Harmonic Source Wavefront Correction for Ultrasound Imaging

Transcription

1 Harmonic Source Wavefront Correction for Ultrasound Imaging by Scott W. Dianis Department of Biomedical Engineering Duke University Date: Approved: Dr. Olaf T. von Ramm, Ph.D., Advisor Dr. Stephen W. Smith, Ph.D. Dr. David S. Enterline, M.D. Dr. Patrick D. Wolf, Ph.D. Dr. Donald B. Bliss, Ph.D. Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2010

2 Abstract (Biomedical Engineering) Harmonic Source Wavefront Correction for Ultrasound Imaging by Scott W. Dianis Department of Biomedical Engineering Duke University Date: Approved: Dr. Olaf T. von Ramm, Ph.D., Advisor Dr. Stephen W. Smith, Ph.D. Dr. David S. Enterline, M.D. Dr. Patrick D. Wolf, Ph.D. Dr. Donald B. Bliss, Ph.D. An abstract of a dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Biomedical Engineering in the Graduate School of Duke University 2010

3 Copyright 2010 by Scott W. Dianis All rights reserved except the rights granted by the Creative Commons Attribution-Noncommercial License

4 Abstract Aberration is a correctable phenomenon that degrades diagnostic quality in a significant number of ultrasound images. Previous aberration correction studies have focused on development of aberration estimation algorithms or on aberration reduction by using harmonic imaging. In the past, a major drawback of aberration estimation algorithms has been the assumptions required about the imaging target, assumptions that can limit clinical application where correction for multiple locations within a scan may be required. Harmonic imaging attempts to reduce the effect of aberration, without making assumptions about the imaging target, by using a lower-frequency transmit beam that is less prone to aberration. However, harmonic imaging does not correct for any aberration that may remain. It is hypothesized that a harmonic source wavefront correction technique is capable of creating a point-like acoustical source that allows for estimation and correction of two-dimensional aberration in a clinical setting. Harmonic source wavefront correction utilizes the reduced aberration of harmonic imaging to create a known acoustical source to satisfy the assumptions of the aberration estimation algorithms, thus improving their clinical application. Generation of a point-like acoustical source in the presence of aberration is demonstrated using both spatially correlated and spatially uncorrelated electronic aberrators varying in strength from 0.25π radians to 1.16π radians RMS focusing error. Beam properties of the 2.08 MHz fundamental, 4.16 MHz generated harmonic, and iv

5 4.17 MHz imaging beams were compared; in the presence of aberration, relative peak beam amplitude of the 4.16 MHz generated harmonic beam was up to 81% higher than the 4.17 MHz imaging beam, while -6 db beam width indicated the 4.16 MHz generated harmonic beam was 88% narrower and more point-like than the 2.08 MHz fundamental beam. The feasibility of harmonic source wavefront correction was demonstrated by correcting for spatially uncorrelated electronic aberrators in a water tank using a point target, specular reflector, and speckle region as correction targets. Harmonic source wavefront correction was paired with a cross-correlation algorithm to estimate corrective delays and was most effective in correcting peak amplitude of the 4.17 MHz imaging beam using a point target (up to 94% improvement), followed by use of a specular reflector (up to 83% improvement), followed by use of a speckle region (up to 47% improvement). Aberration correction is sensitive to signal-to-noise ratio (SNR), and correction utilizing the 2.08 MHz fundamental, which provided higher SNR, was more effective than correction utilizing the more point-like 4.16 MHz harmonic for the experimental setup used. A harmonic SNR of 14 db was estimated as necessary for harmonic-based correction performance to equal or surpass fundamental-based correction, regardless of fundamental SNR. Finally, performance of harmonic source wavefront correction was quantified in a clinical setting. Correction of spatially correlated electronic aberrators was performed using both ex vivo porcine kidneys and the left kidneys of 11 human volunteers as correction targets. Correction utilizing porcine kidney resulted in 10 db greater improvement in peak beam amplitude than correction utilizing the left kidney of human volunteers. Body wall aberration present in the human volunteers was not accounted for during correction and likely caused the disparity in correction performance. An average upper limit for body wall aberration for the human subjects was estimated at 65 ns (±9 ns) RMS. v

6 Contents Abstract List of Tables List of Figures Acknowledgements iv xii xiii xvi 1 Introduction Introduction Hypothesis Preview of Chapters Background Ultrasound Imaging Pulse-echo Imaging Focusing Steering Refraction and Reflection Attenuation Diffraction Imaging Target Types Acoustics Linear Acoustics vi

7 2.2.2 Nonlinear Acoustics Harmonic Generation Image Correction Image Quality Phase Aberration Amplitude Aberration Waveshape Aberration Aberrators Hypothesis Harmonic Source Wavefront Correction Introduction Isoplanatic Patch Correction Methods Time-shift Estimation Cramer-Rao Lower Bound Iterative Correction Harmonic Source Method Source Generation Transmit Amplitude and Frequency Focal Distance Arrival Time Estimation Array Geometry Considerations Aberration and Imaging Beam Distortion Introduction Materials and Methods vii

8 4.2.1 Ultrasound Scanner Ultrasound Transducer Spatially Uncorrelated Aberrators Spatially Correlated Aberrators Beam Plots Formation of B-mode Images Results Aberrators Beam Plots Beam Amplitude Side-lobe Level Beam Width Phantom Images Discussion Aberrators Beam Amplitude Side-lobe Level Beam Width Phantom Images Summary and Conclusion Water Tank Correction Introduction Materials and Methods Ultrasound Scanner Ultrasound Transducer viii

9 5.2.3 Spatially Uncorrelated Aberrators RTV Aberrator Harmonic Source Wavefront Correction Beam Plots Reflectors Off-Axis Correction Data Acquisition System Scan Recalculation Comparison of Fundamental and Harmonic Correction Formation of B-Mode Images Contrast Measurements Results Beam Plots Beam Amplitude Side-lobe Level Beam Width Phantom Images Physical Aberrator Off-Axis Correction Comparison of Fundamental and Harmonic Correction Discussion Beam Plots Beam Amplitude Side-lobe Level Beam Width Phantom Images ix

10 5.4.6 Physical Aberrator Off-Axis Correction Comparison of Fundamental and Harmonic Correction Summary and Conclusion Kidney Correction Introduction Materials and Methods Ultrasound Scanner Ultrasound Transducer Spatially Correlated Aberrators Grouped Element Receive and Interpolation Harmonic Source Wavefront Correction Beam Plots Data Acquisition System Scan Recalculation Porcine Kidney Measurement Setup Human Subject Measurement Setup Body Wall Measurements Amplitude Variation Results Beam Plots Beam Amplitude Side-lobe Level Beam Width Body Wall Measurements Amplitude Variation x

11 6.4 Discussion Beam Plots Beam Amplitude Side-lobe Level Beam Width Body Wall Measurements Amplitude Variation Summary and Conclusion Conclusion Discussion of Results Directions for Future Work Estimating Aberration from Image Distortion Improving System SNR Improving Correction Speed Conclusions Bibliography 142 Biography 148 xi

12 List of Tables 2.1 Acoustic properties of selected biological tissues Relative level of 4.16 MHz harmonic versus focal range Properties of the spatially uncorrelated aberrators Properties of the spatially correlated aberrators Off-axis correction locations Theoretical amplitude loss of RTV aberrator Peak amplitude after iterative correction Side-lobe level after iterative correction db beam width after iterative correction Image contrast after correction Signal-to-noise ratio of fundamental and harmonic correction Relative level of harmonic SNR and correction Measured body wall aberration Regression model of body wall aberration and correction Amplitude variation from porcine kidney and human volunteers Correction time xii

13 List of Figures 2.1 Transmission and reception of acoustic waves with a phased array Time-gain control compensation of attenuation Focusing and steering delays Sector scan lines and B-mode display Reflection and refraction of a plane wave Creating a point-like source Normalized Rayleigh distribution Shock parameter σ Harmonic levels as a function of shock parameter Unaberrated fundamental, harmonic, and imaging beam plots Focusing delays caused by phase aberration Correction of waveshape aberration Aberrated fundamental, harmonic, and imaging beam plots Relative sizes of 1-D, 1.5-D/1.75-D, and 2-D array elements Phase aberration measured by 1-D, 1.5/1.75-D, and 2-D arrays Harmonic source wavefront correction experimental setup Harmonic beam versus transmit amplitude Aberrated harmonic beam versus transmit amplitude Phase closure Ultrasound system bandwidth xiii

14 4.2 Measurement aperture Aberration and imaging beam distortion experimental setup Spatially correlated and uncorrelated electronic aberrators Imaging beam with spatially uncorrelated aberrator applied Imaging beam with spatially correlated aberrator applied Peak amplitude with spatially uncorrelated aberrator applied Peak amplitude with spatially correlated aberrator applied Side-lobe level with spatially uncorrelated aberrator applied Side-lobe level with spatially correlated aberrator applied db beam width with spatially uncorrelated aberrator applied db beam width with spatially correlated aberrator applied Aberrated B-mode images of RMI phantom Flowchart of aberration and correction in Circe Point target corrected beam plots Corrected and aberrated 4.16 MHz harmonic RF RTV aberrated and corrected beam plots Specular reflector corrected beam plots Speckle region corrected beam plots Peak beam amplitude with water tank correction applied Side-lobe level with water tank correction applied db beam width with water tank correction applied Corrected B-mode images of RMI phantom Off-axis correction of RMI phantom B-mode images Comparison of fundamental and harmonic correction Equalized SNR fundamental and harmonic correction xiv

15 6.1 Porcine kidney correction experimental setup Human subject correction experimental setup Porcine kidney and human subject corrected beam plots Peak beam amplitude with porcine kidney correction applied Peak beam amplitude with human subject correction applied Side-lobe level with porcine kidney correction applied Side-lobe level with human subject correction applied db beam width with porcine kidney correction applied db beam width with human subject correction applied xv

16 Acknowledgements I could not have completed this without the support and help of many different people. I would first like to thank my parents, Jack and Linda Dianis, for the innumerable ways they have helped me while pursing my studies at Duke. Second, I would like to thank my current and former lab mates: Derrick Chou, Cooper Moore, and Johnny Kuo. They were always willing to provide advice, lend an extra hand, and accommodate my schedule with using the scanner. I would especially like to thank John Castellucci both for the many fruitful discussions we had and for helping resolve the many undocumented features of the T5 scanner. I would also like to thank the members of the Smith, Trahey, and Nightingale labs, especially Nik Ivancevich, for lending equipment and expertise. Many thanks to my wife Allison for providing love, support, experimental and editorial assistance, and for quickly teaching our newborn daughter Elise to sleep through the night. Finally, I would like to thank the members of my committee for their helpful advice and expertise. I would especially like to thank my advisor, Dr. Olaf von Ramm for providing his support and advice during this project. I have greatly enjoyed working in the von Ramm Diagnostic Ultrasound lab, and hope I have been able to make as valuable of a contribution as so many members of the lab have before me. xvi

17 1 Introduction 1.1 Introduction Pulse-echo ultrasound is a widely used and available diagnostic medical imaging modality. Ultrasound provides a low cost, portable, non-ionizing means to image soft tissue in real time. However, ultrasound is susceptible to defocusing effects, termed aberration, caused by inherent sound speed and attenuation variations in the tissues being imaged. As imaging frequency is increased in a bid to improve image quality, the problem of aberration becomes more significant. Aberration causes distortion to the imaging beam, which degrades image quality and thus diagnostic utility. A number of methods have been described to reverse the effects caused by sound speed variations in the tissues being imaged. However, previous aberration correction studies have had several shortcomings. First, aberration correction has been mainly performed with 1-D arrays. Recently, 1.5-D and 1.75-D arrays have been employed in aberration correction studies; these arrays provide somewhat better correction than 1-D arrays for aberrations encountered in clinical ultrasound scans that vary in two dimensions. Few aberration 1

18 correction methods have been developed and tested for true 2-D arrays. Moreover, previous research in aberration correction has primarily focused on developing algorithms to estimate the compensating delays necessary to correct for aberration, not generating improved signal for aberration estimation. Second, previous aberration correction studies required assumptions about the target tissue being corrected. These assumptions typically involved the presence of either a point-like acoustical source or a speckle region. While aberration correction methods designed for point-like acoustical sources could be adapted for speckle regions (and vice-versa), the focus has primarily been on aberration estimation. Very limited work has been done on the other aspect of aberration correction, ensuring the presence of an acceptable acoustical source in the presence of aberration. Thus, these aberration correction methods perform poorly when applied to aberrators requiring acceptable acoustical sources at multiple arbitrary locations for proper correction. Harmonic imaging has been employed in the past to mitigate the distortion caused by aberration. The low-transmit frequency employed by tissue harmonic imaging reduces the effect of aberration, while the second harmonic, generated as the transmitted pulse propagates, provides resolution comparable to standard ultrasound images. While aberration correction using the generated harmonic has been studied to a limited degree, no investigation has been made of using the generated harmonic from the low-frequency transmit to create a known acoustical source. An aberration correction method that does not require assumptions about the medium being corrected will be described. This method, Harmonic Source Wavefront Correction, creates a point-like acoustical source at a user-specifiable location which allows measurement of the aberration present. This measurement of the aberration present can then be used to improve the performance of any of the many aberration correction techniques previously described. 2

19 1.2 Hypothesis It is hypothesized that harmonic source wavefront correction creates a point-like acoustical source which allows for estimation and correction of two-dimensional aberration in a clinical setting. In proving this primary hypothesis, four more specific points are demonstrated. First, this dissertation quantifies how the generated harmonic beam, fundamental beam, and imaging beam are distorted by electronic aberrators of varying strengths. A minimally aberrated generated harmonic beam is essential to creating a point-like correction source. Second, this work verifies that harmonic source wavefront correction is practicable by correcting for a range of aberration strengths in a water tank using a twodimensional array paired with a point target, specular reflector, and speckle region as correction targets. These three correction target types are the primary target types found in clinical scans. Third, performance of harmonic source wavefront correction, which utilizes the generated harmonic signal, is compared with correction utilizing the fundamental signal. Specifically, the impact of signal-to-noise ratio (SNR) on correction performance is investigated, and the situations where harmonic source wavefront correction provides superior correction performance are determined. Fourth, feasibility of harmonic source wavefront correction is investigated in vitro using porcine kidney as a correction target and in vivo using the left kidney of 11 human volunteers as a correction target. 1.3 Preview of Chapters Chapter 2: Background covers basic principles of ultrasound imaging, linear and nonlinear acoustics, and aberration correction. 3

20 Chapter 3: Harmonic Source Wavefront Correction describes the aberration correction method and improvements made to previous harmonic correction methods. Factors affecting generation of a harmonic source are discussed. Chapter 4: Aberration and Imaging Beam Distortion investigates the effect aberration has on the measurement beam (2.08 MHz fundamental and 4.16 MHz second harmonic) and 4.17 MHz imaging beam. Chapter 5: Water Tank Correction investigates the feasibility of second harmonic correction in an attenuation free environment. Performance of second harmonic correction is compared to fundamental correction performance. Chapter 6: Kidney Correction investigates harmonic correction performance using biological tissue. Second harmonic correction performance, as well as amplitude and body wall aberration are measured for human subjects in a clinical setting. Chapter 7: Conclusion discusses the implications of the results from the previous chapters and considers directions for future work. 4

21 2 Background 2.1 Ultrasound Imaging Pulse-echo Imaging Diagnostic ultrasound images are formed by transmitting and receiving acoustical energy into the body. In pulse-echo imaging, an acoustic pulse is transmitted, and the signal back-scattered or reflected as the pulse propagates is received over time (Figure 2.1). Often, the transmit and receive apertures are located on the same transducer array, although the two apertures need not be the same. Each transmission during pulse-echo imaging yields a received signal over time. The measurement of elapsed time can be converted to a determination of depth by using the propagation speed of the transmitted pulse and received echoes: z = c 2 t R (2.1) where t R is the receive time, c is the sound speed, and z is the depth or round-trip distance. It is difficult to extract structural information from the raw rf signal received by the transducer. The rapid oscillations of the received pulse are typically in the MHz 5

22 a) b) Figure 2.1: Transmission (a) and reception (b) of acoustic waves (W ) with a phased array (E). Electronic delays (D) focus the transmitted pulse (T ) at point P. Electronic delays are again used to focus the received waveform (R). range, making it difficult to pick out the much slower variations due to structure. To extract the structural information from the rf, the received signal is processed with a bandpass filter centered at the transmit frequency in order to remove noise and prevent aliasing, and the signal then is envelope-detected using the Hilbert transform. Due to attenuation, the amplitude of the received signal decreases exponentially with an increase in range. To compensate for attenuation, the detected signal is amplified as a function of range, a process referred to as time-gain control (TGC). By compensating for the effects of attenuation, the relative strength of echoes from varying depths can be compared (Figure 2.2). 6

23 a) Signal Amplitude b) Signal Amplitude Uncompensated Receive Signal Time or Depth Receive Signal After TGC Gain Time or Depth Received Signal Attenuation Envelope TGC Gain Figure 2.2: Time-gain control (TGC) compensates for the increased attenuation of signals received from grater depths Focusing Focusing the transmit and receive beams is essential for the creation of high-resolution two- and three-dimensional images. Focusing improves lateral resolution in the nearfield by essentially shifting the Fraunhofer region (see Section 2.1.6) to the focal plane, thus the beam pattern near the focal plane (D 1 (θ)) is approximated by the Fourier transform of the aperture: D 1 (θ) = FT { P (r)a(r)e jφ(r)} (2.2) where P (r) is the spatial function of the aperture, A(r) is the amplitude weighting across the aperture, and φ(r) is the focusing function. Focusing can be achieved using a physical lens, by bending the aperture to a radius equal to the focal distance (R f ), or by what is more commonly done with phased arrays an application of electronic 7

24 x n R θ d n P Figure 2.3: Focusing delays are calculated from the distance between each element (d n ) and the focal point P. focusing delays. Focusing delays are calculated by determining the path length (d n ) between an element and the desired focal point, while path lengths d n are calculated using the Pythagorean Theorem. For a focal point on the imaging axis, the focusing delays are a quadratic function of position along the aperture. For an off-axis focal point (Figure 2.3), the focusing delays are the sum of a linear function of position and a quadratic function of position: τ 0 = R c (2.3) τ n = d n c = x n sin θ + x2 n(1 + sin 2 θ) + τ 0 c 2cR where x n is the position of element n, R is the focal distance, and θ is the steering angle. The quadratic function of position is referred to as the focusing component of the delay, and is independent of steering angle. The linear function of position is referred to as the steering component of delay, determining the steering angle of the beam, and is the subject section

