Measurement of Kidney Viscoelasticity with Shearwave Dispersion Ultrasound Vibrometry

MEASUREMENT OF KIDNEY VISCOELASTICITY WITH SHEARWAVE DISPERSION ULTRASOUND VIBROMETRY

A THESIS SUBMITTED TO THE FACULTY OF MAYO CLINIC Mayo Graduate School College of Medicine

BY Carolina Amador Carrascal

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY IN BIOMEDICAL SCIENCES AND BIOMEDICAL ENGINEERING

October 2011

ACKNOWLEDGEMENTS

I would like to thank Mayo Graduate School and the Department of Physiology and Biomedical Engineering for providing me the opportunity to pursue my PhD training at Mayo Clinic. I am grateful for the guidance of my thesis advisor Dr. James F. Greenleaf and all the members of my thesis committee: Dr. Lilach O. Lerman, Dr. Kai-Nan An, Dr. Erik L. Ritman and Dr. Michael Romero.

It has been a pleasure to work with the members of the Ultrasound Research Laboratory, I greatly appreciate the guidance, support and assistance of Matthew Urban, Shigao Chen and Randall Kinnick in the experimental aspects of my research. I would like to extent my gratitude to Lizette Warner and John Woollard who provided me with the animal experiment training.

I will be forever grateful to my parents and two brothers, for their unconditional support and encouragement, not only with my education but in all aspects of my life. Finally, I would like to thank every single person that I have had the opportunity to meet through these years and have provided me with great memories.

i ABSTRACT

Kidney mechanical properties such as elasticity are linked to kidney pathology state. Several groups have proposed shear wave propagation speed to quantify tissue mechanical properties. It is well known that biological tissues are viscoelastic materials; therefore velocity dispersion resulting from material viscoelasticity is expected. Shearwave Dispersion Ultrasound Vibrometry (SDUV) is a method that quantifies tissue viscoelasticity by measuring dispersion of shear wave propagation speed. However, there is not a gold standard method for validation. On the other hand, a concern with kidney elasticity imaging is the variability of kidney material properties associated with hemodynamic variables such as renal blood flow (RBF) regardless of kidney pathology. In this thesis the focus is centered in three areas: validate Shearwave dispersion ultrasound vibrometry (SDUV) with a gold standard method, study the feasibility of SDUV to estimate kidney mechanical properties in vitro, study the feasibility of SDUV to estimate kidney mechanical properties in vivo and use SDUV to study kidney mechanical properties during acute gradual decrease of renal blood flow. In this thesis, an independent validation method of elastic modulus estimation by SDUV in gelatin phantoms is presented as well as a method that has the potential to fully quantify viscoelastic parameters in a model independent manner by acoustic radiation force creep and shear wave dispersion ultrasound vibrometry. Moreover, feasibility of SDUV for in vitro measurements of viscoelasticity in healthy swine kidney as well as in vivo measurements of viscoelasticity in healthy swine kidney during acute changes is renal blood flow. Shearwave dispersion ultrasound vibrometry provides a fast, low cost noninvasive tool to measure not only tissue elasticity but tissue viscosity and has the potential to monitor progression of disease with less risk, potential sampling error and cost inherent to biopsies.

ii TABLE OF CONTENTS

LIST OF TABLES...... VII

LIST OF FIGURES...... VIII

LIST OF SYMBOLS AND UNITS...... XVIII

CHAPTER 1 1.1 General introduction...... 1 1.2 Clinical background and significance...... 2 1.3 Current methods to asses kidney function...... 3 1.3.1 Biomarkers...... 3 1.3.2 Renal biopsy ...... 4 1.3.3 Biomedical imaging methods...... 4 1.4 Elasticity imaging...... 5 1.5 Summary of chapters ...... 9

CHAPTER 2

ESTIMATING MECHANICAL PROPERTIES OF VISCOELASTIC MATERIALS: THEORY 2.1 Introduction...... 11 2.2 Behavior of solid materials ...... 11 2.3 Viscoelastic behavior...... 13 2.3.1 Linear viscoelastic models...... 15 2.4 Methods to study viscoelastic behavior ...... 16 2.4.1 Quasi-static indentation ...... 18 2.4.2 Quasi-static creep...... 19 2.4.3 Wave propagation methods...... 22 2.5 Time creep compliance conversion to complex modulus ...... 26

CHAPTER 3

SHEAR ELASTIC MODULUS ESTIMATION FROM SDUV AND INDENTATION ON GELATIN

PHANTOMS 3.1 Introduction...... 28

iii 3.2 Methods and Experiments ...... 30 3.2.1 Gelatin phantom characterization...... 30 3.2.2 Quasi-static indentation ...... 31 3.2.3 Shearwave dispersion ultrasound vibrometry ...... 32 3.3 Results...... 35 3.3.1 Quasi-static indentation ...... 35 3.3.2 SDUV with two transducers...... 36 3.3.3 SDUV with one transducer ...... 41 3.4 Discussion ...... 43 3.5 Conclusion...... 50

