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Improved contrast in ultrasound imaging using dual apodization with cross-correlation
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Improved contrast in ultrasound imaging using dual apodization with cross-correlation
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IMPROVED CONTRAST IN ULTRASOUND IMAGING USING DUAL APODIZATION WITH CROSS-CORRELATION by Chi Hyung Seo A Dissertation Presented to the FACULTY OF THE VITERBI SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (BIOMEDICAL ENGINEERING) December 2008 Copyright 2008 Chi Hyung Seo ii Acknowledgments There are so many people I am grateful for and I wanted to take the time to write the acknowledgment in a way that they deserve and that expresses my most sincere feelings. First and foremost, I would like to thank my advisor, Dr. Jesse Yen for his time, patience, teachings, and supervision through this process. From the very first wavelet and a slab of PZT to the finish line, I am very grateful that he has been there to guide me. I hope I was smart enough to pick some of his wisdom he let fall in my direction. I would also like to thank all the members of my committee for their ideas and support. Special thanks to Jon Cannata and Jay Williams in the Ultrasonic Transducer Resource Center for help with transducer fabrication and Changhong Hu for PCB design and layout. Also thank you, David, for your help with transducer measurements. I could not have gone through this journey at USC without my family. Dad, thanks for always believing in me and praying for me, and for instilling in me a love of learning. You spared no effort to provide me with the best education possible, and for that I am eternally grateful. And Miguel, my best friend and husband, you have been so loving and patient with me. Thank you for teaching me to love the ocean and the "waves". Aren’t you glad that I am not building an "alien probe"? I also want to acknowledge some of the people who are no longer with us. Thanks to Lord Rayleigh for formulating sound wave as a mathematical equation, forming the basis of future practical work in acoustics. iii Thanks to Pierre Curie and Jacques Curie for discovering the piezo-electric effect. Thanks to Sir Arthur Clarke and Gene Roddenberry, for inspiring all the Geeks in the world and proving science is cool! .. and Mom, hope you are proud of me. iv Table of Contents Acknowledgments ii List of Tables vi List of Figures vii Abstract xi Chapter 1: Introduction 1 1.1 Background 1 1.2 Hypothesis 2 1.3 Summary of Chapters 3 Chapter 2: Medical Ultrasound 5 Chapter 3: Dual apodization with cross-correlation 10 3.1 Introduction 10 3.2 Designs 12 3.2.1 Apodization Scheme 1: Uniform and Hanning 15 3.2.2 Apodization Scheme 2: Common midpoint 17 3.2.3 Apodization Scheme 3: Randomly selected aperture 18 3.2.4 Apodization Scheme 4: Alternating 19 3.3 Methods 20 3.4 Results 23 3.4.1 Point target simulation 23 3.4.2 Cyst simulation 27 3.4.3 Cyst experiment 29 3.5 Simulation with 40 MHz quantization 33 3.6 Discussion 36 Chapter 4: Evaluating the robustness of DAX 38 4.1 Introduction 38 4.2 Effect of cross-correlation method on the DAX algorithm 42 4.3 DAX with filtering of weighting coefficients 45 4.4 Methods 46 4.4.1 Simulation parameters 48 4.4.2 Aberration Characterization 49 4.4.3 Experimental setup 51 4.5 Simulation Results 53 4.5.1 Point target simulation in the presence of noise 53 4.5.2. Cyst simulation in the presence of noise 55 v 4.5.3. Point target simulation in the presence of phase aberration 57 4.5.4. Single cyst simulation with Dynamic DAX 59 4.5.5 Multiple cyst simulation with Dynamic DAX 63 4.5.6 Multiple Cyst simulation in the presence of phase aberration 66 4.6 Phantom Experiment Results 69 4.6.1 Cyst experiment in the presence of noise 69 4.6.2 Cyst experiment with pig skin and fat layer 71 4.7 Animal Experiment Results 75 4.7.1 DAX weighting function 75 4.7.2 Excised animal tissue and animal experiments in situ 78 4.8 Discussion 82 Chapter 5: Applications to 3-D imaging 83 5.1 Introduction 83 5.2 Transducer Design 87 5.3 Methods 91 5.3.1 Array fabrication 91 5.3.2 Measurements 93 5.3.3 Imaging Experiments 94 5.3.4 DAX processing 96 5.4 Experimental Results 97 5.5 Discussion 107 Chapter 6: Discussion and future work 110 6.1 Applications to emerging ultrasound technology 111 6.1.1 Real-time 3-D ultrasound 112 6.1.2 High frame rate imaging 112 6.2 Applications to ultrasound systems with reduced receive channels 114 6.3 in-vivo experiments 116 6.4 Low contrast targets 116 Bibliography 118 Appendix A: C++ code for data acquisition with Ultrasonix 124 Appendix B: DAX processing in MATLAB 125 vi List of Tables Table 3.1. 1 × 128 Linear Array and Imaging Parameters 21 Table 3.2. Comparison of Beamwidths and Clutter Levels of the four designs 26 Table 3.3. CNR values of the four designs 35 Table 4.1. Cross-correlation method and size vs CNR improvement 43 Table 4.2. 1 × 128 Linear Array and Imaging Parameters 49 Table 4.3. CNR values with different alternating patterns and dynamic DAX 61 Table 4.4. Dynamic DAX sequence for different focal depths and f-numbers 62 Table 4.5. CNR values of three different sized cysts using dynamic DAX 65 Table 4.6. Experimental CNR values in the presence of phase aberration 74 Table 4.7. Experimental CNR values of the sheep left atrium 80 Table 4.8. Experimental CNR values of the sheep right atrium 80 Table 4.9. Experimental CNR values of the pig carotid artery 82 Table 5.1. Experimental CNR values of the cylindrical cyst 107 Table 6.1. CNR values from a Field II simulation results using a 3 mm anechoic cyst with receive beamforming only 113 Table 6.2. Experimental CNR values of a 3 mm anechoic cyst using fewer receive channels 116 vii List of Figures Figure 2.1. B-mode ultrasound scan using a linear array 5 Figure 2.2. Ultrasonic arrays and their fields of view 7 Figure 2.3. Schematic of standard delay and sum beamforming 8 Figure 2.4. An example of a breast cyst and an Echocardiogram 9 Figure 3.1. General system block diagram for dual apodization with cross-correlation (DAX) 14 Figure 3.2. Uniform and Hanning weighted apertures in continuous wave mode 16 Figure 3.3. Effective apertures of four DAX algorithms 17 Figure 3.4. Point Spread Functions comparing four DAX schemes with standard beamformed data 25 Figure 3.5. RF data in the clutter region 26 Figure 3.6. Cyst simulations with an anechoic region of 3 mm in diameter 29 Figure 3.7. Cyst experiment with an anechoic region of 3 mm in diameter 30 Figure 3.8. Experimental RF data in cyst and speckle region 32 Figure 3.9. Weighting matrix 33 Figure 3.10. Point Spread Functions with 40 MHz quantization 34 Figure 3.11. Cyst simulation with 40 MHz quantization 35 Figure 4.1. CNR vs correlation method 44 Figure 4.2. Weighting matrix with filtering 46 Figure 4.3. System block diagram for the DAX alternating pattern 48 Figure 4.4. Aberration profiles 51 Figure 4.5. Lateral Beamplots with 35 dB, 25 dB and 15 dB SNR 54 viii Figure 4.6. The mean beamwidth with 35 dB, 25 dB and 15 dB SNR 54 Figure 4.7. 3 mm diameter cyst simulations with 35 dB, 25 dB and 15 dB SNR 56 Figure 4.8. Mean CNR values with 35 dB, 25 dB and 15 dB SNR 56 Figure 4.9. Lateral beamplots in the presence aberration 58 Figure 4.10. The mean beamwidth in the presence aberration 59 Figure 4.11. Simulated cyst image using different alternating patterns and dynamic DAX 60 Figure 4.12. Grating lobe magnitude vs receive focus 63 Figure 4.13. Simulated multiple cyst images using standard beamformng with uniform apodization and dynamic DAX 65 Figure 4.14. Simulated multiple cyst images in the presence aberration 68 Figure 4.15. The mean CNR of five realizations in the presence aberration 69 Figure 4.16. Experimental cyst images with different system SNRs 70 Figure 4.17. Mean CNR values with different system SNRs 71 Figure 4.18. Experimental cyst images with no aberrator 72 Figure 4.19. Experimental cyst images in the presence of a skin layer aberration of 3 mm in thickness 73 Figure 4.20. Experimental cyst images in the presence of a fat/muscle layer aberration of 4 mm in thickness 73 Figure 4.21. Experimental cyst images in the presence of a thick muscle layer aberration of 11 mm in thickness 74 Figure 4.22. Several illustrative examples of proposed weightings as function of cross-correlation coefficients 77 Figure 4.23. Image of a dissected sheep heart 78 Figure 4.24. Weighting function profile as a function of the cross-correlation coefficient and depth 79 ix Figure 4.25. Left atrium of a sheep 79 Figure 4.26. Right atrium of a sheep 80 Figure 4.27. Weighting function profile as a function of the cross-correlation coefficient and depth 81 Figure 4.28. Carotid artery of a female pig 82 Figure 5.1. Row-column addressing scheme 87 Figure 5.2. Transmit and Receive Beamforming for 3-D rectilinear imaging 88 Figure 5.3. Modified Tx/Rx circuit 89 Figure 5.4. Simulated beamplots of the row-column transducer 90 Figure 5.5. Two single layer flexible circuits attached to perpendicular sides of the transducer 92 Figure 5.6. Linear weighing function 97 Figure 5.7. Photograph of the finished 256 × 256 2-D array transducer 98 Figure 5.8. Experimental pulse-echo using modified Tx/Rx circuit 99 Figure 5.9. Experimental and simulated electrical impedance 100 Figure 5.10. Experimental and simulated pulse-echo 101 Figure 5.11. Experimental axial wire target images with short axis of the wires positioned in azimuth direction 102 Figure 5.12. Experimental axial wire target images with short axis of the wires positioned in elevation direction 103 Figure 5.13. Lateral wire target response 104 Figure 5.14. Experimental 8 mm anechoic cyst images with short axis of the cyst positioned in azimuth direction 105 Figure 5.15. Experimental 8 mm anechoic cyst images with short axis of the cyst positioned in elevation direction 106 Figure 5.16. Experimental 10 mm anechoic spherical cyst images 107 x Figure 6.1. Field II simulation results using a 3 mm anechoic cyst with receive beamforming only 113 Figure 6.2.Later beamplots with 4 λ pitch 115 Figure 6.3. Experimental results using a 3 mm anechoic cyst with reduced receive channels 115 xi Abstract This dissertation work introduces a novel sidelobe and clutter suppression method in ultrasound imaging called Dual Apodization with Cross-correlation or DAX. DAX dramatically improves the contrast-to-noise ratio (CNR) allowing for easier visualization of anechoic cysts and blood vessels. This technique uses dual apodization or weighting strategies that are effective in removing or minimizing clutter and efficient in terms of computational load and hardware/software needs. This dual apodization allows us to determine the amount of mainlobe versus clutter contribution in a signal by cross- correlating RF data acquired from two apodization functions. Simulation results using a 128 element 5 MHz linear array show an improvement in CNR of 139 % compared to standard beamformed data with uniform apodization in a 3 mm diameter anechoic cylindrical cyst. Experimental CNR using a tissue-mimicking phantom with the same sized cyst shows an improvement of 123 % in a DAX processed image. However, due to the random nature of speckle, artifactual black spots may arise with DAX-processed images. I present several methods to optimize the DAX algorithm. I evaluate the robustness of the optimized DAX in the presence of phase aberration and noise. Simulation results using a 5 MHz 128 element linear array are presented using optimized DAX with aberrator strengths ranging from 25 ns RMS to 45 ns RMS with correlation lengths of 3 and 5 mm. When simulating a 3 mm diameter anechoic cyst, at least 100 % improvement in CNR compared to standard beamforming is seen using optimized DAX except in the most severe case. Aberrating layers of pig skin, fat, and muscle were used experimentally. Simulation and experimental results are also presented xii using optimized DAX in the presence of noise. With a system signal-to-noise ratio (SNR) of at least 15 dB, we have a CNR improvement of over 100 % compared to standard beamforming. An uncut whole sheep heart was imaged to assess the optimized DAX performance with excised animal tissues. The experimental result shows that the optimized DAX improves the visibility of a target with a CNR improvement of at least 56 %. DAX was also able to improve contrast limited applications such as 3-D ultrasound using 2-D array with Row-column addressing. These types of arrays have 1-way focusing thus increasing side lobe level compared to conventional linear arrays with 2-way focusing. Therefore other post processing and filtering techniques in addition to beam steering and beam focusing are needed for image improvement. The CNR improvement utsing the DAX algorithm was at least 55 %. This work shows that optimized DAX is able to reliably improve contrast-to-noise ratio. 1 Chapter 1: Introduction 1.1 Background Virtually every pregnant woman in the world today will have her fetus clinically evaluated with medical ultrasonography. Ultrasound images of the heart are used to examine almost anyone suffering from chest pain. In many parts of the body, suspected tumors are routinely scanned with ultrasound. This widespread use is evidence of the unique advantages offered by ultrasound. Ultrasound not only complements the more traditional diagnostic imaging technologies such as magnetic resonance imaging (MRI), positron emission tomography (PET), and X-rays but also possesses unique characteristics that are advantageous. More specifically, 1) acoustic radiation is nonionizing and produces few or no side effects, 2) it is less expensive than imaging modalities of similar capabilities, 3) it can produce images in real time, with 30 frames/second or more, (4) it has a resolution in the sub-millimeter range for the frequencies being clinically used today (2.5 MHz - 15 MHz), (5) it can yield blood flow information, and (6) it is portable and thus can be easily transported to the bedside of a patient (Shung 2005). Even though ultrasound has been used to image the human body for at least 50 years and is one of the most widely used diagnostic tools in modern medicine, side lobes or clutter inherent in ultrasound imaging are undesirable side effects since they degrade image quality by lowering CNR and the detectability of small targets. Improving the contrast of ultrasound has many clinically significant applications. In breast ultrasound, the main purpose is to differentiate solid and cystic masses (Bassett and Butler 1991). 2 Simple anechoic cysts with fill-in caused by multiple scattering, reverberations and clutter can be misclassified as malignant lesions. Levels of fill-in are increased in the presence of aberrations caused by intermittent layers of fat and tissue. Delineation of carcinoma may also be improved with better signal processing methods that improve contrast. Similar problems arise when imaging other soft tissue. For hepatic imaging, visualization of cystic liver lesions and dilated bile ducts can be improved (Wu et al. 1992). The visualization of prostate cancer may be improved since prostate cancer is usually hypoechoic (Lee et al. 1989). One way to improve CNR is to reduce sidelobe and clutter levels by applying a weighting or shaping function such as a Hanning or Hamming apodization across the transmit and receive apertures. These types of weighting functions are called linear apodization functions since the same weighting is applied to the aperture independent of depth or of imaging line. As a trade-off, they lower the sidelobes at the expense of worse mainlobe lateral resolution. To avoid making this trade-off, there have been several publications in nonlinear sidelobe suppression methods which aim for little or no loss in mainlobe resolution while achieving low clutter levels commonly associated with apodization (Guenther and Walker 2007, Wang 2002, Stankwitz et al. 1995). 1.2 Hypothesis My hypothesis is that an ideal contrast improvement method can be developed which would greatly improve contrast such that lesions are easily visualized without significantly increasing computational complexity, worsening lateral and/or temporal 3 resolution. I present a target-dependent clutter suppression method using pairs of apodization functions. By using certain pairs of apodization functions, we can pass mainlobe signals and attenuate clutter signals using normalized cross-correlation coefficients of RF signals in the axial direction. The amount of attenuation is proportional to the amount of clutter in the signal. A target-dependent weighting matrix is created that will be multiplied to the standard beamformed image. This technique can be adapted to other contrast limited ultrasound imaging with little or no modification. 1.3 Summary of Chapters Chapter 2 describes fundamental ultrasound imaging and transducer concepts that are used throughout the rest of the thesis. Chapter 3 introduces the dual apodization with cross-correlation or DAX algorithm. Four pairs of apodization functions are described. Simulation results are presented using the prescribed four sets of DAX algorithms. They are compared in terms of beamwidth, sidelobe and clutter level using point spread functions and in terms of CNR with an anechoic target simulation. Next, I present experimental results using four sets of DAX algorithms. A 5 MHz 128-element linear probe is used to collect RF signals from a cylindrical lesion phantom containing 3 mm anechoic cyst. The results are compared qualitatively first, then quantitatively in terms of CNR values. Typically, in an experimental setting, an analog RF signal is converted into digitized echo signal using analog to digital converter (ADC) with a sampling frequency of 40-60 MHz. Therefore, another set of simulations were done with 40 MHz sampling and 25 ns delay quantization 4 to model my experimental setup. This introduces delay quantization error and gives us a better understanding of how DAX performs in experimental settings. These simulations also explained some of the discrepancies between the simulation with 200 MHz sampling and experimental results. Chapter 4 tests the robustness of this algorithm in a presence of phase aberration and noise. Several methods to optimize the DAX are presented. These factors include cross-correlation method and parameters, filtering of the cross-correlation coefficients, weighting as a function of cross-correlation coefficient and using depth dependent DAX. Point target and cyst simulations were performed using known aberrators. Experimentally, a subcutaneous pig fat layer was placed between the transducer probe and the phantom to introduce phase aberration. Also, point target and cyst simulations were performed in the presence of -15 dB, -25 dB, and -35 dB random Gaussian noise. Experimentally, an excised sheep heart and a sacrificed pig carotid artery were imaged. Chapter 5 presents results for an application of DAX with 2-D array using row- column addressing. These types of arrays have 1-way focusing thus increasing side lobe level compared to conventional linear arrays with 2-way focusing. Therefore other post processing and filtering techniques in addition to beam steering and beam focusing are needed for image improvement. Chapter 6 describes the implications of this work for future research. This chapter examines other emerging and novel ultrasound or ultrasound-based imaging applications that are contrast limited. Preliminary results show that DAX could be successfully applied to high frame rate imaging and portable ultrasound with reduced receive channels. 