25 The ratio of the focal distance to the aperture size, D, is called the f-number (f/#): f/# = R f D (2.4) and is a common specification for ultrasound systems. For focused circular apertures, lateral resolution is given by the following equation: 1.22λ(f/#) = 1.22 λz D. (2.5) z=rf The depth of focus of an ultrasound beam is often defined as the range over which the beam amplitude varies by less than -6 db. Hunt et al. [21] have computed the depth of focus to be: 9.7λ(f/#) 2 (2.6) for a circular aperture. In transmit, a pulse can only be focused at a single distance, but the received signal is not subject to that limitation. Because focusing is achieved electronically, different focusing delays can be applied to the received signal as it arrives and time/depth increases, keeping the received signal in focus from the beginning to the end of the scan line. Depth of focus is useful to determine the range over which a given set of focusing delays is valid. When the signal begins to arrive from a depth greater than the current focus plus one-half the depth of focus, a new set of focusing delays can be applied. The regions with constant focusing delays are called focal zones Steering To steer an array steering delays can simply be added in to the focusing delays of the focusing function, φ(r) in order to obtain proper focusing at different steering angles (Figure 2.3). A sector scan consists of evenly spaced scan lines steered azimuthally 9

26 Scan Lines Display Figure 2.4: Sector scan lines and B-mode display. between θ 0 and θ 0 relative to the transducer. A B-mode image consists of the envelope-detected data from the scan lines of a sector scan (Figure 2.4). A volume scan consists of sector scans swept from θ 0 to θ 0 azimuthally and from φ 0 to φ 0 in elevation. Volumetric images can be displayed using a number of methods; typically, however, envelope-detected data from one or more arbitrary planes through the volume are displayed. These are referred to as C-mode images [51] Refraction and Reflection Acoustical impedance (Z) of a material is the product of sound speed (c) and the material s density (ρ): Z = ρc. (2.7) When an ultrasound wave encounters an interface between two materials with differing acoustical impedances and a scale greater than one wavelength, a portion of 10

27 θ A θ A Transmittted S Reflected A B Refracted θ B Figure 2.5: Reflection and refraction of a plane wave at interface S between materials A and B. the wave will be reflected and a portion may be transmitted. For a wave of amplitude P normally incident to a boundary S between two materials A and B, the reflected wave will be equal to the product of the reflection coefficient R and the wave amplitude P ; and the transmitted wave will be equal to the product of the transmission coefficient T and the wave amplitude P. The reflection coefficient(r) and transmission coefficient (T ) are each a function of the impedances of materials A and B: R = Z B Z A Z B + Z A T = 1 R. (2.8a) (2.8b) If the incident wave is not normal to the boundary S, as in Figure 2.5, then the angle of the reflected wave will be equal to that of the incident wave, while the angle of the transmitted wave will differ from that of the incident wave wherever the sound speed of the two materials differs. This phenomenon is known as refraction, and the relationship between the angle of the incident wave and the angle of the transmitted 11

28 wave follows Snell s law: sin θ B sin θ A = c B c A. (2.9) For incident angles greater than θ A sin 1 ( c A c B ), no wave will be transmitted through the boundary. For a non-normal incident wave, the reflection coefficient becomes: R = Z B cos θ A Z A cos θ B Z B cos θ A + Z A cos θ B T = 1 R. (2.10a) (2.10b) Attenuation As ultrasound waves propagate through tissue, energy loss occurs, primarily through the process of absorption. This loss leads to attenuation. Attenuation of an ultrasound wave is generally modeled by: p(z) = P 0 e α(f)z (2.11) Where P 0 is the initial amplitude, z is the distance traveled by the wave in centimeters, and α is the frequency-dependent attenuation coefficient, in units of Nepers/cm. In typical diagnostic ultrasound imaging conditions, attenuation is proportional to frequency, such that: α(f) = α 0 βf (2.12) where the conversion factor β equals db/neper, and a value of α 0 equal to 0.3 db/cm-mhz is typically assumed for tissue, although values may range as high as 1.9 db/cm-mhz for breast tissue [17]. Attenuation can be compensated for by applying a corrective gain as a function of depth, process known as range gain control. 12

29 2.1.6 Diffraction Conventional diagnostic ultrasound systems utilize the emission and reception of acoustic waves from a transducer aperture for imaging (Figure 2.1). If p(t) is a pressure disturbance in the aperture, then the pressure at time t and position r 0 is given by the Rayleigh-Sommerfeld integral: P (r 0, t) = ρ 0 2π S ( ) u n t r 0 r 1 c t r 0 r 1 cos (n (r 0 r 1 ))ds (2.13) where n is a unit vector normal to aperture S, u n is the particle velocity normal to S, and r 1 is a point within S. This integral is a mathematical model of Huygens Principle, which states the pressure at a point r 0 in the field is the sum of the spherical wavefronts at point r 1 emitted from the aperture S. Equation (2.13) is not an exact solution for the pressure field, but is reasonably accurate for field points that are not too close to the aperture. Note that for small angles between the aperture and the field point, the obliquity term, cos (n (r 0 r 1 )) vanishes. If we consider only constant frequency disturbances on the aperture, then equation (2.13) may be expressed as: P (r 0 ) = 1 P (r 1 ) ejk r 0 r 1 jλ S r 0 r 1 cos (n (r 0 r 1 ))ds (2.14) or, alternatively, as: where P (r 0 ) = S h(r 0, r 1 )P (r 1 )ds (2.15) h(r 0, r 1 ) = 1 e jk r 0 r 1 jλ r 0 r 1 cos (n (r 0 r 1 )). (2.16) The propagation can be seen as a complex linear filter with impulse response h(r 0, r 1 ) applied to the wavefield in the source aperture. 13

30 Fresnel Approximation Now consider the pressure distribution in an observation plane defined by z = z 0 that results from a disturbance in the aperture plane z = 0. Then r 0 = [x 0, y 0, z 0 ], r 1 = [x 1, y 1, 0], and r 0 r 1 = (x 0 x 1 ) 2 + (y 0 y 1 ) 2 + z 2 0. (2.17) If the distance between the aperture plane and the observation plane is sufficiently large in relation to the extent of the aperture disturbance or observation region, small angle approximations can be introduced: r 0 r 1 = z 0 cos (n (r 0 r 1 )) = 1 h(r 0, r 1 ) = 1 jλz 0 e jk r 0 r 1. (2.18a) (2.18b) (2.18c) The small angle approximation eliminates the obliquity term from the Rayleigh- Sommerfeld equation. The path length defined in equation (2.17) may now be rewritten as: (x0 ) 2 ( ) 2 x 1 y0 y 1 r 0 r 1 = z (2.19) z z After truncation of the binomial expansion given by: the approximate path length is given by: r 0 r 1 = z 1 + b = b 1 8 b (2.20) [ ( x0 x 1 z ) ( ) ] 2 y0 y 1. (2.21) z 14

31 This path length approximation, known as the Fresnel approximation, replaces the spherical wavefront with a quadratic approximation so that h(r 0, r 1 ) = 1 [ [ [ ] e jkz jk 0 (x 2z e y2 1 ]e ) jk (x 2z y2 0 ]e ) jk (x 2z 0 x 1 +y 0 y 1 ) 0. (2.22) jλz 0 Fraunhofer Approximation The propagation filter in equation (2.22) may be simplified further if we assume that It follows that: z k(x2 1 + y1) 2. (2.23) 2 P (r 0 ) = 1 [ ] [ ] e jkz jk 0 (x 2z e y2 0 ) jk (x 2z P (x 1, y 1 )e 0 x 1 +y 0 y 1 ) 0 dx 1 dy 1. (2.24) jλz 0 S Equation (2.24) is known as the Fraunhofer approximation of the propagation integral, also known as the far- field approximation. Except for the scaling term preceding the integration, equation (2.24) is simply the Fourier transform of the aperture function P (x 1, y 1 ) evaluated at spatial frequencies f x and f y P (x 0, y 0 ) FT {P (x 1, y 1 )} f x = x 0 λz 0 f y = y 0 λz 0. (2.25a) (2.25b) (2.25c) For a circular aperture defined by radius a, the far-field beam pattern, D 1 (θ), is given by: D 1 (θ) = FT {P (r)a(r)} = 2J 1(ka sin θ) ka sin θ (2.26) where P (r) is the spatial function of the aperture, A(r) is the amplitude weighting across the aperture, J 1 (x) is a Bessel function of the first kind, and k = 2π/λ is the 15

32 wave number. If lateral angular resolution is to be defined as the first zero crossing of the main lobe of the beam in the plane x 0, y 0 plane (Rayleigh diffraction limit), then lateral angular resolution is: 1.22 λ D. (2.27) Imaging Target Types In a typical diagnostic ultrasound image, the received signal results from the sum of echoes from a large number of reflecting targets. Reflecting targets can be grouped into three main types: point reflectors, specular reflectors, and speckle regions. Diagnostic ultrasound images typically contain all three reflector types, and images of individual structural features may contain a combination of reflector types. Point Reflectors The simplest reflector type is the point reflector, consisting of a zero-dimensional reflecting point in space. When insonified, the point reflector reflects a spherical wave, independent of the transmit beam. Reflections for three-dimensional structures can be determined by spatially convolving the spherical wave response of the point target with the structure, in the manner of Huygens principle. Provided that the structure is small relative to the resolution of the ultrasound system, three-dimensional objects can be considered one-dimensional point reflectors. Because a point reflector always reflects a spherical wave, the signal received from a point reflector with a known location can be used to determine whether any wave distortion has occurred by comparing it to the expected spherical wave. Unfortunately, single point reflectors are rarely encountered in diagnostic ultrasound scans; more often they are mixed in with other confounding three-dimensional structures, which makes measurement of distortion difficult. 16

33 + = Transmit Receive Transmit-Receive Figure 2.6: A point-like source can be created by combining a tightly focused transmit beam with a range-gated receive beam. The signal received from the combined transmit-receive beam originates from the small, point-like region of overlap. Specular Reflectors Specular reflectors occur at the interface between two materials of differing acoustical impedance. As described in section 2.1.4, the reflected wave of an insonified specular reflector is not always directed back toward the transducer. Specular reflectors are two-dimensional objects, and do not reflect perfect spherical waves the way onedimensional point reflectors do. However, when a specular reflector is insonified by a tightly focused beam, reflections originate from only a small region, resulting in a de facto point reflector (Figure 2.6). Speckle Regions Speckle regions consist of a large number of sub-resolution structures acting as scatterers in an insonified volume. The acoustic pulse is reflected and scattered many times off of these structures, resulting in a complex interference pattern that modulates the amplitude of the received echo. The interference pattern results in a grainy overlay to the image, and is called speckle noise. The random scattering in speckle can be modeled as the sum of random-walk component phasors on the complex plane [53]. This model assumes there are a large 17

34 number of scatterers within the resolution volume. The many random-walk components from each scatterer sum to a complex amplitude (A) given by the equation: A = ae jθ = 1 N N k=1 a k e jθ k (2.28) where a k N is the length of the k th component, θ k is the phase of the k th component, and N is the number of speckle components or sub-resolution scatterers. This model makes two simplifying assumptions: (1) that a k and θ k components are statistically independent, and (2) that phase is uniformly distributed between π and π. These assumptions lead to a Rayleigh probability distribution function for speckle brightness (Figure 2.7), described by the equation: where P (a) = a a2 e 2σ σ2 2 (2.29) σ = a2 2 (2.30) The distribution of the detected data amplitude a depends only on the mean-square scattering amplitude. 2.2 Acoustics Linear Acoustics Linear acoustics deals with propagation of small scale disturbances in pressure (p), density (ρ), and particle velocity (u). Acoustical pressure (or density, or particle velocity) refers to the change in pressure from the undisturbed state, according to the equation: p = p p 0 ρ = ρ ρ 0 u = u u 0 18 (2.31a) (2.31b) (2.31c)

35 α Figure 2.7: Normalized Rayleigh distribution for P (α) = αe α2 2, where α = a σ. α where the prime ( ) denotes absolute pressure (or density, or particle velocity), and the 0 subscript indicates the undisturbed state. In a typical diagnostic ultrasound imaging system, u 0 is equal to zero. The relationship between spatial and temporal disturbances in pressure is governed by the wave equation: 2 p 1 c 2 2 p t 2 = 0 (2.32) The wave equation is derived from the linear acoustic equations, which relate 19

36 pressure, density, and particle velocity: ρ t + ρ 0 u = 0 ρ 0 u t = p p = c 2 0ρ ( ) p c 2 0 = ρ S,0 (2.33a) (2.33b) (2.33c) (2.33d) where ( p refers to computing the derivative at constant entropy and evaluation ρ )S,0 at ρ 0. Equation (2.33a) represents the conservation of mass. Equation (2.33b) is Euler s equation, representing flow in the absence of viscosity. Equation (2.33c) is a linearized form of the state equation relating pressure and density, taken from the first term of the Taylor Series expansion of the general pressure-density relationship: p = ρ p 0 ρ 0. (2.34) In the linearized form of the acoustic equations, sound speed is independent of acoustic pressure and particle velocity, depending only on the unperturbed density and adiabatic compressibility, K, of the medium according to: Nonlinear Acoustics c 0 = 1 ρ 0 K. (2.35) The wave equation described in equation (2.32) is valid for small pressure perturbations, and assumes a linear pressure-density relationship. The linear pressuredensity relationship is established by taking only the first-order term of the Taylor Series expansion of the pressure-density state equation. However, ultrasound scanners typically generate pressures in excess of 1 MPa, which is high enough for the 20

37 second-order terms in the Taylor Series to become important [46]. This fact leads to nonlinear propagation. The linear acoustic equations of section assume pressure disturbances of negligible amplitude. For the higher amplitude pressures produced by most modern ultrasound scanners, the approximate pressure-density relationship of equation (2.33c) does not yield valid results. To obtain a reasonably accurate pressure-density relationship, the previously neglected second-order terms must be taken into account when performing the Taylor Series expansion of equation (2.34): ( ) p p = (ρ ρ ρ 0 ) + 1 ( ) 2 p (ρ ρ S,0 2! ρ 2 0 ) (2.36) S,0 This series may be expressed in a more simplified form: ( ) ρ p = A + B ( ) 2 ρ = c 2 ρ 0 2! ρ 0ρ c 2 0 B ρ 0 A ρ2 (2.37) where The ratio B A ( ) P A = ρ 0 ρ B = ρ 2 0 S,0 ρ 0 c 2 0 (2.38a) ( ) 2 P. (2.38b) ρ 2 S,0 characterizes the contribution of finite amplitude effects for a given acoustical medium. Values of B for various biological tissues are given in Table 2.1. A ( ) 2 The presence of the second-order term B ρ 2! ρ 0 invalidates the linear pressuredensity relationship that held true for small-amplitude pressure waves. Using the relation ρ ρ 0 = u c 0, plugging the pressure-density relationship from equation (2.37) into equation (2.33d) and using the truncated binomial expansion from equation (2.20) to determine the sound speed, we see that sound speed is now dependent on local 21

38 Table 2.1: Acoustic properties of selected biological tissues taken from [17, 30]. Tissue Speed of Sound c (m/s) Impedance Z (M rayl) Attenuation α (db/cm/m Hz) Nonlinearity Parameter B/A Water 20 C Blood Fat Kidney Liver Muscle Bone particle velocity: c = c 0 + B u. (2.39) 2A The incorporation of a particle velocity term to sound speed calculation means that sound propagation speed is no longer constant over the course of a pressure wave. In the compression phase of pressure waves, where u is positive, sound travels faster than in the rarefaction phase, where u is negative. This leads to a steepening of the waveform (Figure 2.8), which can eventually form a shock wave Harmonic Generation The steepening of the pressure waveform from nonlinear propagation results in distortion, which in turn shifts energy out of the fundamental (first harmonic) frequency, and into the second and higher harmonic frequencies. The amount of distortion present in a sinusoidal wave is described by the shock number σ, where σ = 0 is undistorted, σ = 1 is weak shock, and σ = 3 is strong shock (Figure 2.8). Diagnostic imaging systems do not typically generate shock waves, and normally operate in the σ < 1 region. Using the shock number σ, it is possible to describe the amplitude of the funda- 22

39 1 σ = 0 σ = π 4π 6π 0 2π 4π 6π a) b) σ = 1 σ = π 4π 6π 0 2π 4π 6π c) d) Figure 2.8: Sinusoidal wave with varying amounts of nonlinear distortion described by shock parameter σ. The undistorted wave (a) and moderately distorted wave (b) have no discontinuities. The first appearance of discontinuity signals weak shock (c), and nonlinear distortion can eventually lead to strong shock (d), transforming a sinusoid into a triangle wave. mental and higher harmonics [18]: p n (σ) = 2p 0 nσ J n(nσ) (2.40) where n is the harmonic number, p 0 is the amplitude of the undistorted fundamental, and J n is the Bessel function of the first kind of order n. As energy is transferred into higher order harmonics, the amplitude of the fundamental will decrease (Figure 2.9). For a spherically focused system, shock number is given by: ( ) ( z σ = R f ln 1 + B ) u k (2.41) R f 2A c where R f is the focal distance and z is the range [48]. Shock increases with range (z), wavenumber (k), acoustic amplitude (u), and the nonlinearity of the acoustic 23

40 0 10 Level (db) Fundamental 2 nd Harmonic 3 rd Harmonic 4 th Harmonic Shock Parameterσ Figure 2.9: Level of fundamental (solid), second harmonic (dash), third harmonic (dash dot), and fourth harmonic (solid) as nonlinear distortion, described by shock parameter σ, increases. medium ( B ). A The transfer of energy into higher harmonics results in creation of harmonic beams from the fundamental beam. Prior to the formation of weak shock (σ < 1), the directivity pattern of these harmonic beams is related to the directivity pattern of the fundamental by [30]: D n (θ) = [D 1 (θ)] n (2.42) where D 1 (θ) is the directivity pattern of the fundamental, given for a circular aperture by equation (2.26). For the second harmonic, the resultant beam is proportional to the square of the fundamental beam (Figure 2.10). It is understood that harmonic beams generated by nonlinear propagation are not transmitted directly by the transducer. Instead, they are generated from the fundamental, thus increasing the spectral content of the transmitted beam. Harmonic 24

41 0 10 Level (db) MHz Transmit 4.16 MHz Harmonic 4.17 MHz Transmit Lateral Position (deg) Figure 2.10: Lateral beam plot of unaberrated 2.08 MHz (dashed) fundamental, 4.16 MHz (dotted) second harmonic, and 4.17 MHz (solid) imaging beams. generation increases with the pressure amplitude of the fundamental, and it is clear that more harmonic will be generated close to the focal point of a converging beam [36]. 2.3 Image Correction Diagnostic ultrasound imaging systems generally operate on the assumption that all tissues in the body have the same acoustical properties. Variations in acoustical properties for different tissues lead to aberration, which degrades the beam through loss of resolution, contrast, and image dynamic range [1]. Beam aberration is caused by distortions in phase, amplitude, and waveshape of both the transmitted and received pulses. As imaging frequency increases, the effect of these distortions on the beam intensifies. 25