CHAPTER 4

SHEAR WAVE DISPERSION ULTRASOUND VIBROMETRY IN SWINE KIDNEY: IN VITRO

STUDY 4.1 Introduction...... 51 4.2 Methods and experiments...... 53 4.2.1 Shearwave dispersion ultrasound vibrometry ...... 53 4.2.2 Experiments ...... 55 4.2.3 Statistical analysis...... 59 4.3 Results...... 60 4.3.1 Linearity study...... 60 4.3.2 SDUV repeatability...... 61 4.3.3 Organ homogeneity ...... 63 4.3.4 Anisotropy study ...... 65 4.3.5 Time influence...... 67 4.4 Discussion ...... 69 4.5 Conclusion...... 73

CHAPTER 5

IN VIVO SWINE KIDNEY VISCOELASTICITY DURING ACUTE GRADUAL DECREASE IN

RENAL BLOOD FLOW: PILOT STUDY 5.1 Introduction...... 74 5.2 Materials and methods...... 76 5.2.1 Shearwave dispersion ultrasound vibrometry (SDUV)...... 76

iv 5.3 Results...... 79 5.4 Discussion ...... 86 5.5 Conclusion...... 89

CHAPTER 6

TISSUE MIMICKING PHANTOMS LOSS TANGENT AND COMPLEX MODULUS ESTIMATED BY

ACOUSTIC RADIATION FORCE CREEP 6.1 Introduction...... 91 6.2 Theory ...... 93 6.2.1 Complex modulus spectrum from creep compliance ...... 93 6.2.2 Displacement and creep compliance relation...... 94 6.2.3 Complex modulus calibration with shear wave dispersion...... 95 6.3 Methods...... 96 6.3.1 Acoustic radiation force creep ...... 96 6.3.2 Shear wave dispersion ultrasound vibrometry ...... 97 6.4 Simulation and experiment...... 97 6.4.1 Simulation ...... 97 6.4.2 Experiment...... 99 6.5 Results...... 100 6.5.1 Simulations ...... 100 6.5.2 Experiments ...... 108 6.6 Discussion ...... 114 6.7 Conclusion...... 116

CHAPTER 7

CONCLUSIONS AND FUTURE DIRECTIONS 7.1 Conclusions...... 118 7.2 SDUV validation ...... 118 7.3 Kidney viscoelasticity ...... 120 7.4 Future directions...... 120 7.4.1 SDUV measurements of the viscoelastic properties of healthy pig kidneys and fibrotic pig kidneys...... 122 7.5 Significant academic achievements...... 126 7.5.1 Peer-reviewed papers...... 126

v 7.5.2 Conference proceedings...... 127 7.5.3 Conference abstracts...... 127 7.5.4 Academic awards ...... 127

REFERENCES ...... 130

vi LIST OF TABLES

Table 2-1: Properties of viscoelastic models when step-stress is applied. 17

Table 2-2: Analytic solution of viscoelastic model’s differential equation when a ramp and hold stress is applied. 21

Table 3-1: Sample characterization for mechanical test. 31

Table 3-2: Shear elastic modulus, kPa (mean ± SD, n = 4), for different sample diameter (d), indenter diameter (2a) and sample thickness. 36

Table 3-3: Coefficients of determination, R2, of the linear regressions between phase estimates and distance, for the 7%, 10% and 15% gelatin phantoms 40

Table 3-4: Shear elastic modulus, kPa (mean ± SD, n = 4), at 10% strain, for different sample diameter (d), indenter diameter (2a) and sample thickness. 44

Table 3-5: Group velocity, phase velocity evaluated at center of gravity and phase velocity evaluated at center frequency. 45

Table 4-1: Description of the tests that were used to study swine kidney viscoelasticity with SDUV. 56

Table 4-2: Shear elastic modulus and viscosity (Mean ± SD of four ROIs) from four kidneys. 65

Table 5-1: Characteristics of the experimental animals. 80

Table 6-1: Viscoelastic parameters used to simulate 104

Table 6-2: Viscoelastic parameters used to simulate 104

vii LIST OF FIGURES

Figure 2.1: Elastic, plastic and viscoelastic strain response to constant stress. 12

Figure 2.2: Characteristics of viscoelastic materials, creep recovery and stress relaxation. 13

Figure 2.3: Regions of creep behavior. Strain, ε, vs. time, t, for different load levels. 14

Figure 2.4: Oscillating stress, σ, strain, ε, and phase lag δ. 15

Figure 2.5: Behavior of a linear spring and linear dashpot. 16

Figure 2.6: Soft tissue indentation based on a Hayes model. F is the indentation force, Δh is the indentation depth, a is the indenter radius, and h is the material thickness. 18

