caudate nucleus (CN), putamen (PT), globus pallidus (GP), substantia nigra (SN), red nucleus (RN), and dentate nucleus (DN) are highlighted with yellow boxes in the susceptibility map and enlarged two to four times for better visualization. 71 Age (years) Control SCD Patients Susceptibility (ppb) Caudate Nucleus p = 0.0001**, r 2 = 0.26 Putamen p <0.0001**, r 2 = 0.45 Globus Pallidus p = 0.0001**, r 2 = 0.27 Substantia Nigra p = 0.0010**, r 2 = 0.20 Red Nucleus p = 0.0043**, r 2 = 0.17 Dentate Nucleus p = 0.0018**, r 2 = 0.23 10 20 30 40 50 10 30 50 70 90 110 10 20 30 40 50 -20 0 20 40 60 80 100 10 20 30 40 50 60 100 140 180 220 260 10 20 30 40 50 0 50 100 150 200 250 10 20 30 40 50 -20 20 60 100 140 180 10 20 30 40 50 -40 0 40 80 120 160 Figure 3.2: Susceptibility increases with age in all deep gray matter structures. Linear regression was performed on the susceptibility measurements with respect to log-transformed age. p-values and r 2 of tting are given. The tted curves and observation bounds of 95% condence intervals are plotted as doted and dashed lines respectively. 72 Age (years) Control SCD Patients 10 20 30 40 50 5 10 15 20 25 30 10 20 30 40 50 10 15 20 25 30 35 10 20 30 40 50 15 20 25 30 35 40 45 50 55 60 10 20 30 40 50 10 15 20 25 30 35 40 45 50 55 10 20 30 40 50 10 15 20 25 30 35 40 45 50 10 20 30 40 50 10 15 20 25 30 35 40 45 50 R2* (s -1 ) Caudate p = 0.07, r 2 = 0.05 Putamen p =0.0001**, r 2 = 0.24 Globus Pallidus p = 0.0003**, r 2 = 0.23 Substantia Nigrav p = 0.0002**, r 2 = 0.24 Red Nucleus p = 0.002**, r 2 = 0.17 Dentate Nucleus p = 0.01*, r 2 = 0.13 Figure 3.3: R2* measurements increase with age in all deep gray matter structures except the caudate nucleus. Linear regression was performed on the R2* measure- ments with respect to log-transformed age. p-values and r 2 of tting are given. The tted curves and bounds of 95% condence intervals are plotted as doted and dashed lines respectively. 73 SCD patient 36 Age : 29 years SCD patient 10 Age : 25 years Control 15 Age : 29 years Control 33 Age : 25 years Susceptibility R2* map T2*w image -250 250 ppb 50 s -1 0 1 0 A B ROI Healthy controls SCD patients d P Susceptibility (ppb) Caudate nucleus 57.7 (14.4) 60.4 (17.5) 0.17 0.55 Putamen 29.7 (13.7) 40.7 (15.3) 0.76 0.009** * Globus pallidus 150.9 (29.1) 164.9 (30.8) 0.47 0.10 Substantia nigra 110.4 (30.9) 134.3 (36.9) 0.70 0.017* Red nucleus 67.4 (30.2) 92.4 (28.3) 0.86 0.005** Dentate nucleus 48.0 (24.5) 63.5 (25.7) 0.62 0.057 R2* (s -1 ) Caudate nucleus 18.0 (3.1) 18.4 (3.7) 0.12 0.64 Putamen 21.5 (3.2) 21.9 (2.7) 0.13 0.59 Globus pallidus 35.9 (4.4) 37.5 (5.7) 0.31 0.27 Substantia nigra 31.8 (4.5) 35.0 (5.8) 0.62 0.034* Red nucleus 29.7 (4.4) 32.1 (6.2) 0.44 0.14 Dentate nucleus 29.0 (4.6) 31.9 (4.8) 0.62 0.048* Figure 3.4: SCD patients exhibit higher susceptibility and R2* in multiple sub- cortical nuclei, compared with age-matched controls. (A) Average susceptibility (in parts per billion (ppb)) and R2* (in s 1 ) of deep gray matter ROIs in SCD patients and healthy controls. Values are reported as mean (standard deviation). All values were corrected for age and sex. d is Cohen's eect size, which is dened as the dierence between group means divided by the pooled standard deviation. **: p < 0:01. *: p < 0:05. (B) Examples of susceptibility and R2* maps in the regions of substantia nigra and red nucleus. Susceptibility maps (top), R2* maps (middle) and T2*-weighted images at TE = 20 ms (bottom) are shown. Blue and pink dashed boxes highlight the regions of substantia nigra and red nucleus respec- tively. The left two columns compare an SCD patient with a control who are both 29 years old, and the right two columns compare two subjects who are both 25 years old. 74 50 100 150 200 0 250 Susceptibility (ppb) Caudate Nucleus Putamen Globus Pallidus Substantia Nigra Red Nucleus Dentate Nucleus Control SCD Patients SCI - SCI + B ** ** Susceptibility (ppb) Substantia Nigra Hemoglobin (g/dL) Hemoglobin (g/dL) A Hemoglobin (g/dL) Red Nucleus Dentate Nucleus 6 8 10 12 14 16 50 100 150 200 6 8 10 12 14 16 20 50 80 110 140 170 6 8 10 12 14 16 0 20 40 60 80 100 120 Figure 3.5: Susceptibility values of multiple subcortical nuclei increase with sever- ity of anemia and white matter damage. (A) Age corrected susceptibility measure- ments present signicant negative correlation with hemoglobin in substantia nigra (p = 0:008, r 2 = 0:14), red nucleus (p = 0:028, r 2 = 0:10), and dentate nucleus (p = 0:023, r 2 = 0:13). Dotted lines show the linear regression of the data and shaded areas delimit the 95% condence interval. (B) Susceptibility of the globus pallidus and substantia nigra (after correction for age and sex) is higher in SCD patients with silent infarcts (SCI+), compared to patients with normal appearing white matter (SCI-). Mean and standard deviation of globus pallidus susceptibility are 180.529.8 ppb in the SCI+ group and 149.323.7 ppb in the SCI- group. **: p = 0:007. Mean and standard deviation of substantia nigra susceptibility are 151.735.5 ppb in the SCI+ group and 115.329.1 ppb in the SCI- group. **: p = 0:010. 