42 2.3.1 Image Quality There are several metrics used to evaluate image quality in ultrasound images, although evaluation of ultrasound images is generally a subjective matter. Even objective image quality measures, such as image dynamic range, contrast resolution, and spatial resolution, depend on a subjective choice of regions over which such evaluations are made [56]. Image quality is primarily a function of imaging beam quality, and the three metrics above are largely functions of three different aspects of the imaging beam. Image dynamic range, defined as the range between the noise floor of the image and the maximum brightness, is primarily determined by the peak amplitude of the imaging beam s main lobe. Contrast resolution, or the ability to differentiate between objects with different brightness levels, is determined largely by the side-lobe level of the imaging beam, and is calculated by C = 20 log ( B1 B 0 ) (2.43) where B 1 and B 0 are the mean brightness of two regions of interest (ROIs). Spatial resolution, the ability to distinguish two objects separated in space, is a function of beam width. Using the relationships between imaging beam properties and image quality factors, it is possible to measure properties of the aberrated and corrected imaging beams (amplitude, side-lobe level, beam width), and to use these measurements to infer the effect on image quality factors (image dynamic range, contrast resolution, spatial resolution) Phase Aberration Phase aberrations are caused by differences between the speed of sound assumed by the imaging systems (c = 1540 m/s) and the speed of sound of the tissues being imaged (from 1420 m/s for fat to 1580 m/s for blood; see Table 2.1) [1]. The varying 26

43 A Figure 2.11: The aberrating layer (A) introduces arrival time variations in the received signal (R). These arrival time variations are not compensated by the focusing delays (D), leading to out-of-phase summation of the individual pulses and a distorted output pulse S. sound speed of the tissues being imaged leads to refraction and errors in arrival time that degrade both the transmit and receive beams (Figure 2.11). These aberrations may be expressed as: D 1 (θ) = FT { P (r)a(r)e j[φ(r)+ε(r)]} (2.44) where ε(r) represents the arrival time errors. These arrival time errors are generally dependent only on the position and acoustical properties of the tissues being imaged, and are independent of frequency. However, as imaging frequency is increased, the arrival time errors become more significant relative to the period of the imaging frequency, increasing beam degradation. Ultrasound systems are particularly sensitive to phase aberration, as small arrivaltime errors can cause noticeable decreases in beam amplitude (reduced image dynamic range), increased side-lobe level (decreased contrast resolution), and increased beam width (decreased lateral resolution) [1]. Phase aberrations can be corrected by applying a time delay to compensate for the difference between expected and actual pulse arrival time. 27

44 2.3.3 Amplitude Aberration Amplitude aberrations are a result of the difference between the attenuation assumed by the imaging system (0.3 db/cm-mhz) and the attenuation of the tissues being imaged (0.15 db/cm-mhz for blood to 1.3 db/cm-mhz for muscle (Table 2.1). Variations in attenuation cause the signal received at different positions along the transducer to vary in amplitude: D 1 (θ) = FT { P (r)a(r)ε A (r)e jφ(r)} (2.45) where ε A (r) represents the amplitude fluctuations across the aperture. Attenuation is frequency-dependent, and an increase in frequency leads to greater amplitude fluctuations. Amplitude aberrations lead to the same problems as those caused by phase aberration: decreased beam amplitude, increased side-lobe level, and increased beam width, although the effects are usually relatively much less severe [38]. Amplitude aberration can be corrected by multiplying the received signal by an appropriate gain factor to match the expected value, which is typically constant across the aperture Waveshape Aberration Waveshape aberration occurs when the shape of the transmit or receive pulse is altered. Nonlinear acoustic propagation effects are not considered waveshape aberration. Waveshape aberration is often due to multi-path reception effects, such as reverberation or refraction [10]. The effect on the imaging beam is highly dependent on the source of the shape distortion and on the shape of the initial pulse used. Correction of waveshape aberration requires the transmission of an altered pulse that, after being subject to the distorting effects of the imaging medium, attains the desired pulse shape (Figure 2.12) [10]. Waveshape aberration correction is outside the scope of this work. 28

45 a) b) T D A P Figure 2.12: a) As a pulse (P ) passes through an aberrator (A) its shape can become distorted (D) prior to being received by the transducer (T ). b) To compensate for waveshape distortion an altered pulse shape must be transmitted that, after passing through the aberrating layer, achieves the desired pulse shape Aberrators The term aberrator can refer to the cause of aberration, i.e. the varying acoustic properties of tissue, or it can refer to the mathematical model used to describe those variations. Aberrators usually belong to one of two types: near-field or distributed. Both aberrator types are typically described by the root-mean square (RMS) focusing errors they cause. The correction strategy for both types of aberrators is the same, although distributed aberrators can be more challenging to correct. Near-field Aberrators A near-field aberrator occurs when aberrating effects (sound speed or amplitude variations) are confined to depths close to the transducer, in its near-field. The simplest near-field aberrator is a phase-amplitude screen: a layer of zero thickness located at the face of the transducer that causes time delays and amplitude variations. The time delay and amplitude variations due to the phase screen generally vary with position across the transducer. However, due to the screen s lack of thickness and its 29

46 position, the aberrations are independent of the received path, and thus of steering angle and focal depth. In abdominal imaging, the body wall, consisting of layers of skin, fat, muscle, and connective tissue, sits between the transducer and the target organ (liver, kidney, uterus, etc.). The body wall can be considered a near-field aberrator due to the varying acoustical properties of its layers, which are located close to the transducer [19, 20]. Distributed Aberrators Unlike near-field aberrators, the varying acoustical properties of distributed aberrators are not confined to a single region near the transducer. In a distributed aberrator, the aberration present at a transducer element is highly dependent on the acoustical path taken from each element to the focal point. Therefore, changes in steering angle and focal depth can alter the phase and amplitude distortions present. It is possible to model a distributed aberrator as a series of phase-amplitude screens located at varying distances from the transducer [28]. The finite distance from the screen to the transducer ensures that aberration is path-dependent. For example, breast tissue is often described as a distributed aberrator, with intermixed regions of adipose, glandular, and connective tissues [42]. 2.4 Hypothesis It is hypothesized that the generated second harmonic beam creates a point-like acoustical source that allows for estimation and correction of two-dimensional aberration. Generated second harmonic beams have advantages for imaging when aberration is present over beams that are transmitted directly at the second harmonic frequency. A primary advantage for harmonically generated beams over those directly transmitted at the second harmonic frequency is that harmonic beams are generated from lower frequency fundamental transmits, which are less susceptible to 30

47 0 5 Level (db) MHz Transmit 4.16 MHz Harmonic 4.17 MHz Transmit Lateral Position (deg) Figure 2.13: Lateral beam plot of 2.08 MHz (dashed) fundamental, 4.16 MHz (dotted) second harmonic, and 4.17 MHz (solid) imaging beams in presence of a grooved Lucite aberrator. aberration effects [49]. This feature is advantageous when faced with either nearfield or distributed aberrators, as the transmit beam will be less aberrated and can generate a more concentrated beam at the second harmonic frequency than can be obtained through direct transmission (Figure 2.13) [4]. Moreover, harmonic beams are generated close to the focal point of the fundamental beam, past the near-field [48]. If a near-field aberrator is present that does not significantly distort the low-frequency fundamental transmit beam, then a nearly unaberrated second harmonic beam will be generated. The generated second harmonic beam will still be subject to aberration while passing through the near-field as it is received. When a two-dimensional array used to receive the generated second harmonic, the aberrated signal can be used to estimate, and then correct, the aberrator present. 31

48 Harmonic Source Wavefront Correction Introduction Pulse-echo ultrasound is in widespread use as a diagnostic tool. However, a significant number of patients do not make high-quality ultrasound images. Often, these patients have a thick layer of fat that results in a degraded image due to increased scattering, increased attenuation, and wavefront distortion. The distortions, or phase aberrations, include not just timing or phase delays, but also amplitude and waveshape distortions. Imaging systems generally operate on the erroneous assumption that all tissues in the body have the same sound speed. The variations in sound speed that exist for different tissues degrade the imaging beam, leading to a loss in resolution, contrast, and image dynamic range [1]. As imaging frequency increases, the subsequent decrease in wavelength causes arrival-time variations to become more significant, and these more significant arrival-time variations result in greater focusing errors. It is known that by applying wavefront correction the imaging beam can be improved. The problem has been to determine the necessary correction functions for the imaging beam[45]. 32

49 Many wavefront correction methods have been suggested [10, 11, 13, 28, 37, 41], but each of these requires the presence of a specific acoustical target, such as a point reflector or an active ultrasound source acting as a transponder. Point reflectors are very rarely encountered during a diagnostic scan. A new approach, using the generated harmonic to create an operator-specifiable active source, overcomes these limitations. A wavefront correction method utilizing the generated harmonic was previously described by Gauss and Trahey in 1999 [12, 13, 14, 15]. This method assumes that the signal from a generated harmonic beam is less aberrated than that from a beam transmitted directly at the harmonic frequency, and the generated harmonic beam was paired with a cross-correlation method to estimate the actual timing delays. The harmonic signal was extracted using pulse inversion, and then used to estimate the adjustments required to correctly focus the received harmonic rf data. This method applied corrections to images formed from the received harmonic signal, but did not attempt to improve standard imaging transmit and receive beams. Gauss s method, like most aberration correction work, uses a form of a onedimensional array. While the elements are small in the direction of the array (azimuthal direction), they can be from 15 to over 50 times larger in the elevation dimension (Figure 3.1). For any waveform distortion correction to be valid, the wave s distortion must be constant across the surface of the transducer element. Studies have shown that in most instances, distortions are usually constant over, at most, a few elements in the azimuthal direction [14, 37, 39, 47, 52]. However, because most one-dimensional array elements are many times taller than they are wide, the distortion is not constant across an element s elevation dimension, severely limiting the ability of one-dimensional arrays to correct in vivo wavefront distortions. As previously stated, phase aberration is caused by variations in soft tissue; it should not be assumed to be limited to a single dimension. If aberration were assumed to vary 33

50 1-D 1.5 / 1.75-D 2-D Figure 3.1: Relative size of typical transducer elements for 1-D, 1.5/1.75-D and 2-D arrays. The square 2-D elements can sample a signal equally well in azimuthal and elevation directions. The rectangular 1.5/1.75-D elements do not sample signals as well in the elevation direction as the azimuthal direction. one-dimensionally it would not necessarily be aligned with the arbitrary orientation of a transducer. Instead, optimal in vivo correction of aberration will be obtained through utilization of a two-dimensional transducer. This chapter will describe a new aberration correction method which addresses the shortcomings of previous methods by creating a point-like acoustical source and using a 2-D array to measure aberration. The presented method uses a harmonic beam generated from a low-frequency transmit in order both to avoid distortion from aberrating layers and to achieve a tight focus. The effects of focal range, transmit frequency, and transmit amplitude on the harmonic beam are demonstrated. This correction method can be paired with any of a number of well-described focusing delay estimation algorithms in order to determine aberration correction. Lastly, correction can be applied to standard transmit and receive imaging beams, or to subsequent measurement beams to improve aberration correction accuracy Isoplanatic Patch An important concept when describing aberrators is that of the isoplanatic patch. An isoplanatic patch is a region over which phase aberration (arrival time error) is constant. This can refer to a region of the aperture over which phase aberration is constant for a given focal point (aperture isoplanatic patch), or it can refer to a region of the target where a change in steering angle or focal depth does not change the phase aberration at a particular transducer element (target isoplanatic patch). 34

51 A set of corrective arrival time delays is only valid within an isoplanatic patch. For a near-field aberrator that can be described as a phase-amplitude screen, a set of corrective delays valid for any one focal point are valid for all other focal points. A single target isoplanatic patch encompasses the entire scan area of a target subject to a phase-amplitude screen, because aberration is not dependent on acoustic path. For a distributed aberrator, however, aberration is dependent on acoustic path, which in the extreme means that each target isoplanatic patch is the size of a single focal spot. As a result, calculation of corrective delays is necessary for potentially every steering angle-focal depth combination. It is important to note that aperture isoplanatic patch size is independent of target isoplanatic patch size. Aperture isoplanatic patch size can vary from the size of the entire aperture to smaller than a single element. Only one compensating time delay and amplitude correction can be applied to each element. For that correction to be successful the phase and/or amplitude aberration must be constant across the element; otherwise, the aberration will not be properly compensated. To achieve phase aberration correction, array element size must be smaller than the aperture isoplanatic patch size. Phase aberration is caused by variations in soft tissue, and is thus not expected to change rapidly. Therefore, aperture isoplanatic patch size is likely to be larger than the element sizes required to image in the MHz range [47]. However, tissue distributions, and thus aperture isoplanatic patches, are by nature two-dimensional. Transducer elements from one-dimensional arrays can be 50 times larger in the non-imaging dimension (elevation) than the imaging dimension (azimuth), making them potentially larger than the aperture isoplanatic patches, and consequently poor choices for aberration correction [8, 9, 14, 15, 35, 37, 47, 52]. To correct properly for two-dimensional tissue distributions that lead to two-dimensional aperture isoplanatic patches, a two-dimensional array is required (Figure 3.2). 35

52 360 ns 260 ns 160 ns a) b) 60 ns -60 ns -160 ns -260 ns c) d) -360 ns Figure 3.2: Two-dimensional aberration function (a) measured by 51-element 1-D array (b), 5x51 element 1.5-D/1.75-D array (c), and a 512-element 2-D array (d) Correction Methods Aberration correction is fairly straightforward: application of compensating delays to arrival time errors and corrective gains to address amplitude fluctuations. The challenge lies in estimating the corrective factors. The focus of this section will be on estimating corrective focusing delays, as phase aberration tends to have a greater impact on beam quality than amplitude aberration [38]. A number of arrival time estimation methods have been described; these methods share a common requirement for a known source of received signal, often a point reflector or source. 36

53 3.1.3 Time-shift Estimation If we assume that the signal received by the transducer array originated from a single area (either a point reflector or a tightly focused transmit beam), then the signal received by any two transducer elements will be the same except for time shift and noise effects: s 1 (t) = p(t) + n 1 (t) s 2 (t) = p(t + τ) + n 2 (t) (3.1) where p(t) is the reflected pulse, and n 1 and n 2 are independent stationary noise processes. To determine the time shift τ, Flax and O Donnell [11] proposed taking the maximum of the cross-correlation of s 1 and s 2 : ( T ) max s 1 (τ)s 2(t + τ)dτ 0 (3.2) where T is the observation interval. The cross-correlation method is ideally suited for extracting delays from pulses reflected from a point target, where the signal received at each element is the same except for a time delay. Signal originating from a specular reflector is handled well by the cross-correlation method, despite the minor shape distortions in the received signal resulting from the finite extent of the insonified reflector. Extraction of delays for a signal received from speckle regions is the most challenging for the cross-correlation method, as the original transmit pulse shape has been transformed into a pattern of peaks and nulls that varies across the receive aperture. The signal received by two neighboring elements is often very similar, however, and it is therefore possible to extract the time shift by cross-correlating the signal received at one element with that received at neighboring elements [39] Cramer-Rao Lower Bound All time-shift estimation methods, including the cross-correlation method, produce some error between the estimate and the true time shift. The standard deviation 37

54 of the error is called jitter, and provides a measure of the quality of the estimate. The Cramer-Rao lower bound is the limit on the smallest variance an estimator can obtain and is used to quantify the maximum accuracy of the estimator. For the cross-correlation method proposed by Flax and O Donnell, the Cramer-Rao lower bound of the jitter is given by: ( σ(ˆτ τ) 3 2f0 3 π 2 T (B B) 1 ρ 2 ( ) 2 1) SNR 2 (3.3) where f 0 is the imaging center frequency, T is the observation time, B is the -6dB fractional bandwidth, ρ is the correlation coefficient between two signals, and SN R is the signal-to-noise ratio of the data [54]. For a zero-mean process, SNR can be expressed in terms of the correlation coefficient [40]: Iterative Correction ρ SNR = 1 ρ. (3.4) Due to the inherent error present in time shift estimation, application of corrective delays may not achieve the desired improvement in beam quality. To further compensate for phase aberration, an iterative correction approach is necessary. Iterative correction takes the corrected beam from the initial arrival time measurement and uses it to repeat the arrival time measurement process. This second measurement iteration should further improve the arrival time estimate, because it uses a lessaberrated measurement beam, which results in higher SNR and thus reduced jitter (equation (3.3)) [34]. The iterative correction process is repeated until either the desired level of correction is attained, or further correction iterations do not improve the beam. When applying iterative correction to the imaging beam, it is important to guard against the beam wandering in range or laterally over the course of multiple 38

55 iterations. To address the issue of beam wandering, the constant range component and the linear steering component are subtracted from the arrival time estimates before the remaining focusing correction component is applied to the corrected beam. These components are determined by fitting the estimated arrival times across the aperture to a plane using least-mean-squares. 3.2 Harmonic Source Method Unlike the method proposed by Gauss and Trahey, harmonic source wavefront correction consists of two distinct phases: measurement and imaging (Figure 3.3). During the measurement phase, a pulse is transmitted at one-half the imaging frequency. The relatively long wavelength of this lower-frequency measurement pulse, termed the fundamental, minimizes the impact of the aberrating layers of soft tissue. The nonlinear propagation effects of tissue cause the fundamental beam to generate a harmonic beam at twice the frequency of the fundamental frequency, which is equal to the imaging frequency [2]. This harmonic beam is generated primarily in the region just prior to the focal point of the fundamental [3, 50]. Because the fundamental beam is not significantly affected by aberrating layers, the fundamental beam pattern near the focal point has very little distortion. This beam pattern in turn results in a harmonic beam that is nearly undistorted as well, but has a tighter, more concentrated focus than the fundamental beam [24]. Both the fundamental and harmonic pulses are reflected from the focal point. As they travel back to the transducer, both pulses are subject to distortion from any aberrating layers. The returning pulse contains both the fundamental and the harmonic. The harmonic portion of the pulse is extracted from the returning pulse. Any of a number of methods can then be used on the harmonic pulse to calculate corrective delays to compensate for phase aberration. The harmonic pulse s origin from a relatively concentrated, point-like focus makes it ideal as a basis for deter- 39

56 Isolate 4.16 MHz Harmonic Calculate Corrective TX Delays Apply Corrective RX Delays Transducer Transducer Aberrating Layer 2.08 MHz TX 2.08 MHz & 4.16 MHz RX 4.17 MHz TX 4.17 MHz RX Target 1. Measure 2. Image Figure 3.3: Diagram of experimental setup. Wavefront correction consisted of two phases: (1) measurement and (2) imaging. mination of necessary corrections. Once corrective factors have been calculated, the second, or imaging, phase of harmonic source wavefront correction begins. Corrective transmit delays are applied to an imaging pulse transmitted at the same frequency as the harmonic (i.e., twice the frequency of the fundamental). As it propagates, the relatively high-frequency imaging pulse is subject to aberration. The corrective delays previously calculated cancel out the aberration, so that the imaging beam is nearly undistorted at the focal point. The imaging pulse is then reflected from the focal point, and is again subject to aberration as it travels back to the transducer. Corrective receive delays are applied to compensate for distortion introduced between the focal point and the transducer. Ideally, the product of the corrective transmit and receive delays is an unaberrated imaging beam. The harmonic source wavefront correction method can be repeated at as many points as necessary to correct a larger field of view. 40