Figure 2.7: Non-dimensional geometric factor κ as a function of aspect ratio a/h for two different Poisson ratio ν. 19

Figure 2.8: The linear strain and compliance response at various step-stresses for (a-b) Maxwell, (c-d) Kelvin-Voigt and (e-f) standard linear solid. 20

Figure 2.9: Ramp and load stress. 21

Figure 2.10: Correction factor as a function of time ratio. (a) Maxwell model, (b) Kelvin-Voigt and standard linear solid. 22

Figure 2.11: SDUV implementations. (a) Mechanical actuator and single element transducer, (b) Mechanical actuator and array transducer, (c) Push transducer and single element transducer, (d) Array transducer to push and detect. 25

Figure 2.12: Push toneburst repeated at frequency PRFp produces shear wave at PRFp and its harmonics. 26

Figure 3.1: (a) Illustration of the experimental set up to do SDUV with two transducers. (b) Implementation of SDUV with a curved array transducer. SDUV applies a localized force

viii generated by a ‘Push Transducer’ (1) or by electronically focused push (Push beam) coupled to the phantom, transmitting repeated tonebursts of ultrasound. (a) A separate transducer acts as the detector, ‘Detect Transducer’ (2), and is moved to detect shear wave motion at several spatial locations or (b) same transducer is used to detect phantom response (Detection beams). 33

Figure 3.2: Force-displacement data for one sample of each gelatin phantom (Sample type 1, refer to Table 3-1). The four symbols (o, x, Δ,+) represent the linear region for the four gelatin phantoms (7%,8%,10%,15%). The four line types (-, --, ···, -·-) represent the raw data for the four (7%,8%,10%,15%) gelatin phantoms. 35

Figure 3.3: Displacement amplitude estimates over 50 ms for 7% gelatin phantom. The curves (-, --, -·-) represent three sets of the measured amplitude for 4, 6 and 8 mm away from the vibration center. 36

Figure 3.4: Displacement amplitude estimates over 20 ms for the 15% phantom with PRF of 1.6 kHz and 3.2 kHz. The three curves (-, --, -·-) represent three sets of the measured amplitude for 4, 6 and 8 mm away from the vibration center. 37

Figure 3.5: Magnitude spectra of the velocity signals over 200 ms. The three symbols (o, *, Δ) represent 7, 10 and 15% gelatin phantoms. 38

Figure 3.6: Time shift estimates over 3 to 8 mm away from the vibration center. The three symbols (o, *, Δ) represent 7, 10 and 15% gelatin phantoms. 39

Figure 3.7: Phase estimates over 3 to 8 mm away from the vibration center for 7% gelatin phantom. The four symbols (o, *, , Δ) represent four sets of estimated phase changes over the distance for four vibrations with frequencies from 100 Hz to 400 Hz. The solid line represents linear regression. 40

Figure 3.8: Mean shear wave speed, cs, of four repeated measurements from 50 Hz to 400 Hz. The three symbols (o, *, Δ) represent 7, 10 and 15% gelatin phantoms. Error bars represent standard deviation of four repeated measurements. The solid lines are fits from the Kelvin-Voigt dispersion model, which gives estimates of shear elastic modulus (G) and viscosity (η) shown at the bottom of this figure. 41

ix Figure 3.9: Shear wave profiles (-,-·-·, -·-,···, --) from different time points (1.5 ms, 3.0 ms, 4.5 ms, 6.0 ms and 7.5 ms) after the transmission of the push pulse. 41

Figure 3.10: (a) Magnitude spectra of the velocity signal over 20 ms. (b) Time shift estimates over 2 to 10 mm away from the vibration center. 42

Figure 3.11: (a) Phase estimates for the 8% gelatin phantom over 2 to 8 mm away from vibration center at 100 Hz (o), 200 Hz (*), 300 Hz ( ) and 400 Hz (Δ). (b) Mean shear wave speed, cs, of four repeated measurements from 50 Hz to 400 Hz. Error bars represent standard deviation of four repeated measurements. The solid line is the fit from Kelvin-Voigt dispersion model, which gives estimates of shear elastic modulus (G) and viscosity (η) shown at the bottom of this figure. 43

Figure 3.12: Two dimensional Fourier transform of displacement response for (a) 7%, (b) 10%, (c) 15% and (d) 8% gelatin phantoms. Vertical axis represents the one dimensional spatial Fourier space, where kx is the spatial Fourier transform variable. Horizontal axis represents the one dimensional temporal Fourier space. 47

Figure 3.13: Shear elastic modulus comparison between phase velocity, indentation test and group velocity. Mean ± SD, n=4. 48