5 Chapter 2: Medical Ultrasound The simplest method of obtaining an ultrasound image is the pulse-echo B-mode (brightness mode) scan (Figure 2.1), in which a focused source of pulsed ultrasound is translated parallel to the skin of the patient or rotated to achieve a sector scan. Figure 2.1. B-mode ultrasound scan using a linear array A coupling gel ensures better matching in terms of acoustic impedance between transducer and skin. When an ultrasonic wave travels through a biological medium, the interaction of the wave with inhomogeneities in the medium leads to absorption and scattering of the incident wave (Shung 2005). The total scattered wave is the sum of all waves scattered from within the medium. The received RF signals are filtered, envelope detected, and displayed forming the desired image. In modern clinical use, most current medical ultrasound imaging scanners form B- mode images using phased or linear arrays. These allow the ultrasound beam to be Skin Direction of electronic scanning Tissues Coupling gel 6 steered over a range of angles and focused at any depth without the need to physically move the transducer. 1-D linear arrays have a number of elements which are narrow in the azimuth direction and wide in the elevation direction. Figure 2.2 (a) shows a typical 1-D linear array and its field of view where line A is created using the on-axis or center subaperture, indicated by the gray shading, and line B is creating using an off-axis subaperture. The acoustic lens of a 1-D array focuses the beam at a single, predetermined depth. The beam is well focused in elevation at this depth, but diverges at depths away from the focus degrading image quality due to the increase in slice thickness. 2-D arrays, on the other hand, have equal focusing capability in both lateral directions (Figure 2.2 b), which make them capable of producing a thinner slice thickness since dynamic elevation focusing is possible. Line A is created using the on-axis or center subaperture, indicated by the gray shading, and line B is creating using an off-axis subaperture. Overall, 2-D arrays have advantages of higher speed, more reliability, and better elevational resolution through electronic focusing. A fully sampled 2-D array would have up to 256 x 256 = 65,536 elements. At this time, constructing such a large fully sampled 2-D array would be an unrealistic goal due to difficulty in fabricating such a large number of elements, high electric impedance of the small array elements and interconnection problems. Therefore there have been many publications with novel designs to overcome these problems (Yen et al. 2004, Yen and Smith 2004, Seo and Yen 2007, Jeong et al. 2007). One of them is using row-column addressing scheme which will be discussed in Chapter 5. 7 (a) (b) Figure 2.2 Ultrasonic arrays and their fields of view (a) 1-D linear array. (b) 2-D rectilinear array. In a typical diagnostic ultrasound system, an image line is created by a process of electronically focusing, also known as beamforming, an array of ultrasound elements. The standard method of beamforming, termed delay and sum beamforming, involves calculating distances between the array element locations and the focal point (Figure 2.3). Assuming an average sound velocity of 1540 m/s in tissue, time arrival differences can be calculated and proper delays can be applied to each element in the array to achieve good focusing. Delayed data from individual elements is then summed to form an image line. However the true speed of sound deviates from the assumed value by up to 10% in soft tissues and much more in bone (Goss et al. 1978). The issues of phase aberration will be further discussed in Chapter 4. 8 Figure 2.3. Schematic of standard delay and sum beamforming One striking feature of medical ultrasound images, as shown in Figure 2.4, is the granular appearance known as speckle. Speckle can be observed in any coherent imaging system when the target contains many random, subwavelength scatterers per resolution cell. The brightness of a single pixel in the image is determined by the vector sum of the contributing scatterers. Modeling this as a random walk in the complex plane (Goodman 1984), the central limit theorem predicts circular Gaussian statistics as the number of scatterers per resolution cell becomes large. The pixel intensities are thus Rayleigh distributed, making the background appear grainy. However, unlike the laser beam which is totally coherent, ultrasound beam is partially coherent and the speckle patterns contain useful diagnostic information and play an important role in aberration correction. The resolving power of an ultrasound scanner is not evaluated solely by its ability to identify closely spaced point targets. 9 For diagnostic purposes, it may be more important to be able to pick out small, anechoic scatter-free regions surrounded by speckle. Thus, low side lobe and clutter level is at least as important as a narrow main lobe width. (a) (b) Figure 2.4. An example of a (a) breast cyst (Stavros 2004), and an (b) Echocardiogram (UCSD medical center) 10 Chapter 3: Dual apodization with cross-correlation 3.1 Introduction The ultimate goal of beamforming is to focus ultrasound energy to one location only, but this is not truly achievable with standard delay and sum beamforming. Thus, ultrasound image contrast can be reduced due to off-axis sidelobes and clutter. These side lobes or clutter inherent in ultrasound imaging are undesirable side effects since they degrade image quality by lowering CNR and the detectability of small targets. One way to improve CNR is to apply a weighting or apodization function. There are plethora of apodization functions reported (Harris 1978). Windows such as Hanning, Kaiser, Blackman, Hamming are based on a trade-off between the window design parameters, which are the main lobe width, the total side lobe energy, and the peak side lobe level. These types of weighting functions are called linear apodization functions since the same weighting is applied to the aperture independent of depth or of imaging line. To avoid making this tradeoff there have been several publications in other types of side lobe suppression techniques including array pattern synthesis technique and nonlinear apoodization method which aim for little or no loss in main lobe resolution while achieving low clutter levels commonly associated with apodization (Guenther and Walker 2007, Wang 2002, Stankwitz et al. 1995). In recent work, Guenther and Walker (2007) developed optimal apodization functions using constrained least squares theory. This method creates apodization functions with the goal of limiting the energy of the point spread function (PSF) outside a certain area and maintaining a peak at the focus. A point target simulation was performed 11 using a linear array with 192 elements with 200 µm element pitch and a transmit frequency of 6.5 MHz. Using this method, a 5-10 dB reduction in sidelobe levels compared to a Hamming apodization was achieved. Wang (2002) used a comparator to select the minimum magnitude from two or more sets of data using various apodization methods, such as uniform, Hanning or Hamming. By taking the minimum magnitude on a pixel-by-pixel basis, this method preserves the mainlobe resolution of the uniformly apodized data and lowers sidelobes similar to a Hanning or Hamming apodized data. Stankwitz et al. (1995) developed a spatially variant nonlinear apodization (SVA) technique, which uses the lateral phase differences between Hanning and uniformly apodized data to distinguish between mainlobe and clutter signals. This is accomplished by taking advantage of the properties of raised-cosine weighting functions and finding the optimal apodization function on a pixel-by-pixel basis. An ideal contrast improvement method would greatly improve contrast such that lesions are easily visualized without significantly increasing computational complexity, worsening lateral and/or temporal resolution. This chapter introduces a target-dependent clutter suppression method using pairs of apodization functions. By using certain pairs of apodization functions, we can pass mainlobe signals and attenuate clutter signals using normalized cross-correlation coefficients of RF signals in the axial direction. The amount of attenuation is proportional to the amount of clutter in the signal. A target-dependent weighting matrix is created that will be multiplied to the standard beamformed image. 12 3.2 Designs Assuming linearity, any ultrasound echo signal can be thought of as the sum of two signals: one signal is the mainlobe contribution which is desired and one signal from the sidelobes, grating lobes, and other forms of clutter which reduces image contrast. The amount of mainlobe contribution and sidelobe contribution depends on two factors: 1) the ratio of the mainlobe amplitude to the sidelobe amplitude and 2) the strength of the scatterers within the mainlobe versus the strength of the scatterers in the clutter region. To improve contrast, one would like to remove or at least minimize contributions from clutter. Our approach to removing clutter is to distinguish the mainlobe dominated signals from clutter signals by developing two point spread functions using two different apodization functions. These two apodization functions give similar mainlobe signals and very different clutter patterns. Therefore, echoes from a target, such as speckle or a point target, which comprises primarily of mainlobe components will look similar to each other, but echoes from a target, such as a cyst, which are mainly clutter will appear different from each other. Signals from a target which consists of a comparable contribution from both mainlobe and clutter will be partially similar. The degree of similarity can be quantified using normalized cross-correlation (NCC) between the two signals RX1 and RX2 from two PSFs. Normalized cross- correlation is performed using segments of RF data along the axial direction at zero lag. The normalized cross-correlation coefficient ρ at zero lag is calculated for every sample and used as a target-dependent pixel-by-pixel weighting matrix, which passes mainlobe dominated signals and attenuates clutter dominated signals (3.1). The post beamformed 13 RF data is then multiplied by this weighting matrix. (3.1) In (3.1), index i indicates the i th sample in image line j. The total cross-correlation segment length is 2A+1 samples. Normalized cross-correlation coefficients range from -1 to 1. Two signals are identical if the cross-correlation coefficient is 1 and they are considered uncorrelated if the coefficient is near or below zero. Signals would be somewhat correlated if ρ is in between 0 and 1. In the proposed method, if the coefficient is greater than or equal to a set threshold value ε > 0, then the sample value will be multiplied by the cross-correlation coefficient. If the coefficient is less than the threshold value ε, the sample value is multiplied by the threshold value ε. This algorithm is called dual apodization with cross-correlation or DAX. A general system block diagram is shown in Figure 3.1. ∑ ∑ ∑ + − = + − = + − = = A i A i k A i A i k A i A i k j k RX j k RX j k RX j k RX j i 2 2 ) , ( 2 ) , ( 1 ) , ( 2 ) , ( 1 ) , ( ρ 14 Figure 3.1. General system block diagram for dual apodization with cross-correlation (DAX). Numbers indicate steps described in the text. RX1 and RX2 are two data sets created with two apodization functions. * The combined RF data can be obtained by taking the minimum magnitude of RX1 and RX2 or the sum of RX1 and RX2. In Figure 3.1, the delayed data is processed with two receive apodization functions to create beamformed RF data sets RX1 and RX2. RX1 and RX2 can be combined in different ways. One way to combine is through a minimum function as done in dual apodization described by Wang (2002) and Stankwitz et al. (1995). This min function is used to select the minimum magnitude at each sample between the two data sets. Another way to combine is to add them. This is the case when the two apodization functions are complementary shown later in this section. Simply adding the two data sets from the complementary apodization functions would give us the same data from a standard receive aperture. If the cross-correlation value is less than a threshold value ε, the value will be replaced with the set threshold value (3.2). This signal is considered to be mainly clutter and needs to be suppressed. Signals having a comparable mixture of mainlobe and clutter will receive a reduction in amplitude between ε and 1. The cross- Delayed RF data Apodization 2 Bandpass Filter Hilbert transform/ Log compression RX 1 RX 2 DAX RF data DAX applied image Apodization 1 NCC Thresholding Combine RF data * 4 2 5 6 7 3 1 15 correlation matrix is multiplied to the combined RF data (* in Figure. 3.1). (3.2) where ρ is calculated using (3.1). We investigated the performance of four pairs of apodization functions, where each pair has a well correlated mainlobe response and a different or uncorrelated sidelobe response. All methods use echo datasets formed from each apodization and calculate a weighting matrix by cross-correlating image pairs. All apodization pairs have the same goal of suppressing clutter levels, thus increasing CNR, while maintaining mainlobe resolution. 3.2.1 Apodization Scheme 1: Uniform and Hanning Motivated by Stankwitz (1995), my first choice is using a pair of apodization functions that are common in ultrasound imaging practice. An aperture with a uniform amplitude weighting or a rect apodization function gives a sinc function shaped beam. This will lead to sidelobes at -26 dB. The Hanning window, given in (3.3), is a special case of generalized raised cosine windows with n the element number, N the total number of elements in the aperture (Harris 1978). (3.3) DAX CC = ε, ρ < ε ρ, ρ >= ε )) 2 cos( 0 . 1 ( 5 . 0 ) ( π N n n w + = 16 With an apodization function smoother than uniform apodization such as Hanning apodization, the sidelobe level is lowered from -26 dB to -57 dB but has a larger -6 dB beamwidth compared to uniform weighting (Figure 3.2). Figure 3.2. Uniform and Hanning weighted apertures in continuous wave (CW) mode. We can circumvent this trade-off between mainlobe width and sidelobe level, by axially cross-correlating segments of RF data from the two data sets obtained using these two apodization methods. The RF signals in the sidelobes of the beamformed point target image of these two data sets are quite different, giving near zero or negative cross- correlation values. The cross-correlation coefficient at each image sample is calculated. After thresholding, this matrix becomes the weighting matrix which can be multiplied to the combined RF data at each sample. Figure 3.3 (a) shows two apertures where the first receive aperture has a uniform weighting, and where the second receive aperture has a Hanning apodization. 17 (a) (b) (c) (d) Figure 3.3. All algorithms use a common uniform transmit aperture. The lateral location of the focus is marked with the arrow. The interelement distance, or pitch, is one wavelength. Four pairs of receive apertures used with DAX, (a) Uniform and Hanning, (b) Common midpoint, (c) Random, and (d) Alternating pattern 3.2.2 Apodization Scheme 2: Common midpoint Borrowing concepts from common midpoint apertures (Haun et al. 2004, Li 1997), spatial compounding (Trahey et al. 1986, O'Donnell and Silverstein 1988, Dahl et al. 2005) and translating apertures algorithm (Walker 2001), the next pair of apodization functions to be investigated is two uniformly weighted apertures that have a fractional translation of the active subaperture. The speckle patterns obtained from the two apertures with a large number of common elements are still well correlated. This cross- correlation will decrease in the clutter region due to a steering of the sidelobes in opposite directions. The degree of steering or the amount of decorrelation will depend on the number of elements translated. This design is demonstrated first using a simple 1 × 8 linear array shown in Figure 3.3 (b). The main idea is that an equal amount of steering in opposite directions is RX1 RX2 RX1 RX2 RX1 RX2 RX1 RX2 18 purposely introduced. With a desired focused subaperture of 8 elements, only the first 6 elements or from channel 1 to 6 are activated for the first data set. This first image is a steered version of the standard beamformed image. Then, another set of data is acquired using the latter 6 elements, or from channel 3 to 8. The second image will also be a steered version of the standard beamformed image. The mainlobes will still be well cross- correlated with each other, but the sidelobes and the clutter portions are less correlated with each other. By calculating the cross-correlation coefficient at each image sample, this matrix becomes the “weighting factor” which can be multiplied to the minimum of the two images. For the simulation and experiment, we used a 64 element subaperture with an 8 element translation. With an 8 element translation or 14 % translation, we expect the speckle correlation obtained from the two apertures to be roughly 0.98 (Dahl et al. 2005). However, in the cystic region dominated by clutter and sidelobes, we expect the cross-correlation to be lower. 3.2.3 Apodization Scheme 3: Randomly selected aperture In this scheme, by randomly selecting the two receive apertures with no common elements, a similar mainlobe with quite different clutter can be obtained. Since the two receive apertures are sparse, high clutter levels are expected where the amplitude of the clutter will depend on the sparseness of each aperture (Davidsen et al. 1994). For the purpose of this paper, four different permutations were done in a point target simulation and the best random sparse aperture in terms of beamwidths and sidelobe level was chosen for subsequent cyst simulations and experiments. In Figure 3.3 (c), a simple 1 × 8 19 linear array is used to demonstrate the two receive apertures. Four random elements are selected to receive for the first data set. Then for the second data set, unused elements from the first case are used. The cross-correlation coefficient at each image sample is calculated to generate a matrix and this matrix becomes the weighting factor. This is multiplied to the sum of the two images which is the standard beamformed image with uniform receive apodization. 