57 3.3 Source Generation The main feature that sets harmonic source wavefront correction apart from other wavefront correction schemes is the use of the generated harmonic to create a pointlike source. A true point source emits signal from an infinitesimally small region in the lateral and range dimensions. A tightly focused transmit beam insonifies a small region in the lateral dimension. Range-gating the received signal retains only those echoes that originate from a small region in the range dimension. Combining a tightly focused transmit beam with range-gating provides a method to isolate echoes from a small region in both the lateral and range dimensions, essentially creating a point-like source (Figure 2.6). Both range-gating and a tightly focused transmit beam are necessary to create a point-like source. Range-gating is relatively simple to implement: a time window is applied to the receive signal to isolate a specific range. Creating a tightly focused transmit beam can be more challenging. In the presence of aberration, this is not a trivial task, as distortion degrades the focus of the beam and spreads out the transmit energy. However, aberration decreases as transmit frequency decreases. By transmitting at a sufficiently low frequency, it is possible to create an undistorted or minimally distorted focus. Unfortunately, lateral beam width increases as transmit frequency decreases, counteracting the improvement from reduced distortion. However, due to the nonlinear pressure-density relationship of tissue, a high-amplitude/low-frequency transmit will generate harmonic beams that, like the low-frequency fundamental, are nearly undistorted and also have decreased lateral beam width [16]. In addition to the tighter focus, the harmonic beams have reduced side-lobe level compared to the fundamental beam [5] (Figure 2.10). The result is that more energy is concentrated near the focal point, yielding a better point-like target than the low-frequency fundamental beam could provide. 41

58 3.3.1 Transmit Amplitude and Frequency While a high-amplitude, low-frequency pulse will generate a tightly focused harmonic beam for use as a point-like source, exactly how low of a frequency and how high an amplitude are necessary depends on the aberrator present. Harmonic source wavefront correction typically uses a measurement pulse that is one-half the frequency of the imaging pulse. To justify harmonic correction, aberration of the imaging beam must be severe enough to warrant correction, but mild enough such that the measurement beam, at one-half the imaging frequency, is not significantly distorted. This balancing act will be investigated in Chapter 4, where the effects of a variety of aberrators on the fundamental measurement beam, the generated harmonic beam, and the imaging beam will be demonstrated. Determining the ideal amplitude for the measurement pulse is straightforward. Due to nonlinear effects, increased transmit amplitude leads to an increase in generated harmonic beam level relative to the fundamental measurement pulse (Figure 3.4). Increased harmonic beam level leads to increased SNR of the received signal, and thus to more accurate corrective delay estimation (equation (3.3)). The upper limit of measurement pulse amplitude is typically governed by either physical limits of the ultrasound system, such as maximal input power of the transducer, or regulatory limits, such as the FDA limit on integrated pulse intensity [7]. Simulations performed by groups headed by Bjøn Angelsen and Svein-Erik Måsøy have suggested that for the case of a near-field aberrator, an additional benefit of increased measurement pulse amplitude is decreased distortion of the generated harmonic beam [50]. This effect has been investigated experimentally [6], and while the shape of the fundamental measurement beam is not affected by an increase in amplitude, distortion of the generated harmonic beam is indeed decreased (Figure 3.5). Using the highest possible measurement-pulse amplitude will therefore yield more accurate correction 42

59 10 20 V TX = 80 V V TX = 40 V V TX = 20 V Level (db) Level (db) Lateral Position (degrees) a) b) Range (mm) Figure 3.4: Lateral (a) and rage (b) beam plots of the 4.16 MHz harmonic beam level relative to the fundamental as transmit voltage is increased. estimation through increased received signal SNR and creation of a less distorted, more point-like harmonic source Focal Distance The amplitude of the measurement pulse is not the only factor that has a significant effect on the amplitude of the generated harmonic beam; the focal distance of the measurement beam is also important. As focal distance increases, so does the distance over which the measurement pulse is subject to nonlinear propagation, causing harmonic beam level increases. However, as nonlinear propagation begins shifting some of the harmonic beam energy into higher harmonics, greater focal distances lead to diminishing returns in harmonic beam level. Additionally, greater focal distances subject the reflected harmonic pulse to increased tissue-induced attenuation. Greater focal distances therefore incur a trade-off between the benefit of increased harmonic beam level and the detriment of greater tissue-induced attenuation. Measured levels of the 4.16 MHz second harmonic generated by a 2.08 MHz measurement pulse for 43

60 0 5 V TX = 80 V V TX = 20 V Unaberrated 0 5 Level (db) Level (db) a) Lateral Position (degrees) b) Lateral Position (degrees) Figure 3.5: Beam plots of 4.16 MHz harmonic in presence of 11 mm thick Lucite aberrator (a) and 24 mm Lucite aberrator (b). As transmit voltage is increased, the aberrated beam approaches the unaberrated beam. Table 3.1: Peak amplitude of the 4.16 MHz harmonic beam relative to the 2.08 MHz fundamental for increasing focal distance at constant transmit voltages. Incremental increase is the increase in harmonic level from previous focal distance. Net increase is the incremental increase minus 2.4 db of attenuation to the receive signal. Focal Distance (mm) Harmonic Level (db) Incremental Increase(dB) Net Increase (db) the T5 ultrasound system are summarized in Table 3.1. Assuming tissue-induced attenuation equal to the FDA suggested value of 0.3 db/cm-mhz (1.2 db/cm at 4.16 MHz), the optimal focal distance for our system is between mm. Aberration correction is typically performed to improve image quality around features of interest, and a focal range of 60 mm was chosen for harmonic source wavefront correction experiments as it is common to encounter biological structures of interest at that range when performing an abdominal scan. 44

61 Figure 3.6: The sum of relative time shifts between adjacent elements (arrows) on a path from the reference element (bottom left) to each element equals the arrival time (squares). Phase closure implies that arrival time will be the same for any path, as shown by the red and blue paths. 3.4 Arrival Time Estimation The goal of harmonic source wavefront correction is to generate a positionable pointlike source. The signal received from that point-like source can then be used with any of a number of algorithms to estimate the corrective factors necessary to compensate for aberration. Of the numerous methods proposed to estimate corrective focusing delays, the cross-correlation method proposed by Flax and O Donnell [11], the speckle brightness method proposed by Nock and Trahey [37], and the backpropagation method proposed by Liu and Waag [28] are some of the best known. The cross-correlation method proposed by Flax and O Donnell has inspired a number of similar corrective delay estimation algorithms, which are evaluated and summarized by Måsøy [33]. As cross-correlation is both straightforward and easy to implement with existing laboratory equipment, it was chosen to estimate corrective focusing delays while evaluating harmonic source wavefront correction performance. Corrective delay estimation accuracy can be enhanced by applying the concept of phase closure to the cross-correlation method. Phase closure states that the relative 45

62 arrival times along any closed loop of array elements will sum to zero. The relative arrival time between two adjacent elements can be calculated using cross-correlation; between any two non-adjacent elements, the relative arrival time is equal to the sum of relative arrival times for a path of adjacent elements between the two. Phase closure implies that this sum, the relative arrival time, does not depend on the particular path chosen (Figure 3.6) [29]. Due to noise present in the received harmonic signal, the cross-correlation algorithm produces errors in arrival time estimations. To enforce phase closure despite these errors, a least-mean-squares fit is applied to the relative delay profile: T = (M T M) 1 M T D (3.5) where T is the vector of unknown arrival times for each element, D is the estimated differential time shift vector between pairs of elements calculated using crosscorrelation, and M is the model matrix relating arrival times to time shift estimates between element pairs [22, 29]. The matrix M is determined from array geometry and indicates which elements are spatially near each other. This over-determined system of equations helps reduce the effect of errors in the differential time shift vector, D [29]. 3.5 Array Geometry Considerations A high signal-to-noise ratio in the received harmonic signal is important to accurate estimation of arrival times. When wavefront correction is performed on biological tissue, the measurement pulse is subjected to frequency-dependent attenuation. This attenuation reduces the harmonic received signal indirectly by reducing the amplitude of the fundamental beam that generates it, and directly by attenuating the reflected harmonic pulse. In addition to attenuation, biological tissue often lacks strong reflectors, limiting the signal reflected from the generated harmonic beam s 46

63 focus and further reducing the signal received by the array. Due to the often weak harmonic signal received by the transducer, the signal-to-noise ratio is typically too low to permit accurate arrival time estimation. To improve SNR, multiple receive elements can be grouped together, resulting in an N/ N increase in SNR. By overlapping groups of receive elements, accurate arrival times for individual elements can be interpolated from arrival times measured for the various element groups. The increased SNR of grouped receive elements comes at the expense of decreased spatial sensitivity to change in aberration. For grouped receive elements to produce useful signal for the arrival time estimation algorithm, the aberration present at each element in the group must be similar to the aberration present in the group as a whole. Thus, the spatial extent of the element group must be smaller than the aperture isoplanatic patch for a given aberrator [26, 27]. The aperture isoplanatic patch of an aberrator is typically described by the correlation length of focusing errors as a function of aperture position. As phase aberration is caused by variations in soft tissue, aperture isoplanatic patch size is expected to be large relative to small groups of elements, and grouped elements should provide increased SNR without sacrificing spatial sensitivity. 47

64 Aberration and Imaging Beam Distortion Introduction To justify harmonic correction, aberration of the imaging beam must be severe enough to warrant correction, of course; but it also must be mild enough such that the measurement beam, at one-half the imaging frequency, is not significantly distorted. This balancing act is highly dependent on the aberration present. Simulations performed by Christopher [4] investigated the effect of aberrators modeled on the body wall had on the measurement beam, the generated harmonic beam, and the imaging beam. However, Christopher s simulations were limited to only two aberrators, and did not investigate the effect of variation in aberration strength on the measurement, generated harmonic, and imaging beams. To investigate the effect of aberration strength experimentally on beam distortion, electronic aberrators of varying severity are used to determine if a general relationship between aberration and the resultant distortion exists for the measurement, generated harmonic, and imaging beams. Two different classes of electronic aberrators are used: (1) spatially uncorrelated 48

65 aberrators, and (2) spatially correlated aberrators. Spatially uncorrelated aberrators provide a first-order approximation of tissue-induced aberration. These uncorrelated aberrators can be categorized both by the probability distribution from which focusing errors are drawn, and by RMS focusing error. The second class of electronic aberrators, spatially correlated aberrators, produced a more realistic simulation of tissue-induced aberration because focusing errors can be represented as a smooth function of spatial position. The use of spatially correlated aberrators also permits grouping of receive elements to achieve improved harmonic SNR, a feature that is essential to improving correction performance in biological tissue. Spatially correlated aberrators can be described by a combination of the probability distribution from which the focusing errors were drawn, the RMS focusing error, and the spatial correlation length. Spatial correlation length is defined as the distance when autocorrelation of the aberrating function has fallen by to half its maximal value. The autocorrelation function, R(x, y) is defined as: R(x, y) = A(x, y )A (x + x, y + y)dx dy (4.1) where A(x, y) is the function of aberrating phase delays. The measurement beam, generated harmonic beam, and imaging beam are measured for multiple examples of each class of aberrator and for a range of aberration severity. The details of and results from these aberration experiments are presented in the following sections. Beam characteristics caused by various aberrators are assessed in terms of peak amplitude of the main beam, relative side-lobe level, and beam width at -6 db. The relation of these beam properties to image quality is also explored. 49

66 4.2 Materials and Methods Ultrasound Scanner All measurements were conducted using T5, the Duke University phased-array scanner, with a custom-built two-dimensional array. The Duke University ultrasound scanner T5 was constructed entirely at Duke University as a test bed system for advanced ultrasound imaging experiments, and is capable of real-time three-dimensional scanning. The system features 512 independent transmit channels with programmable transmit waveforms, and 1024 independent receive channels with 32-to-1 parallel processing. System bandwidth is in excess of 9 MHz with radio frequency (rf) sampling at 50 MHz. The system is capable of synthetic aperture imaging and features a highly capable and flexible display system. The Duke scanner permits acquisition and simultaneous display of multiple images, interactive manipulation of real-time volume-rendered images, and display of various cut-planes of volumes. Echo data from each of the receive channels can be easily accessed to permit measurements necessary to implement wavefront corrections. All beam steering and focusing data is under software control, with wavefront corrections determined and calculated using a separate computer system and then downloaded into the T5 beam steering computer Ultrasound Transducer The two-dimensional array was used with a roughly circular aperture with diameter of 15.3 mm. The aperture was sampled by 1024 square elements with dimension 0.3 mm each. Of the 1024 elements, 512 were shared, operating in both transmit and receive, and 512 elements were used in receive mode only. Elements were spaced 0.6 mm in both the azimuth and elevation dimensions. The array s bandwidth was such that it was possible both to transmit and to receive at 2.08 MHz and 4.16/

67 0 2 Level (db) Frequency (MHz) Figure 4.1: Ultrasound system bandwidth is largely governed by transducer bandwidth. Response at 2.08 MHz and 4.16/4.17 MHz is marked with circles. MHz with less than 5 db loss relative to the array s center frequency of 3.57 MHz (Figure 4.1). System limitation required transmission at 4.17 MHz (rather than 4.16 MHz). For measurements performed in the presence of both the spatially uncorrelated and spatially correlated aberrators, the transmit and receive apertures were identical, and consisted of the 512 shared elements (Figure 4.2). The 512 receive-only elements were not used in these experiments Spatially Uncorrelated Aberrators In order to evaluate harmonic wavefront correction performance for a phase-screen, electronic aberrators had to be created. These were created by assigning focusing delay errors to each element from a probability distribution. Focusing delay errors were drawn from a uniform random distribution. These electronic aberrators were spatially uncorrelated; thus, the focusing error assigned to each element was independent of errors assigned to nearby elements. Without spatial correlation, neighboring elements cannot be grouped together when making measurements to improve 51

68 Figure 4.2: The measurement aperture consisted of 512 elements sampling the transducer in a circular pattern. Elements operated in both transmit and receive. signal-to-noise ratio (SNR) over individual elements. However, that lack of coherent spatial structure in spatially uncorrelated aberrators makes investigation of the effects of aberration strength on beam distortion simpler. For these experiments fifteen spatially uncorrelated aberrators each were generated from one of five uniform random distributions, ranging from: (1) 0 to 2π/3, (2) 0 to π, (3) 0 to 4π/3, (4) 0 to 5π/3, and (5) 0 to 2π radians at 4.17 MHz. Respectively, these aberrators resulted in root-mean-squared (RMS) phase errors of 0.39π, 0.58π, 0.78π, 0.97π, and 1.16π radians, all at 4.17 MHz. A total of 75 electronic aberrators were created (15 aberrators x 5 aberration levels). The same focusing errors were applied in both transmit and receive. 52

69 4.2.4 Spatially Correlated Aberrators Frequency-dependent attenuation of signals in biological tissue (e.g. porcine kidney and human abdomen) measurements results in a decreased SNR. The lower SNR presented a challenge to accurate aberration estimation and correction; to address this, elements were grouped to compensate for signal loss. For grouped elements to result in increased SNR, a spatially correlated aberrator was required. For a spatially correlated aberrator, the focusing errors at each of the elements comprising a patch take on similar values, due to the spatial proximity of the elements. Spatial correlation is described by the correlation length, defined as the distance over which the autocorrelation of the spatial data decreases to one-half its maximum value. Spatially correlated electronic aberrators were calculated by assigning focusing delay errors to each element from a uniform random distribution. Spatial correlation was achieved through a two-step process. First, focusing delay errors were set to zero for approximately 70% of the array elements. This was necessary to provide a good mix of peaks and valleys in the final aberrator profile. In the second step, a circular spatial averaging filter, with a radius of eight elements, was applied to the transducer aperture, resulting in spatially correlated focusing errors. Aberrators were given mean focusing delay errors of zero by subtracting the average focusing error from the focusing error applied to each element. A total of 33 spatially correlated electronic aberrators at three different levels were created: 11 aberrators with an average RMS error of 0.25π radians, 11 aberrators with an average RMS error of 0.44π radians, and 11 aberrators with an average RMS error of 0.87π radians, all at 4.17 MHz Beam Plots Beam plots are measurements of the directivity pattern as a function of angle of the imaging beam in the focal plane (Equation (2.26)). Lateral beam plots were 53

70 T5 Transducer Hydrophone Translation Stage Figure 4.3: Experimental setup for measuring lateral beam plots. The hydrophone acted as a point reflector and was swept laterally using the translation stage. measured in a water tank at 22 C (c = 1480 m/s) using the beam-formed receive signal from the Duke T5 scanner. The measured rf signal of lateral beam plots was displayed on an Agilent DSO-6034-A digital oscilloscope. Measurement of the 2.08 MHz, 4.16 MHz, and 4.17 MHz beam levels was made using the displayed FFT of the measured signal. Lateral beam plots were measured by sweeping a hydrophone, acting as a point reflector, laterally in the azimuthal plane using a translation stage (Figure 4.3). A fixed focus of 60 mm was used in the transmit and receive modes. Measurements of the transmit-receive beam were made in lateral increments of 0.25 mm. Lateral beam plots were measured for the unaberrated beam, and then for the beam with each of the electronic aberrators applied. Unaberrated lateral beam plots were simulated using the FIELD II software package [23] as a comparison to the 54

71 experimental measurements. Aberrated beam amplitude was measured relative to the unaberrated beam. Aberrated side-lobe level was measured relative to the mainlobe for the higher of the two side-lobes. Aberrated beam width was measured as the width of the main-lobe in degrees at 6 db below its peak Formation of B-mode Images B-mode images were captured with aberrators at various aberration levels applied in order to gain insight into the relationship between image quality and RMS focusing error magnitude. Images were captured of an RMI resolution phantom (Middleton, WI, model 415), which provided a variety of targets to permit evaluation of image quality. A B-mode image of the phantom was captured with an aberrator from each aberration level applied (0.39π, 0.58π, 0.77π, 0.97π, and 1.16π radians RMS at 4.17 MHz for the spatially uncorrelated aberrator; and 0.25π, 0.44π, and 0.87π radians RMS at 4.17 MHz for the spatially correlated aberrator). A reference B- mode, with no aberration applied, was also captured. During B-mode acquisition, the transducer was held stationary relative to the phantom using a ring stand clamp. B-mode images were formed using a 2-cycle 4.17 MHz pulse focused at 60 mm in transmit and receive. The formed images consisted of 120 lines scanning 12 cm deep, and spanned an arc of -45 to 45 degrees in the azimuth dimension. Range gain control and overall image brightness were optimized for the unaberrated B-mode image. These gain settings were kept constant for all subsequent aberrated B-mode images to facilitate comparison of image quality. 4.3 Results Aberrators Assignment of focusing errors for each aperture element from a uniform distribution created spatially uncorrelated aberrators with the desired RMS error. An example 55