Figure 3.14: Linear correlation comparing shear elastic modulus, G, estimated from quasi-static indentation test with group velocity (◊, --) and SDUV phase velocity ( ,···). The continuous line represents an ideal correlation (o). 49

Figure 4.1: (a) Illustration of the experimental set up to make SDUV measurements with two transducers in swine kidney. (b) Implementation of SDUV with a curved array transducer. SDUV applies a localized force generated by a ‘Push Transducer’ or by a electronically focused push (‘Push Beam’) coupled to the tissue, transmitting repeated ultrasound tone bursts of ultrasound. To detect shear wave propagation, (a) a separate transducer acts as the detector (‘Detection Transducer’) and is moved to detect the shear wave motion at several spatial locations or (b) the same transducer is used to detect tissue response (‘Detection Beams’). 54

Figure 4.2: (a) B-mode image along zx-plane. The beam was focused at 3 locations (white arrows). Tissue motion was tracked at 5 regions along x-axis (white squares) of 5 x 5 mm2.

x (b) Curved array B-mode image along zx-plane. Shear waves propagating perpendicular to blood vessels (tangential direction or x-direction in this figure) were generated by a push beam focused at x = 0 (ROI 1 and 2). Shear waves propagating parallel to blood vessels (radial direction or z- direction in this figure) were generated by a push beam focused at the edge of the kidney (ROI 3). 57

Figure 4.3: (a) Illustration of SDUV measurements every 45º respect to z-axis. (b) Illustration of shear wave propagation in two different directions. The blood vessels are running vertically (z-axis) in the kidney section shown. In the tangential direction (y-axis), the shear wave propagates in a direction perpendicular to blood vessels, and in the radial direction (z- axis) the shear wave propagates in a direction parallel to blood vessel orientation. 58

Figure 4.4: (a) Displacement amplitude estimates over 20 ms. Symbols (-,+,·,*) represent four different excitation voltage amplitudes (3.0 V, 2.6 V, 2.1 V and 1.5 V) in one excised kidney (Kidney #1, refer to Table 4-1). (b) Tissue peak displacement versus voltage squared. The solid line is a linear fit to the experimental data (*). 60

Figure 4.5: Shear wave propagation speed (Mean ± SD) of a 5 x 5 mm2 region as a function of frequency. The bars (left to right) represent four different excitation voltage amplitudes (3.0 V, 2.6 V, 2.1 V and 1.5 V) on one excised kidney (Kidney #1, refer to Table 4-1). 61

Figure 4.6: SDUV repeatability when using (a) two transducers or (b) curved linear array transducer. The symbols (x) represent shear wave propagation speed (Mean ± SD) as a function of frequency measured along x-axis in a 5 x 5 mm2 patch (ROI1) five repeated times (Kidney #1, refer to Table 4-1) and four repeated times (Kidney #8, refer to Table 4-1). The solid line is the fit from Kelvin-Voigt model (Equation 3.3). 62

Figure 4.7: Box and whisker diagram for (a) shear elastic modulus and (b) viscosity of a 5 x 5 mm2 patch in eight kidneys. The box and whisker diagrams were made with five repeated measurements (Kidney #1-7, refer to Table 4-1) and four repeated measurements (Kidney #8, refer to Table 4-1) of one ROI. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group. 62

xi Figure 4.8: (a) Shear wave propagation speed (Mean ± SD) as a function of frequency, (b) shear elastic modulus and (c) viscosity box and whisker diagram of five ROI’s in one kidney (Kidney #2, refer to Table 4-1). The solid line is the fit from Kelvin-Voigt model (Equation 3.3). The box and whisker diagrams were made with five measurements on each individual region. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group. 64

Figure 4.9: Box and whisker diagram for (a) shear elastic modulus and (b) viscosity in ROI2 every 1 x 5 mm2 along z- axis in one kidney (Kidney #2, refer to Table 4-1). The box and whisker diagrams were made with five repeated measurements on each individual region. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group. 65

Figure 4.10: Box and whisker diagram for (a) shear elastic modulus and (b) viscosity in one kidney (Kidney #8, refer to Table 4-1) from 8 different angles of scanning respect to z- axis. The box and whisker diagrams were made with four repeated measurements at each individual angle. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group. 66

Figure 4.11: (a) Shear wave propagation speed (mean ± SD, 4 repeated measurements) as a function of frequency measured in a 5 x 5 mm2 patch for both (*) tangential and (Δ) radial excitation (Refer to Figure 4.3b) of one kidney (Kidney #8, refer to Table 4-1). (b) Shear elastic modulus and (c) viscosity measurements made in one kidney (Kidney #8, refer to Table 4-1) with shear waves propagating along the (*) tangential direction and (Δ) radial direction (refer to Figure 4.3b). 67