75 Chapter 4 Eect of low spatial resolution on quantitative susceptibility mapping 4.1 Introduction Quantitative susceptibility mapping (QSM) is an MRI technique that provides di- rect quantication of tissue susceptibility by solving a dipole deconvolution problem [74, 75]. Histology studies have shown that QSM measurements in deep gray mat- ter nuclei with high concentration of iron strongly correlated with iron staining [62, 80, 159]. QSM have been widely applied to evaluate brain iron overload in normal aging [73] and a large range of neurodegenerative diseases [48, 160]. Venous blood susceptibility measured by QSM can be converted into venous oxygen satura- tion. Validation studies showed that the change of oxygenation state in healthy vol- unteers can be indicated by QSM-based saturation measurement [83, 114, 115, 116]. QSM shows promise in the investigation of abnormal oxygenation in stroke [175], tumor and multiple sclerosis [176]. Despite the wide applications of QSM, the long scan time remains one of the major challenges in the clinical translation of QSM. Current QSM protocol usually requires long scan times (4-10 minutes) due to the use of long echo times, broad spatial coverage, and submillimeter spatial resolution [74, 75]. Long echo times (20 76 to 40 ms, usually around the T2* of targeted tissue) are needed to achive optimal sensitivity of susceptibility measurement [177]. Broad spatial coverage has also been shown to be critical to the accuracy of QSM measurement [178]. However, the eect of spatial resolution is still not clear. Zhou et al. [179] modeled the eect of low spatial resolution on susceptibility measurement as a voxel sensitiv- ity function, which predicted that susceptibility underestimation at low resolution originated from decreased phase contrast. Through numerical simulation and phan- tom experiments using Gadolinium-lled balloons, they demonstrated that partial voluming eect depended on a large range of factors including object geometry, orientation, imaging echo time, eld strength, and magnitude contrast. Karsa et al. [178] simulated QSM acquisition with slice thickness from 1 mm to 6 mm using ve high-resolution volunteer datasets. They conrmed the ndings by Zhou et al. by showing that susceptibility map contrast decreased with increasing slice thick- ness. Existing investigations on spatial resolution were either based on phantoms or datasets of small sample size, both of which have limited coverage of susceptibility values and ROI geometries typically found in human subjects. Furthermore, the sensitivity of QSM-based venous oxygen saturation quantication to low spatial resolution has never been evaluated. This study aimed to investigate the importance of spatial resolution on QSM measurements for brain iron and brain oxygen saturation evaluation. 40 QSM datasets were acquired at sub-millimeter resolution for brain iron quantication. 39 one-millimeter resolution QSM datasets were acquired at dierent oxygenation conditions for venous oxygen saturation quantication. We retrospectively trun- cated the rawk-space data of these high-resolution QSM datasets to simulate lower resolution acquisitions. Susceptibility measurements in six subcortical nuclei and the straight sagittal sinus were investigated over varying resolution. Numerical sim- ulations were also performed to evaluate the accuracy of susceptibility estimation in small veins at low spatial resolution. 