72 a) b) 240 ns ns 160 ns 120 ns 80 ns 40 ns Count c) d) 0 ns Delay Magnitude (ns) 300 ns ns ns 0 ns -100 ns -200 ns -300 ns Count Delay Magnitude (ns) Figure 4.4: Focusing delay errors applied to the aperture from a single spatially uncorrelated (a) and spatially correlated (c) aberrators. The focusing error distributions for the spatially uncorrelated (b) and spatially correlated (d) aberrators are modeled (dashed line) as a uniform and normal distribution respectively. Table 4.1: RMS focusing errors of the spatially uncorrelated aberrators. RMS (± SD) (π radians RMS (± SD) (ns) Range at 4.17 MHz) 1.16(±0.03) 138.6(±3.9) 0 ns to 240 ns 0.97(±0.03) 115.5(±3.2) 0 ns to 200 ns 0.77(±0.02) 92.4(±2.6) 0 ns to 160 ns 0.58(±0.02) 69.3(±2.0) 0 ns to 120 ns 0.39(±0.01) 46.2(±1.4) 0 ns to 80 ns 56

73 Table 4.2: RMS focusing errors of the spatially correlated aberrators. RMS (± SD) (π radians at 4.17 MHz) RMS (± SD) (ns) Range Correlation Length (± SD) (mm) 0.87(±0.09) 104.4(±10.7) -320 ns to 320 ns 4.64 (±0.37) 0.44(±0.04) 52.8(±4.6) -160 ns to 160 ns 4.63 (±0.37) 0.25(±0.02) 30.0(±2.7) -100 ns to 100 ns 4.61 (±0.35) aberrator with delays ranging from 0 to 240 ns demonstrates a lack of spatial correlation (Figure 4.4a), while a histogram of the focusing errors closely matches the uniform distribution from which they were drawn (Figure 4.4b). Minimal variation in RMS error was found within each of the five aberration levels, as shown in Table 4.1. It should be noted that RMS focusing error magnitude values are reported for the 4.17 MHz imaging beam. RMS focusing error magnitude for the 2.08 MHz measurement beam is one-half those reported for the imaging beam, as the measurement beam is one-half the frequency of the imaging beam. Although focusing errors for the spatially correlated aberrators were initially drawn from a uniform distribution, the spatial filter implemented in the spatial correlation process produced a Gaussian-like distribution of focusing errors. An example aberrator with delays ranging from -320 ns to 320 ns demonstrates spatial correlation of the focusing errors (Figure 4.4c), while a histogram of the focusing errors approaches a Gaussian distribution near the mean (Figure 4.4d). Despite spatial structure that varied significantly among individual aberrators, RMS focusing error and correlation length were both consistent among aberrators within the same aberration level, as shown in Table Beam Plots As the focusing error magnitude of the spatially uncorrelated electronic aberrator increased, the quality of the 4.17 MHz imaging beam decreased (Figure 4.5). The beam plots in Figure 4.5 show measurements from a single example of each aberration 57

74 Unaberrated Simulation 0.39 π RMS Error 0.58 π RMS Error 0.78 π RMS Error 0.97 π RMS Error 1.16 π RMS Error Level (db) Lateral Position (degrees) Figure 4.5: Plot of 4.17 MHz imaging beam unaberrated, simulated, and one example each where spatially uncorrelated electronic aberrators of increasing RMS focusing error are applied. range for the spatially uncorrelated aberrator, as well as the unaberrated beam, and a beam simulated using Field II. Aside from a slight difference in right sidelobe level, likely due to a slight misalignment between the transducer axis and the measurement axis, there is a close match between the unaberrated and simulated beams. This indicates that reported experimental parameters were accurate. An increase in relative side-lobe level with concomitant decrease in beam amplitude, as focusing error magnitude increases, is seen for the single examples which are representative of each level of aberration as determined by the RMS error. Although not shown, beam plots of the 2.08 MHz measurement and 4.16 harmonic beams exhibited the same trends seen in the beam plots for the 4.17 MHz imaging beam, 58

75 Unaberrated 0.25 π RMS Error 0.44 π RMS Error 0.87 π RMS Error 30 Level (db) Lateral Position (degrees) Figure 4.6: Plot of 4.17 MHz imaging beam unaberrated and one example each where spatially correlated electronic aberrators of increasing RMS focusing error are applied. although they were less affected for a given aberration level. As the focusing error magnitude of the spatially correlated electronic aberrator increased, the quality of the 4.17 MHz imaging beam decreased (Figure 4.6). Figure 4.6 shows beam plots measurements from a single example of each of the three aberration levels, as well as an unaberrated beam. As was the case with the spatially uncorrelated aberrator, an increase in relative side-lobe level, with concomitant decrease in beam amplitude as focusing error magnitude increases, is seen for the example beam plotted. These single examples are representative of the other beam plots for each level of aberration. Although not shown, beam plots of the 2.08 MHz fundamental and 4.16 MHz harmonic beams also exhibited the same trends seen in 59

76 Level (db) MHz Fundamental Beam 4.16 MHz Harmonic Beam 4.17 MHz Imaging Beam RMS Focusing Error (π radians) Figure 4.7: Plot of average peak level relative to the unaberrated beam for 2.08 MHz fundamental beam (diamonds), 4.16 MHz second harmonic beam (triangles), and 4.17 MHz imaging beam (circles) with spatially uncorrelated aberrators applied. Error bars represent a range of two standard deviations. the beam plots for the 4.17 MHz imaging beam, although they were less affected for a given aberration level Beam Amplitude From Figure 4.7, it can be seen that in the presence of spatially uncorrelated aberrators, an increase in RMS focusing error causes a decrease in beam amplitude. The overlap between the 2.08 MHz curve and the 4.17 MHz curve suggests that a frequency-independent relationship exists between beam amplitude and RMS focusing error. The 4.16 MHz harmonically-generated beam shows a relationship between amplitude and RMS focusing error similar to that seen for the directly transmitted 2.08 MHz and 4.17 MHz beams, however the loss in amplitude for the 4.16 MHz harmonic beam is significantly less. 60

77 Level (db) MHz Fundamental Beam 4.16 MHz Harmonic Beam 4.17 MHz Imaging Beam RMS Focusing Error (π radians) Figure 4.8: Plot of average peak level relative to the unaberrated beam for 2.08 MHz fundamental beam (diamonds), 4.16 MHz second harmonic beam (triangles), and 4.17 MHz imaging beam (circles) with spatially correlated aberrators applied. Error bars represent a range of two standard deviations. From the amplitude plot of beams subject to spatially correlated aberrators, a number of features common to beams subjected to spatially uncorrelated aberrations become apparent, as shown in Figure 4.8. Specifically, an increase in RMS focusing error resulted in decreased amplitude for the 2.08 MHz measurement, the 4.17 MHz imaging, and the 4.16 MHz harmonic beams. Like the spatially uncorrelated case, there is also overlap between the 2.08 MHz curve and the 4.17 MHz curve. Finally, the 4.16 MHz harmonically generated beam is, again, less distorted than the 4.17 MHz imaging beam, evidenced by a consistently smaller drop in beam amplitude across all aberration levels. 61

78 0 5 Side-lobe Level (db) MHz Fundamental Beam 4.16 MHz Harmonic Beam 4.17 MHz Imaging Beam RMS Focusing Error (π radians) Figure 4.9: Plot of side-lobe level relative to the main lobe for 2.08 MHz fundamental beam (diamonds), 4.16 MHz second harmonic beam (triangles), and 4.17 MHz imaging beam (circles) with spatially uncorrelated aberrators applied. Error bars represent a range of two standard deviations Side-lobe Level As indicated in Figure 4.9, the 2.08 MHz measurement beam, in terms of side-lobe level, suffers least from distortion due to spatially uncorrelated aberrators of the three beams. Unlike with beam amplitude measurement, the relationship between side-lobe level and RMS error does not appear to be the same for the 2.08 MHz beam as for the 4.17 MHz beam, indicating that the relationship between these two factors is frequency-dependent. Side-lobe levels of the 4.16 MHz harmonic beam are lower than those of the 4.17 MHz imaging beam for all but the most severe aberration (1.16π radians RMS error). Figure 4.10 shows that RMS focusing error has the same relative effect on side- 62

79 0 Side-lobe Level (db) MHz Fundamental Beam 4.16 MHz Harmonic Beam 4.17 MHz Imaging Beam RMS Focusing Error (π radians) Figure 4.10: Plot of side-lobe level relative to the main lobe for 2.08 MHz fundamental beam (diamonds), 4.16 MHz second harmonic beam (triangles), and 4.17 MHz imaging beam (circles) with spatially correlated aberrators applied. Error bars represent a range of two standard deviations. lobe level for all three beams. This result appears to contradict the unique relationship that each beam had between side-lobe level and RMS focusing error in the presence of spatially uncorrelated aberrators. However, the small sample size (three aberration levels) used here makes subtle trends impracticable to analyze. It is clear, however, that neither the 4.17 MHZ imaging beam nor the 4.16 harmonic beam (once subjected to spatially correlated aberrators) provides a significant advantage In terms of side-lobe level Beam Width Figure 4.11 shows that the -6 db beam width is not significantly affected by the spatially uncorrelated aberrators. Representation of the width of the 2.08 MHz 63

80 4 6 db Beam Width (degrees) MHz Fundamental Beam 4.16 MHz Harmonic Beam 4.17 MHz Imaging Beam Normalized 2.08 MHz Fundamental Beam RMS Focusing Error (π radians) Figure 4.11: Plot of -6 db beam width for 2.08 MHz fundamental beam (diamonds), normalized 2.08 MHz fundamental beam (squares), 4.16 MHz second harmonic beam (triangles), and 4.17 MHz imaging beam (circles) with spatially uncorrelated aberrators applied. Error bars represent a range of two standard deviations. measurement beam, due to its lower frequency, has been decreased by one-half to facilitate its comparison with the 4.17 MHz imaging beam. This beam width normalization is derived from Equation (2.26), which states that doubling the frequency of a beam results in a decrease in beam-width by one-half. A similar relationship is seen between the normalized beam width of the 2.08 MHz measurement beam and that of the 4.17 MHz imaging beam. The harmonic beam is slightly wider than the 4.17 MHz beam. While the width of the harmonic beam is noticeably degraded by the 1.16π radians aberrators, it should be noted that the 4.17 MHz beam was degraded to such an extent by these aberrators that no meaningful beam width could be measured (see the example beam in Figure 4.5). Figure 4.12 reveals what appears to be a correlation between increased beam 64

81 4.5 6 db Beam Width (degrees) MHz Fundamental Beam 4.16 MHz Harmonic Beam 4.17 MHz Imaging Beam Normalized 2.08 MHz Fundamental Beam RMS Focusing Error (π radians) Figure 4.12: Plot of -6 db beam width for 2.08 MHz fundamental beam (diamonds), normalized 2.08 MHz fundamental beam (squares), 4.16 MHz second harmonic beam (triangles), and 4.17 MHz imaging beam (circles) with spatially correlated aberrators applied. Error bars represent a range of two standard deviations. width and increased RMS focusing error of the spatially correlated aberrators. It should be noted that beam width for the 2.08 MHz fundamental was again decreased by one-half to allow direct comparison with the width of the 4.17 MHz beam. The beam width versus RMS focusing error for the 2.08 MHz fundamental and the 4.17 MHz imaging beams appear to overlap. However, as was the case with side-lobe level, the small sample size makes it difficult to clearly identify trends. From the beam plots of Figure 4.6, it is clear that the slight increase in width for the 4.17 MHz imaging beam as RMS focusing error increases is a symptom of the much greater distortion that is present. 65

82 a) Unaberrated b) Uncorrelated 1.16π radians c) Uncorrelated 0.97π radians d) Uncorrelated 0.77π radians e) Uncorrelated 0.58π radians f) Uncorrelated 0.39π radians g) Correlated 0.87π radians h) Correlated 0.44π radians i) Correlated 0.25π radians Figure 4.13: B-mode images of an RMI resolution phantom made with an 4.17 MHz imaging beam unaberrated (a), with spatially uncorrelated electronic aberrators applied (b-f), and with spatially correlated electronic aberrators applied (g-i). 66

83 4.3.6 Phantom Images The RMI phantom contained four types of targets: (1) a large anechoic cyst, (2) a group of closely spaced point targets, (3) hyper-echoic cysts of varying size, and (4) point targets spaced at constant intervals in range. Each of these four target types demonstrates a different aspect of system imaging quality. The anechoic cyst acts as a specular reflector and demonstrates imaging system contrast; the closely spaced point targets demonstrate spatial resolution for the image; the hyper-echoic cysts also demonstrate image system contrast; and the targets spaced in range demonstrate how imaging system resolution varies over range. As electronic aberrators of increasing RMS focusing error magnitude are applied, these four target types initially grow less distinct, and then disappear from the images. Overall image brightness and contrast also decrease with aberration. The B-mode images in Figure 4.13 were formed using the beams shown in Figure 4.5 and Figure 4.6. Application of the strongest spatially uncorrelated aberrator (1.16π radians RMS focusing error) and the strongest spatially correlated aberrator (0.87π radians RMS focusing error) caused extreme distortion, making all but the most general features of the phantom impossible to discern. While it is possible to detect the large anechoic cyst, there is no way to determine where it is located. With the slightly less severe 0.97π radians RMS spatially uncorrelated aberrator, however, we can begin to determine the location of the anechoic cyst, though it is still somewhat uncertain, and the image permits only minimal detection of the closely spaced point targets. In images formed with the remaining spatially uncorrelated aberrators (0.77π radian, 0.58π radian, and 0.39π radians RMS focusing error) and spatially correlated aberrators (0.44π radians and 0.25π radians RMS focusing error), all four target types are detectable and can be localized; targets become clearer as aberration level decreases. 67

84 4.4 Discussion Aberrators Investigation of the relationship between aberration and beam distortion required aberrators of different types and strengths. The spatially uncorrelated aberrators provided a good sampling of aberration strength, ranging from mild (0.39π radians RMS at 4.17 MHz) to severe (1.16π radians RMS at 4.17 MHz). A fairly large number of unique aberrators (fifteen) was created for each aberration level to reduce uncertainty in beam distortion measurements. To facilitate comparison of beam distortion measurements among aberration levels, the random seeds used to generate each of the fifteen unique aberrators were re-used for each of the five aberration levels. Therefore, the fifteen unique aberrators at each aberration level were similar, with variations due to scaling and quantization of the focusing errors. Focusing error quantization occurred because the Duke T5 scanner can only implement delays in 20 ns increments. Finally, the small standard deviation in RMS focusing error magnitude within each aberration level in Table 4.1 is attributable to the large sample size of elements in the aperture (512) to which focusing errors were applied. The large sample size was also responsible for the close match of focusing error distribution to the uniform distribution from which focusing errors were selected (Figure 4.4b). The spatially correlated aberrators provided a semi-structured delay profile across the aperture. Spatially correlated aberrators were created for fewer aberration levels than spatially uncorrelated aberrators were, but this smaller quantity still provided mild (0.25π radians RMS at 4.17 MHz), moderate (0.44π radians RMS at 4.17 MHz), and strong (0.87π radians RMS at 4.17 MHz) aberration strength. As with generation of the spatially uncorrelated aberrators, the random seeds that had been used to generate each of the eleven unique spatially correlated aberrators were reused for each of the three aberration levels. Thus, the general features of any of the eleven 68

85 unique aberrators are the same at each of the three aberration levels, except for scaling of focusing delay magnitude and quantization. This similarity accounts for the comparable spatial correlation lengths for each of the three aberration levels (Table 4.2). The distribution of spatially correlated focusing errors followed a normal distribution, despite the fact that focusing delays matched a uniform distribution prior to the spatial correlation processing. The spatial average filter used to achieve spatial correlation is responsible for this outcome. The spatial filter calculated the mean of focusing delays from nearby elements (each delay represents a random variable) to determine a new focusing delay for each element. Therefore, the distribution of spatially correlated focusing delays is the result of the mean of several random variables that, according to the central limit theorem, will tend toward a normal distribution. This distribution is evident in Figure 4.4d Beam Amplitude The beam amplitude versus RMS focusing error magnitude plots show that beam amplitude is sensitive to aberration magnitude. For all three beams and both aberration types, a drop in amplitude occurs that accelerates as the aberration level increases. This drop in amplitude versus RMS focusing error magnitude seems to follow the same curve for the two beams transmitted directly: the 2.08 MHz fundamental and 4.17 MHz imaging beam. This result suggests that a common, frequency-independent relationship exists between beam amplitude loss and aberration level. As peak beam amplitude is lost, acoustic energy is moved out of the imaging beam s main lobe, and contributions from off-axis targets to the image increase, resulting in image clutter. Thus, a combination of image brightness and image clutter can be used to indirectly measure the magnitude of aberration present in an image. Comparison of actual image brightness to expected image brightness can be used to estimate the drop in peak beam amplitude. However, a drop in peak beam amplitude 69

86 can be caused by not only aberration but also by increased attenuation. Comparison of actual image clutter to expected image clutter could be used to estimate the loss of peak beam amplitude due to aberration and not attenuation. An estimate of aberration magnitude could be made using the relationship between peak amplitude loss and aberration level. Comparison of data presented in Figure 4.7 and Figure 4.8, however, show that the beam amplitude versus RMS focusing error magnitude curve governing the directly transmitted beams subject to spatially uncorrelated aberrators is different from the curve followed by beams subject to spatially correlated aberrators. This difference indicates that the relationship between amplitude loss and aberration level, while independent of beam frequency, is dependent on the nature of the aberrator. Therefore, indirect measurements of aberration level using image brightness would require some assumption about the structure and distribution of focusing errors present. A common feature to the plots of beam amplitude versus RMS focusing error magnitude is the lesser loss of amplitude suffered by the 4.16 MHz harmonically generated beam compared to that suffered by the 4.17 MHz imaging beam. This result indicates that the harmonically generated 4.16 MHz beam is less affected by aberration than the directly transmitted 4.17 MHz beam. In fact, harmonic beam amplitude is within 10 db of its unaberrated level, even with 0.9π radians RMS focusing error present for the spatially uncorrelated aberrators and 0.5π radians RMS focusing error present for the spatially uncorrelated aberrators. These beam amplitude measurements demonstrate both that the 4.16 MHz harmonically generated beam is less affected by aberration than the 4.17 MHz imaging beam, and that harmonic beam amplitude does not drop significantly even in the presence of mild to moderate aberration. 70