Figure 4.12: (a) Renal cortex shear elastic modulus and (b) viscosity as a function of time after sacrifice from two kidneys (Kidney #5-6, refer to Table 4-1). The different symbols represent mean ± standard deviation of four 5 x 5 mm2 regions in ( ) kidney #5 and (Δ) kidney #6. 68

Figure 4.13: (a) Shear wave propagation speed (mean ± SD) as a function of frequency measured in 17 different ROI’s (*) before

xii and (Δ) after formalin immersion of one kidney (Kidney #7, refer to Table 4-1). (b) Shear elastic modulus and (c) viscosity values made in one kidney (Kidney #7, refer to Table 4-1) before and after formalin immersion. Both shear elastic modulus and viscosity were significantly different when comparing normal versus formalin (p < 0.001). 69

Figure 5.1: Illustration of the experimental set up for in vivo SDUV measurements in kidney. (a) An electromechanical actuator was placed in contact with the surface of the kidney and a linear array transducer was used to detect shear wave propagation. (b) A linear curved array transducer is used to generate shear wave with localized acoustic radiation force with push beams and detect shear wave propagation with detect beams. 78

Figure 5.2: B-scan coronal plane image (cross-section) of the kidney with Verasonics V1 system equipped with linear curved array transducer at baseline of renal blood flow. 80

Figure 5.3: (a) Amplitude of displacement response at 100 Hz excitation with mechanical actuator at three locations 1.8 mm apart during baseline of renal blood flow. (b) Magnitude spectrum of displacement estimates from (a). (c) Phase estimates over 2 to 7 mm away from vibration center at 100 Hz (o), 200 Hz (*), 300 Hz (□) and 400 Hz (Δ). (d) Shear wave phase velocity as a function of frequency averaged from three repeated measurements at baseline of renal blood flow. 81

Figure 5.4: Shear wave dispersion from three repeated measurements for (a) animal 1, (b) animal 2 and (c) animal 3. The color bars represent the baseline renal blood flow, 25, 50, 75 and 100% of baseline renal blood flow. 82

Figure 5.5: (a) Velocity estimates as a function of distances generated by acoustic radiation force toneburst at t = 0.5 ms, 1.5 ms and 2.5 ms. (b) Velocity estimates as a function of time generated by acoustic radiation force toneburst at x = 7.4 mm, 8.5 mm and 9.5 mm. (c) Wave number – frequency diagram from two-dimensional Fourier transform applied to velocity estimates. (d) Shear wave phase velocity as a function of frequency from wave number – frequency diagram at baseline of renal blood flow. 83

Figure 5.6: Shear wave dispersion from three repeated measurements for (a) animal 4 and (b) animal 5. The color

xiii bars represent the baseline renal blood flow, 25, 50, 75 and 100% of baseline renal blood flow. 84

Figure 5.7: Shear wave phase velocity (mean ± SEM of 5 animals) as a function of acute gradual decrease of renal blood flow at 100 Hz and 400 Hz excitation. 84

Figure 5.8: (a) Shear elastic modulus and (b) viscosity as a function of acute and gradual decrease in renal blood flow. The error bars represent the standard error of the mean (SEM) of the group of animals. 85

Figure 5.9: B-scan coronal plane image (cross-section) of one kidney with Verasonics V1 system equipped with linear curved array transducer. (a) At baseline renal blood flow. (b) At 100% decrease in baseline renal blood flow. 85

Figure 5.10: (a) Renal cortex thickness as a function of distance along x-direction for each renal blood flow period. (b) Average renal cortex thickness over 40 mm as a function of change in renal blood flow from base line. The error bars represent the standard deviation. 86

Figure 6.1: Illustration of the pulse sequences used to induce and monitor creep and recovery. The small (blue and green) arrows represent tracking beams and large (red) arrows represent pushing beams. 97

Figure 6.2: Illustration of (a) Kelvin-Voigt and (b) Standard linear solid models. Springs represent the elastic elements with assigned elastic properties E, E1 and E2. Dashpots represent viscous elements with assigned viscous properties η. 98

Figure 6.3: Creep compliance response for E, E1 and E2 of 9 kPa, η of 10 Pa.s (blue and continuous curve) and 100 Pa.s (green and continuous curve with *) for Kelvin-Voigt model (a-b) and standard linear solid model (c-d). The time vector in (a) and (c) starts at t1 of 0.001 s and Fs of 1 kHz. The time vector in (b) and (d) starts at t1 of 0.0001 s and the sampling rate was 10 kHz. 101

Figure 6.4: Moduli as a function of frequency from Kelvin-Voigt model creep compliance. (a) η = 10 Pa.s, t1 = 0.001 s or Fs = 1 kHz, (b) η = 10 Pa.s, t1 = 0.0001 s or Fs = 10 kHz, (c) η = 100 Pa.s, t1 = 0.001 s or Fs = 1 kHz, (d) η = 100 Pa.s, t1 = 0.0001 s or Fs = 100 kHz. The red curve is the loss modulus, El, and the

xiv blue curve is the storage modulus, Es. The estimated moduli is a continuous line and the theoretical modulus is a continuous line with *. 102