3.2.4 Apodization Scheme 4: Alternating In this scheme, the first receive aperture has alternating elements enabled. The second receive aperture will use the alternating elements that are not used in the first receive aperture. With these two apodizations, we purposely create grating lobes which are 180 º out of phase with each other. Then, by using cross-correlation we can distinguish between signals coming from a mainlobe and clutter signals. In our current scheme, signals with cross-correlation coefficients less than 0.001 are multiplied by 0.001 or reduced by 60 dB. Echoes with higher cross-correlation coefficients have more mainlobe signal and are multiplied by the cross-correlation coefficient. Figure 3.3 (d) is an illustration of a pair of receive apertures with a pitch of one wavelength λ. RX1 uses an alternating pattern of 2 elements on, 2 elements off. RX2 uses the opposite alternating pattern of 2 elements off, 2 elements on. These receive apertures are essentially sparse arrays with a four wavelength pitch. Thus, grating lobes are expected to be present in the PSF. The location of the nth grating lobe is given by 20 (3.4) where n is the nth grating lobe, λ is the ultrasound wavelength, and d is the interelement distance or pitch. The cross-correlation coefficient at each image sample is calculated to generate a matrix, and this matrix becomes the weighting factor. By summing data from these two receive apertures, we get the same data as from a uniformly weighted receive aperture. This RF data will then be weighted by the cross-correlation matrix. Instead of a 2-element alternating pattern as shown, any N-element alternating pattern can be used where N is less than half of the number of elements in the subaperture. The main difference between these configurations will be the location of the grating lobe. Increasing N will move the grating lobes closer to the mainlobe. 3.3 Methods I have performed computer simulations using Field II to generate lateral beamplots for all four designs (Jensen and Svendsen 1992). A 5 MHz Gaussian pulse with 50 % bandwidth was used as the transmit pulse and a delta function as the element impulse response. For a point target simulation, an RMS energy value was calculated from the received voltage trace. All RMS energy values were converted to decibels after normalizing to the maximum energy level. The transmit and receive focus was fixed at 30 mm for the point target simulation. Since there is rarely a point target in a clinical environment, we have also done a simulation using a cylindrical 3 mm diameter anechoic ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ = − d n n λ θ 1 sin 21 cyst located at 30 mm depth embedded in a 3-D phantom of scatterers. The parameters for the simulation are listed in Table 3.1. Parameter Value Number of elements in subaperture 64 Center Frequency 5 MHz Bandwidth 50 % Azimuthal element Pitch 300 µm Elevation Element Height 5 mm Sound speed 1540 m/s Transmit Focus 30 mm Lateral beam spacing (beamplot simulation) 30 um Lateral beam spacing (cyst) 150 um Receive focal delay step (cyst) 0.1 mm Table 3.1. 1 × 128 Linear Array and Imaging Parameters For the experimental setup, individual element RF signals were collected for off- line processing from an ATS spherical lesion phantom (ATS laboratories, Bridgeport, CT, Model 549) containing a 3 mm anechoic cyst using an Ultrasonix Sonix RP ultrasound system (Ultrasonix Medical Corporation, Richmond, BC, Canada) having 40 MHz sampling frequency. This system has great flexibility allowing the researcher to control parameters such as transmit aperture size, transmit frequency, receive aperture, filtering, and Time-Gain Compensation. In this experiment, a 128-element, 300 µm pitch, L14-5/38 linear array was used. A 1-cycle transmit pulse of 5 MHz and an f- 22 number = 1.5 was used. In receive, element data was collected and receive beamforming was done off-line using Matlab (The MathWorks, Inc. Natick, MA). Dynamic receive focusing was used with focal updates every 0.1 mm. The image line spacing is 150 µm. Data from each channel was collected 32 times and averaged to minimize effects of electronic noise. In an experimental setting as describe above, an analog RF signal is digitized with a sampling frequency of 40-60 MHz. Additional simulations were done with 40 MHz delay quantization in transmit and receive beamforming to model our experimental setup. This introduces delay quantization error and gives us a better understanding of how DAX performs on a commercially available system. All signals in the experiments are bandpass filtered using a 64-tap finite impulse response (FIR) bandpass filter with frequency range limited to the -6 dB bandwidth of the transducer. After the signals are bandpass filtered, delayed, apodized and summed to create RX1 and RX2, the two sets of data are cross-correlated. The cross-correlation value is sent to a thresholding operator. If the value is less than or equal to ε, or 0.001 in our case, then the value is replaced with 0.001. If it is greater than 0.001, then the value remains unchanged. A second filter, which has the same passband window as the first filter, might be required to reduce sharp discontinuities in images that might be caused by multiplication of the weighting matrix. The Hilbert transform is used for envelope detection, and all images are displayed on a log scale. 23 3.4 Results 3.4.1 Point target simulation Figure 3.4 shows simulated lateral beamplots using Field II of a standard transmit/receive beam with uniform weighting compared to the four DAX schemes. The beamplots of all four methods have mainlobe widths basically equal to the mainlobe of the uniform apodization. At the same time, clutter near the mainlobe has dropped dramatically down to below -100 dB for all four methods. The -6, -20, -40, and -60 dB beamwidths are listed in Table 3.2. The -6 and -20 dB beamwidths are similar for all cases. For the uniform-Hanning and common midpoint schemes, the -6 dB beamwidths are 0.40 and 0.35 respectively or 11 % and 24 % smaller compared to the standard beamformed case. For the uniform-Hanning case, only portions of the two mainlobes are well correlated. For the common midpoint scheme, the two beams are steered and the overlap of the two beams is smaller than in random or alternating pattern schemes. Thus, having a cross-correlation value of slightly less than 1 and by multiplying this value by the minimum of the two data sets, the mainlobe width or the -6 dB beamwidth is narrower than in standard beamformed case. The -40 dB and – 60 dB widths are also narrowest for uniform-Hanning and common midpoint schemes. The -6 dB beamwidths for the randomly selected aperture and the alternating pattern are the same as the beamwidth for the case of standard beamforming. Figure 3.5 shows the RF data inside the clutter and grating lobe regions for RX1 and RX2 for the four DAX schemes. It is interesting to note the effect of different apodizations on the clutter and grating lobe regions. For the uniform-Hanning 24 apodization scheme, we see the amplitude of a Hanning apodized receive aperture is about 30 dB lower than the amplitude of a uniformly apodized receive aperture. With the common midpoint scheme, the two RF data are shifted by about 1 wavelength with respect to each other. In the randomly selected aperture scheme, the two data are “mirrored” versions of each other giving a 180 º phase shift approximately. In the alternating pattern scheme, we also clearly see the two grating lobe regions are basically 180 º out of phase with respect to each other. Although perhaps counterintuitive, using a larger alternating pattern can result in a better beam with DAX since the grating lobes here are beneficial since they narrow the beam particularly down at the -40 to -60 dB level. Cross-correlating these two signals would yield a cross-correlation coefficient near -1 and therefore a reduction of 60 dB in magnitude. The weighting matrix will be applied to the sum of these data sets. 25 (a) (b) (c) (d) Figure 3.4. Point Spread Functions comparing four DAX schemes with standard beamformed data. The standard beamformed PSF is compared with (a) uniform-Hanning scheme, (b) common midpoint scheme, (c) random scheme, and (d) the alternating pattern scheme. -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard Randomly selected -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard 8-8 Alternating -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard Uniform-Hanning -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard Common midpoint 26 Standard Uniform- Hanning Common midpoint Randomly selected Alternating pattern -6 dB (mm) 0.46 0.40 0.35 0.46 0.45 -20 dB (mm) 0.80 0.89 0.79 0.81 0.79 -40 dB (mm) 2.67 0.99 1.00 1.89 2.05 -60 dB (mm) 8.58 1.08 1.92 2.12 2.20 Residual sidelobes Clutter <-80 <-60 <-60 <-100 Table 3.2. Comparison of Beamwidths and Clutter Levels of the four designs (a) (b) (c) (d) Figure 3.5. RF data in the clutter region of (a) Uniform-Hanning scheme (b) Common midpoint scheme (c) Randomly selected aperture scheme and (d) Alternating pattern scheme. 30.8 31 31.2 31.4 31.6 31.8 32 32.2 32.4 32.6 -4 -3 -2 -1 0 1 2 3 4 x 10 -3 Axial distance (mm) Normalized amplitude RF data in the grating lobe RX 1 RX 2 30.8 31 31.2 31.4 31.6 31.8 32 32.2 32.4 32.6 -4 -3 -2 -1 0 1 2 3 4 5 x 10 -4 Axial distance (mm) Normalized amplitude RF data in the clutter RX 1 RX 2 30.8 31 31.2 31.4 31.6 31.8 32 32.2 32.4 32.6 -5 -4 -3 -2 -1 0 1 2 3 4 5 x 10 -4 Axial distance (mm) Normalized amplitude RF data in the clutter RX 1 RX 2 30.8 31 31.2 31.4 31.6 31.8 32 32.2 32.4 32.6 -8 -6 -4 -2 0 2 4 6 8 10 x 10 -4 Axial distance (mm) Normalized amplitude RF data in the clutter RX 1 RX 2 27 3.4.2 Cyst simulation It is important to remember that the proposed algorithms are spatially varying and target-dependent. Therefore, although beamplots or PSFs are more intuitive, they are not exactly indicative of imaging performance for diffuse scatterers such as biological tissue. To further test the performance of these algorithms, Figure 3.6 shows simulated images of a 3 mm diameter anechoic cyst with standard beamforming with uniform apodization, Hanning apodization and the four DAX schemes. To quantify improvement, the CNR for each of the images was calculated. CNR is defined as the difference between the mean of the background and the cyst in dB divided by the standard deviation of the background in dB (O'Donnell and Flax 1988), (3.5) where is the mean of the target, is the mean of the background and is the standard deviation of the background. Signals coming from the speckle region are dominated by the mainlobe, thus giving a cross-correlation coefficient near 1. In the case of an anechoic cyst where the signal contribution from the mainlobe will be small, the sidelobes and grating lobes will be dominant giving a very low or negative cross- correlation value. The CNRs for the six images are 5.24, 6.85, 12.62, 12.92, 7.44, and 11.28 for standard beamforming with uniform apodization, Hanning apodization, uniform-Hanning, common midpoint, randomly selected and alternating pattern respectively. Regions used to calculate CNR are shown in the white and black rectangles b b t S S CNR σ − = t S b S b σ 28 for the target and background respectively. The figures are shown with 80 dB dynamic range. Qualitatively, the cyst using uniform weighting is most difficult to see (Figure 3.6. a). Using Hanning apodization, the cyst has a better contrast but the speckle size is larger due to a widened mainlobe (Figure 3.6. b). Using DAX processing, the cyst becomes more visible without affecting the mainlobe resolution (Figure 3.6. c-f). The uniform-Hanning approach shows a dark cyst with a well defined boundary. This approach gives the highest CNR when multiplying the cross-correlation matrix with Hanning apodized data. In fact, multiplying by the minimum of the two data sets lowered the CNR below 10. The common midpoint approach shows a darker cystic region but the left and right edges show clutter. The amplitude of the clutter region is around 60 dB below the peak signal in the image. The randomly selected aperture approach also shows a darker cyst with some clutter. The alternating pattern approach performs as well as uniform-Hanning apodization scheme. All of the DAX schemes create some dark “pits” in the speckle region due to the randomness of the speckle. Methods to reduce these artifacts will be discussed later. 29 (a) (b) (c) (d) (e) (f) Figure 3.6. Cyst simulations with an anechoic region of 3 mm in diameter (a) Standard beamforming with uniform apodization (b) Hanning apodization, (c) Uniform-Hanning (d) Common midpoint (e) Randomly selected (f) Alternating pattern. The CNR values are (a) 5.24, (b) 6.85 (c) 12.92, (d) 7.44, (e) 11.28, and (f) 12.62 3.4.3 Cyst experiment Figure 3.7 shows the result from the cyst experiment using the Ultrasonix Sonix RP system and ATS tissue-mimicking phantom containing a 3 mm diameter anechoic cyst. The images are displayed with a 55 dB dynamic range after delay and sum beamforming, digital bandpass filtering, envelope detection and log-compression. The target region is marked with a white rectangle and the background region is marked with a black rectangle in the first image. Qualitatively, the cyst using standard beamforming with uniform apodization is the most difficult to see (Figure 3.7. a). Using Hanning apodization, there is some improvement in 30 CNR, and the speckle size is larger due to a widened mainlobe (Figure 3.7. b). The uniform-Hanning, common midpoint, random all have some amount of “fill in”. The alternating pattern has the highest CNR at 11.64 compared to 5.23, 5.56, 7.02, 7.11, 11.39 for uniform, Hanning, uniform-Hanning, common midpoint, and random cases respectively. These CNR values are in very good agreement with the simulation results except for the Hanning apodization and uniform-Hanning scheme. This issue will be discussed in section 3.5. (a) (b) (c) (d) (e) (f) Figure 3.7 Experimental cyst images in a tissue-mimicking phantom. The cysts are 3 mm in diameter (a) Standard beamformed with uniform apodization (b) Hanning apodization (c) Uniform-Hanning (d) Common midpoint (e) Randomly selected (f) Alternating pattern. The CNR values are (a) 5.23, (b) 5.56, (c) 7.02, (d) 7.11, and (e) 11.39 (f) 11.64 31 Figure 3.8 shows experimental RF data from speckle region (left column) and inside the cyst (right column). In the speckle region, the waveforms from RX1 and RX2 are very similar yielding a cross-correlation coefficient near 1. For the cyst region, with uniform- Hanning scheme, the amplitude for Hanning apodized data (Figure 3.8. b. RX2) is smaller than uniformly apodized data (Figure 3.8. b. RX1). However, two sets of RF data are still correlated, and this fact does not agree with our point target and cyst simulation results. For the common midpoint scheme (Figure 3.8. d), the two RF data are shifted relative to each other, but not as dramatically as in the simulation. For the randomly selected aperture (Figure 3.8. f), and alternating pattern scheme (Figure 3.8. h), the waveforms appear nearly 180 ° out of phase resulting in negative cross-correlation coefficients. Note that graphs in the left column of Figure 3.8 are not on the same vertical scale as the graphs on the right column and that the echo magnitude inside the cyst is about 30 or 40 dB lower than the magnitude in the speckle region. Figure 3.9 shows the weighting matrices after the thresholding operation used for simulation and for the experiment using the DAX alternating pattern scheme. All cross- correlation values less than 0.001 were replaced with 0.001 to create the final weighting matrix. The cyst is clearly visible in the weighting matrix and the CNR values are 19.98 for simulation and 14.43 for experiment. Therefore, it may be possible to use these matrices as cross-correlation based images to locate a target, but this requires further investigation. 32 (a) (b) (c) (d) (e) (f) (g) (h) Figure 3.8. RF data in the (a) speckle with Uniform-Hanning scheme (b) cyst with Uniform-Hanning scheme (c) speckle with common midpoint scheme (d) cyst with common midpoint scheme (e) speckle with randomly selected aperture scheme (f) cyst with randomly selected aperture scheme (g) speckle with alternating pattern scheme (h) cyst with alternating scheme 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -1000 -800 -600 -400 -200 0 200 400 600 800 Axial distance (mm) Digitized echo amplitude RF data inside the cyst (experiment) RX1 RX2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 x 10 4 Axial distance (mm) Digitized echo amplitude RF data in the speckle region (experiment) RX 1 RX 2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 x 10 4 Axial distance (mm) Digitized echo amplitude RF data in the speckle region (experiment) RX1 RX2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -1.5 -1 -0.5 0 0.5 1 1.5 x 10 4 Axial distance (mm) Digitized echo amplitude RF data in the speckle region (experiment) RX 1 RX 2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -800 -600 -400 -200 0 200 400 600 800 Axial distance (mm) Digitized echo amplitude RF data inside the cyst (experiment) RX 1 RX 2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -1500 -1000 -500 0 500 1000 1500 Axial distance (mm) Digitized echo amplitude RF data inside the cyst (experiment) RX 1 RX 2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -1.5 -1 -0.5 0 0.5 1 1.5 x 10 4 Axial distance (mm) Digitized echo amplitude RF data in the speckle region (experiment) RX 1 RX 2 25.6 25.8 26 26.2 26.4 26.6 26.8 27 27.2 27.4 -800 -600 -400 -200 0 200 400 600 800 1000 Axial distance (mm) Digitized echo amplitude RF data inside the cyst (experiment) RX 1 RX 2 33 (a) (b) Figure 3.9. Weighting matrix used for a) simulation b) experiment. Color bar shows the range of cross-correlation coefficients. 