87 4.4.3 Side-lobe Level The side-lobe level plots of Figures 4.9 and 4.10 show that side-lobe level increases, and thus degrades, as aberration increases. The spatially uncorrelated and correlated aberrators demonstrated different relationships between side-lobe level and aberration level for the three beams. Degradation of side-lobes seemed to occur at lower average RMS focusing error magnitude for the spatially correlated aberrator. In general, there was little difference in side-lobe level for either the 4.16 MHz harmonic beam or the 4.17 MHz imaging beam for a given aberration level. This result differs from the simulations of aberrated harmonic and imaging beams performed by Christopher [4], which predict lower side-lobe levels for the harmonic beam. The difference between simulated and experimental side-lobe performance is likely due to the specific choice of aberrator studied; from Figures 4.11 and 4.12 it is clear that a change in aberrator structure alters the relationship between side-lobe level and RMS focusing error. Another feature of the plots in Figures 4.11 and 4.12 is that the sidelobe level versus RMS focusing error magnitude curves for the directly transmitted 2.08 MHz measurement and 4.17 MHz imaging beams show much less overlap than in the beam amplitude plots. This result indicates that if a frequency-independent relationship exists between side-lobe level and RMS focusing error magnitude for directly transmitted beams, it is much more subtle than the one governing beam amplitude. The relationship between side-lobe level and RMS focusing error shows trends that are similar to, but more muted than, trends observed in the relationship between beam amplitude and aberration level. These less clearly defined trends are due, in part, to the different effect aberration has on side-lobe level than it has on peak beam amplitude. Unlike beam amplitude, which always degrades in the presence of aberration, side-lobe level can actually improve when aberrating conditions are 71

88 optimal. This improvement, however, comes with additional losses in both beam amplitude and beam width. While side-lobe level will, on average, degrade with increased aberration, improvement in side-lobe level occurs frequently enough to confound this trend. This makes side-lobe level relative to the main lobe a poor indicator of the aberration present Beam Width The plots in Figures 4.11 and 4.12 show that -6 db beam width is not significantly affected by aberration level for any of the three beams. Both spatially uncorrelated and spatially correlated aberrators resulted in similar -6 db beam widths for each of the three beams. For the spatially uncorrelated aberrators, there is no change in beam width as aberration strength increases. This finding is especially well illustrated by the 4.17 MHz imaging beam, where beam width does not vary until RMS focusing error magnitude reaches 1.16π radians, at which point the main beam practically disappears, and beam width can no longer be measured. For the spatially correlated aberrators, beam width did increase as aberration strength increased, but the effect of aberration on the width measurement was slight. These results, unlike those for sidelobe level, are in good agreement with the simulations performed by Christopher [4]. This agreement in between Christopher s simulations and these experiments for beam width but not for side-lobe level can be explained by comparing Figures 4.11 and 4.12 to Figures 4.9 and Unlike side-lobe level, the relationship between beam width and RMS error is not significantly altered by a change in aberrator structure. Thus we expect similar results between Christopher s simulations and these experimental measurements, despite the structural differences of the aberrators used. The beam widths of directly transmitted 2.08 MHz measurement and 4.17 MHz imaging beams were normalized using Equation (2.26), and there was some overlap for their normalized beam width versus RMS focusing error curves. This result 72

89 indicates that a frequency-independent relationship between beam width and RMS focusing error magnitude exists for the directly transmitted beams. However, the weak dependence of beam width on aberration strength would make use of beam width to measure aberration strength impracticable. Finally, it should be noted that, like side-lobe level, beam width does not always increase in the presence of aberration Phantom Images The B-mode images in Figure 4.13 formed using the 4.17 MHz imaging beam show the effect of aberration on image quality. By comparing the B-mode images to the beams used to form them in Figures 4.5 and 4.6, we gain insight into the effect both different aspects of the beam (peak amplitude, side-lobe level, and beam width) and strength of aberration affect image quality. For example, the lack of a clear main lobe for the 1.16π radians RMS focusing error imaging beam results in an image of the anechoic cyst with a laterally smeared appearance. For the most part, however, the B-mode images are consistent with the amplitude, side-lobe level, and beam width measurements. Image brightness follows the trend of the 4.17 MHz imaging beam amplitude, dropping off quickly as aberration strength is increased. On the other hand, resolution, which is related to the imaging beam s width, does not seem to vary significantly with aberration strength. This observation is corroborated by looking at the closely spaced point targets which follow the trend of -6 db beam width; they appear relatively constant across the aberration levels. The effect of side-lobe levels on image quality is not easily demonstrated with these B-mode scans. The difficulty of determining the effect arises from the fact that side-lobe level is relatively constant for the 4.17 MHz imaging beam for aberration levels where multiple phantom targets are visible. 73

90 4.5 Summary and Conclusion Distortion to the 2.08 MHz measurement beam, the 4.16 MHz harmonic beam, and the 4.17 MHz imaging beam was measured over a range of aberration strengths for unstructured and semi-structured (spatially uncorrelated and spatially correlated) electronic aberrators. Distortion was quantified using three measurements: (1) beam amplitude, (2) side-lobe level, and (3) -6 db beam width. These measurements are related to the image quality parameters of brightness/dynamic range, contrast, and spatial resolution, respectively. Experiments demonstrated that beam amplitude is most sensitive to aberration strength, while side-lobe level is less affected, and beam width nearly unaffected. Overall, the 4.16 MHz harmonic beam was the least distorted of the three beams at any given aberration level, making it an attractive correction source. Results for the directly transmitted beams (2.08 MHz measurement and 4.17 MHz imaging) indicate that a frequency-independent relationship may exist between distortion and aberration strength. If true, such a relationship would provide a method of estimating the severity of aberration present directly from diagnostic images by comparing image brightness and clutter to expected values. Finally, the images in Figure 4.13 illustrate how decreases in beam amplitude, increases in side-lobe level and -6 db beam width, as well as other unmeasured effects of aberration (seen in the beam plots of Figures 4.5 and 4.6), combine to affect image quality. These images provide a guide as to the decrease in image brightness, increase in image clutter, and decrease in image contrast that result for different levels of aberration. 74

91 5 Water Tank Correction 5.1 Introduction The beam distortion experiments discussed in Chapter 4 demonstrate the effect of aberration on beam quality for the measurement, harmonic, and imaging beams. Evaluation of beam amplitude, side-lobe level, and -6 db beam width all indicated that the harmonically generated beam was less distorted than the imaging beam. The advantages of the harmonically generated beam were especially noticeable in cases where imaging beam distortion caused degradation in image quality severe enough to warrant correction. These advantages provided strong rationale to use the received harmonic beam to correct for aberration. In this chapter, aberration correction using the harmonic beam is carried out, both on the spatially uncorrelated electronic aberrators studied in the previous chapter, and on a physical aberrator. Correction utilizing the 4.16 MHz harmonic beam is compared with that utilizing the 2.08 MHz fundamental signal, and the effect of SNR on correction performance is discussed. Because biological tissue contains a combination of reflector types, evaluation 75

92 of harmonic correction includes each of the three major classes of reflectors: point, specular, and speckle. Harmonic correction is performed in a water tank environment in order to eliminate the effect of motion and attenuation. As there is no attenuation in the water tank, use of spatially correlated aberrators (to allow grouped receive elements) is unnecessary. The 4.17 MHz imaging beam that resulted from application of harmonic correction is used to evaluate the effectiveness of harmonic correction. The three beam properties studied in the previous section (beam amplitude, sidelobe level, and -6 db width) are measured over a range of aberration strengths. The effect of correction on image quality is also investigated. 5.2 Materials and Methods Ultrasound Scanner See Section Ultrasound Transducer See Section Spatially Uncorrelated Aberrators See Section RTV Aberrator A physical aberrator was created to provide a model of body-wall aberration superior to that which a phase-screen aberrator provided. The physical aberrator consisted of a slab of RTV (c=940 m/s, α = MHz) created to simulate an aberrating layer with finite thickness and attenuation, and thus one that would yield multiple target isoplanatic patches and amplitude aberration. RTV was poured into a mold carved from soap, and then degassed in a vacuum for 30 minutes to remove air bubbles. A heavy, flat metal block, wrapped in plastic wrap to prevent adhesion, 76

93 was pressed onto the mold to squeeze out excess RTV during the curing period. The aberrator was 3 mm thick on average, with random thickness variations of approximately 0.5 mm randomly distributed across it both lengthwise and crosswise in two dimensions. The RTV aberrator was placed parallel to and in contact with the face of the array. RMS focusing error attributable to the aberrator was estimated to be 0.17π radians at 4.17 MHz Harmonic Source Wavefront Correction The wavefront correction process comprised two phases: measurement and imaging. During the first phase, a six-cycle measurement pulse was transmitted at 2.08 MHz. The aberrator had a minimal effect on this relatively low-frequency pulse. Through nonlinear propagation, this measurement pulse produced a minimally aberrated 4.16 MHz harmonic component [50]. The six-cycle pulse was narrowband, preventing overlap between the fundamental and harmonic bandwidths. The fundamental and harmonic pulses both reflected from a target or speckle region, and the 4.16 MHz harmonic pulse was isolated in order to estimate the aberrating delays present. The second phase of correction, the imaging process, consisted of a two-cycle imaging pulse transmitted and received at 4.17 MHz with corrective time delays applied, as determined from the received harmonic pulse, to compensate for the aberrating delays (Figure 3.3). Each electronic aberrator or body wall measurement consisted of 512 six-cycle transmits at 2.08 MHz using the full transmit aperture. For each transmit pulse, a separate receive channel group (either individual channels or nine-element patches) was digitized at 50 MHz for 20 μs; the 20 μs recording window included the focal point. After 512 transmits, the entire receive aperture had been measured and digitized. This measurement process was repeated in order to obtain a total of 16 measurements for each receive element. The measurements were averaged to- 77

94 gether to reduce noise. The averaged signal measurements were bandpass-filtered at 4.16 MHz to isolate the harmonic signal from the 2.08 MHz fundamental signal. The aberrating delays were estimated using the multi-lag, least-means-squares cross-correlation algorithm of equation (3.5). The vector D can be determined by any of the many arrival-time estimation techniques in existence; cross-correlation of signals from neighboring elements was implemented here, as this approach is both straightforward and effective [33]. Correction of aberrating time delays was implemented by subtracting the resultant delays, T, from the current aberration function. Proper correction results in a minimized focusing error. A 4.17 MHz beam was then transmitted and received in the water tank with correction applied. Lateral beam plots of the corrected 4.17 MHz beam were made in the water tank using the corrective delays from each electronic aberrator and correction target combination. Multiple correction iterations were accomplished by applying corrective delays to the 2.08 MHz transmit and repeating the delay estimation process. The delays calculated from the second correction iteration were then subtracted from the residual focusing error that remained after the first correction iteration, and beam plots were measured Beam Plots See Section Reflectors Medical ultrasound images result from reflections from a variety of targets. These reflectors include point reflectors, specular reflectors, and regions of pure speckle. These three types of reflectors were used in water tank experiments to evaluate performance of the harmonic correction technique for each type. The point reflector consisted of the tip of a hydrophone (radius=1 mm) placed in the water tank at 78

95 60 mm from the transducer. The specular reflector consisted of a sheet of Lucite (c=2650 m/s) approximately 24 mm thick placed in the water tank so that the first surface was parallel to and 60 mm away from the transducer face. A custom phantom constructed by Professor Ernie Madsen of the University of Wisconsin- Madison, with a large number of sub-resolution scatterers (c=1540 m/s), was used as a speckle target. Data was recorded from a speckle region 60 mm away from the transducer Off-Axis Correction The majority of harmonic source wavefront correction in this chapter was performed with the correction target located on the imaging beam axis (0 elevation, 0 azimuth). Aberrators encountered in a clinical setting generally have multiple target isoplanatic patches [52], thus harmonic source wavefront correction must be able to correct using targets off the imaging beam axis. The ability of harmonic source wavefront correction to correct using off-axis correction targets was evaluated using a finite thickness RTV aberrator (from Section 5.2.4) paired with a point correction target. Correction was performed at seven locations: point target at 18, 12, 6, 0, 6, 12, 18 azimuth, all at 0 elevation. No modification of the harmonic source wavefront correction method was necessary for off-axis correction. To evaluate the improvement in image quality from correction, B-mode images of the RMI phantom were captured with the RTV aberrator present and correction from each of the seven locations applied. A corrected image was created by taking the scan lines around the correction point from each of the seven off-axis corrected B-modes and combining those scan lines to form an composite image (see Table 5.1). 79

96 Table 5.1: Location of the six off-axis and one on-axis correction points. Correction from each point was applied to scan lines within about 3 degrees of the correction point. Correction Position Scan Lines in Angular Range in (degrees) Composite Image Composite Image (degrees) Data Acquisition System The summed rf signal from T5 was sampled using a Signatec (Corona, CA) PDA12A data acquisition card with a 50 MHz sample rate. A custom-built buffer amplifier was used to match the 1 MW output impedance of T5 to the 50 W impedance of the data acquisition card. During each transmit, 512 samples were recorded from the summed rf signal, representing a μs time window (approximately 15 mm range). The sampling range was set so that 12-bit samples were acquired from +500 mv to -500 mv. The signal from each element was averaged over multiple measurements (typically 16), before being output as a binary file to be processed by custom Matlab code for delay estimation Scan Recalculation Correction of electronic aberrators was achieved by adjusting the original aberrated focusing delay to account for the estimated focusing delay. A file consisting of the difference between aberrated and estimated focusing delays for each element was then uploaded via FTP to T5 and a new scan calculated using the custom written Circe scan software (Figure 5.1). The Circe scan software was developed over a number of years by the von Ramm Diagnostic Ultrasound Laboratory. Circe uses 80

97 Scan Parameters (c, scan angle, element position, focal distance, etc.) Circe Focusing Delays Aberrating Delay File Corrective Delay File Scan File Figure 5.1: Focusing delays are calculated in Circe using scan parameters before being output as part of the scan file. Aberrating and corrective delays are added to the focusing delays. Proper corrective delays will cancel out aberrating delays to zero. scan parameters from an input file to calculate a file that will execute the desired scan on T Comparison of Fundamental and Harmonic Correction The 4.16 MHz harmonic beam is more point-like than the 2.08 MHz fundamental beam, but suffers from decreased SNR relative to the fundamental. To determine the relative importance of the opposing effects of beam width and SNR, the correction performance of the 2.08 MHz fundamental was compared to that of the 4.16 MHz harmonic beam. To determine whether fundamental or harmonic correction performed 81

98 better when using the T5 scanner with the two-dimensional transducer, correction of the spatially uncorrelated electronic aberrators, described in Section 5.2.5, was performed using a region of the speckle phantom as a correction target. A modification to the harmonic wavefront correction method described in Section 5.2.5, i.e. the substitution of the fundamental for the harmonic beam, was used to perform the correction. The 2.08 MHz fundamental signal was bandpass-filtered from the received signal and fed to the delay estimation algorithm instead of the 4.16 MHz signal. Peak amplitude of the corrected 4.17 MHz imaging beam was measured for both fundamental and harmonic correction. Signal-to-noise ratio (SNR) is an important factor to be considered in any correction scheme. Signal-to-noise ratio is measured by calculating the average correlation coefficient for the array using equation (3.4). The correlation coefficient for each element is determined for the signal received at each element from successive measurements; the average correlation coefficient for the array is the average of these element correlation coefficients. To investigate the effect a relative increase in harmonic SNR had on correction performance, correction of a speckle region was performed in the water tank. Correction of fifteen 0.39π radians electronic aberrators was performed in a water tank on a sponge acting as a speckle region. The water tank provided greater harmonic SNR relative to the fundamental than the speckle phantom due to a combination of decreased attenuation and increase nonlinear propagation of water. Peak amplitude of the corrected 4.17 MHz imaging beam was measured for both fundamental and harmonic correction. To further investigate the impact SNR had on correction performance, correction was performed using the 2.08 MHz fundamental and the 4.16 MHz harmonic signals of equal SNR. Decreasing the SNR of the 2.08 MHz fundamental to the level of the 4.16 MHz harmonic simulates the case where overall system SNR is high enough that the increased SNR of the 2.08 MHz fundamental over the 4.16 MHz harmonic does 82

99 not affect correction performance. Comparing correction performance between the 2.08 MHz fundamental and 4.16 MHz harmonic before and after SNR equalization will indicate the impact SNR has on correction. Fifteen spatially uncorrelated electronic aberrators with 1.16π radians RMS focusing error were corrected using a specular reflector as a correction target. Correction was first performed using the 4.16 MHz harmonic, and the signal-to-noise ratio of the 4.16 MHz harmonic was measured. Transmit amplitude was then decreased until the SNR of the 2.08 MHz fundamental beam was equal to the value measured for the 4.16 MHz harmonic beam. Correction using this decreased transmit amplitude was then performed using the 2.08 MHz fundamental. Peak amplitude of the corrected 4.17 MHz imaging beam was measured for both fundamental and harmonic correction. Peak amplitudes of the corrected imaging beam, after fundamental and harmonic correction were applied, were analyzed using a one-sided, paired-sample Student s t-test Formation of B-Mode Images See Section Contrast Measurements Contrast was evaluated by measuring the average brightness between two regions of interest (ROIs) of equal area. One of these ROI was located inside the anechoic cyst target, a region nearly free of scatterers. Thus, the anechoic cyst provided a good measurement of quality of the imaging beam s off-axis response, as any received signal necessarily originated from off-axis scatterers. The other ROI selected was located in a speckle region adjacent to the anechoic cyst. The brighter speckle ROI provided a measurement of the peak amplitude of the imaging beam, as from equation (2.29) brightness increases with beam amplitude. The speckle ROI was located at the same 83

100 Level (db) Unaberrated 1 st Correction Iteration 2 nd Correction Iterration 1.16π RMS Error Lateral Position (degrees) 4 6 Figure 5.2: Plot of unaberrated (squares), and one example of the electronically aberrated (circles) and corrected (diamonds and asterisks) 4.17 MHz imaging beams using a point reflector as a correction target. range as the anechoic cyst ROI; therefore, the effect of attenuation on both ROIs was the same. 5.3 Results Beam Plots The beam plots in Figure 5.2 show the imaging beam without aberration (squares), in the presence of a 1.16π radians RMS focusing error magnitude electronic aberrator (circles), and with correction applied using signal received from a point reflector (diamonds and asterisks). These beam plots represent the aberrated and corrected beams for a single aberrator from the strongest aberration level examined here. As 84