77 4.2 Methods 4.2.1 Data acquisition The protocol was approved by our Institutional Review Board, and written informed consent was obtained for each participant in this study. To investigate the eect of low resolution on susceptibility quantication of deep gray matter structures, 20 healthy subjects and 20 anemia patients (15 male; age range, 10{37 years; mean, 21 years) were scanned using a 3D multi-echo gradient echo sequence on the Philips 3T Achieva system with a 32-channel head coil. Se- quence parameters: spatial resolution = 0:6 0:6 1:3 mm 3 ; FOV = 22 22 12 cm 3 ; four echo times = 5, 10, 15, 20 ms; TR = 30 ms; SENSE rate of 2 in the right-left direction and 1.29 in the head-feet direction. Total scan time was 6 min 40 sec. The scanner-reconstructed, post-coil combination magnitude and phase im- ages were Fourier transformed to k-space. Six levels of spatial resolution (Table 4.1) were simulated by truncating the acquired data in k-space. To investigate the eect of low resolution on susceptibility quantication of straight sagittal sinus, 39 QSM datasets were acquired on 13 healthy subjects (7 male; age range, 24-55 years; mean, 29 years) under baseline conditions and two gas challenges - hypoxia and hypercapnia. Gas challenge setup and scan protocols were the same as Chapter 2. Sequence parameters: spatial resolution= 1 1 1:3 mm 3 ; FOV = 21 19 11 cm 3 ; TE = 4.2:7.0: 25.2 ms; TR = 31 ms; SENSE rate of 2 in the right-left direction and 1.29 in the head-feet direction. Images were zero-padded to have reconstruction voxel size of 0:46 0:46 1:3mm 3 ;. Flow was compensated for all echoes along all spatial axes. Total scan time was 3.5 min. Five levels of spatial resolution (Table 4.1) were simulated by truncating the acquired data in k-space. 78 Figure 4.1: Segmentation of deep gray matter structures on quantitative suscepti- bility map. Example axial (a to c) and coronal slices (d to f) of the susceptibility map are displayed. Locations of the slices are indicated in the sagittal view of T1- weighted image (top left). Structures of the caudate nucleus (CN), putamen (PT), globus pallidus (GP), substantia nigra (SN), red nucleus (RN), and dentate nucleus (DN) are highlighted with yellow boxes in the susceptibility map and enlarged two to four times for better visualization. 4.2.2 Image processing Before QSM processing, all datasets were zero-padded to have the same matrix size as the full-resolution reference data. B 0 eld was computed by tting the multi-echo phase images. Laplacian phase unwrapping was performed [77]. Background eld was removed using project onto dipole eld (PDF) [71]. Unreliable phase points were excluded [62]. L1-norm constrained reconstruction [73] was used to derive susceptibility map from local B 0 eld ( = 4 10 4 ). All ROI masks were rst dened on the full-resolution reference susceptibility maps and then applied to simulated low-resolution datasets. 3D ROI masks for the caudate nucleus (CN), putamen (PT), globus pallidus (GP), red nucleus (RN), substantia nigra (SN), and dentate nucleus (DN) were dened based on T1-weighted 79 Table 4.1: Simulated spatial resolution levels for susceptibility quantication of deep gray matter structures and straight sagittal sinus. Voxel size (in mm) along the three spatial dimensions is listed. A-P: anterior-posterior dimension; R-L: right-left dimension; F-H: feet-head dimension. ROI Spatial Spatial resolution levels dimension 1 2 3 4 5 6 Deep gray matter structures A-P 1.0 1.5 1.5 2.0 2.0 2.5 R-L 1.0 1.5 1.5 2.0 2.0 2.5 F-H 1.3 1.3 2.0 1.3 2.0 2.5 Straight sagittal sinus A-P 1.0 1.5 1.5 2.0 2.5 R-L 1.0 1.5 1.5 2.0 2.5 F-H 2.0 1.3 2.0 2.0 2.5 images, and registered to the QSM datasets. Figure 4.1 shows the segmentation of the six ROIs in both axial and coronal views. 3D ROI masks of the straight sagittal sinus were manually drawn. At each spatial scale, average susceptibility within the ROI was computed and compared against the reference. Error was computed as ref , where and ref are the intra-ROI average susceptibility in the low-resolution and the reference data respectively. One-sample student t-test was performed on measurement error. 4.2.3 Numerical phantom simulation Numerical phantoms were generated to simulate the eect of low resolution on susceptibility quantication of small vessels. The phantom contained a cylinder oriented perpendicular to the main magnetic eld. Instead of calculating the phase directly using the analytic formula for an innitely long cylinder, we performed a process analogous to the MRI image acquisition. We started by generating high- resolution complex image on a 512 x 512 x 512 grid representing a physical resolution of 0.0625 mm isotropic. The cylinder had 32-voxel diameter in the 512 cubic matrix and therefore represented a physical diameter of 2 mm, which is typical size of internal cerebral vein. T2* of the cylinder and background were set to 20 ms and 80 50 ms, representing typical T2* of venous blood and gray matter. Susceptibility of the cylinder varied from 0.1 to 1 ppm, while the background had susceptibility of 0 ppm. Magnetic eld variation, B 0 , was computed by convolving the susceptibility model with the dipole kernel. Taken all the parameters together, high-resolution complex image was generated using: m(r;TE) =e TE T2(r) e i B 0 (r)TE (4.1) We then obtained the lower-resolution version of the complex image by truncating the simulated data in k-space. For example, to simulate acquisition with a spatial resolution of 0:5 0:5 1:0 mm 3 , the k-space was truncated to keep the central 64 64 32. Data generated in this manner exhibits the usual experimental artifacts such as Gibbs ringing and partial volume eects. Phase was extracted from the low-resolution complex images and converted to susceptibility map using L1-regularized eld-to-susceptibility inversion. Simulations were performed at three levels of spatial resolution (0:50:51:0, 0:250:250:5, 0:1250:1250:25 mm 3 ) and at four echo times (TE = 5, 10, 15 and 20 ms). In each case, the simulation was performed 10 times, with complex Gaussian noise (SNR = 20 at TE = 0 ms) added independently. 4.3 Results 4.3.1 Deep gray matter structures The 40 full-resolution datasets for deep gray matter susceptibility quantication covered a broad range of susceptibility values: CN (0.03{0.09 ppm), PT (0.01{0.07 ppm), GP (0.09{0.23 ppm), SN (0.05{0.20 ppm), RN (0.03{0.14 ppm), and DN (0.02{0.13 ppm). Figure 3 shows the average susceptibility estimation error in the six gray matter ROIs at dierent spatial resolution levels. For CN, PT and 81 GP, down-sampling to a spatial resolution level of 2.0 mm isotropic still produced acceptable susceptibility quantication error (< 5 ppb) (Figure 4.2) and nonsigni- cant estimation bias (Figure 4.3). For smaller gray matter ROIs, spatial resolution of 2.0 mm isotropic induced signicant susceptibility underestimation (Figure 4.3). When the voxel size was 2:0 2:0 1:3 mm 3 , estimation error was < 5 ppb in SN and DN. For RN, spatial resolution of 1:5 1:5 2:0 mm 3 or higher was required for acceptable quantication (error < 5 ppb). -10 -5 0 5 10 CN DN GP PT RN SN 1 2 3 4 5 6 -10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10 -10 -5 0 5 10 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6 ) b p p ( r o r r E ) b p p ( r o r r E Resolution level index Figure 4.2: Mean susceptibility measurement error at dierent spatial resolutions for gray matter ROIs. The horizontal axis represents six levels of spatial resolution detailed in Table 1. The range of acceptable error,5 ppb is denoted as gray area. When the voxel dimension along all three axes was leq 2.0 mm, estimation error was < 5 ppb in CN, PT and GP. When the voxel size was 2:0 2:0 1:3 mm 3 , estimation error was < 5 ppb in SN and DN. For RN, spatial resolution of 1:5 1:5 2:0 mm 3 or higher is required. 82 40 60 80 CN Ref -12 -8 -4 0 4 8 12 2.2 -0.36 -2.9 20 40 60 80 PT Ref 1.8 -0.22 -2.2 50 100 150 200 GP Ref 3.2 -0.02 -3.2 50 100 150 200 SN Ref 0.99 -3.0 -7.1 20 60 100 140 RN Ref 2.5 -4.3 -11 100 DN Ref -0.38 -3.2 -6.0 -12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12 -12 -8 -4 0 4 8 12 0 50 Error (ppb) Error (ppb) Figure 4.3: Bland-Altman plot of susceptibility measurement error at spatial reso- lution of 2:02:02:0 mm 3 for gray matter ROIs. Solid and dashed lines represent the mean and the 95% condence interval (i.e. mean 2.03 SD) of measurement error. Signicant measurement bias (p< 0:05, t-test) is labeled in red. 4.3.2 Straight sagittal sinus Datasets acquired for venous blood susceptibility quantication in the straight sagittal sinus covered a broad range of susceptibility (0.17 { 0.60 ppm) and venous oxygen saturation (50-76%). All simulated spatial resolution produced signicant underestimation of susceptibility and corresponding overestimation of saturation. Figure 4.4 shows that, when the voxel size was 1:5 1:5 2:0 mm 3 , susceptibil- ity estimation error was [-33, 3.4] ppb, which corresponds to saturation estimation error of [-0.2, 2.2] % (saturation unit). 83 4.3.3 Small vessel At echo time of 5 ms, susceptibility underestimation was mainly due to partial vo- luming, and the relative error varied insignicantly across the susceptibility range from 0.1 to 1.0 ppm. Spatial resolution of 0:5 0:5 1:0 mm 3 produced suscep- tibility underestimation by about 30% at echo time of 5 ms. When the echo time increased, intra-voxel phase aliasing started to contribute to additional susceptibil- ity underestimation. When the true susceptibility was larger than 0.6 ppm and the echo time longer than 15 ms, the trend of estimation error was somewhat arbitrary (red arrows in Figure 4.5). 