3.5 Simulation with 40 MHz quantization The disparity between the CNRs of the simulated cyst and experimental cyst was further investigated with Field II simulations having 40 MHz quantization. The integrated lateral beamplots are shown in Figure 3.10 and a cyst simulation with 40 MHz quantization is shown in Figure 3.11. Using standard beamforming with uniform apodization, the anechoic cyst still shows some “fill in” due to clutter. The CNRs are 5.39, 6.45, 10.45, 7.34, 11.03, 12.53 for standard beamforming, Hanning apodization, uniform-Hanning, common-midpoint, randomly selected and alternating pattern respectively. The effect of quantization is most prominent in the uniform-Hanning scheme. This can be explained considering quantization error as essentially a focusing error. In the other three apodization schemes, some or all elements in the receive aperture are different. Therefore if there are any focusing or quantization errors, each aperture sees different error contributions which are poorly correlated. However in the uniform- Weighting matrix (Simulation) Lateral position (mm) Axial position (mm) -5 -4 -3 -2 -1 0 1 2 3 4 5 28 29 30 31 32 33 34 35 36 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 34 Hanning scheme, both apertures will be equally affected by any quantization errors introduced. These errors would be highly correlated. Table 3.3 summarizes the CNR values for two cyst simulations and experiment. (a) (b) (c) (d) Figure 3.10. Point Spread Functions comparing four DAX schemes with standard beamformed data with 40 MHz quantization. The standard beamformed PSF is compared with (a) uniform-Hanning scheme, (b) common midpoint scheme, (c) random scheme, and (d) the alternating pattern scheme. -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard Uniform-Hanning -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard Common midpoint -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard Randomly selected -6 -4 -2 0 2 4 6 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 Lateral position (mm) Amplitude (dB) Standard 8-8 Alternating 35 (a) (b) (c) (d) (e) (f) Figure 3.11 Cyst simulation with 40 MHz quantization (a) Standard beamformed with uniform apodization (b) Hanning apodization (c) Uniform-Hanning (d) Common midpoint (e) Randomly selected (f) Alternating pattern. The CNR values are (a) 5.39, (b) 6.45, (c) 10.45, (d) 7.34, (e) 11.03 and (f) 12.53 respectively. Standard Hanning Uniform- Hanning Common midpoint Randomly selected Alternating CNR (simulation) 5.27 6.92 12.92 7.44 11.28 12.62 CNR (experiment) 5.23 5.56 7.02 7.11 11.39 11.64 CNR (simulation with 40 MHz quantization) 5.39 6.45 10.45 7.34 11.03 12.53 Table 3.3: CNR values of the four designs 36 3.6 Discussion I have presented our Dual Apodization with Cross-correlation (DAX) technique that suppresses sidelobes and lowers clutter, thus improving CNR, without compromising spatial resolution in ultrasound imaging. The main idea behind this method is to use a pair of apodization schemes that are highly cross-correlated in the mainlobe but have low or negative cross-correlation in the sidelobe region. DAX uses two sets of beamformed data acquired with two different receive apertures and cross-correlates segments of RF data. This cross-correlation matrix serves as a pixel-by-pixel weighting function which will be multiplied to the minimum or to the sum of the two data sets. Theory and simulation were validated in ultrasound tissue-mimicking phantoms where contrast improvement in terms of CNR was 139 % in simulation and 123 % experimentally. Lateral and axial resolution are not sacrificed to improve CNR. The alternating pattern showed the highest CNR experimentally. This alternating pattern purposely creates two sets of grating lobes which are 180 º out of phase with respect to each other. While grating lobes have long been a potential source for clutter in ultrasound imaging, DAX uses gratings lobes to help distinguish between mainlobe and clutter signals. Occasionally, DAX will add artificial dark spots in the speckle region. In fact, the DAX algorithm slightly lowers the speckle SNR, defined as the ratio of mean to standard deviation of the scattered signal for fully developed speckle (Burckhardt 1978), by 4-11 %. The SNR in the speckle region before applying the DAX algorithm was 1.91. The SNR in the speckle region after the DAX algorithm was applied were 1.81, 1.70, 1.84 and 1.77 for Uniform-Hanning, Common midpoint, Random and Alternating pattern 37 respectively. In cystic regions, it may be possible that clutter signals will have a high cross-correlation coefficient. In this situation, minimal or no improvement in contrast will be seen. The occurrence of both of these artifacts could be minimized by several straightforward options. Using a moving average or median filter on the cross- correlation coefficients is one approach. Since this process is a smoothing of the weighting matrix, the speckle pattern is not smeared. We have also briefly investigated the effect of correlation window on the cyst. A longer correlation window produced a poorly delineated cyst but with fewer dark spots in the speckle region. If the window size was too small, the speckle had more pits due to greater variation in cross-correlation coefficients. Empirically, 20-30 samples, which is roughly two wavelengths, performed best in terms of CNR. Lastly, the threshold and weighting as a function of ρ could be adjusted. All of these methods may help eliminate dark spots but may also lower CNR. This will be investigated in future work. Preliminary attempts with 1-D lateral cross- correlation gave us a slightly lower CNR than using 1-D axial cross-correlation. 2D cross-correlation gave us a comparable improvement to 1D axial cross-correlation but with increased computational load. The methods to optimize DAX will be discussed in the next chapter. 38 Chapter 4: Evaluating the robustness of DAX 4.1. Introduction Ultrasound systems assume a nominal tissue sound speed of 1540 m/s for beamforming. However, different sound speeds in different tissues result in poor focusing of the beam since echoes do not arrive at the focus simultaneously. These effects, generally known as phase aberration, result in lower amplitude of the main lobe, a broadening of the main lobe, and increased clutter levels. There are two main models for aberrations which differ in the aberrator location. The near-field aberration model assumes that the aberrations that contribute most to image degradation occur right at the transducer surface. The aberrations are modeled entirely by changes in the arrival time of the signals at the face of the transducer. However, a more realistic model would incorporate the variations throughout the tissue. This distributed aberration model assumes the aberration varies in range through the imaging plane and is distributed throughout the medium. Many phase aberration correction algorithms are based on a near-field screen model. Arrival times for each of the elements are calculated based on the geometric relationship between the array elements and the receive focus. The arrival time errors are computed for each element and used to generate an aberration profile. This profile can be used to correct the aberration by adding compensating delays. Methods to improve image quality in the presence of phase aberration in medical ultrasound images of diffuse targets include cross-correlation of neighboring element data (Flax and O’Donnell 1988, O'Donnell and S. W. Flax 1988), maximization of mean speckle brightness (Nock et al. 39 1989, Zhao and Trahey 1991), and direct estimation using a k-space approach (Rachlin 1990, Li 1997, Li et al. 1997). After several iterations, these methods seek to converge to a resulting image that is equivalent to an image without phase aberration. In the nearest-neighbor cross-correlation method (NNCC) (Flax and O’Donnell 1988, O'Donnell and S. W. Flax 1988), phase aberration correction is based on cross-correlation measurements between neighboring elements to estimate the relative time shifts. These time shifts are integrated across the array to calculate improved focusing delays. Since the original transmit focus is degraded by uncompensated aberration, the procedure requires iteration. Nock et al. (1989) and Zhao and Trahey (1991) adjusted the element delays based on speckle brightness. Since a widening of the imaging point spread function caused by aberration decreases the average speckle brightness in the image (Nock et al. 1989), this method aims to improve image quality by sequentially adjusting the delay at each array element for maximum speckle brightness. Another approach to delay estimation uses the strong correlation between common midpoint signals when single array elements are used for transmitting and receiving. In their published algorithms, both Rachlin (1990) and Li (1997) perform cross-correlations of common- midpoint signals. This method uses the fact that transmitter and receiver elements spaced about the common midpoint of the array have similar spatial frequency responses, and a redundant estimate of the time delay at each element can be computed. Focusing imperfections reduce the coherence of the received signal and decrease CNR by raising side lobes and clutter. Another group of adaptive imaging methods do not attempt to estimate and correct for the focusing errors but instead minimize the 40 effects of phase aberration, namely the higher sidelobes. These groups include coherence factor (CF) (Hollman et al. 1999), generalized coherence factor (GCF) (Li and Li 2000, Wang et al. 2007) spatially variant apodization (SVA) (Stankwitz et al. 1995), parallel adaptive receive compensation algorithm (PARCA) (Li et al. 1993), and a modified version of PARCA, PARCA2 (Krishnan et al. 1998). The coherence factor is defined in the literature (Hollman et al. 1999) as: (4.1) where S(i) is the received signal at channel i and N is the total number of channels. A CF value of 1 indicates perfect coherence and a value of 0 means incoherence. Li expanded the idea of coherence factor to develop the generalized coherence factor (GCF) (Li and Li 2000). The GCF is calculated by first performing the Fourier Transform on channel data after receive delays have been applied. The GCF assumes that the low frequency component of the element domain spectrum corresponds to the coherent portion of the received data, and the high frequency component corresponds to the incoherent portion. The coherence factor matrix is calculated as the ratio of the spectral energy within a low frequency region to the total energy and is used as a pixel-by-pixel weighting of the image. In synthetic aperture radar (SAR), Stankwitz proposed a spatially variant nonlinear apodization technique, which uses the lateral phase differences between data from Hanning and uniform apodizations. This is accomplished by taking advantage of the properties of raised-cosine weighting functions to find the optimal apodization function ∑ ∑ − = − = = 1 0 2 2 1 0 ) ( ) ( N i N i i S N i S CF 41 on a pixel-by-pixel basis (Stankwitz et al. 1995). Another well known adaptive imaging method is parallel adaptive receive compensation algorithm (Li et al. 1993). Using total least squares (TLS), this method works well with a point target, but the improvement is uncertain with speckle targets. A modified version, PARCA2, was also proposed where the parallel beam formation is approximated by Fourier transform of the aperture data and an iterative scheme is used to simplify the calculation in PARCA (Krishnan et al. 1998). Since DAX is adaptive or target-dependent, it can be considered to fall under this latter group. In this chapter, I present several options to optimize DAX. These factors include cross-correlation method and parameters, filtering of the cross-correlation coefficients, weighting as a function of cross-correlation coefficient and using depth dependent weighting functions. I describe results from computer simulations and phantom experiments to evaluate optimized DAX performance in the presence of phase aberration and noise. Simulation and experimental results using a 5 MHz 128 element linear array show that DAX is able to lower sidelobe levels and significantly reduce clutter levels in the presence of phase aberration. Experimentally, a subcutaneous pig fat layer was interposed between the ultrasound transducer and phantom to emulate the effects of phase aberration. CNRs are calculated to quantify improvements and identify the limitations of DAX. To examine the effects of electronic noise, simulation and experimental results are presented with 35 dB, 25 dB and 15 dB system SNRs. Lastly, excised animal tissue and a carotid artery of a sacrificed pig were imaged to further assess the optimized DAX performance. 42 4.2 Effect of cross-correlation method on the DAX algorithm I investigated the effect of different cross-correlation methods and cross- correlation segment size on contrast-to-noise ratio (CNR) using the DAX algorithm. For 1-D axial cross-correlation, axial segments of RF data from the two beamformed RF data sets are cross-correlated to determine the amount of mainlobe dominated signal and to create a weighting matrix (4.2). For 1-D lateral cross-correlation, lateral segments of RF data from the two beamformed RF data sets are cross-correlated (4.3). For 2-D cross- correlation, 2-D kernels of RF data from the two beamformed RF data sets are cross- correlated (4.4). The post beamformed RF data is then multiplied by one of these weighting matrices. (4.2) (4.3) (4.4) ∑ ∑ ∑ ∑ ∑ ∑ + − = + − = + − = + − = + − = + − = = A i A i k B j B j l A i A i k B j B j l A i A i k B j B j l j k RX j k RX j k RX j k RX j i 2 2 ) , ( 2 ) , ( 1 ) , ( 2 ) , ( 1 ) , ( ρ ∑ ∑ ∑ + − = + − = + − = = A i A i k A i A i k A i A i k j k RX j k RX j k RX j k RX j i 2 2 ) , ( 2 ) , ( 1 ) , ( 2 ) , ( 1 ) , ( ρ ∑ ∑ ∑ + − = + − = + − = = B j B j l B j B j l B j B j l j k RX j k RX j k RX j k RX j i 2 2 ) , ( 2 ) , ( 1 ) , ( 2 ) , ( 1 ) , ( ρ 43 In the above equations, index i indicates the i th sample in image line j. The total cross- correlation segment length is 2A+1 samples axially (4.2) and 2B+1 samples laterally (4.3) for 1-D axial and 1-D lateral cross-correlation respectively. For 2-D cross- correlation, the 2-D kernel size is 2A+1 samples axially × 2B+1 samples laterally. Using the experimental anechoic cyst data set from the Chapter 3, I performed 1-D axial cross- correlation with segment sizes varying from 0.42 mm to 3.50 mm. 1-D lateral cross- correlation was performed with segment size varying from 0.45 mm to 1.95 mm. I also performed 2-D cross-correlation with sizes varying from 0.42 mm (axially) × 0.45 mm (laterally) to 3.50 mm (axially) × 1.95 mm (laterally). The Figure 4.1 shows CNR vs cross-correlation size. When using 1-D axial cross-correlation, an axial segment size of 1.73 mm gave us the highest CNR of 125 % improvement. Using 1-D lateral cross- correlation showed a 91 % improvement in CNR with segment size of 1.05 mm. 2-D cross-correlation showed a 145 % improvement with segment size of 1.2 mm axially × 0.45 mm samples laterally. This is summarized in Table 4.1. Cross-correlation method Cross-correlation size CNR improvement 1-D axial cross-correlation 1.73 mm 125 % 1-D lateral cross-correlation 1.05 mm 91 % 2-D cross-correlation 1.2 mm × 0.45 mm 145 % Table 4.1. Cross-correlation method and size vs CNR improvement 44 (a) (b) (c) Figure 4.1. CNR vs correlation method. (a) CNR vs 1-D axial cross-correlation segment size (b) CNR vs 1-D lateral cross-correlation segment size (c) CNR vs 2-D cross- correlation segment size 45 4.3 DAX with filtering of weighting coefficients In Figure 3.10, I showed the cross-correlation matrices from the simulated (Figure 3.10 a) and experimental (Figure 3.10 b) cyst. In simulation, the mean cross-correlation coefficients are 0.968 and 0.012 for the background and target respectively while the experiment had cross-correlation coefficients of 0.859 and 0.0053 respectively. The grayscale maps coefficients from 0 (black) to 1 (white) on a linear scale. The dark spots in the speckle region above the cyst are most likely due to the random nature of speckle. As a solution, the matrix of cross-correlation coefficients could be modified by a 1-D or 2-D median filter, 1-D or 2-D moving average filter, or other types of low-pass filters. In case of median filter, this filter replaces the center value in the window with the median value of all the points within the window. This window size should be an odd number and long enough to remove the effect of pits but short enough not to introduce blurring in the speckle region. Average filter is similar to median filter. However, the output pixel is set to an average of the pixel values in the neighborhood of the corresponding input pixel instead of being determined by the median of the neighborhood pixels. With DAX artifacts, the median filter gave us better result since it is much less sensitive than the mean to extreme values of dark pits or fill-in inside the cyst. Median filters are the most effective non-linear rank ordered filters that reliably remove salt and pepper like impulse noises while still preserving the edge details (Jain 1989). Since this process is a smoothing of the weighting matrix and not of the received RF data, the speckle pattern will not be smeared. Figure 4.2 shows an example of modified weighting matrices with 2-D median filtering and 2-D average filtering. The artifacts almost disappear with 2-D median filtering of 46 window size of 1.2 mm axially and 0.45 mm laterally and the cyst itself becomes smoother. Average filtering with 1.2 mm axially and 0.45 mm laterally also smoothes out speckle region. However, cyst looks blurrier than unfiltered case and this will affect CNR. (a) (b) (c) Figure 4.2. Weighting matrix with filtering (a) Original weighting matrix, (b) 2-D median filter with window size of 1.2 mm axially and 0.45 mm laterally and (c) 2-D average filter with window size of 1.2 mm axially and 0.45 mm laterally 4.4 Methods In all simulations and experiments, I used an alternating pattern of enabled elements in receive mode to create the two apodization functions which, in combination, were shown to have the highest CNR experimentally. A detailed system block diagram of the alternating pattern is shown in Figure 4.3. For transmit, a uniformly weighted subaperture of 64 elements was used to focus at a single depth of 30 mm. On receive, signals from transducer elements in the darker gray shading were delayed and summed to create RX1. The signals from elements with lighter shading were delayed and summed to create RX2. If clusters of 8 elements are used, I call this pattern the 8-on, 8-off pattern, or 8-8 alternating pattern. Axial segments of RF data, roughly two to four wavelengths long, from the two beamformed RF data sets are cross-correlated to determine the amount 47 of mainlobe dominated signal and to create a weighting matrix. Due to the random nature of speckle, artifacts in the form of black spots may arise with DAX-processed images. To minimize these occurrences, the weighting matrix was median filtered. Median filtering is a simple way to suppress impulse noise (Jain 1989). This window size was chosen to be large enough to remove the effect of most artifacts but small enough to minimize blurring of the weighting matrix. The standard delay-and-sum beamformed data with uniform apodization, labeled as “Standard beamformed data” in Figure 4.3, are given by the sum of RX1 and RX2. After bandpass filtering, the standard beamformed data is multiplied by the thresholded and filtered cross-correlation coefficients to yield a DAX RF dataset. For animal experiments, 2-D segment size of 1.2 mm axially × 0.67 mm laterally from the two beamformed RF data sets are cross-correlated to determine the amount of mainlobe dominated signal and to create a weighting matrix. I found using a slightly longer lateral cross-correlation length in the animal experiments was more efficient in reducing artifacts without extra computation burden. The weighting matrix was median filtered with the window size of 1.2 mm axially × 0.67 mm laterally, the same size as cross-correlation kernel. After bandpass filtering, the standard beamformed data is multiplied by the depth dependent weighting matrix to yield the DAX RF dataset. This data set will go through additional standard signal processing steps such as bandpass filtering, envelope detection, and log compression. 48 Figure 4.3. System block diagram for the DAX alternating pattern 4.4.1 Simulation parameters To begin our evaluation, simulations with a point target and cyst with varying aberration and noise strengths were performed using Field II (Jensen and Svendsen 1992). A 5 MHz Gaussian envelope pulse with 50 % bandwidth was used as a transmit pulse, and a delta function was used as the element impulse response. For a point target simulation, an RMS energy value was calculated from the received voltage trace. All RMS energy values were converted to decibels after normalizing to the maximum energy level. The focus for both transmit and receive was fixed at a 30 mm depth for the point target simulations. Since point targets are rarely found in the clinical environment and DAX is a target-dependent technique, I have also performed simulations using cylindrical 2, 3, and 4 mm diameter anechoic cysts located at depths of 20, 30 and 40 mm 49 respectively embedded in a 3-D phantom of scatterers. Based on a previously published analysis (Oosterveld et al. 1985), I used 10 scatterers per resolution cell to create a 10 mm × 40 mm × 50 mm (elevation × lateral × axial) phantom filled with speckle generating scatterers. The following array imaging parameters in Table 4.2 were used. These imaging parameters were chosen to model the Ultrasonix Sonix RP ultrasound system (Ultrasonix Medical Corporation, Richmond, BC, Canada) and L14-5/38 linear array used in the experimental component of this paper. Parameter Value Number of elements in subaperture 64 Center Frequency 5 MHz Bandwidth 50 % Azimuthal Element Pitch 300 µm Azimuthal Element Width 279.8 µm Elevation Element Height 5 mm Sound speed 1540 m/s Transmit Focus 30 mm Lateral beam spacing 75 µm Receive focal delay step (cyst) 100 µm Table 4.2. 