101 concluded from the discussion in Chapter 4, the beams resulting from aberrators with decreasing strength are less distorted, with improved amplitude and side-lobe level. The corrected beams for aberrators of decreasing strength are also less distorted and approach the unaberrated beam, as will be discussed later in this section. Beam plots showing aberrated and corrected beams for the strongest aberration level examined are used throughout this section in order to better illustrate the improvement from correction. Correction using a point target is the ideal case for the cross-correlation delay estimation technique [11], and a significant improvement in the imaging beam is observed after just one round of correction (Figure 5.2 diamonds). We can see the effect of correction in the focused rf shown in Figure 5.3. Almost all the focusing errors present in the rf for the aberrated beam (Figure 5.3a) are eliminated, resulting in near-simultaneous arrival time for the receive pulse seen in the corrected rf (Figure 5.3b). However, it is clear that even the corrected rf still includes small residual focusing errors. A second correction iteration compensates for these residual errors, resulting in a beam (Figure 5.2 asterisks) that is a near-match to the unaberrated beam. The beam plots in Figure 5.4 show aberration and correction of the imaging beam for a physical aberrator using a point target as a correction source. The physical aberrator, molded from RTV, has multiple target isoplanatic patches, providing a closer model of the aberrating tissue layers encountered in the human body than electronic aberrators. The physical aberrator had an estimated 0.17π radians RMS focusing error, and resulted in the aberrated beam (represented in the figure with circles). The corrected beam (diamonds) is an improvement over the aberrated beam, but the corrected beam s peak amplitude is noticeably lower than that of the unaberrated beam. The disparity in peak amplitude between the corrected and unaberrated beams is partially due to residual focusing errors, but much of the 85

102 100 Element a) Sample 100 Element b) Sample Figure 5.3: Aberrated (a) and corrected (b) rf data measured from the point reflector after bandpass filtering to extract the 4.16 MHz harmonic signal. The aberrated rf signal in (a) corresponds tot he aberrated curve in Figure 5.2, while the corrected rf signal in (b) corresponds to the first correction iteration curve in Figure 5.2. difference in amplitude can be explained by attenuation within the RTV aberrator and reflection at the water-rtv interface (Table 5.2). When these loss mechanisms are compensated for, the peak amplitude of the corrected beam is within 1 db of the peak amplitude of the unaberrated beam. The beam plots in Figure 5.5 show the imaging beam without aberration (squares), in the presence of an electronic aberrator with 1.16π radians RMS focusing error mag- 86

103 Level (db) Unaberrated Corrected RTV Physcial Aberrator Lateral Position (degrees) Figure 5.4: Plot of unaberrated (squares), aberrated (circles), and corrected (diamonds) for the 4.17 MHz imaging beam in the presence of the RTV aberrator. Table 5.2: Estimated and actual difference in peak amplitude after correction based on attenuation and reflection from the RTV aberrator. Alpha Average Thickness Expected Attenuation RTV Impedance Loss at RTV-Water Interface Total Expected Loss Peak Amplitude Difference 10.7 db/cm 3 mm 6.42 db Mrayl 0.38 db 6.80 db 7.15 db 87

104 0 10 Unaberrated Corrected 1.16π RMS Errror Level (db) Lateral Position (degrees) Figure 5.5: Plot of the unaberrated (squares), and one example of the electronically aberrated (circles) and corrected (diamonds) 4.17 MHz imaging beams using a specular reflector as a correction target. nitude (circles), and with correction applied using signal received from a specular reflector (diamonds). As mentioned for the point reflector, the beam plots shown in the figure are the results for a single aberrator at the strongest aberration level. The characteristics of beams corrected for aberrators of varying aberration strengths will be discussed later in this section. It should be noted that correction using a specular reflector leaves greater residual focusing errors than correction using a point target. The beam plots in Figure 5.6 show the imaging beam without aberration (squares), in the presence of a 1.16π radians RMS focusing error magnitude electronic aberrator (circles), and with correction applied using the signal received from a speckle region (diamonds). Signal received from speckle regions presents the greatest chal- 88

105 0 10 Unaberrated Corrected 1.16π RMS Error Level (db) Lateral Position (degrees) Figure 5.6: Plot of the unaberrated (squares), and one example of the electronically aberrated (circles) and corrected (diamonds) 4.17 MHz imaging beams using a speckle region as a correction target. lenge for the cross-correlation method to extract corrective delays accurately. As a result, correction effectiveness varied within each aberration level significantly more for speckle region reflectors than for point or specular reflectors. The peak amplitude of the corrected beam in Figure 5.6 was actually higher than the peak amplitude of the beam corrected using a specular reflector in Figure 5.5. On average, however, peak amplitude of beams corrected using speckle regions was lower than for those corrected using specular reflectors Beam Amplitude As discussed earlier, the results of Section demonstrated that peak beam amplitude is very sensitive to beam distortion. Figure 5.7 illustrates the impact on 89

106 Peak Amplitude (db) Point Target Correction Specular Reflector Correction Speckle Region Correction Aberrated RMS Focusing Error (π radians) Figure 5.7: Plot of average peak beam level relative to the unaberrated beam for the 4.17 MHz imaging beam when a point reflector (squares), specular reflector (diamonds), and speckle region (crosses) were used as targets to correct the aberrated beam (circles). Values from fifteen beams were averaged for each point; error bars represent a range of 2 standard deviations. peak beam amplitude of correction using a point target (squares), a specular reflector (diamonds), and a speckle region (crosses). An increase in peak amplitude of the corrected imaging beam is observed over the range of aberration strengths studied, indicating effective aberration correction. As the figure illustrates, correction using signal from a point target was most effective, followed by correction using a specular reflector, and finally by correction using of speckle region. For all target types, the ratio of improvement in the peak amplitude of the corrected beam over peak amplitude of the aberrated beam decreases as aberration strength diminished. This result indicates that an iterative correction technique would yield diminishing returns on peak beam amplitude improvement, however a second correction iteration performed 90

107 Table 5.3: Peak amplitude of the 4.17 MHz imaging beam after iterative correction of the 1.16π RMS aberrators. Aberrated 1 st Correction 2 nd Correction Peak Beam Amplitude (db) (±3.05) (±0.60) (±0.27) on the 1.16π radians RMS aberrators (Table 5.3) does result in an additional 4 db of improvement in peak beam amplitude Side-lobe Level The effect of correction on side-lobe level for a range of aberration strengths is illustrated in Figure 5.8. In general, side-lobe level of the corrected beams improved 0 Side-lobe Level (db) Point Target Correction Specular Reflector Correction Speckle Region Correction Aberrated RMS Focusing Error (π radians) Figure 5.8: Plot of side-lobe level for the 4.17 MHz imaging beam when a point reflector (squares), specular reflector (diamonds), and speckle region (crosses) were used as targets to correct the aberrated beam (circles). Values from fifteen beams were averaged for each point; error bars represent a range of 2 standard deviations. 91

108 Table 5.4: Side-lobe level of the 4.17 MHz imaging beam after iterative correction of the 1.16π RMS aberrators. Aberrated 1 st Correction 2 nd Correction Side-lobe Level (db) (±3.30) (±2.89) (±2.27) (decreased in value) as aberration strength decreased. The exception to this trend is for correction of weak aberrators using a point target. For correction using a point target (squares) or specular reflector(diamonds), side-lobe level is improved relative to the aberrated beam (circles). Correction using a speckle region (crosses), however, actually degrades side-lobe level to a slight degree. Although the trend of continual improvement in side-lobe level for decreasing aberration strength is not as marked compared to the improvement seen with peak beam amplitude, application of iterative correction (Table 5.4) using a point target does result in additional improvement in side-lobe level Beam Width As discussed in Section 4.4.4, beam width was observed to have little dependence on aberration strength. In Figure 5.9, corrected beam width likewise does not show much dependence on aberrator strength, and trends for corrected beam width as aberration strength varies appear conflicted for different correction targets. In general, corrected beams are slightly wider than aberrated beams. Corrected beam width also matches expected performance for the correction targets, with point target correction (squares) performing better than specular reflector correction (diamonds), and specular reflector correction performing better than speckle region correction (crosses). It should be noted, however, that while imaging beam width is degraded by correction, beam width is never degraded more than 13 percent, even for the imaging beam corrected using a speckle region. The improvement observed from a second correction iteration (Table 5.5) indicates that iterative correction can reverse 92

109 db Beam Width (degrees) Point Target Correction Specular Reflector Correction Speckle Region Correction Aberrated RMS Focusing Error (π radians) Figure 5.9: Plot of -6 db beam width for the 4.17 MHz imaging beam when a point reflector (squares), specular reflector (diamonds), and speckle region (crosses) were used as targets to correct the aberrated beam (circles). Values from fifteen beams were averaged for each point; no -6 db width could be measured for 1.16π radians aberrated beams. Error bars represent a range of 2 standard deviations. beam width degradation Phantom Images The images in Figure 5.10 are B-mode scans of an RMI phantom. Figure 5.10a is a scan of the phantom using an unaberrated beam, while Figure 5.10b shows a diagram of the targets present in the phantom. Phantom targets of particular interest are Table 5.5: Beam width of the 4.17 MHz imaging beam after iterative correction of the 1.16π RMS aberrators. Aberrated 1 st Correction 2 nd Correction -6 db Beam Width (degrees) N/A (±0.070) (±0.031) 93

110 the anechoic cyst (1), the closely spaced point targets (2), the hyper-echoic cysts of varying size (3), and the point targets spaced at constant intervals in range (4). The third image, Figure 5.10c, is the resulting image after a 1.16π radians RMS aberrator is applied to the imaging beam. This image was formed using the aberrated beam (circles) shown in Figure 5.2 (the same aberrated beam shown in Figures 5.5 and 5.6 as well). The images in Figure 5.10d, e, & f were formed by applying correction to the imaging beam measured from a point target, a specular reflector, and speckle region, respectively. The imaging beams used to form the B-mode scans in Figure 5.10d, e, & f are the same as the corrected beams (diamonds) shown in the beam plots of Figures 5.2, 5.5, and 5.6 respectively. It is clear that aberration has severely degraded the image in Figure 5.10c. In the aberrated B-mode scan, the anechoic cyst is visible, but it is impossible to determine its location. Harmonic source wavefront correction significantly improves the aberrated image. The image formed using point target correction is very close to the unaberrated image. All four major target types are clearly visible in this image. Specular reflector and speckle region correction was not quite as effective as point target correction. Image quality for both the specular-reflector-corrected and speckle-region-corrected images is somewhat less than that of the point-targetcorrected images. However, specular-reflector-corrected and speckle-region-corrected images are still greatly improved compared to the aberrated images, and allow the viewer to distinguish three of the four main target types of the RMI phantom. Analysis of the interior of the anechoic cyst and neighboring speckle region measured the contrast that is provided by the imaging beams shown in Figures 5.2, 5.5, and 5.6. The results in Table 5.6 clearly show that correction increases contrast, making the interior of the anechoic cyst darker while brightening the neighboring speckle. The greatest contrast improvement of the B-mode images in Figure 5.10 occurred when a point target was used as a correction target, followed by improve- 94

111 Table 5.6: Contrast between anechoic cyst and surrounding speckle before and after corrective delays from different correction targets are applied. Image Contrast (db) Unaberrated (Fig 5.10a) Aberrated (Fig 5.10c) 1.26 Point Target Corrected (Fig 5.10d) Specular Reflector Corrected (Fig 5.10e) Speckle Region Corrected (Fig 5.10f) 9.96 ment seen with use of a specular reflector as a correction target, and finally with use of a speckle region as a correction target. It should be noted that the values in Table 5.6 were calculated on the detected data, not the compressed data displayed in Figure Physical Aberrator Off-Axis Correction The aberrated and corrected images of the RMI phantom with the RTV aberrator present in Figure 5.11 clearly show that off-axis correction was effective at restoring image quality. The resolution targets (1), anechoic cyst (2), and range targets (3) are all visibly improved when off-axis correction is applied to the RTV aberrated scan. Comparing the corrected B-mode image with the unaberrated B-mode image, the most conspicuous difference is the greater brightness of the unaberrated B-mode. This brightness difference is due largely to attenuation of the imaging beam by the RTV aberrator (see Table 5.2) and is not a byproduct of correction. In addition to the difference in brightness, the phantom targets generally appear crisper in the unaberrated image than the corrected image, indicating that there is some residual error present in the off-axis corrected image Comparison of Fundamental and Harmonic Correction Peak amplitude of corrected imaging beams using a speckle region as a correction target is shown in Figure 5.12 when corrective delays are estimated from the 2.08 MHz 95

112 a) Unaberrated b) RMI Phantom Targets c) Aberrated d )Point Reflector e) Specular Reflector f) Speckle Reflector Figure 5.10: B-mode images of an RMI phantom showing unaberrated image (a) and position of the phantom targets (b). Images formed with an 1.16π RMS spatially uncorrelated electronic aberrator present (c) as well as corrections obtained from a point reflector (d), specular reflector (e), and speckle region (f) are shown. Brightness of unaberrated, aberrated, and corrected images was normalized. 96

113 a) Unaberrated b) RTV Aberrated c) Corrected Figure 5.11: B-mode images of an RMI phantom showing an unaberrated image (a), an image with the RTV aberrator applied (b), and an image with off-axis correction applied (c). Off-axis correction was performed at 7 locations between -18 and 18 degrees. Each range marker represents 1 cm. 97

114 Peak Amplitude (db) MHz Fundamental Correction 4.16 MHz Harmonic Correction Aberrated RMS Focusing Error (π radians) Figure 5.12: Plot of average peak beam level relative to the unaberrated beam for the 4.17 MHz imaging beam comparing correction using the 2.08 MHz fundamental (squares) and 4.16 MHz harmonic (crosses) returned from a speckle region correction target. Values from fifteen beams were averaged for each point; error bars represent a range of 2 standard deviations. fundamental (squares) and from the 4.16 MHz harmonic (crosses). As Figure 5.12 shows, the 2.08 MHz fundamental provides much better correction than the 4.16 MHz harmonic. While the 4.16 MHz harmonic signal comes from a more pointlike region than the 2.08 MHz fundamental (a direct consequence of the relatively narrower harmonic beam), the 2.08 MHz fundamental has a significantly higher SNR than the 4.16 MHz harmonic. The Cramer-Rao lower bound on jitter, as calculated from equation (3.3), is a reasonable match to the RMS residual error measured for both the fundamental and harmonic. This result suggests that the higher SNR of the fundamental signal is responsible for the improved estimates for corrective delays (Table 5.7). Indeed, when the gap in SNR of the 2.08 MHz fundamental and

115 Table 5.7: Comparison of signal-to-noise ratio, estimated RMS error, and actual RMS error for correction using the 2.08 MHz fundamental and 4.16 MHz harmonic. A speckle region was used as a correction target. Aberration SNR (db) Jitter Lower Residual Error (ns) (radians at Bound (ns) 4.16 MHz) Fund. Harm. Fund. Harm. Fund. Harm. 1.16π π π π π Table 5.8: Impact of signal-to-noise ratio on correction. The phantom speckle correction region provides low harmonic SNR relative to the fundamental, while the water tank speckle correction region provides higher harmonic SNR relative to the fundamental. Phantom Speckle Water Tank Speckle SNR (db) Improvement (db) SNR(dB) Improvement (db) Fundamental (±0.27) (±0.19) Harmonic (±0.55) (±0.17) MHz harmonic is reduced, results of speckle region correction in the water tank demonstrate that the difference in fundamental and harmonic correction is reduced Table 5.8. Furthermore, when SNR of the 2.08 MHz fundamental and 4.16 MHz harmonic signals is equalized, we see that correction of peak beam amplitude utilizing a specular reflector as a correction target is 3 db more effective when using the 4.16 MHz harmonic beam instead of the 2.08 MHz fundamental beam (Figure 5.13). A Student s t-test analysis of correction performance using fundamental and harmonic beams with equalized SNR indicates that the improvement in correction of the 4.16 MHz harmonic over the 2.08 MHz fundamental is statistically significant, with p <

116 Peak Amplitude (db) Fundamental Harmonic Figure 5.13: Box-and-whisker plot showing peak amplitude of 4.17 MHz imaging beams corrected using 2.08 MHz fundamental and 4.16 MHz harmonic signals of equal signal-to-noise ratio. Values were averaged from 15 measurements on the 1.16π radians aberrator, a specular reflector was utilized as the correction target. The box indicates the interquartile range, the dashed line indicates the mean value, and the whiskers indicate twice the interquartile range. 5.4 Discussion Beam Plots The beam plots in Section present an aberrated beam severely distorted by the 1.16π radians RMS aberrator. It would be nearly impossible to obtain an acceptable image with such a beam, as the high side-lobes and weak main-lobe would obscure all but the largest and brightest structures. However, correction of the imaging beam greatly improves its quality. In the case of point reflector correction, the initial correction has nearly restored the main-lobe and side-lobes to their unaberrated 100

117 state. A subsequent correction iteration produces a corrected beam that is essentially aberration-free. When we observe the aberrated rf received by the transducer in Figure 5.3, the success of correction for the point-target case is not surprising. Examination of the signal received by each element reveals nearly identical pulses except for varying time shifts. This ensemble of waveforms is exactly what we would expect from a spherical wave reflected by the point target, and cross-correlation is the optimal method for estimating delays. Although correction of the imaging beam using a specular reflector or speckle region was not as effective as correction with a point target, it did result in a corrected imaging beam that was not significantly distorted, despite the presence of a strong aberrator. Corrections using a specular reflector or speckle region were made using received rf that began to exhibit changes in waveform shape as well as time delays. The plots in Figure 5.4 of beams aberrated and corrected in the presence of a physical aberrator demonstrate an important limitation of aberration correction: while corrective delays restored the peak amplitude of the beam to within 1 db of perfect correction, over 6 db of signal is irreversibly lost due to attenuation by the RTV aberrator. Aberration correction can improve both beam amplitude and shape, but it cannot restore signal lost through attenuation or other mechanisms. This limitation results in reduced receive signal amplitude, and can significantly impact image quality, especially when imaging in the presence of highly attenuating tissues, such as bone (α = 13 db / cm / MHz) [17] Beam Amplitude The results of harmonic source correction on peak beam amplitude indicate that a significant amount of the main-lobe energy dispersed by the aberrator is being re-concentrated back into the main lobe. Correction effectiveness in terms of beam amplitude varies for each of the target types. The impressive correction performance 101

118 provided by the point target is not surprising. The point target produces a strong spherical-wave reflection, the ideal signal for cross-correlation-based delay estimation. The specular reflector achieves correction performance almost as impressive as the point target. This result would indicate that the measurement beam is generating a harmonic source on a spatial scale similar to that of the point target. The relatively poor correction performance provided by the speckle region, compared to those of the point target and specular reflector, is due largely to two important differences between speckle region and the point target and specular reflector. First, the speckle region provides significantly less received harmonic signal for delay estimation than either of the other two. This relatively low amount of received harmonic signal is a result of the decreased reflectivity of the speckle region compared to that of the point target and specular reflector, each of which have much higher reflectivity. Additionally, propagation of the 2.08 MHz measurement pulse through the speckle phantom produces less second-harmonic signal than is produced in the water tank through a combination of attenuation and a decreased coefficient of nonlinearity. The second important difference between the speckle region and the point target and specular reflector is that the signal received from the many sub-resolution point scatterers appears to come from an incoherent, diffuse source, meaning that the shape of the received signal varies from element to element across the aperture. This variation can be described by the Van Cittert-Zernicke theorem, which states that the spatial receive correlation function of signal received from a speckle region is equal to the autocorrelation function of the transmit aperture [31, 55]. Thus variation between the signals received by any two elements increases as the separation between those elements increases. Variation also increases with aberration, further degrading the performance of the cross-correlation delay estimation algorithm. Application of a more speckle-appropriate delay estimation algorithm, such as the FDORT method described by Robert and Fink [43] would address this issue. 102