4.4 Discussion This study evaluated the eect of spatial resolution on QSM-based susceptibility quantication in deep gray matter structures and medium- and small-size veins. The in-vivo datasets for gray matter nuclei quantication were acquired from sub- jects with a broad range of age, and the datasets for venous blood susceptibility quantication were acquired at a broad range of venous oxygen saturation. Both groups of datasets fully covered the range of susceptibility values reported by the literature [62, 114, 115, 116]. Through down-sampling simulation on the 40 sub-millimeter datasets, we found that susceptibility estimation error was below 5 ppb for CN, PT and GP at spatial resolution of 2.0 mm isotropic. Although the susceptibility quantication of SN, RN and DN required higher resolution, sub-millimeter acquisition might still be unnecessary. For example, when the voxel size was 2:0 2:0 1:3 mm 3 , estimation error was < 5 ppb in SN and DN. By down-sampling the 39 datasets acquired for venous oxygen saturation, we observed that saturation estimation error below 2.2% (saturation unit) for the straight sagittal sinus at spatial resolution of 1:51:52:0 mm 3 . The ndings indicated an opportunity to signicantly shorten scan time by 84 simply lowering spatial resolution, when deep gray matter structures or the straight sagittal sinus are the target of QSM study. High resolution in most QSM protocols has been largely motivated by a phantom study by Dong et al [179], using Gadolinium contrast. The study showed suscepti- bility underestimation by about 30% when the gadolinium balloons (6.7 cm 3 big) were imaged at 1.8 mm isotropic spatial resolution at 3T. The balloons had similar size of the gray matter ROIs investigated in this study. However, our experimental nding contradicts the prediction by Dong et al. The Gadolinium phantom study involved high susceptibility values, ranging from 0.41 ppm to 3.26 ppm, which were much higher than what is typically encountered in basal ganglia nuclei. Moreover, the usage of T1-shortening contrast agent produced high magnitude signal (more than 9 times higher than the background), whereas gray matter nuclei usually have lower magnitude signal than the background. Since the magnitude contrast can aect the extent of partial voluming, the phantom study might overestimate the eect of low spatial resolution by creating magnitude contrast that was unrealistic for gray matter ROIs. In recent literature on the repeatability of brain QSM, Lin. et al [180] and Santin. et al [181] showed within-site variance of about 5 ppb in deep gray matter nuclei; Deh. et al [182] showed a within-site variance above 12 ppb. In this study, we used 5 ppb as an acceptance threshold of QSM measurement for gray matter iron characterization. Repeatability study on QSM-based venous oxygen saturation quantication was scarce. In an unpublished study, we observed an inter-session variance of 2.3% when using QSM to measure venous oxygen saturation in healthy volunteers. Therefore, we used 2.3% as the acceptance threshold of measurement error. However, future study is needed to determine the clinical signicance of such measurement errors. For small cylindrical objects, our simulation showed remarkable susceptibility underestimation even at a voxel-to-diameter ratio of 4. At short echo times (e.g. 5 85 ms), partial voluming caused a constant relative estimation error. However, at long times (e.g. 15 ms or longer), intra-voxel phase aliasing caused additional suscepti- bility quantication error that was no longer a constant factor: the ratio of underes- timation varied depending on the true susceptibility. This is concerning particular for applications where the susceptibility of venous blood is intrinsically dierent across subjects. For example, anemic patients with low hemoglobin usually have lower venous blood susceptibility than healthy controls. Due to the proportional susceptibility underestimation, oxygen saturation measurement might produce sig- nicantly dierent values even if an anemic patient has the same venous oxygen saturation as a healthy subject. One limitation of this study is that simulations were only performed for a cer- tain selection of voxel sizes regardless of the geometry of ROI. Both the deep gray matter structures and the vessels have unequal aspect ratios, which indicates that the ROIs have dierent sensitivity to spatial resolution along dierent dimensions. Acquisition at lower resolution might be more tolerable along the longer dimension of the ROI. Future studies investigating asymmetric voxel sizes can help improve the accuracy of susceptibility quantication at low spatial resolution. Another lim- itation is the usage of ROI masks that were dened on the full-resolution reference datasets. For prospective low-resolution data acquisition, ROI