1 × 128 Linear Array and Imaging Parameters 4.4.2 Aberration Characterization Aberrations can be characterized with the following parameters: 1. RMS (root-mean-square) Residual time value: The strength of an aberration generally is reported as the RMS amplitude of the aberrating function, in nanoseconds. 50 2. FWHM (full-width-half-maximum) autocorrelation length: The spatial frequency content of an aberration is indicated by the FWHM value of the aberrator’s autocorrelation function. This parameter is referred to as the correlation length, in millimeters. There are two basic models for aberrations differing in the aberration location. The near- field aberration model states that the aberrations that contribute the most to image degradation occur right against the surface of the transducer (i.e. fat layer). However, a more realistic model would incorporate the variations throughout the tissue. The distributed aberration model assumes the aberration varies in range through the imaging plane and is distributed throughout the medium. In this thesis, I assume a near-field aberration model for all simulations and experiment. Aberration parameters ranging from 25 - 45 ns root-mean-square (RMS) and 3 mm and 5 mm correlation lengths were used. To test the performance of DAX in the presence of aberration, 100 realizations of each aberrator were used for a point target simulation. Because of limited computing resources and a large number of scatterers present in the 3- D phantom, we performed five realizations of each aberrator for a cyst target simulation. Figure 4.4 shows examples of the three aberration profiles. These aberrators are created by convolving Gaussian distributed random numbers with a Gaussian function which is applied to both transmit and receive (Dahl et al. 2005). For all cysts targets, performance was evaluated using the CNR in equation (4.5): (4.5) b b t S S CNR σ − = 51 where is the mean of the target, is the mean of the background and is the standard deviation of the background of the envelope-detected, log-compressed image. To test the performance of DAX in the presence of noise, 100 realizations of random zero-mean Gaussian noise were added to achieve a system SNR of 35, 25, and 15 dB. Integrated beamplots and cyst images with SNRs of 35, 25, and 15 dB were created and evaluated quantitatively in terms of beamwidths, clutter level and CNR. Figure 4.4. Aberration profiles of 25 ns RMS 5mm FWHM (solid line), 35 ns RMS 5mm FWHM (dashed line) and 45 ns RMS 3mm FWHM (dotted line) 4.4.3 Experimental setup For our experimental setup, individual element RF signals were collected for offline processing from an ATS spherical lesion phantom (ATS laboratories, Bridgeport, CT, Model 549) containing 2, 3, and 4 mm anechoic cysts using an Ultrasonix Sonix RP t S b S b σ 52 ultrasound system having 40 MHz sampling frequency. This system has great flexibility allowing the researcher to control parameters such as transmit aperture size, transmit frequency, receive aperture, filtering, and time-gain compensation. In this experiment, a 128-element, 300 µm pitch, L14-5/38 linear array was used. A 1-cycle transmit pulse with a center frequency of 5 MHz, and a subaperture size of 64 elements, or 19 mm, was used. On receive, element data was collected, and receive beamforming was done offline with a constant f-number = 1.5 using Matlab (The MathWorks, Inc. Natick, MA). Dynamic receive focusing was used with focal updates every 100 µm in range and an image line spacing of 75 µm. Data from each channel was collected 32 times and averaged to minimize the effects of electronic noise in all experiments. To mimic a near field aberration of the body wall consisting of skin fat, muscle encountered in clinical ultrasound imaging, 3 mm - 11 mm thick layers of pork belly were used (99 Ranch Market, San Gabriel, CA). To mimic a weak aberrator, only a 3 mm thickness of skin from the pork belly was used. Next, a 4 mm thickness of fat and muscle aberrator was used. Lastly, a 11 mm thickness of fat and muscle was used. To simulate different levels of noise, I added Gaussian white noise to achieve system SNRs of 35, 25, and 15 dB. For animal experiments with an uncut whole sheep heart (Bio Corporation, Alexandria, MN) and a carotid artery of a sacrificed pig, a 2-cycle transmit pulse with a center frequency of 5 MHz, and a subaperture size of 64 elements, or 19 mm, was used. The same data acquisition method as previous phantom experiments was used to collect averaged data sets. On receive, element data was collected, and receive beamforming was done offline with a constant f-number = 1.5 using Matlab (The MathWorks, Inc. Natick, 53 MA). Dynamic receive focusing was used with focal updates every 1 mm in range and an image line spacing of 75 µm. 4.5 Simulation Results 4.5.1 Point target simulation in the presence of noise Figure 4.5 shows one of the 100 realizations with system SNRs of 35, 25 and 15 dB before and after applying the DAX 8-8 alternating algorithm. The noise level was determined with respect to the peak value of RF data. From these results, we can see that the DAX is able to suppress noise by a factor of 30 dB assuming that the noise on each channel is uncorrelated. The mean reduction in the clutter level was from -36 dB to -67 dB, from -26 dB to -56 dB and from -16 dB to -46 dB with system SNR of 35 dB, 25 dB and 15 dB respectively. The noise suppression capability of DAX algorithm can be explained as follows. The cross-correlation of two sets of uncorrelated noise will have an expectation value of zero. However, after thresholding of the cross-correlation coefficients, the new expectation value will be greater than zero. I have empirically quantified the new expectation value by performing 2000 realizations of the cross- correlation and thresholding. The mean reduction was 0.0316 or -30 dB. Figure 4.6 shows the mean beamwidths with three different system SNR levels. The error bars span ± 1 standard deviations from the mean beamwidth. 55 4.5.2. Cyst simulation in the presence of noise Cyst simulations were also performed in the presence of the same noise levels. Figure 4.7 shows the simulation results with 3 mm diameter cyst with 35 dB, 25 dB and 15 dB system SNRs before and after applying the DAX 8-8 alternating algorithm. The logarithmically compressed images are displayed with 50 dB dynamic range. Regions used to calculate CNR are shown in the white and black rectangles for the target and background respectively. With 35 dB SNR, clutter inside the cyst with standard beamforming is increased which results in a lower CNR value (Figure 4.8). With 25 dB SNR, clutter inside the cyst with standard beamforming is further increased which results in lower CNR value. When the SNR is further decreased to 15 dB, it is harder to see the cyst in standard image due to raised clutter inside the cyst. DAX is able to improve CNR by over 100 % in all cases and restore visibility of the cyst. From these results, I can see that the DAX algorithm is able to suppress noise-dominated signals at SNRs of 15 dB or greater. The CNR values are shown in Figure 4.8. The error bars span ± 1 standard deviations from the mean CNR. 56 Figure 4.7. 3 mm diameter cyst simulations with (a) 35 dB SNR, (b) 25 dB SNR, and (c) 15 dB SNR Figure 4.8. Mean CNR values of 100 realizations for cyst simulations with different levels of system SNR The error bars span ± 1 standard deviations from the mean CNR. (c) (b) (a) 57 4.5.3. Point target simulation in the presence of phase aberration Figure 4.9 shows one of 100 simulated beamplots using standard beamforming with uniform receive apodization and with the DAX 8-8 alternating pattern in the presence of no aberration and aberrators with 25 ns RMS, 5 mm correlation length, 35 ns RMS, 5 mm correlation length, and 45 ns RMS, 3 mm correlation length. In the case of no aberration, DAX removes most of the clutter below -40 dB. With the 25 ns RMS, 5 mm correlation length aberrator, DAX is able to remove most of the clutter below -30 dB. Since this is considered a fairly weak aberrator, similar performance to the case of no aberration is seen. With the 35 ns RMS, 5 mm correlation length aberrator, higher side lobes and clutter levels are seen. DAX is effective in lowering clutter levels away from the main lobe by more than 40 dB. Lastly, with the 45 ns RMS, 3 mm correlation length aberrator which is a severe aberration, high sidelobes are seen. Most of the clutter away from the main lobe has been removed using DAX. Figure 4.10 shows the mean -6, -20, -40, and -60 dB beamwidths for all three aberrators from 100 realizations. The error bars span ± 1 standard deviations from the mean beamwidth. In all cases, DAX is able to decrease the beamwidths and clutter. 58 Figure 4.9. Lateral beamplots in the presence of (a) no aberration, (b) 5mm FWHM 25 ns RMS, (b) 5mm FWHM 35 ns RMS, and (d) 3mm FWHM 45 ns RMS aberration. Beamplot for RX1 is shown in dashed/dotted line, beamplot for RX2 in dotted line, standard beamforming with uniform apodization in dashed line, and DAX 8-8 alternating pattern in solid line. (a) (c) (d) (b) 60 on the distance away from the transmit focus. For example, by observing the range where artifacts appear, DAX would not be used at depths less than 19 mm if the transmit focus is located at 30 mm. A 2-2 alternating pattern would be used for depths between 19-25 mm, 4-4 would be used for depths 25-29 mm, 8-8 would be used for 29-33 mm. 4- 4 would then again be used from 33- 42 mm, and 2-2 is used from 42-60 mm. The result is essentially a composite image from Figure 4.11 (a)-(c) and is shown in Figure 4.11 (d). Figure 4.11. Simulated cyst image using (a) 2-2 (b) 4-4 (c) 8-8 alternating patterns and (d) dynamic DAX (b) (d) (a) (c) 61 2-2 4-4 8-8 Dynamic DAX CNR 8.57 12.02 12.55 12.60 Table 4.3. CNR values with different alternating patterns and dynamic DAX The sequences used for dynamic DAX lead us to hypothesize that these black spots arise when the grating lobe signal is the dominant portion of the signal since grating lobe and clutter levels rise at depths away from the transmit focus. To test this hypothesis, I performed Field II simulations to examine the magnitude of grating lobes of the beam at each depth. Depths ranging from 15 – 50 mm at 1 mm increments were used. DAX with alternating patterns of 2-2, 4-4, and 8-8 were done. Figure 4.12 shows the grating lobe beam magnitude versus depth for each alternating pattern. The receive focus was set to the specific depth of interest, and the transmit focus was always set to 30 mm. As expected, the grating lobe magnitude increases with distance away from the transmit focus located at 30 mm and also with an increasing alternating pattern. The magnitude of the grating lobe is not symmetrical around the focus but decreases with depth. This implies that we could use a wider range of larger alternating patterns after the transmit focus. Examining where the peak of the grating lobes become greater than -25 dB in Figure 4.12 closely relates to the depth at which black spots in the images appear in Figure 4.11. This is not a surprising result since signals with a grating lobe signal that is comparable to a main lobe signal in magnitude would give a wide variation of cross- correlation coefficients. Therefore, the following dynamic DAX sequence has been used 62 for all simulations and experiments when the transmit focus was at 30 mm with an f- number of 1.5: 1) DAX is not used at depths less than 19 mm. 2) A 2-2 alternating pattern is used for depths between 19-25 mm, 3) A 4-4 alternating pattern is used for depths 25-29 mm, 4) An 8-8 alternating pattern is for 29-33 mm. 5) A 4-4 alternating pattern is then again used from 33- 42 mm, and 6) A 2-2 alternating pattern is used from 42-60 mm. The DAX sequence will depend on the transmit focus and the f-number. If we shift the transmit focal depth, then the pattern will be shifted by the same amount. If we reduce or increase the f-number, the depth of field will be decreased or increased by factor of the f- number squared. This allows us to use a larger range for the 8-8 pattern in this focal region. Table 4.4 shows an example of how to determine a particular dynamic DAX sequence. f-number 1.5, transmit focus @ 30 mm f-number 2, transmit focus @ 41 mm Dynamic DAX sequence < 19 mm < 30 mm No DAX 19-25 30-36 2-2 25-29 36-39 4-4 29-33 (4 mm) 39-46 (7 mm) 8-8 33-42 46-53 4-4 42-50 - 2-2 Table 4.4. Dynamic DAX sequence for different focal depths and f-numbers 63 Figure 4.12. Grating lobe magnitude vs receive focus when the transmit focus is set to 30 mm depth 4.5.5 Multiple cyst simulation with Dynamic DAX To examine the effect of dynamic DAX, a simulation with multiple cysts was used. Three cysts with diameters 2, 3, and 4 mm were placed at a depth of 20, 30, and 40 mm respectively. These cysts were chosen to simulate the ATS tissue mimicking phantom used in the experimental component of this paper. The transmit focus was fixed at a 30 mm depth for the simulation. Dynamic receive focusing was used with focal updates every 100 µm for both standard and dynamic DAX images with f-number of 1.5. Figure 4.13 shows the results of the simulation. The cyst images obtained by using dynamic DAX processing are more visible than the images obtained with standard beamforming. Regions used to calculate CNR are shown in the white and black rectangles for the target and background respectively. The CNR for the 2 mm cysts is 64 1.84 for the standard beamformed case, and DAX yields a slight improvement to 2.16. Qualitatively, the cyst is only slightly more visible using DAX. For the 3 mm cyst, a CNR of 5.69 for standard beamforming is improved to 13.40 using dynamic DAX. The 4 mm cyst also shows a significant improvement in CNR from 2.90 to 9.40. I could use a larger alternating pattern after the transmit focus, which may explain why there is a larger CNR improvement with the 4 mm cyst located after the transmit focus than with the 2 mm cyst located before the transmit focus. The 4 mm cyst exhibits a large amount of clutter which resulted in a smaller looking less circular cyst, but this is also seen in the standard beamformed case. Using an additional transmit focus here may restore the circular shape of the cyst. The CNR values are listed in Table 4.5. 65 Figure 4.13. Simulated multiple cyst images using standard beamformng with uniform apodization and dynamic DAX Standard with uniform apodization Dynamic DAX 2 mm 3 mm 4 mm 2 mm 3 mm 4 mm CNR 1.84 5.54 2.90 2.16 13.10 9.40 Table 4.5. CNR values of three different sized cysts using dynamic DAX Dynamic DAX zones No DAX 2-2 4-4 8-8 4-4 2-2 66 4.5.6 Multiple Cyst simulation in the presence of phase aberration To further examine the effect of dynamic DAX in the presence of phase aberration, the same multiple cyst phantom was used with the aberrators shown in Figure 4.14. I have performed five realizations of Field II simulations to assess the performance of DAX in the presence of phase aberration. I have also compared the DAX algorithm with GCF (Li and Li 2000) in terms of CNR. Figure 4.14 show simulated cysts using standard beamforming with uniform receive apodization, GCF with M 0 = 2 (using Li’s notation) and with dynamic DAX in the presence of aberrators with 25 ns RMS, with 5 mm correlation length, 35 ns RMS, with 5 mm correlation length, and 45 ns RMS, with 3 mm correlation length. The images are displayed over 50 dB dynamic range. The transmit focus was fixed at a 30 mm depth for the simulation. Dynamic receive focusing was used with focal updates every 100 µm for both standard and dynamic DAX images with f-number of 1.5. With a 25 ns, 5mm aberrator, an improvement in CNR from 1.72 ± 0.19 to 2.29 ± 0.17, from 3.66 ± 0.34 to 9.86 ± 0.80 and from 2.27 ± 0.44 to 10.05 ± 0.62 is seen for the 2 mm, 3 mm and 4 mm cysts respectively. Qualitatively, the 3 mm cyst which is located at the transmit focus appears circular, but not the 2 mm and the 4 mm cysts which are away from the transmit focus. Some clutter at the top right corner of the 4 mm cyst can also be seen. In the case of a 35 ns, 5 mm FWHM aberrator, a CNR improvement from 1.45 ± 0.19 to 1.96 ± 0.30, from 3.42 ± 0.61 to 10.17 ± 0.71 and from 2.28 ± 0.81 to 7.91 ± 0.91 is seen for the 2 mm, 3 mm and 4 mm cysts respectively. Again, the 3 mm cyst which is located at the transmit focus appears circular but not the cysts which are away from the 67 transmit focus. The 4 mm cyst has clutter at the top left corner. More black spots can also be observed away from the focus. In the case of a 45 ns, 3 mm FWHM aberrator, a CNR improvement from 1.01 ± 0.25 to 1.38 ± 0.37, from 1.65 ± 0.50 to 2.41 ± 1.62 and from 0.96 ± 0.13 to 4.47 ± 0.95 is seen for the 2 mm, 3 mm and 4 mm cysts respectively. DAX is not able to completely remove clutter inside the cysts. Overall, a more significant improvement in CNR is seen for the 4 mm cyst than the 2 mm cyst. This can possibly be explained by the fact that the 4-4 pattern was used for the 4 mm cyst which gives a higher CNR than the 2-2 pattern which was used for the 2 mm cyst. Also, it is typically easier to detect a larger lesion. The mean CNR values for each aberrating case are shown in Figure 4.15. The error bars span ± 1 standard deviations from the mean CNR. 68 Figure 4.14. Simulated multiple cyst images with standard beamforming with uniform apodization, GCF and dynamic DAX in the presence of (a) 25 ns RMS 5 mm FWHM aberrator, (b) 35 ns RMS 5 mm FWHM aberrator and (c) 45 ns RMS 3 mm FWHM aberrator a) b) c) 70 further increased with standard beamforming. With DAX, CNR is increased by 130 %. When the noise level is further increased to -15 dB, it is harder to see the cyst in standard image due to raised clutter inside the cyst and variation in the speckle region. DAX is able to improve CNR by over 140 % and restore the visibility of the cystic region. However, the black artifacts in the speckle region are also increased. From these results, DAX could be used for SNR greater than 15 dB. The mean CNR values are shown in Figure 4.17. The error bars span ± 1 standard deviations from the mean CNR. Figure 4.16. Experimental cyst images with standard beamforming with uniform apodization and DAX 8-8 alternating pattern with (a) 35 dB SNR (b) 25 dB SNR and (c) 15 dB SNR (b) (c) (a) 71 Figure 4.17. Mean CNR values of 100 realizations for cyst experiments with different levels of system SNR. The error bars span ± 1 standard deviations from the mean CNR. 4.6.2 Cyst experiment with pig skin and fat layer To test the effects of phase aberration experimentally, a subcutaneous pig skin layer was placed in between the ultrasound transducer and the ATS cylindrical lesion phantom containing 2 mm, 3 mm and 4 mm anechoic cysts to induce phase aberrations and beam distortion, to determine whether DAX reduces the effect of beam distortion and image clutter. I have also compared DAX with the GCF algorithm with M 0 = 2 in terms of CNR. At 24 °C, the speed of sound of pig fat is 1420-1444 m/s and of pig skin/muscle varies from 1720 m/s to 2000 m/s (Chivers R. C. and Parry 1978). The temperature of the test phantoms and the pig fat layer was approximately 22 °C (room temperature, normal testing conditions) during the experiment. Images with no aberration of the ATS phantom are shown in Figure 4.18. CNR improves with dynamic DAX for all three cysts. The improvement is more dramatic for the 3 mm diameter cyst which is located at the transmit focus and where the 8-8 alternating pattern was used (Table 4.6). For all 72 experimental images, the dynamic DAX images were generated using the same sequence used for simulation, where the 8-8 pattern was used for the transmit focal region. The transmit focus was always set to the depth of the 3 mm diameter cyst. Figure 4.18. Experimental cyst images with no aberrator With a skin layer of 3 mm thickness and a fat/muscle aberrator of 4 mm in thickness, a dramatic improvement in CNR can be observed (Figures 4.19 - 4.20 Table 4.6). The transmit focus was set to 33 mm and 34 mm for the 3 mm and 4 mm aberrators respectively to maintain a focus at the 3 mm diameter cyst. Lastly, the thick 11 mm fat/muscle aberrator created the most clutter in the cysts, but dynamic DAX was yet able to improve CNR (Figure 4.21, Table 4.6). Here, the transmit focus was set to a depth of 41 mm. 73 Figure 4.19. Experimental cyst images in the presence of a skin layer aberration of 3 mm in thickness Figure 4.20. Experimental cyst images in the presence of a fat/muscle layer aberration of 4 mm in thickness 74 Figure 4.21. Experimental cyst images in the presence of a thick muscle layer aberration of 11 mm in thickness Uniform Apodization GCF Dynamic DAX 2 mm 3 mm 4 mm 2 mm 3 mm 4 mm 2 mm 3 mm 4 mm No aberrator 1.72 4.40 4.11 2.18 6.02 5.41 2.12 10.64 7.65 Skin layer 2.01 3.84 2.89 2.65 5.01 3.90 2.03 10.04 7.52 Fat/muscle layer 2.24 3.34 3.72 2.52 4.51 4.84 2.28 7.39 6.74 Thick muscle 1.59 2.63 2.05 2.22 3.26 2.98 1.83 4.62 3.59 Table 4.6. Experimental CNR values in the presence of phase aberration 75 4.7 Animal Experiment Results Until now, the experiments have been performed using a commercial phantom with cylindrical anechoic regions. To assess the DAX technique in a setting closer to a clinical environment, an uncut whole sheep heart embedded in gelatin was first imaged. 