Figure 6.5: Moduli as a function of frequency from standard linear solid model creep compliance. (a) η = 10 Pa.s, t1 = 0.001 s or Fs = 1 kHz, (b) η = 10 Pa.s, t1 = 0.0001 s or Fs = 10 kHz, (c) η = 100 Pa.s, t1 = 0.001 s or Fs = 1 kHz, (d) η = 100 Pa.s, t1 = 0.0001 s or Fs = 100 kHz. The red curve is the loss modulus, El, and the blue curve is the storage modulus, Es. The estimated moduli is a continuous line and the theoretical modulus is a continuous line with *. 103

Figure 6.6: Kelvin-Voigt model (a) creep strain response and (b) creep compliance response to 1 kPa (*) and 3 kPa (o) step- stress input. Estimated complex modulus (c) C*(ω), from creep strain, and (d) E*(ω), from creep compliance response to 1k Pa and 3 kPa step-stress input. Tan(δ) from estimated complex modulus using (e) creep strain and (f) creep compliance response to 1k Pa and 3 kPa step-stress input. 105

Figure 6.7: Kelvin-Voigt model tan(δ) for(a) fixed η = 100 Pa.s and elastic modulus of 6 kPa (-), 9 kPa (*) and 12 kPa (o), (b) fixed E = 9 kPa and viscosity of 20 Pa.s (-), 40 Pa.s (*) and 60 Pa.s (o). 106

Figure 6.8: Standard linear solid model (a) creep strain response and (b) creep compliance response to 1 kPa (*) and 3 kPa (o) step-stress input. Estimated complex modulus (c) C*(ω), from creep strain, and (d) E*(ω), from creep compliance response to 1k Pa and 3 kPa step-stress input. Tan(δ) from estimated complex modulus using (e) creep strain and (f) creep compliance response to 1k Pa and 3 kPa step-stress input. 107

Figure 6.9: Standard linear solid model tan(δ) for(a) fixed η = 100 Pa.s and elastic modulus of 6 kPa (-), 9 kPa (*) and 12 kPa (o), (b) fixed E = 9 kPa and viscosity of 20 Pa.s (-), 40 Pa.s (*) and 60 Pa.s (o). 108

Figure 6.10: CIRS 1 phantom (a) mean creep displacement, (b) estimated storage moduli, (c) loss moduli and (d) loss tangent of a 1.6 μs (o) and 3.2 μs (*) push duration. Average of 5 repeated measurements over a window of 3 mm in axial direction and 1 mm in lateral direction. The dashed lines represent the standard deviation of 5 repeated measurements. 109

xv Figure 6.11: CIRS 3 phantom (a) mean creep displacement, (b) estimated storage moduli, (c) loss moduli and (d) loss tangent of a 1.6 μs (o) and 3.2 μs (*) push duration. Average of 5 repeated measurements over a window of 3 mm in axial direction and 1 mm in lateral direction. The dashed lines represent the standard deviation of 5 repeated measurements. 110

Figure 6.12: Loss tangent (average of 5 measured locations) as a function of frequency for CIRS 1 (*) and CIRS 3 (o) phantom. The dashed lines represent the standard deviation of 5 measured locations in each phantom. 111

Figure 6.13: CIRS 1 phantom (a) shear wave dispersion estimated by SDUV, (b) shear wave attenuation estimated by SDUV and acoustic radiation force creep using Equations 6.7- 6.11 and 6.16, (c) model free complex moduli estimated by shear wave phase velocity and shear wave attenuation, (d) complex moduli estimated by Kelvin-Voigt model fit to SDUV shear wave dispersion. 112

Figure 6.14: CIRS 3 phantom (a) shear wave dispersion estimated by SDUV, (b) shear wave attenuation estimated by SDUV and acoustic radiation force creep using Equations 6.7- 6.11 and 6.16, (c) model free complex moduli estimated by shear wave phase velocity and shear wave attenuation, (d) complex moduli estimated by Kelvin-Voigt model fit to SDUV shear wave dispersion. 113

Figure 6.15: Vector diagrams of the relationship between loss angle, δ, complex modulus, G*, storage modulus, Gs, and loss modulus, Gl. The complex modulus, G*, is independent of tan(δ) when Gs and Gl change independently; (a) changing Gs and Gl in opposite direction cause tan(δ) to change and G* remains the same; (b) changing Gs and Gl in the same direction and magnitude causes G* to change but tan(δ) remains the same. 115

Figure 7.1: (a) In vivo pig kidney transcoutaneos set up for SDUV measurements. (b) B-scan image with sample grid of points (yellow circles) for SDUV measurements. 121