denition might be aected by the blurriness of tissue boundary, causing additional error to suscepti- bility quantication. In conclusion, we evaluated the eect of low spatial resolution on the susceptibil- ity quantication of gray matter nuclei and medium- to small-size veins. Through down-sampling simulation on in-vivo datasets, we demonstrated that sub-millimeter resolution was unnecessary for QSM-based iron quantication in subcortical nuclei and oxygenation quantication in straight sagittal sinus. Numerical simulations re- vealed that signicant susceptibility underestimation and corresponding saturation overestimation existed for small cylindrical objects even when they were imaged at 86 sub-millimeter resolution. Special image processing and partial voluming model- ing might be required to obtain accurate oxygen saturation quantication in small veins. 87 200 300 400 500 600 Susceptibility Ref (ppb) -120 -100 -80 -60 -40 -20 0 20 40 -2.7 -12 6.2 200 300 400 500 600 -120 -100 -80 -60 -40 -20 0 20 40 1.0 -12 -26 200 300 400 500 600 -120 -100 -80 -60 -40 -20 0 20 40 3.4 -15 -33 200 300 400 500 600 -120 -100 -80 -60 -40 -20 0 20 40 -4.6 -35 -65 200 300 400 500 600 -120 -100 -80 -60 -40 -20 0 20 40 -8.6 -63 -120 Susceptibility Error (ppb) A. 1.0 x 1.0 x 2.0 B. 1.5 x 1.5 x 1.3 C. 1.5 x 1.5 x 2.0 D. 2.0 x 2.0 x 2.0 E. 2.5 x 2.5 x 2.5 50 60 70 80 S v O 2 Ref (%) -10 -5 0 5 10 50 60 70 80 -10 -5 0 5 10 50 60 70 80 -10 -5 0 5 10 50 60 70 80 -10 -5 0 5 10 50 60 70 80 -10 -5 0 5 10 0.20 -0.45 0.85 0.89 -0.04 1.8 S v O 2 Ref (%) S v O 2 Ref (%) 1.1 -0.22 2.3 S v O 2 Ref (%) 2.5 0.32 4.7 4.5 0.68 8.3 S v O 2 Ref (%) S v O 2 Error (%) Susceptibility Ref (ppb) Susceptibility Ref (ppb) Susceptibility Ref (ppb) Susceptibility Ref (ppb) Susceptibility Error (ppb) S v O 2 Error (%) Susceptibility Error (ppb) S v O 2 Error (%) Susceptibility Error (ppb) S v O 2 Error (%) Susceptibility Error (ppb) S v O 2 Error (%) Figure 4.4: Eect of spatial resolution on the accuracy of susceptibility and S v O 2 measurements in the straight sinus. Bland-Altman plots of susceptibility and S v O 2 measurement errors at dierent spatial resolution levels are shown in (A) to (E). Solid and dashed lines represent the mean and the 95% condence interval (i.e. mean 2.03 SD) of measurement error. Signicant measurement bias (p < 0:05, t-test) is labeled in red. Error of saturation measurement was 2.3% (saturation unit), when the voxel dimension along all three axes was 1:5 1:5 2:0 mm 3 . 88 Figure 4.5: Numerical simulation of susceptibility underestimation at low spatial resolution for a cylindrical ROI with physical diameter of 2 mm and orientation perpendicular to the main magnetic eld. Estimated susceptibility of the cylinder (A) and relative estimation error (B) are plotted against the true susceptibility. Solid lines represent the mean values of the 10 measurements with complex Gaussian noise. Simulations at three levels of spatial resolution (blue: 0:5 0:5 1:0, red: 0:25 0:25 0:5, yellow: 0:125 0:125 0:25 mm 3 ) and at four echo times (TE = 5, 10, 15 and 20 ms) are shown. Simulated susceptibility underestimation depends on not only the spatial resolution but also the echo time. Intra-voxel phase aliasing produces additional eect on susceptibility quantication (black arrows). 89 Chapter 5 Conclusion and ongoing work This dissertation contributes to the development, validation, and clinical translation of susceptibility-weighted MRI. Project outcomes can advance the evaluation of brain oxygenation and brain iron in sickle cell disease. 1) Susceptibility-based MR oximetry was validated in vivo with the clinical stan- dard for the rst time and compared with T2-based oximetry across a broad range of physiological states. With jugular vein catheterization as the true reference, sys- tematic biases in susceptibility-based and T2-based oximetry were revealed. Sources of variance in susceptibility-based and T2-based oximetry were quantitatively eval- uated. The results emphasize the limitations of absolute venous oxygen saturation measurements using these two techniques. 2) Brain iron quantication is another application of susceptibility-weighted MRI. Quantitative susceptibility mapping (QSM) enabled brain iron quantication with high sensitivity and spatial specicity. With QSM, brain iron overload in SCD patients was revealed for the rst time. Iron accumulation with age was accelerated in multiple subcortical nuclei in SCD. Increased brain iron correlated with severity of anemia and presence of silent stroke. By studying the accumulation and dis- tribution of brain iron in SCD, we may increase our understanding of progressive brain tissue damage and develop new therapeutic strategies. 