4.7.1 DAX weighting function With animal experiments, 8-8 or even dynamic DAX proved to be too aggressive. I investigated a new weighting function that depends on the cross-correlation coefficient as well as depth. Figure 4.22 (a) shows the original weighting as a function of cross- correlation described in Chapter 3. Here, the weighting value was equal to the cross- correlation coefficient when the coefficient was greater than 0.001 and equal to 0.001 when the cross-correlation coefficient was less than 0.001. Other proposed weighting functions are shown in Figures 4.22 (b)-(e). Figure 4.22 (b), lowering the threshold to - 0.2 for example is a possible method to minimize these artifacts. This lower threshold value can be chosen by the cross-correlation value of the dark pits in the speckle region of the pre-thresholded cross-correlation matrix. As we further decrease this threshold, the weighting function will eventually look like Figure 4.22 (c). Figure 4.22 (c) shows a linear mapping curve. Low positive correlation coefficients will receive a higher weighting than the original weighting function. This may help minimize black pits, but would also raise the amplitude within cystic regions. This weighting function is less aggressive than the original thresholded weighting function and will be most suitable for row-column arrays or high frame rate imaging where side-lobes are higher due to 1-way focusing. This 1-way focusing imaging would also raise grating lobe magnitude in each 76 of the two sparse receive apertures used in DAX. Signals with grating lobe signal that are comparable to main lobe signal in magnitude would give a wide variation of cross- correlation coefficients and the original weighting function would introduce black artifacts. Figure 4.22 (d) is a log weighting function. Since most of the ultrasound B- mode images are displayed in a log scale with dynamic ranges varying from 40-70 dB, the weighting function could be a linear mapping between the cross-correlation coefficient and weighting in a log scale. The mapping is biased toward lower weighting values and will help reduce the artifacts caused by a high cross-correlation coefficient in the cystic region. The curve shown in Figure 4.22 (d) is plotted in linear scale having a weighting function shape of: 10 (4.6) where gl is the magnitude of the grating lobe, which is set to 60 dB in this example, and ρ is the cross-correlation coefficient. Lastly, a natural extension of this log weighting function would be having a continuum of weighting functions dependent on the cross- correlation coefficients and depths. These weighting functions can be generated using the data from the Figure 4.12. For example, Figure 4.22 (e) shows weighting functions with DAX 2-2 alternating pattern, generated every 5 mm. 20 2 2 gl gl − ⋅ ρ 77 (e) Figure 4.22. Several illustrative examples of proposed weightings as function of cross- correlation coefficients. The last image shows weightings as a function of cross- correlation coefficients and depth. (a) (b) (c) (d) 78 4.7.2 Excised animal tissue and animal experiments in situ Figure 4.23 shows the image of a dissected sheep heart. A depth dependent logarithmic weighting function with a 2-2 alternating pattern was used in all DAX processed images (Figure 4.24). I have also compared the DAX algorithm with GCF (Li and Li 2000) in terms of CNR. Similar to depth dependent DAX weighting functions, M 0 parameter was varied as a function of depth for GCF as well. For example, GCF was not used for depth less than 15 mm and greater than 50 mm if the transmit focus was set to 30 mm. In the focal region between 25 mm and 35 mm, M 0 =3 was used. Every 5 mm away from the focal region, M 0 was increased by 1. Figure 4.23. Image of a dissected sheep heart Cross-sectional views of atria are shown in Figures 4.25 and 4.26. Regions used to calculate CNR are shown in the white and black rectangles for the target and background respectively. Both GCF and DAX images show images with improved 79 contrast compared to uniform weighted image. However, they also create more variation in the speckle region. Table 4.7 and 4.8 list CNR values. (a) (b) Figure 4.24. Weighting function profile as a function of the cross-correlation coefficient and depth plotted in (a) 2-D matrix format and (b) 1-D plots, shown here only at 15 mm, 30 mm and 45 mm for visibility Figure 4.25. Left atrium of a sheep 80 Figure 4.26. Right atrium of a sheep Uniform GCF DAX CR 32.17 53.96 66.87 Background standard deviation 6.75 7.91 7.05 CNR 4.76 6.82 9.49 Table 4.7. Experimental CNR values of the sheep left atrium Uniform GCF DAX CR 29.83 46.92 53.26 Background standard deviation 6.57 6.97 6.63 CNR 4.54 6.73 8.04 Table 4.8. Experimental CNR values of the sheep right atrium 81 Next, a carotid artery of an 80 lbs female pig was sacrificed and imaged in situ. Figure 4.27 shows a depth dependent logarithmic weighting function with a 2-2 alternating pattern when the transmit focus was set at 20 mm. In Figure 4.28, both GCF and DAX images show contrast improvement compared to the uniform weighted image. Part of the jugular vein can also be seen on the top right side. Table 4.9 lists CNR values. (a) (b) Figure 4.27. Weighting function profile as a function of the cross-correlation coefficient and depth plotted in (a) 2-D matrix format and (b) 1-D plots, shown here only at 10 mm, 20 mm and 30 mm for visibility 82 Figure 4.28 Carotid artery of a female pig UniformGCF DAX CR 13.21 22.2625.25 Background standard deviation 5.96 7.38 7.24 CNR 2.22 3.01 3.49 Table 4.9. Experimental CNR values of the pig carotid artery 4.8 Discussion Optimized DAX has been shown to improve contrast in anechoic cysts in the presence of phase aberration and electronic noise. The improvement in CNR was shown through simulation and experiments using a commercial phantom and excised porcine tissue. The DAX algorithm was also compared with GCF with M 0 = 2 in the presence of phase aberration in terms of CNR. DAX performed better than GCF in most cases, especially at the transmit focus. Lastly excised sheep heart and pig carotid in situ were imaged to assess the performance of DAX and compared with GCF. 83 Chapter 5: Applications to 3-D imaging 5.1 Introduction A recent major innovation in ultrasound imaging technology is 3-D imaging. 3-D ultrasound has several advantages over 2-D ultrasound, providing orientations and slices not available with 2-D ultrasound, more accurate volume measurements and improved detection of cystic or cancerous masses (Fenster and Downey 1996). For example, 2-D breast ultrasound is routinely used for identifying cysts and solid nodules (Bassett and Butler 1991). 3-D ultrasound has the potential to demonstrate the delineation of these lesions and to reduce the need for biopsy (Moskalik et al. 1995). When a biopsy becomes necessary, 3-D ultrasound-guided breast biopsy procedures may help doctors by giving 3- D spatial location of the applied needle since the needle no longer has to be aligned within a single scan plane (Smith et al. 2001). Another application of 3-D ultrasound is ultrafast ultrasound in vascular imaging (Palombo et al. 1998). This 3-D vascular system can be expected to improve assessment of luminal geometry and disease process, since a 3-D data set can be freely rotated and examined along multiple planes and tomographic sections. Current 3-D ultrasound systems may contain mechanically moving 1-D array transducers or fully or partially populated 2-D array transducers. Volumetric images are then captured by physical movement of 1-D array or by electronic scanning in the case of a 2-D array. Mechanical translation of a 1-D array has a slow data acquisition rate and poor spatial resolution in the elevation direction, which in turns degrades image quality and limits accuracy of the volume measurement (Fenster and Downey 1996). A fully- 84 sampled 2-D array consisting of 128 × 128 = 16,384 or 256 × 256 = 65,536 elements would serve as an ideal probe for 3-D rectilinear ultrasound imaging of near-field targets such as breast, carotid artery and abdomen. Such a fully sampled 2-D array would give a substantial improvement over a traditional 1-D linear array in image quality in 3-D imaging with a wide field of view near the transducer. However, it has not been demonstrated whether developing a fully sampled 2-D array would be feasible because of the difficulty in fabricating an array with such a large number of elements. The high electrical impedance due to the small size of each element would result in signal loss. To handle such a large array, one would need as many as 65,536 channels and tens of thousands of coaxial cables in an imaging system create a major challenge. One well established technique to overcome these difficulties is by using a sparse 2-D array (Yen et al. 2000, Yen and Smith 2001, Yen and Smith 2004). Yen and Smith (2000) investigated several sparse 2-D array designs for real time volumetric imaging and used the Mills-cross design to build a curvilinear array for 3-D ultrasound (2001). In the later version of the rectilinear 3D scanner, a sparse periodic array with receive mode multiplexing was built to improve spatial resolution performance (2004). However, extreme sparseness, with less than 10 % active elements, causes grating lobes and high clutter levels. This results in degradation of image contrast and hence limits the diagnostic value of the exam. Taking advantage of integrated circuit (IC) fabrication techniques, recent commercial systems use integrated electronics to allow connecting to approximately 3,000 individual elements before funneling the signals from these elements into 128 system channels via switches and preliminary beamformation within 85 the handle (Savord and Solomon 2003). The preliminary beamformation is located within the transducer handle using application specific integrated circuits (ASICs). The second stage of beamformation is done by a traditional 128 channel system digital beamformer providing dynamic focusing. Tamano et al. developed a convex 2-D array in which switches connect elements in rings around the beam center similar to an annular array (Tamano et al. 2003, Tamano et al. 2004). Changing a steering direction or transmit focus is accomplished by reconfiguring the switches. Another emerging array technology is capacitive micromachined ultrasonic transducers (CMUTs). This technology is suitable for 3-D imaging with 2-D arrays since the challenges associated with small element size in conventional array fabrication are not present. CMUT technology makes use of advanced IC fabrication processes and enables the easy manufacture of large 2-D transducer arrays with individual electrical connections. With through-wafer interconnects and a 420 µm element pitch, Oralkan et al. (2003) fabricated and demonstrated this technology with an experimental prototype, a 32 × 64-element portion of the 128 × 128-element array. Ermert et al. (2000) presented an ultrasound transmission camera using two separate linear crossed arrays. A transmit array consisting of transducer elements with a horizontal orientation are focused vertically. In receive, the vertical orientation of the second array focuses horizontally. This transmission ultrasound system has real-time capability and a reduced number of channels. It is an alternative to an earlier design of transmission camera with a 2-D array. Morton and Lockwood (2003) presented a crossed-electrode array that has two 86 identical hemispherically shaped linear array electrode patterns oriented perpendicular to each other on opposite sides of a 1-3 composite. Using this design, transmit beamforming in one direction and receive beamforming in the other direction could be achieved. This transducer acquires a pyramidal volume by emitting a fan shaped beam suitable for cardiac imaging. In similar work, we presented a row-column addressing technique to simplify interconnections of a flat 40 mm × 40 mm 2-D transducer array and verified its performance through simulations and experiments (Seo and Yen 2007). This transducer array is essentially a 1-3 composite with vertical and horizontal electrodes on the top and bottom respectively. Transmit and receive switching between the vertical and horizontal electrodes was accomplished with a simple diode circuit. In another realization of the row-column or cross-electrode array design, we proposed a dual-layer transducer array design which uses perpendicular 1-D arrays for 3-D imaging (Jeong et al. 2007). This dual-layer design uses one piezoelectric layer for transmit and another separate co- polymer layer for receive. Each layer is an elongated 1-D array with transmit and receive elements oriented perpendicular to each other. Both of these row-column transducers scan a rectilinear volume with a wide field of view close to the transducer and are useful for abdominal, breast, or vascular imaging. In this chapter, based on our previous works with Mills cross and row-column addressing scheme, we present simulation and experimental results from a 5 MHz 256 × 256 (38.4 mm × 38.4 mm) 2-D array transducer for rectilinear volumetric imaging. 87 5.2 Transducer Design First, we describe this design using a simplified 8 × 8 2-D array (Figure 5.1). This design utilizes a two-layer electrode pattern where the bottom layer consists of a series of vertical electrodes (Figure 5.1 (a)) and the top layer consists of a series of horizontal electrodes (Figure 5.1 (b)). In transmit, the vertical electrodes serve as the “ground” and the top electrodes serve as the “transmitters”. Figure 5.1. Row-column addressing scheme. The transmit side consists of 8 horizontal electrodes. The receive side consists of 8 vertical electrodes which serve as ground in transmit. Transmit beamforming is done in the vertical or elevational direction while receive beamforming is done horizontally or azimuthally. In this example, we excite transmit channel D as indicated by the arrow to the right of channel D in Figure 5.1 (b). This row of elements, shown in the gray shading in Figure 5.1 (c), then emits a cylindrical wavefront into the field. In elevation, the wavefront Elevation Azimuth (a) (b) (c) (d) (f) (e) 88 appears omnidirectional since the aperture behaves like a single small element. In the azimuth direction, the emitted beam is a planar wavefront because all elements fire simultaneously, and the aperture behaves as a single long element. For receive mode, receive channels A-H are active and the desired receive column is selected (Figure 5.1 (d)). In receive mode, the individual elements along one column (gray shading) will be used to record the echoes (Figure 5.1 (f)). With this design, transmit beamforming can be done in the vertical or elevational direction while receive beamforming can be done horizontally or azimuthally. A schematic illustrating this beamforming method is shown in Figure 5.2. Multiple rows could be used for elevational beamforming in transmit and multiple columns can be used for azimuth beamforming in receive. By stepping transmit subapertures across the array with multiple receive beams within the transmit beam, a 3- D rectilinear volume can be acquired (Morton and Lockwood 2003). Figure 5.2. Transmit and Receive Beamforming for 3-D rectilinear imaging To implement this design, we have modified a typical transmit/receive circuit such that an entire row acts as a single transmit element and an entire column acts as a single receiver (Petersen et al. 2004, Christensen, 1998). A typical Tx/Rx circuit uses the same 89 electrode for ground in both transmit and receive. The modified Tx/Rx circuit uses one electrode as ground in transmit and the other electrode as ground in receive (Figure 5.3 b) Since the effective size of the element is increased by a factor of N (where N is the number of elements in one direction in the N × N 2-D array transducer), the high electrical impedance associated with a single 2-D array element is eliminated. This modified transmit/receive circuit is illustrated in Figure 5.3 (a) using a simpler 2 × 2 array. (a) (b) Figure 5.3. (a) Modified Tx/Rx circuit where entire row acts as a single transmit element and an entire column acts as a single receiver and (b) Circuit diagram used to verify performance of the modified Tx/Rx circuit using a single element transducer. In this circuit, the row electrodes act as transmitters and are connected to the transmitters. The column electrodes are not connected directly to ground, but a pair of parallel reversed diodes serves as a low impedance path to ground. When either Tx1 or Tx2 emits a high voltage transmit pulse along the row electrodes, approximately ± 50-100 V, one of the diodes in each pair is forward biased with a ± 0.7 V drop with respect to ground. The TX RX Trasnducer 90 remaining voltage drops across the transducer, and the column electrodes serve as a ground through the forward-biased diodes. In