Figure 7.2: In vivo transcutaneous swine kidney (a) displacement as a function of time and space, (b) displacement as a function of time for 3 lateral position, (c) time to peak of displacement response. 122

xvi Figure 7.3: Excised swine kidney (a) mean creep displacement, (b) estimated loss tangent of 5 repeated measurements in 4 locations, the dashed lines represent the standard deviation of 5 repeated measurements. (c) Mean creep displacement and (d) loss tangent of 5 locations, dashed lines represent the standard deviation of 4 locations. 124

Figure 7.4: Excised swine kidney (a) shear wave dispersion estimated by SDUV, (b) shear wave attenuation estimated by SDUV and acoustic radiation force creep, (c) complex moduli estimated by shear wave phase velocity and shear wave attenuation, (d) complex moduli estimated by Kelvin-Voigt model fit to SDUV shear wave dispersion. 125

xvii LIST OF SYMBOLS AND UNITS

σ Direct stress, [Pa]

ε Direct strain, [dimensionless]

t Time, [s]

E Young’s modulus o Relaxation modulus, [Pa]

η Viscosity, [Pa.s]

J Creep compliance, [1/Pa]

ω Angular frequency, [Rad/s] i Imaginary number

δ(t) Delta function

Es Storage modulus, [Pa]

El Loss modulus, [Pa]

Js Storage compliance, [Pa]

Jl Loss compliance, [Pa]

F Force, [N], Acoustic radiation force, [N/m3]

Δh Indentation depth, [m]

a Indenter radii, [m]

h Material thickness, [m]

G Shear elastic modulus, [Pa]

xviii ν Poisson ratio, [dimensionless]

κ Geometric factor in Hayes’ model, [dimensionless]

t1 Rise time, [s]

CF Correction factor, [dimensionless]

τ Time constant, [s]

u Displacement, [m]

k Wave number, [1/m]

kr Real wave number, [1/m]

ki Imaginary wave number, [1/m]

cs Shear wave phase velocity, [m/s]

αs Shear wave attenuation coefficient, [1/m]

Gs Shear storage modulus, [Pa]

Gl Shear loss modulus, [Pa]

ρ Density, [Kg/m3] r Radial distance, [mm]

φ Phase, [rad] f Frequency, [Hz]

E* Complex modulus, [Pa]

G* Shear complex modulus, [Pa]

J* Complex compliance, [1/Pa]

xix k* Complex wave number, [1/m] x Lateral distance, [mm]

U Discrete Fourier transform of u v Spacial discrete Fourier transform variable

π Mathematical constant n index x(n) Function

X(v) Spacial discrete Fourier transform of x(n)

N Length of data set

δ Loss angle, [degrees]

cg Shear wave group velocity, [m/s]

Δt Time difference, [s]

d Sample diameter, [mm]

PRF Pulse repetition frequency, [Hz]

fp Center frequency, [Hz]

ω p Angular center frequency, [rad/s]

fc Center of gravity, [Hz]

ω c Angular center of gravity, [rad/s]

R2 Coefficient of determination, [dimensionless]

xx kx Spatial Fourier transform variable, [1/m]

λ Wavelength, [m]

Δφ Phase difference, [rad/s] or [degress]

Δr Radial distance difference, [mm]

ω Angular shear wave frequency, [rad/s] s

α Absorption coefficient of medium, [Np/m]

I Temporal average intensity, [W/m2]

c Speed of sound, [m/s]

P Pressure, [N/m2]

V Voltage, [Volts]

p Statistical significance, [dimensionless]

z Axial distance, [mm]

β Proportionality constant

L Length, [m]

C* Extracted complex modulus, C* = βG*, [Pa]

Cs Extracted storage modulus, Cs = βGs, [Pa]

Cl Extracted loss modulus, Cl = βGl, [Pa]

xxi Chapter 1

Introduction

1.1 General introduction Elasticity imaging is an emerging imaging modality that has the potential to assess renal fibrosis in patients with chronic kidney disease (CKD) by using the elasticity of kidney as the contrast mechanism in images. Fundamental material properties of soft tissues, such as elasticity, are closely related to the state of health of the tissue and can be used as an indicator for medical diagnosis.

The kidney, like many other soft tissues, can be modeled as a viscoelastic material, that is, the kidney has both elastic and viscous characteristics. Shear wave based methods have been developed to quantitatively evaluate the viscoelastic material properties of tissue using noninvasive imaging modalities. A method called Shearwave Dispersion Ultrasound Vibrometry (SDUV) that utilizes measurements of the shear wave speed as it varies with frequency, or dispersion, can characterize of the shear elasticity and viscosity of soft tissues.