119 While improvement in beam amplitude for the corrected beams over the aberrated beams is impressive, especially with use of the point target, corrected beam amplitude never reaches that of the unaberrated beam. Residual focusing errors in the corrected beam account for the discrepancy between corrected and unaberrated peak amplitude, and this finding suggests that additional correction iterations may be necessary. The results from one additional correction iteration on the 1.16π radians RMS focusing error aberrator demonstrate that further improvement in beam amplitude can be achieved. The corrected curves in Figure 5.7 show consistent improvement in beam amplitude over the range of RMS focusing error magnitude studied. This finding provides strong rationale for performing additional correction iterations if the initial correction does not achieve desired imaging beam quality. It should be noted that the relative improvement in peak beam amplitude from aberrated to corrected decreases as RMS focusing error magnitude decreases. This relationship suggests that each of the three correction targets has a correction ceiling beyond which further correction iterations will not yield improvement in peak beam amplitude. However, for the water tank correction experiments, this correction ceiling appears to be within 5 db of the unaberrated beam s peak amplitude, and thus is not a significant concern Side-lobe Level A reduction in side-lobe level relative to the main lobe generally indicates that more energy is being concentrated into the main lobe. A comparison of the relative side-lobe level versus aberration strength curves of the corrected beams shown in Figure 5.8 to their respective peak beam amplitude curves as shown in Figure 5.7 indicates that, for the most part, a rise in peak beam amplitude corresponds to a decrease in relative side-lobe level for the corrected imaging beams. The main exception to this trend is for the speckle-region-corrected beams, which show an increase, 103

120 not decrease, in relative side-lobe level after correction. As mentioned in the preceding section, the speckle region presented the greatest challenge to the correction algorithm. While correction successfully transferred energy from off-axis into the main beam, as seen in the increased peak beam amplitudes in Figure 5.7, the increased residual error of the speckle-corrected beam has apparently led to a greater amount of that energy ending up in the side lobes than occurred for the point target or specular reflector corrected beams. Additional correction iterations would likely result in improved side-lobe levels, levels more in line with those seen for the point target and specular reflector corrected beams. Iterative correction of the 1.16π radians RMS focusing error aberrator using the point target as a correction source did result in further improvement in side-lobe level. Relative side-lobe levels resulting from the second correction iteration were more than would be expected based on RMS focusing error alone. RMS residual focusing error after the first correction was 0.35π radians RMS. Based on RMS focusing error alone, the side-lobe level versus RMS focusing error relationship in Figure 4.9 predicts side-lobe levels after the second correction iteration to be -25 db. Actual side-lobe levels after the second correction iteration, however, were -28 db. It seems likely that the unexpected improvement in side-lobe level arises from improvement of the aberrating delay distribution. In Section 4.3.4, we saw evidence that side-lobe level depends on a combination of aberration strength (as measured by RMS focusing error magnitude) and aberration delay distribution. Thus, despite the absence of a clear trend of continual improvement in side-lobe level for decreasing aberration strength, additional correction iterations will likely yield further improvement in side-lobe levels for other correction targets and aberration strengths. 104

121 5.4.4 Beam Width Wavefront correction has the unexpected effect of increasing -6 db beam width for the point-target-, specular-reflector-, and speckle-region-corrected imaging beams. This increase in beam width, however, was modest, and likely has little impact on image quality. For example, the greatest increase observed in corrected beam width comes from speckle region correction of the 0.58π radians RMS focusing error aberrators. In this case, -6 db beam width at a focal distance of 60 mm increases from 1.89 mm (1.81 ) to 2.14 mm (2.05 ), an increase of about 13 percent. The increase in beam width for all other corrected beams was usually significantly less than this value. The corrected imaging beam width curves in Figure 5.9 corroborate the findings of Section in suggesting that -6 db beam width is not strongly affected by RMS focusing error magnitude. As with side-lobe level, -6 db beam width seems to depend on the distribution of aberrating delays. Thus, it is not surprising to see improvement in beam width after a second correction iteration if improvement is presumed to result from improvement in the aberrating delay distribution rather than a reduction in RMS focusing error magnitude. Therefore, additional correction iterations will likely yield improvement in beam width by improving the aberrating delay distribution Phantom Images B-mode images were used to illustrate the effect of aberration and its correction on image quality. However, the two-dimensional array used in these experiments can also be employed to acquire three-dimensional images, and it is anticipated that harmonic source wavefront correction will also improve 3-D images. The effect of correction on aberrated 2-D images is shown in Figure The 2-cycle 4.17 MHz imaging beams used to form each of these images are very similar to the 6-cycle 4.17 MHz imaging beams shown in Figures 5.2, 5.5, and 5.6, with the main difference between 105

122 the two being improved range resolution for the 2-cycle beam. The aberrated image Figure 5.10c was formed by applying one of the 1.16π radians RMS focusing error aberrators to both the transmit and receive apertures. Nearly all the features of the RMI phantom became obscured by 1.16π radians RMS focusing error aberrator. Because a single set of focusing errors was used, there was a single target isoplanatic patch; consequently, a single set of corrective delays could be applied regardless of scan angle or depth. Application of corrective delays from each of the reflectors significantly improved the image. Based on the peak amplitude of the corrected imaging beams (diamonds) in Figures 5.2, 5.5, and 5.6, we would expect the image formed using point target correction to be brighter than the images formed using either specular reflector or speckle region correction. However, image brightness is often normalized, as was done in Figure Normalizing brightness allows comparison of fine detail among the images formed using the three correction targets, but doing so also makes it impossible to determine if the point-target-corrected image is indeed brighter than the specular-reflector- or speckle-region-corrected images. Brightness, however, is not the only image parameter expected to increase with peak beam amplitude. Penetration depth-the maximum depth at which structures are visible-should be greater when imaging with the point-target-corrected beam and its higher peak amplitude than when imaging with the specular-reflector or speckle-region-corrected beams. Indeed, this is the result illustrated in Figures 5.10d, e, and f, as we can make out the third row of hyper-echoic cysts in Figure 5.10d but not in Figures 5.10e and f. Thus, based on the average peak beam amplitude in Figure 5.7, point-target-corrected images can be expected to have greater penetration depth than specular-reflector-corrected images, which in turn should have greater penetration depth than speckle-regioncorrected images. Based on the relative side-lobe levels and -6 db beam widths for the corrected 106

123 beams (diamonds) in Figures 5.2, 5.5, and 5.6, one might expect to find similar contrast and spatial resolution for the corrected images in Figures 5.10d, e, and f. One would further expect that contrast for the speckle-region-corrected image would be slightly less than for the point-target- and specular-reflector-corrected images. Indeed, it is difficult to distinguish any difference in contrast between the images in Figures 5.10d, e, and f, although this is because the brightness curve applied to the images was chosen in order to emphasize the general features of the RMI phantom instead of contrast. It is possible, however, to modify the brightness curve of an image to emphasize even slight differences in contrast: in fact, an analysis of the detected rf used to form the images in Figure 5.10 indicates that the point-targetcorrected image has greater contrast than the specular-reflector-corrected image, and the specular-reflector-corrected image has greater contrast than the speckle-regioncorrected image. A comparison of the closely spaced point targets found in the point-target-, specular-reflector-, and speckle-region-corrected images, does not yield any noticeable differences. The closely spaced point targets can be resolved into individual targets equally well in all the corrected images. Therefore, spatial resolution is deemed to be nearly the same for the three correction targets. The average -6 db corrected imaging beam widths in Figure 5.9 are unaffected by changes in correction target choice or aberration strength, thus similar corrected beam spatial resolution would likely result regardless of the correction target utilized or initial aberration strength Physical Aberrator Off-Axis Correction Off-axis correction was successful at compensating for the focusing errors that varied with scan angle caused by the finite thickness RTV aberrator. While harmonic source wavefront correction can be applied at any scan angle, correction performance is expected to degrade as the angle between the correction target and the imaging 107

124 beam axis increases. This is due to the angular response of the transducer elements, V i = εp i cos θ i (5.1) where P i is the acoustic pressure wave received at element i, V i is the output voltage produced by element i, ε is piezoelectric conversion factor between acoustic pressure and voltage and θ i is the angle between element i and the source of acoustic pressure P i. The angular response described by equation (5.1) is ideal, the angular response of most transducer elements degrades more rapidly than cos θ. Therefore, correction performed off-axis will suffer from reduced transmit and receive amplitude due to the element angular response. These reduced amplitude lead in turn to reduced SNR, degrading correction performance. It should be noted, however, that grating lobes, a common concern when steering a beam off-axis, are greatly suppressed by the nonlinear generation of the second harmonic beam Comparison of Fundamental and Harmonic Correction With the current experimental setup, correction using the 2.08 MHz fundamental was actually more effective than when using the 4.16 MHz harmonic, despite the larger, less point-like region insonified by the fundamental beam. The improved performance of the 2.08 MHz fundamental beam was due to its increased SNR over the 4.16 MHz harmonic, which is characteristic of nonlinear acoustics. According to equation (3.3), increased SNR reduces the theoretical lower bound of error estimates, and these estimated lower bounds are matched well for both the 2.08 MHz fundamental and 4.16 MHz harmonic beams by the residual error present after correction. However, Table 5.7 and Figure 5.12 show that increases in SNR led to diminishing improvements in correction, both in terms of remaining residual error and peak beam amplitude. In particular, Figure 5.12 shows that in the presence of weak aberrators, where the SNR of both the fundamental and harmonic beams is relatively high, the 108

125 difference between correction using the 2.08 MHz fundamental and correction using the 4.16 MHz harmonic becomes quite small. The results of correction of a speckle region in the water tank Table 5.8 demonstrate that as the gap in SNR between the fundamental and harmonic signals is reduced relative to overall SNR, the gap fundamental and harmonic correction performance is reduced as well. Thus, for a clinical implementation of harmonic source wavefront correction that provides sufficiently high values of SNR, the increased SNR of the 2.08 MHz fundamental over the 4.16 MHz harmonic will have negligible impact on correction performance. When SNR of the 2.08 MHz fundamental and 4.16 MHz harmonic signals is equalized, correction using the 4.16 MHz harmonic is more effective than correction using the 2.08 MHz fundamental. The correction target used, a specular reflector, provided a good tool with which to evaluate quality of the fundamental and harmonic beams. As the focus of a beam narrows, the area of the specular reflector that is insonified shrinks, becoming more and more like a point target. As the area of the specular reflector that is insonified becomes more like a point target, the received signal increasingly assumes the shape of a spherical wave, improving performance of the delay estimation algorithm. Thus, the improved correction performance of the 4.16 MHz harmonic proves that the harmonic beam creates a more point-like source than the 2.08 MHz fundamental. 5.5 Summary and Conclusion Distortion of the 4.17 MHz imaging beam caused by spatially uncorrelated electronic aberrators was reduced using harmonic source wavefront correction. Correction was performed using the three main types of targets found in clinical scans: point targets, specular reflectors, and speckle regions. Harmonic source wavefront correction was effective at increasing peak amplitude of the 4.17 MHz imaging beam, leading to increased brightness and greater penetration depth in images. Correction of the 109

126 aberrated imaging beam resulted in improved (decreased) side-lobe levels when utilizing the point target or specular reflector as correction targets, but actually tended to degrade (increase) side-lobe levels when utilizing the speckle region as a correction target. Correction of the aberrated imaging beam, surprisingly, degraded (increased) -6 db beam width when the point target, specular reflector, and speckle region were utilized as correction targets, but did so only slightly. An additional correction iteration resulted in improvements to peak beam amplitude, side-lobe level, and -6 db beam width, indicating degraded side-lobe level or beam width caused by the initial correction iteration could be improved by performing subsequent corrections. Improvements to peak amplitude and side-lobe level of the imaging beam from correction resulted in improvements in image quality, such as increased penetration depth and higher contrast. While most correction in this chapter was performed using correction targets on the imaging beam axis, correction of the RTV aberrator using point targets spaced azimuthally from -18 to 18 demonstrated that harmonic source wavefront correction is also effective with off-axis correction targets. For all aberrators studied, wavefront correction of the 4.17 MHz imaging beam using a point target was most effective, followed by correction using a specular reflector, followed by correction using a speckle region. With the current ultrasound system, correction utilizing signal from the 2.08 MHz fundamental was more effective than correction utilizing signal from the 4.16 MHz harmonic. The increased SNR of the fundamental compared to the harmonic, a byproduct of nonlinear propagation, resulted in more accurate corrective delay estimation for the fundamental than for the harmonic. The increased SNR of the fundamental compared to the harmonic is only significant when the overall SNR of the ultrasound system is low at the fundamental and harmonic frequencies. For the experimental setup used, low SNR resulted from use of a transducer designed to operate at 3.57 MHz transmitting and receiving at 2.08 MHz and 4.16 MHz. The results 110

127 of correction using a speckle region in the water tank demonstrate that as the gap in SNR between the fundamental and harmonic shrinks relative to overall SNR, correction performance of the fundamental and harmonic begins to equalize. If overall system SNR can be improved, such as by utilizing a transducer designed specifically for harmonic imaging, the increased SNR of the fundamental will no longer result in a significant advantage in correction effectiveness compared to the harmonic. With reasonably high SNR for both the 2.08 MHz fundamental and 4.16 MHz harmonic, results show correction is improved by using signal from a more tightly-focused 4.16 MHz harmonic beam for delay estimation instead of signal from the 2.08 MHz fundamental. Overall, these water tank correction experiments demonstrate that harmonic source wavefront correction should be feasible when applied to biological tissue. 111

128 6 Kidney Correction 6.1 Introduction The water tank correction experiments in Chapter 5 demonstrated the effectiveness of harmonic source wavefront correction in an ideal environment. However, correction of a biological tissue target introduces attenuation, increased scattering, and other effects that combine to reduce correction effectiveness. To be clinically practicable, harmonic source wavefront correction must provide worthwhile improvement in imaging beam quality despite the additional challenges introduced by biological tissue. In this chapter, the performance of harmonic source wavefront correction is evaluated over a range of aberration strengths using ex vivo porcine kidney tissue as a correction target. Additionally, harmonic source wavefront correction using the more challenging correction target of the left kidney of human subjects is evaluated. Due to the increased attenuation of biological tissue, receive aperture elements must be grouped together to maintain adequate 4.16 MHz harmonic SNR for correction. Grouped receive elements necessitate the use of spatially correlated aberrators to allow determination of individual element delays from the estimated delays of the 112

129 larger element groups. Correction of spatially correlated aberrators over a range of strengths using porcine kidney as a correction target is evaluated using the three principal beam properties of the 4.17 MHz imaging beam studied in the previous chapters (peak beam amplitude, side-lobe level, and -6 db width). The clinical feasibility of harmonic source correction is investigated by performing full correction of a spatially correlated electronic aberrator and the measurement phase of correction on body wall aberration of a number of human subjects. 6.2 Materials and Methods Ultrasound Scanner See Section Ultrasound Transducer See Section Spatially Correlated Aberrators See Section Grouped Element Receive and Interpolation To compensate for reduced SNR during porcine tissue and human subject experiments, measurements were recorded from nine-element groups rather than from single elements. These nine-element groups had a high degree of overlap and led to a N/ (N) improvement in SNR, but suffered a 12 db SNR penalty due to the fact that multiple receive boards were active simultaneously instead of only one at a time. For the isoplanatic patch assumption discussed in Section to hold, the correlation length of the aberrator being measured must be substantially greater than the diameter of the nine-element groups [26, 27]. None of the nine-element groups had a diameter greater than 2.3 mm, while the spatially correlated electronic aberrators 113

130 had correlation lengths of between 4.4 mm and 4.8 mm. Therefore, the assumption that each nine-element patch was part of an isoplanatic patch was acceptable. Individual measurements from each element were not possible, so grouped-element patches were used. The group measurements were assigned physical locations according to the geometric center of the nine-element patches. The patch centers were not regularly spaced, necessitating the use of Shepard two-dimensional interpolation [44]. Interpolation from the patch measurements allowed calculation of arrival times for individual elements Harmonic Source Wavefront Correction See Section Beam Plots See Section Data Acquisition System See Section Scan Recalculation See Section Porcine Kidney Measurement Setup Frozen porcine kidneys were obtained from Cliff s Meat Market in Carrboro, NC. After thawing, three kidneys were vacuum sealed together using a Ziploc Vacuum Seal bag. The bag was then placed in a 165 mm wide x 255 mm long x 170 mm deep box with an open top. The box walls permitted volumetric containment of the kidney tissue in order to achieve scan depths greater than 30 mm (Figure 6.1). The 114

131 Transducer Porcine Kidney (vacuum sealed) Figure 6.1: Setup for aberration correction experiments using porcine kidney as a correction target. Porcine kidney was volumetrically constrained by the Lucite box, allowing scan depths over 30 mm. vacuum seal bags were acoustically transparent and prevented experimental setup contamination during scanning of the porcine tissue Human Subject Measurement Setup Electronic aberrator correction and body wall measurements were made on 11 healthy volunteers (10 male and 1 female, aged 26 to 29 years). Subjects lay prone on their stomachs while the transducer was adjusted to place their left kidney in the center of the field of view of a B-mode image. After securing the transducer with a ring stand and clamp, measurements were made on the spatially correlated electronic aberrator and body wall (Figure 6.2). The measurement process was as described 115

132 T5 Transducer Volunteer (#8) Figure 6.2: Setup for aberration correction experiments using the left kidney of human volunteers as a correction target. During correction volunteers lay prone on a cot while the transducer was clamped in place with a ring stand. in Section Subjects were instructed to hold their breath to minimize kidney motion during the acquisition of each set of 16 measurements, a process taking from 20 to 30 seconds per set. For each subject, 24 data sets were acquired with the spatially correlated electronic aberrator, and 10 data sets were acquired for the body wall. The measurement window was centered at 6 cm depth, which located it within the kidney for all subjects; due to individual variations in the thickness of body wall, however, the 6 cm depth was not always at the center of the kidney Body Wall Measurements Body wall measurements were made with the transducer focused at the center of the kidney with zero electronic aberration applied in transmit and receive. The recorded signal was then processed using the time delay estimation algorithm (equation (3.5)). 116