receive, the relatively low output impedance of the transmitter and a 1 k Ω pull-down resistor (R1) provide a path to ground and the diodes are turned off assuming none of the echoes have an magnitude greater than 0.7 V. Thus, the row electrodes effectively become the ground electrodes. Using this row-column addressing scheme, we performed a point spread function simulation using Field II (Jensen and Svendsen 1992) (Figure 5.4). The transmit aperture is a 1-D array with azimuthal pitch of λ/2 = 0.15 mm and elevational height of 256 λ/2 = 38.4 mm. The receive aperture has an elevational pitch of λ/2 = 0.15 mm and an azimuthal length of 38.4 mm. A Gaussian pulse with center frequency of 5 MHz and a -6 dB fractional bandwidth of 50 % was used. For cross-sectional scanning, a 128-element subaperture was used in both transmit and receive and focused on-axis to (x,y,z) = (0,0,30) mm. The highest clutter levels, around -30 to -40 dB, are seen along the azimuth and elevation axes. The -6 dB and -20 dB beamwidths are 0.55 mm and 2.39 mm respectively. Figure 5.4. Simulated beamplots of the row-column transducer (a) 3-D beamplot and (b) Contour plot with lines at -10, -20, -30, -40 and -50 dB. (a) (b) 91 5.3 Methods 5.3.1 Array fabrication The 1-3 composite device was manufactured using the conventional dice and fill technique (Savakas et al. 1981). To fabricate this 2-D array substrate, a 50 mm × 50 mm wafer of 600 μm thick PZT-5H was mounted on a 3 × 3 inch glass plate using melted wax. The PZT was diced in perpendicular directions to a depth of 325 μm with a 150.23 μm element-to-element distance and a 35 μm kerf. The kerfs were filled with Epotek 301, a low viscosity epoxy. This initial pitch size of 150.23 μm was calculated to take into account epoxy shrinkage during the fabrication process to achieve a final pitch of 150 μm. Next, any excess epoxy was lapped away, and a gold and chrome layer was sputtered on the top side. A diamond wheel dicing saw was used to scratch dice a few microns into the epoxy filler to form columns. The PZT was then flipped over and lapped to a final desired thickness near 300 μm. After sputtering the bottom side, row electrodes were created by scratch dicing. The final array pitch is equal to the composite pitch, or 150 μm, where a line of square ceramic pillars is connected by a single electrode, forming one array element. Two prototype flexible circuits (Microconnex, Snoqualmie, WA), oriented perpendicular to each other were bonded using Epotek 301 on opposite faces of the composite (Figure 5.5) using a pressure of approximately 100 psi. The flexible circuits consist of a 104 μm thick polyimide, 9 μm thick copper, 1 μm thick nickel and 1 μm thick gold. The polyimide layer of the flexible circuit has an acoustic impedance of 3.4 MRayl and was attached to the front of the transducer as a matching layer. Polymer films have been previously used 92 as a coupling matching layer previously (Hadimioglu and Khuri-Yakub 1990). The flexible circuit was connected to a custom printed circuit board (PCB) (Sunstone Circuits, Mulino, OR) by a Samtec connector (Samtec, Inc. New Albany, IN). The parallel reversed diode pairs (Figure 5.3 a) are located on the receive PCB. Figure 5.5 Two single layer flexible circuits attached to perpendicular sides of the transducer. A 12 mm thick lossy epoxy backing consisting of 45 g of tungsten oxide (Cerac Specialty Inorganics, Milwaukee, WI), 7.875 g of LP-3 (Morton International, Chicago, IL), 1.688 g of phenolic balloons (Union Carbide, Danbury, CT), 4.5 g of Zeeospheres (3M, St. Paul, MN), 14.625 g of Dow Epoxy Resin 332 and 5.063 g of Dow Epoxy Hardener 24 (Dow Chemical Company, Midland, MI) was bonded using a FINISH-CURE™ 20 min epoxy (Sheldons Hobbies, San Jose, CA) onto the flexible circuit behind the transducer. The calculated acoustic impedance was 4.5 MRayl and the attenuation in the backing was measured using the method by Selfridge (1985) and was 10 dB/cm at 5 MHz. Front Flex circuit (Transmit) 2-D array Samtec connector Back Flex circuit (Receive) 93 5.3.2 Measurements We have verified the operation of the modified circuit (Figure 5.3. a) experimentally using the Ultrasonix Sonix RP ultrasound system (Ultrasonix Medical Corporation, Richmond, Canada,) with a Panametrics 5 MHz piston transducer (Figure 5.3. b). In a standard setup, the echo was received from a glass plate using a standard Tx/Rx channel from the Ultrasonix RP system, a 5 MHz Panametrics piston transducer and a pair of parallel, reversed diodes. In a switched case, one channel was used as a transmitter only and another channel is used in receive only to receive echo. The voltage trace is measured across a pair of parallel, reversed diodes on the receive board. An Agilent (Santa Clara, CA) precision impedance analyzer (model 4294A) was used for impedance analysis. Since the individual pillars of the composite are not individually accessible, all electrodes of one side from the transducer were grounded while the other side was used to measure electrical impedance. The device is similar to an elongated 1-D array. Pulse-echo measurements, using an aluminum plate reflector and a Panametrics 5072PR pulser/receiver (Waltham, MA) were taken in the same manner as for the impedance measurements. The pulse was acquired using a Tektronix oscilloscope (TDS 5054) and Fast Fourier Transform done in Matlab (Mathworks, Natick, MA) to yield the spectrum. Nearest-neighbor crosstalk measurements of the arrays were made by applying a 200 mV p-p 5 MHz 20-cycle burst using an Agilent 33250A function generator on one element and measuring the voltage on the neighboring element with 1 M Ω coupling on the oscilloscope. The system signal-to-noise ratio (SNR) at the transmit focus was measured using the method described in (Üstüner and Holley 2003). The composite 94 transducer array was interfaced with the Sonix RP ultrasound system using a custom printed circuit board to acquire data from a tissue mimicking phantom. Next, the transmitters were turned off to acquire only electronic noise data. After band-pass filtering, standard beamforming, envelope detection and log compression, the difference between a signal mean and a noise mean image was calculated to get the system SNR. 5.3.3 Imaging Experiments After transducer testing, the composite transducer array was interfaced with the Sonix RP ultrasound system using a custom printed circuit board. This system allows the researcher to control imaging parameters such as transmit aperture size, transmit frequency, receive aperture, filtering, and time-gain compensation. In these experiments, one row was connected to one channel of the Sonix system. This channel was used in transmit mode only. A two-cycle, 5 MHz transmit pulse was used. Sixty-four receive columns were each connected to individual system channels configured to operate in receive mode only. With a 40 MHz sampling frequency, data from each receive channel was collected 100 times and averaged to minimize effects of random noise. A different set of 64 receive elements was used until data from all 256 receive elements were collected. This process is repeated until all transmit and receive element combinations were acquired. The data was then imported into Matlab for offline 3-D delay-and-sum beamforming, signal processing and image display. Dynamic transmit (azimuth) and receive (elevation) focusing was done with 0.5 mm increments with a constant f-number of 2. The image line spacing was 150 µm. All signals in the experiments were bandpass 95 filtered using a 64-tap finite impulse response (FIR) bandpass filter with frequency range of 3.75 - 6.25 MHz. A 3-D volume was acquired by moving the transmit subapertures in azimuth and receive subapertures in elevation to focus a beam directly ahead. We imaged homemade 70 × 70 × 70 mm tissue mimicking gelatin phantoms containing 5 pairs of nylon wire targets with axial separations of 0.5, 1, 2, 3 and 4 mm. The bottom wire in each pair was shifted laterally by 1 mm with respect to the top wire. The diameter of the nylon wire was 400 μm. The background material of the wire phantom consisted of 400 g of DI water, 36.79 g of n-propanol, 0.238 g of formaldehyde and 24.02 g of gelatin. These ingredients and quantities are based on recipes given in the literature for evaluating strain imaging techniques (Hall et al. 1997). The second phantom imaged was an 8 mm diameter cylindrical anechoic cyst phantom where the cyst was located at a depth of 30 mm. The cylindrical cyst was made using the same ingredients as the background of the wire phantom. The tissue mimicking material surrounding the cyst used the same ingredients as the wire phantom but with 3.89 g of graphite powder added to provide scattering. The dimensions of the acquired volumes were 40 (azimuth) × 40 (elevation) × 45 (axial) mm. The third phantom imaged was a 9 mm diameter spherical anechoic cyst phantom where the cyst was located at a depth of 35 mm. The spherical cyst was made using the same ingredients as the cylindrical cyst. The tissue mimicking material surrounding the cyst used the same ingredients as the cylindrical and wire phantoms but with 3.89 g of graphite powder added to provide scattering. The dimensions of the acquired volumes were 40 (azimuth) × 40 (elevation) × 45 (axial) mm. 96 5.3.4 DAX processing For axial wires data, I used an 8-8 alternating pattern of enabled elements in receive mode to create the two apodization functions. An axial 1-D segment size of 1.6 mm from the two beamformed RF data sets are cross-correlated to determine the amount of mainlobe signal and to create a weighting matrix. If the coefficient is greater than or equal to a set threshold value 0.001, then the sample value is multiplied by the cross- correlation coefficient. For the cyst data, I used a 2-2 alternating pattern of enabled elements in receive mode to create the two apodization functions. 2-D segment size of 1.2 mm axially × 1.35 mm laterally from the two beamformed RF data sets are cross-correlated to determine the amount of mainlobe signal and to create a weighting matrix. A linear mapping weighting function with a 2-2 alternating pattern was used (Figure 5.6). The weighting matrix was median filtered with the window size of 1.2 mm axially × 1.35 mm laterally, the same size as cross-correlation kernel. After bandpass filtering, the standard beamformed data is multiplied by the filtered weighting matrix to yield the DAX RF dataset. This data set can go through additional standard signal processing steps such as bandpass filtering, envelope detection, and log compression. Images were then log-compressed and displayed with a dynamic range of 20 to 35 dB. Azimuth and elevation B-scans are displayed along with C-scans which are parallel to the transducer face. 97 Figure 5.6. Linear weighing function 5.4 Experimental Results Figure 5.7 shows the photograph of the final transducer. The final pitch was 150 μm. Two perpendicular flexible circuits can also be seen in this figure. 98 Figure 5.7. Photograph of the finished 256 × 256 2-D array transducer Figure 5.8 shows the pulse-echo result from the experiment to verify the operation of the modified circuit (Figure 5.3). The solid line in Figure 5.8 is the echo received from a glass plate using a standard Tx/Rx channel from the Ultrasonix RP system, a 5 MHz Panametrics piston transducer and a pair of parallel, reversed diodes. The dashed line is the echo where one channel was used as a transmitter only and another channel is used in receive only. Since the ground of the transducer is switched between transmit and receive, the echo using the new circuit is inverted compared to when a traditional transmit/receive circuit is used. Elevation Azimuth 40 mm Top Flexible circuit (Transmit) Bottom Flexible circuit (Receive) Active area 99 Figure 5.8. Experimental pulse-echo using modified Tx/Rx circuit and a 5 MHz Panametrics piston transducer. The solid line is the echo received from a glass plate using a standard Tx/Rx channel. The dashed line is the echo where one channel was used as a transmitter only and another channel is used in receive only. Figure 5.9 shows the typical electrical impedance of a transducer element measured experimentally using an Agilent precision impedance analyzer and in simulation using the 1-D KLM model (Krimholtz et al. 1970). The simulated impedance magnitude was 100 Ω at a series resonance frequency of 5.3 MHz while the experimental impedance curve showed a series resonance of 104 Ω at 5.4 MHz. The phase plots peak at 6.4 MHz for the KLM simulation and at 6.1 MHz in the experimental case. 100 Figure 5.9. Experimental (solid lines) and simulated (dashed lines) electrical impedance (a) magnitude plots and (b) phase angle plots Figure 5.10 shows the simulated and experimental time and frequency responses of the pulse-echo signals. In simulation, the center frequency was 5.2 MHz with a -6 dB fractional bandwidth of 67 %. Experimentally, the spectrum of the pulse has a center frequency of 5.3 MHz and a -6 dB fractional bandwidth of 53 %. At 5 MHz, the average nearest neighbor crosstalk was -25 dB. This level of crosstalk is acceptable in use for conventional linear array imaging, where the acoustic beam is not steered (Cannata et al. 2005). The SNR at the transmit focus at a depth of 30 mm (f-number = 1.5) was measured to be 30 dB (Üstüner and Holley 2003). (a) (b) 101 Figure 5.10. Experimental (solid lines) and simulated (dashed lines) (a) pulse and (b) spectra of the row-column transducer. The pulse plots were zoomed in to clearly see the two pulses. Figure 5.11 (a)-(c) show the azimuth B-scan, elevation B-scan, and C-scan of the wire phantom respectively when the short axis of the wires is in the azimuth direction. All images are log-compressed and shown on a 20 dB dynamic range. The elevation B- scan (Figure 5.11 b) shows the pair of wires with 1 mm axial separation. The two wires are discernible. The C-scan was taken at a depth of 35 mm. Here, one can also see the presence of sidelobes along side the wires. Figure 5.11 (d)-(f) show DAX processed images with reduced clutter. Figure 5.12 (a)-(c) show the axial wire target phantom with the short axis of the wires in the elevation direction. The pair of wires with 1 mm axial separation is discernible in the azimuth B-scan while the short-axis view is shown in Figure 5.12 (b). Figure 5.12 (c) shows the C-scan where sidelobes are present. DAX processed images in Figure 5.12 (d)- (f) again show sharper point targets with reduced clutter. (a) (b) 102 (a) (b) (c) (d) (e) (f) Figure 5.11. Experimental axial wire target images. The images are acquired with short axis of the wires positioned in azimuth direction. (a)-(c) show standard beamformed images and (d)-(f) show corresponding DAX processed images. All images are log- compressed and shown with 20 dB dynamic range 103 (a) (b) (c) (d) (e) (f) Figure 5.12. Experimental axial wire target images. The images are acquired with short axis of the wires positioned in elecvation direction. (a)-(c) show standard beamformed images and (d)-(f) show corresponding DAX processed images. All images are log- compressed and shown with 20 dB dynamic range Figure 5.13 shows the lateral wire target response in azimuth (Figure 5.13 a). The wire nearest the transducer was used. The -6 dB beamwidth was 0.68 mm in azimuth and 0.70 mm in elevation compared to an expected beamwidth of 0.55 mm calculated from Field II simulations. In both cases, there are sidelobes at -13 dB and some clutter below -20 dB. The -6 dB beamwidth of DAX processed image was 0.60 mm in azimuth and 0.63 mm in elevation. DAX was able to suppress high clutter and reduce sidelobes. 104 (a) (b) Figure 5.13. Lateral wire target response in azimuth direction (a) and in elevational direction (b). The dashed lines is a Field II simulated beamplot and the solid line is the experimental beamplot Figure 5.14 contains images of the cyst phantom. Figure 5.14 (a)-(f) show two perpendicular B-scans and a C-scan with the short axis of the cyst in azimuth and corresponding DAX processed images. Figure 5.15 (a)-(f) show two perpendicular B- scans and a C-scan with the short axis of the cyst in elevation and corresponding DAX processed images. All images in Figure 5.14 and 5.15 are log-compressed and are shown with 35 dB dynamic range. Figure 5.14 (a) and Figure 5.14 (e) show the cysts in cross- section. The cyst is not perfectly circular because of mechanical compression of the phantom to prevent motion during the data acquisition process. In the elevational B-scan and C-scan, the cylindrical cyst appears as a rectangle. The C-scans were taken at a depth of 30 mm. The bright spots are probably due to air bubbles in the phantom surrounding the cystic region. Regions used to calculate CNR are shown in the white and black rectangles for the target and background respectively. Qualitatively, the cyst using 105 uniform weighting has high clutter due to 1-way focusing. The DAX shows a dark cyst with a well defined boundary. CNR improved by 105 % from 2.08 to 4.27. Figure 5.15 (a)-(f) show the cyst with short axis in elevation. The C-scans were taken at a depth of 30 mm. Although some clutter is present, the cyst is visible in all images. DAX processed image show CNR improvement of 56 % from 1.79 to 2.79. Lastly, Figure 5.16 (a)-(f) show the spherical cysts. DAX improved CNR in azimuth direction by 76 % and in elevation direction by 72 %. Table 5.1 lists CNR values. (a) (b) (c) (d) (e) (f) Figure 5.14. Experimental 8 mm anechoic cyst images. (a)-(c) are acquired with short axis of the cyst positioned in azimuth direction with standard beamforming. (d)-(f) show DAX processed images. All images are log-compressed and shown with 35 dB dynamic range 106 (a) (b) (c) (d) (e) (f) Figure 5.15. Experimental 8 mm anechoic cyst images. (a)-(c) are acquired with short axis of the cyst positioned in elevation direction with standard beamforming. (d)-(f) show DAX processed images. All images are log-compressed and shown with 35 dB dynamic range 107 (a) (b) (c) (d) (e) (f) Figure 5.16. Experimental 10 mm anechoic spherical cyst images. (a)-(c) are with standard beamforming. (d)-(f) show DAX processed images. All images are log- compressed and shown with 35 dB dynamic range Row-column DAX CNR (cylindrical cyst in the azimuth direction) 2.08 4.27 CNR (cylindrical cyst in the elevation direction) 1.79 2.79 CNR (spherical cyst in the azimuth direction) 1.68 2.95 CNR (spherical cyst in the elevation direction) 0.55 0.95 Table 5.1. Experimental CNR values of the cylindrical and spherical cysts 5.5 Discussion I have experimentally verified the feasibility of a row-column device for 3-D imaging using a 5 MHz 256 × 256 2-D array. The array was made using a modified 1-3 108 composite fabrication process. My experimental results indicate the feasibility of 3-D imaging using a row-column transducer array with a reduced fabrication complexity and a decreased number of channels compared to a fully sampled 2-D array of comparable size. Rectilinear volumetric scans with a wide field of view close to the transducer could prove more useful for abdominal, breast, or vascular imaging when overlying bone is absent from the field of view. The impedance and pulse-echo measurements showed good agreement between simulation and experiment. Using this row-column addressing scheme, the high electrical impedance associated with small elements in a typical 2-D array was avoided. The small differences may be partially due to additional parasitic cable capacitance not included in the KLM model. In simulation, the center frequency was 5.2 MHz with a -6 dB fractional bandwidth of 67 %. Experimentally, the spectrum of the pulse has a center frequency of 5.3 MHz and a -6 dB fractional bandwidth of 53 %. The lower experimental bandwidth is believed to be a result of variation in bond thickness since it is quite difficult to achieve highly uniform pressure over a 40 mm × 40 mm area. Using the wire target phantom, the -6 dB beamwidth was 0.68 mm in azimuth and 0.70 mm in elevation compared to an expected beamwidth of 0.55 mm calculated from Field II simulations. In both cases, there are sidelobes at -13 dB and some clutter below -20 dB. The -6 dB beamwidth of DAX processed image was 0.60 mm in azimuth and 0.63 mm in elevation. DAX was able to suppress high clutter and reduce sidelobes. Using anechoic cyst phantoms, DAX improved visibility of the target and the CNR by at least 56 %. Sidelobes from the wire targets and clutter in the anechoic cyst regions are present, which may be due to the variability of element-to-element performance in terms of sensitivity 109 and bandwidth. If these issues can be addressed, DAX should be able to improve the CNR further. In theory, real-time 3-D rectilinear imaging is possible if enough system channels and parallel beamformers are available. In this experiment, I acquired data and beamformed synthetically due to a limited channel count. Data acquisition takes about 2 hours in the current implementation. Future work includes improving transducer element uniformity and obtaining 3-D images of in-vitro and excised tissue specimens. 