90 3) The eect of spatial resolution on tissue susceptibility quantication was evaluated. Based on down-sampling simulations of in-vivo datasets, error bounds were provided on susceptibility measurement at low spatial resolution. The results showed that sub-millimeter resolution was unnecessary for accurate susceptibility measurement in subcortical nuclei, indicating the potential to shorten scan time by simply lowering spatial resolution. QSM-based venous oxygen saturation measure- ment in straight sagittal sinus also produced acceptable measurement with one- millimeter resolution. In comparison, signicant susceptibility underestimation of small veins existed with sub-millimeter resolution. The results indicate practical guidelines on the choice of spatial resolution in clinical settings where scan time is limited. Background eld is one of the biggest confounders in susceptibility-based MR oximetry. Current implementations of background eld estimation including low spatial order tting [112], spherical harmonic ltering [82], and dipole eld pro- jection [71] all face challenges at the superior sagittal sinus, which is the biggest draining vein of the brain and therefore bears signicant clinical interest. In the fu- ture, modeling the background eld with subject-specic susceptibility models [183] and prior knowledge of scanner shimming can improve accuracy of susceptibility- based oximetry. T2-based oximetry is used for a wide range of clinical studies, and it is imperative to consider the systematic bias introduced by T2-Hct-saturation calibration. Existing calibration models were derived in vitro using static blood with xed gas conditions. In the future, calibration for T2-based oximetry should be improved by incorporating blood ow and blood gas condition. In-vivo calibra- tion may be plausible using a gas control system such as RespirAct [184]. With the end-tidal O 2 and CO 2 strictly controlled and measured by RespirAct, the T2 of cerebral arterial blood measured by MRI can be calibrated with the oxygen saturation measured by pulse oximetry. 91 Multiple cerebrovascular conditions can potentially contribute to increased brain iron deposition in SCD patients. In our observation, the dierence of brain iron be- tween SCD patients and controls were more apparent in older subjects (>25 years). The small sample size of old patient subjects limited our statistical power to analyze the correlates of brain iron abnormality in SCD patients. In the future, studies over older age ranges are required to investigate the potential linkages among brain iron overload, chronic hypoxia, and brain tissue damage in SCD patients. Furthermore, the inclusion of non-SCD anemia patients may help discriminate the physiological factors of sickle cell disease and chronic anemia on brain iron deposition. Lastly, it is important to investigate the neurocognitive correlation with brain iron given that SCD is associated with progressive neurocognitive impairment and brain iron overload can contribute to neurodegeneration. If a correlation exists, this knowl- edge would be critical for developing treatment plans such as iron chelation therapy to eectively improve neurocognitive function. Figure 5.1: (a) Susceptibility measurement of internal cerebral vein as a function of hematocrit (%). (b) Compared with healthy controls, venous oxygen saturation of internal cerebral vein is signicantly lower (p< 0:05) in both SCD and non-SCD anemia patients. Mean venous oxygen saturation of internal cerebral vein in the three groups: CTL = 73.9%, ACTL = 73.6% and SCD = 69.3%. ACTL: non- SCD anemia controls (pink dots), CTL: healthy controls (green dots), and SCD: sickle-cell disease patients (red dots). Boxes represent 95% condence interval of the mean in each group. Statistical signicance is denoted as **. 92 For QSM-based susceptibility quantication in subcortical nuclei, improvement of scan eciency with low-resolution acquisition needs to be evaluated prospec- tively. Inevitable susceptibility underestimation might make QSM unsuitable for venous oxygen saturation measurement in small veins. Figure 5.1 plots susceptibil- ity of the internal cerebral veins as a function of hematocrit in 11 healthy controls and 23 anemia patients (16 SCD patients and 7 non-SCD anemia patients). It was obvious that anemia patients have lower venous blood susceptibility due to low hematocrit. After conversion of venous blood susceptibility to oxygen saturation, a group dierence of venous oxygen saturation