110 Chapter 6: Discussion and Future work In summary, I have presented the Dual Apodization with Cross-correlation (DAX) technique that suppresses sidelobes and lowers clutter, thus improving CNR, without compromising spatial resolution in ultrasound imaging. The main idea behind this method is to use a pair of apodization schemes that are highly cross-correlated in the mainlobe but have low or negative cross-correlation in the sidelobe region. DAX uses two sets of beamformed data acquired with two different receive apertures and cross- correlates segments of RF data. This cross-correlation matrix serves as a pixel-by-pixel weighting function which will be multiplied to the sum of the two data sets. Theory and simulation were validated in ultrasound tissue-mimicking phantoms where contrast improvement in terms of CNR was 139 % in simulation and 123 % experimentally. Lateral and axial resolutions are not sacrificed to improve CNR. The alternating pattern showed the highest CNR experimentally. Occasionally, DAX will add artificial dark spots in the speckle region. In cystic regions, it may be possible that clutter signals will have a high cross-correlation coefficient. In this situation, minimal or no improvement in contrast will be seen. Using multiple transmit foci and using DAX at depths near the transmit foci would lower the frame rate. However, it will give higher overall CNR throughout the image and might be more robust with stronger aberrators. I investigated methods to minimize the occurrence of both of these artifacts when only a single transmit focus is available. Using a 2-D cross-correlation, a 2-D median filtering of the cross-correlation coefficients, a modified weighting function and a depth dependent weighting function, I was able to reduce the 111 artifacts without affecting the CNR and without extra computation burden. The optimized DAX has been shown to improve contrast in anechoic cysts in the presence of phase aberration and electronic noise. The improvement in CNR was shown through simulation and experiments using a commercial phantom and excised porcine tissue. The DAX algorithm was also compared with GCF with M 0 = 2 in the presence of phase aberration in terms of CNR. DAX performed better than GCF in most cases, especially at the transmit focus. Dynamic DAX would be most effective when we have a single anechoic target at a focal region. However, as the animal experiments showed, an alternating pattern greater than 2-2 might be too aggressive in an in-vivo situation. A 2-2 DAX alternating pattern with depth dependent weighting function turned out to be the best solution. Lastly, I was also able to apply the DAX to 3-D ultrasound with at least 56 % improvement in CNR. With a row-column array, since the focusing is done only in one direction, higher grating lobes are present in each of the two sparse receive data set used in DAX. Thus a linear mapping weighting function worked well with 1-way focusing. One area of future work is to investigate other areas where DAX can be successfully applied and to obtain images in vivo. Another area of work is to combine DAX with other speckle reduction algorithms to improve CNR in low contrast targets. 6.1 Applications to emerging ultrasound technology In the past several years, novel ultrasound imaging methods such as real-time 3-D ultrasound and high frame rate ultrasound have been proposed where two-way beamforming is not used or is not possible. Most of these newer methods essentially use 112 one-way beamforming where focusing is only done in receive mode. As a result, these newer methods can have high clutter levels making low contrast targets difficult to detect. These novel ultrasound imaging methods are briefly discussed below. 6.1.1 Real-time 3-D ultrasound As demonstrated in chapter 5, DAX was successfully applied with row-column array imaging. In theory, real-time 3-D rectilinear imaging is possible if enough system channels and parallel beamformers are available. If more improvements can be made in transducer fabrication and hardware, DAX could further improve contrast in anechoic lesions. 6.1.2 High frame rate imaging Among the factors which govern the performance of the ultrasound image, frame rate is the rate of image acquisition. It is ultimately limited by the speed of sound in the medium being imaged, the depth of acquisition and number of scan lines required or number of transmit firings. We do not have much flexibility with the first two parameters. For a particular transmit event, enough time must be allowed for the ultrasound pulse to make a round trip for the desired depth. If higher frame rates can be achieved, there is less blurring of the image from motion of the subject. In elasticity imaging, the ultrasound frames acquired during tissue deformation are analyzed to estimate the internal displacements and strains. If the deformation rate is high, high-frame-rate imaging techniques are required to avoid severe decorrelation between the neighboring ultrasound images (Bercoff et al. 2001). Because only one transmission is 113 required to construct images, this method may achieve a high frame rate. Since the frame rate is inversely proportional to the number of transmit events, in case of N transmits, a frame rate improvement of a factor of N can be achieved. To explore the utility of DAX for high frame rate imaging, I have performed a Field II simulation where a plane wave is used in transmit and beamforming is done only in receive (Lu 1997, Bercoff et al. 2001). Figure 6.1 compares standard 1-way beamforming with GCF and DAX. The CNR values are listed in Table 6.1. DAX was able to improve CNR by 125 %. Although we do not have capability to perform DAX processing in real-time at this time, this work demonstrates the feasibility of performing high frame rate imaging with improved contrast performance. Figure 6.1. Field II simulation results using a 3 mm anechoic cyst with receive beamforming only. Standard GCF DAX 2-2 CNR 2.41 4.76 5.42 Table 6.1. CNR values from a Field II simulation results using a 3 mm anechoic cyst with receive beamforming only. 114 6.2 Applications to ultrasound systems with reduced receive channels Receive channels are much more expensive than transmitters. Reducing receive channels will allow the transducer to be smaller, portable and cost-effective at the expense of contrast and spatial resolution. Preliminary results with the DAX algorithm proved that this technology can also be used with sparse array transducers with reduced receive channels. Figure 6.2 shows the lateral beamplot simulation with 4 λ pitch. The grating lobes that I purposely created were successfully suppressed after DAX operation. However, the second pair of grating lobes that are caused by a 4 λ pitch remain. Using the experimental cyst data set from the chapter 3, when the receive channels are reduced by a factor of 4, results showed that that DAX can successfully improve CNR. Figure 6.3 shows the experimental cyst images with reduced receive channels. Table 6.2 lists CNR values. Future work will also include evaluating DAX with sparse receive channels in the presence of phase aberration and with in-vivo data. 115 Figure 6.2.Later beamplots with 4 λ pitch. The dotted and Dash-dot lines are RX 1 and RX 2 respectively. Standard beamformed data is plotted in a dashed line. DAX is plotted in a solid line. (a) (b) Figure 6.3. Experimental results using a 3 mm anechoic cyst with (a) 16 receive channels with a λ pitch and (b) effective 16 receive channels with a 4 λ pitch. -10 -8 -6 -4 -2 0 2 4 6 8 10 -100 -90 -80 -70 -60 -50 -40 -30 -20 -10 0 lateral position (mm) amplitude (dB) RX 1 RX 2 Standard DAX Grating lobes I created Grating lobes due to 4 λ pitch 116 StandardGCF DAX CNR (16 receive channels with λ pitch) 4.35 5.23 8.71 CNR (4 λ pitch, effective 16 receive channels) 4.02 5.57 10.61 Table 6.2. Experimental CNR values of a 3 mm anechoic cyst using fewer receive channels 6.3 in-vivo experiments Future work will also focus on evaluating DAX using in vivo data. Although the CNR values are generally reported as a performance indicator of an algorithm in the literature and are directly related to fundamental quality of an image, it is up to the clinicians and radiologist to ultimately provide diagnosis. Therefore, the interpretation of the images will be also done by an experienced clinician or a trained radiologist. 6.4 Low contrast targets One limitation of the current DAX algorithm is that it does not improve contrast of hyper-echoic or hypo-echoic lesions since signals are well-correlated inside and outside the lesions. These low contrast targets comprise of not only clutter signal but also mainlobe signals or speckle. A more generalized DAX algorithm which adjusts the weighting as a function of cross-correlation could be developed to improve contrast of hyper–echoic or hypo-echoic targets. Another area to explore is a possibility of hybrid method by combining DAX with other speckle reduction algorithms. Compounding algorithms such as spatial compounding, frequency compounding and phase compounding improve speckle SNR at the expense or worse spatial resolution (Abott and Thurstone 1979). 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Control, vol. 38, 125-132, March 1991. 124 Appendix A: C++ code for data acquisition with Ultrasonix bool createSequence1(texo &tex,int ti,int ri) { int j; texoTransmitParams tx; texoReceiveParams rx; tx.centerElement = ((ti) * 10) + 5; rx.centerElement = ((ri) * 10); tx.aperture = 64; tx.focusDistance = 30000; tx.angle = 0; tx.frequency = 5000000; strcpy(tx.pulseShape, "+-+-"); tx.useManualDelays = false; tx.tableIndex = -1; rx.aperture = 32; rx.angle = 0; rx.maxApertureDepth = 20000; rx.acquisitionDepth = 60000; rx.speedOfSound = 1540; rx.channelMask[0] = 0; rx.channelMask[1] = 1; rx.applyFocus = false; rx.useManualDelays = false; rx.decimation = 0; rx.customLineDuration = 0; rx.lgcValue = 4000; rx.tgcSel = 0; rx.tableIndex = -1; for(j = 0; j < 32; j++) { // 0 = on, 1 = off rx.channelMask[0] = ~(1 << j); lineSize = tex.addLine(rfData, tx, rx); if(lineSize == -1) return false; } return true; } 125 Appendix B: DAX processing in MATLAB %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: f_dax_alternating_1DAxial.m % 2. Author: Chi Hyung Seo % 3. Version: 1.0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 4. Inputs: % total standard beamformed data % total1 RX1 % total2 RX2 % thr threshold % segment cross-correlation length % 5. Description: % Performs 1D axial cross-correlation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function f_dax_alternating_1DAxial (total, total1, total2, thr, segment) rf_matrixa = total1'; rf_matrixb = total2'; mean_rf=total'; rf_matrixa = rf_matrixa/max(max(rf_matrixa))+1e-20; rf_matrixb = rf_matrixb/max(max(rf_matrixb))+1e-20; mean_rf = mean_rf/max(max(mean_rf))+1e-20; cc=ones(size(rf_matrixa)); rf_matrixnla1 = zeros(size(rf_matrixa)); for j=1:min(size(rf_matrixa)); for i=1+segment:max(size(rf_matrixa))-segment; a = rf_matrixa(i-segment:i+segment,j); b = rf_matrixb(i-segment:i+segment,j); cc(i,j)= sum(a.*b)/sqrt(sum(dot(a,a))*sum(dot(b,b))); if (cc(i,j)<thr) cc(i,j)=thr; end end end 126 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: f_dax_alternating_1DLateral.m % 2. Author: Chi Hyung Seo % 3. Version: 1.0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 4. Inputs: % total standard beamformed data % total1 RX1 % total2 RX2 % thr threshold % segment cross-correlation length % 5. Description: % Performs 1D lateral cross-correlation %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function f_dax_alternating_1DLateral (total, total1, total2, thr, segment) rf_matrixa = total1'; rf_matrixb = total2'; mean_rf=total'; rf_matrixa = rf_matrixa/max(max(rf_matrixa))+1e-20; rf_matrixb = rf_matrixb/max(max(rf_matrixb))+1e-20; mean_rf = mean_rf/max(max(mean_rf))+1e-20; cc=ones(size(rf_matrixa)); rf_matrixnla1 = zeros(size(rf_matrixa)); for i=1:max(size(rf_matrixa)) for j=1+segment:min(size(rf_matrixa))-segment; a = rf_matrixa(i,j-segment:j+segment); b = rf_matrixb(i,j-segment:j+segment); cc(i,j)= sum(a.*b)/sqrt(sum(dot(a,a))*sum(dot(b,b))); if (cc(i,j)<thr) cc(i,j)=thr; end end end 127 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: f_dax_alternating_2Dlinear.m % 2. Author: Chi Hyung Seo % 3. Version: 1.0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 4. Inputs: % total standard beamformed data % total1 RX1 % total2 RX2 % segmentlateral lateral cross-correlation length % segmentaxial axial cross-correlation length % start start location in mm to apply DAX % stop stop location in mm to apply DAX % fs sampling frequency % 5. Description: % Performs 2D cross-correlation with linear mapping %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function f_dax_alternating_2Dlinear (total, total1, total2, thr, segmentlateral, segmentaxial, start, stop, fs) rf_matrixa = total1'; rf_matrixb = total2'; mean_rf=total'; rf_matrixa = rf_matrixa/max(max(rf_matrixa))+1e-20; rf_matrixb = rf_matrixb/max(max(rf_matrixb))+1e-20; mean_rf = mean_rf/max(max(mean_rf))+1e-20; cc=ones(size(rf_matrixa)); rf_matrixnla1 = zeros(size(rf_matrixa)); for j=1+segmentlateral:min(size(rf_matrixa))-segmentlateral; for i=1+segmentaxial:max(size(rf_matrixa))-segmentaxial; i_mm =floor(((i)*1.54)/(fs*2)); clear cc2dnorm a = rf_matrixa(i-segmentaxial:i+segmentaxial,j- segmentlateral:j+segmentlateral); b = rf_matrixb(i-segmentaxial:i+segmentaxial,j- segmentlateral:j+segmentlateral); cc2dnorm= sum(sum(a.*b))/sqrt(sum(dot(a,a))*sum(dot(b,b))); if (i_mm>= start && i_mm<= stop) cc(i,j)=0.5*cc2dnorm+0.5; 128 end end end 129 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: f_dax_alternating_2Dlog.m % 2. Author: Chi Hyung Seo % 3. Version: 1.0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 4. Inputs: % total standard beamformed data % total1 RX1 % total2 RX2 % segmentlateral lateral cross-correlation length % segmentaxial axial cross-correlation length % start start location in mm to apply DAX % stop stop location in mm to apply DAX % fs sampling frequency % 5. Description: % Performs 2D cross-correlation with log mapping %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% function f_dax_alternating_2Dlog (total, total1, total2, thr, segmentlateral, segmentaxial, start, stop, fs) load('F:\DEFENSE2008\GLmag_RXfoc_DAX22_TXfocus30mm.mat'); log_vector=ceil(abs(GLmag));%RXfoci_vector=[15:50] mm depth_vector=RXfoci_vector; rf_matrixa = total1'; rf_matrixb = total2'; mean_rf=total'; rf_matrixa = rf_matrixa/max(max(rf_matrixa))+1e-20; rf_matrixb = rf_matrixb/max(max(rf_matrixb))+1e-20; mean_rf = mean_rf/max(max(mean_rf))+1e-20; cc=ones(size(rf_matrixa)); rf_matrixnla1 = zeros(size(rf_matrixa)); for j=1+segmentlateral:min(size(rf_matrixa))-segmentlateral; for i=1+segmentaxial:max(size(rf_matrixa))-segmentaxial; i_mm =floor(((i)*1.54)/(fs*2)); log_vector_index=find(depth_vector==i_mm); clear cc2dnorm 130 a = rf_matrixa(i-segmentaxial:i+segmentaxial,j- segmentlateral:j+segmentlateral); b = rf_matrixb(i-segmentaxial:i+segmentaxial,j- segmentlateral:j+segmentlateral); cc2dnorm= sum(sum(a.*b))/sqrt(sum(dot(a,a))*sum(dot(b,b))); if (i_mm>= start && i_mm<= stop) cc(i,j)=10.^((log_vector(log_vector_index)/2*cc2dnorm- log_vector(log_vector_index)/2)/20); end end end
Abstract (if available)
Abstract
This dissertation work introduces a novel sidelobe and clutter suppression method in ultrasound imaging called Dual Apodization with Cross-correlation or DAX. DAX dramatically improves the contrast-to-noise ratio (CNR) allowing for easier visualization of anechoic cysts and blood vessels. This technique uses dual apodization or weighting strategies that are effective in removing or minimizing clutter and efficient in terms of computational load and hardware/software needs. This dual apodization allows us to determine the amount of mainlobe versus clutter contribution in a signal by crosscorrelating RF data acquired from two apodization functions. Simulation results using a 128 element 5 MHz linear array show an improvement in CNR of 139 % compared to standard beamformed data with uniform apodization in a 3 mm diameter anechoic cylindrical cyst. Experimental CNR using a tissue-mimicking phantom with the same sized cyst shows an improvement of 123 % in a DAX processed image.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Seo, Chi Hyung
(author)
Core Title
Improved contrast in ultrasound imaging using dual apodization with cross-correlation
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Biomedical Engineering
Publication Date
12/02/2008
Defense Date
10/20/2008
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
3-D ultrasound,contrast improvement,cross-correlation,OAI-PMH Harvest,ultrasound imaging
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Yen, Jesse T. (
committee chair
), Cannata, Jonathan Matthew (
committee member
), Kim, Eun Sok (
committee member
), Liu, Brent J. (
committee member
), Shung, Kirk (
committee member
)
Creator Email
chiseo@gmail.com,chiseo@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-m1851
Unique identifier
UC1194621
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etd-Seo-2520 (filename),usctheses-m40 (legacy collection record id),usctheses-c127-131768 (legacy record id),usctheses-m1851 (legacy record id)
Legacy Identifier
etd-Seo-2520.pdf
Dmrecord
131768
Document Type
Dissertation
Rights
Seo, Chi Hyung
Type
texts
Source
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
Repository Name
Libraries, University of Southern California
Repository Location
Los Angeles, California
Repository Email
cisadmin@lib.usc.edu
Tags
3-D ultrasound
contrast improvement
cross-correlation
ultrasound imaging