appears between healthy controls and anemia patients. The observed group dierence could be induced by physiol- ogy. However, systematic bias must be evaluated before making any physiological interpretations because susceptibility underestimation due to low spatial resolution was more remarkable for higher susceptibility values (Chapter 4). In the future, susceptibility of small vessels may be quantied with specialized methods such as CISSCO (Complex Image Summation around a Spherical or a Cylindrical Object) [185]. Magnitude information can also be incorporated to resolve the partial vo- luming eect [186]. The beauty of susceptibility contrast is its simple linear indication of biological parameters. By providing a direct quantication of tissue magnetism, susceptibility- weighted MRI makes a unique tool to study the brain of sickle cell disease. 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Abstract (if available)

Abstract Sickle cell disease (SCD) is a genetic disorder characterized with abnormal hemoglobin that polymerizes upon deoxygenation, creating rigid, sickle-shaped red blood cells. Recurrent red blood cell sickling causes anemia and vasculopathy, which have the most devastating consequences in the brain. Silent cerebral infarction (SCI) is a common and progressive problem in SCD and is linked to high stroke risks and neurocognitive deficits. However, the prediction and pathogenesis of SCI is still obscure. This thesis aims to develop a brain oxygenation marker to predict SCI and to investigate brain iron deposition in its correlation with SCD and SCI. ❧ Susceptibility-weighted magnetic resonance imaging (MRI) provides noninvasive quantification of the magnetic property of brain tissue, which can be exploited for the assessment of brain oxygenation and brain iron deposition in SCD. Cerebral venous oxygen saturation measurement using susceptibility-weighted MRI has the advantages of model simplicity and calibration exemption. However, the technique has seldom been validated in a controlled manner under a broad range of physiological states. In this thesis, I cross-validated susceptibility-based oximetry (SBO) with both the clinical gold standard (jugular vein catheterization) and a relaxation-based oximetry (RBO) technique widely used in SCD literature. Systematic bias between SBO and RBO was revealed and analyzed. Error bonds of SBO and RBO were placed for the first time based on the comparison with the clinical standard. ❧ Brain iron has been shown to increase with recurrent ischemic-reperfusion injuries, chronic hypoxia and microvasculature damage, which are common conditions in SCD. As a consequence, excessive brain iron could potentially aggravate white matter damage and accelerate neurodegeneration. In the second part of this thesis, susceptibility-weighted MRI was applied to measure the brain iron in SCD patients. Increased brain iron accumulation in multiple subcortical nuclei was observed in SCD patients. Iron concentration in deep gray matter demonstrated correlation with severity of anemia and the presence of SCI. ❧ Given the potential clinical translation of susceptibility-weighted MRI, practical consideration on the trade-off between scan time and spatial resolution becomes important, especially in SCD pediatric imaging. The third part of the thesis investigated the effect of spatial resolution on susceptibility-based brain oxygenation and brain iron quantification. Susceptibility quantification errors due to low spatial resolution were bounded based on both simulation and in-vivo data. Practical guidelines on shortening scan time by lowering spatial resolution were provided.

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Creator Miao, Xin (author)

Core Title Susceptibility-weighted MRI for the evaluation of brain oxygenation and brain iron in sickle cell disease

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 01/18/2019

Defense Date 10/23/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag brain iron,brain oxygenation,MRI,OAI-PMH Harvest,quantitative susceptibility mapping,sickle cell disease,susceptibility-based oximetry

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nayak, Krishna S. (committee chair), Wood, John C. (committee chair), Coates, Thomas D. (committee member), Khoo, Michael Chee-Kuan (committee member)

Creator Email xinm@usc.edu,xinmiao1990@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-115336

Unique identifier UC11675380

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Legacy Identifier etd-MiaoXin-7023.pdf

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