A concern with kidney elasticity imaging is the variability of kidney material properties associated with hemodynamic variables such as renal blood flow (RBF) regardless of kidney pathology. Moreover, elasticity imaging methods have not been strictly validated to gold standard methods.

In this thesis the focus is centered in three areas:

1 - Validate Shearwave dispersion ultrasound vibrometry (SDUV) against a gold standard method

- Study the feasibility of SDUV to estimate kidney mechanical properties in vitro

- Study the feasibility of SDUV to estimate kidney mechanical properties in vivo and use SDUV to study kidney mechanical properties during acute gradual decrease of renal blood flow.

1.2 Clinical background and significance Chronic kidney disease (CKD) encompasses a long-term decrease in function of the kidneys. The prevalence of CKD has shown to increase in the years 1999-2004 compared to that during the period of 1988-1994 from 10.0% to 11.5% in adults aged 20 and over [1], more than 20 million people. Another stark reality concerning CKD is that patients with this affliction carry 2-5 times the disease burden of non-CKD patients; CKD precipitates and promotes cardiovascular disease (CVD) [2] and hypertension [3]. If diagnosed, treatment of the earlier stages of CKD can be effective in slowing the progression of the disease as it progresses to kidney failure or development of CVD [4].

CKD can progress to kidney failure or end-stage renal disease (ESRD), and at the end of 2007, 527,283 patients were receiving ESRD therapy, which includes hemodialysis or kidney transplant [5]. The incidence of patients beginning ESRD therapy in 2007 was estimated to be 111,000 [5]. In 2007, the care of patients who have CKD or ESRD totaled 32% of the Medicare budget, and projections show that the ESRD population could double over the next decade [5]. Among the patients with ESRD, there were 87,812 deaths reported in 2007. It is suggested that early detection and prevention strategies should be addressed to reduce the long-term burden of ESRD.

One treatment for ESRD is kidney transplant. The number of transplants performed in the United States 2009 was 16,829, but as of August 26, 2010 91,434 patients were on a waiting list [6]. Patient and graft survival rates have increased over the past two decades [6], but long-term survival of grafts is still

2 an issue. The patient survival probabilities for patients receiving deceased- or living-donor transplants are higher than the graft survival rates, indicating that the patient will often outlive the graft and have to be retransplanted or undergo dialysis treatment.

1.3 Current methods to asses kidney function It is critical to assess kidney function in management of CKD and ESRD patients in order to save and prolong life, improve quality of life, and reduce care costs. Indicators of the health of the kidney are critically important towards evaluating diagnosis and prognosis for these patients. Various indicators such as serum biomarkers, renal biopsies, and noninvasive imaging methods are utilized to provide clinicians with feedback on the health of a patient’s kidneys. The ideal indicator would be noninvasive and able to be used frequently enough for clinical feedback to be obtained on disease progression and treatment regimens.

1.3.1 Biomarkers Creatinine is an amino acid compound that is released into the plasma at a relatively constant rate. In general, serum creatinine (SCr) levels are inversely proportional to glomerular filtration rate. High levels of SCr are used as a first- order indicator of an impairment of kidney function [7]. However, SCr levels are modified by different factors such as age, sex, ethnicity, dietary intake, and muscle mass [7, 8]. The SCr levels alone as indicators have been found to be inadequate in certain populations, particularly in the elderly [9].

Glomerular filtration rate (GFR) is considered the best overall index of kidney health and disease [1, 5]. The gold standard for measurement of GFR is inulin clearance, but using inulin is expensive and difficult in clinical practice so other agents have been used for clearance studies such as 125I-iothalamate, 99mTc- diethylenetriaminepentaacetic acid (DPTA), and 169Yb-DPTA [10, 11]. However, direct measurement of GFR is not easily performed in clinical practice so equations have been developed that include the SCr or serum cystatin levels, age, race, sex, and body size to estimate GFR [1, 10, 12-15]. Estimated glomerular filtration rate (eGFR) and albumin/creatinine ratio (ACR) are used as a basis for staging CKD patients [4, 5].

3 1.3.2 Renal biopsy Renal biopsy is a valuable procedure for the diagnosis of renal disease, and the results from biopsies can help guide treatment and establish a prognosis, especially in assessing allograft rejection by evaluating the degree of fibrosis or inflammation [16-22]. Biopsies are performed on native kidneys in patients with CKD to assess kidney health within the chronic disease process. The tissue from renal biopsy is examined using histological methods to determine the structural morphology and integrity of the renal tissue at the cellular level. Factors that are taken into account are the presence and severities of interstitial fibrosis, inflammation, tubular atrophy, among others. Fibrosis leads to renal scarring and loss of functional tissue, which occurs in late stages of disease [23-25].

Renal biopsies are largely considered to be safe, but are associated with complications such as small and large hematomas, gross hematuria, arteriovenous fistula, and even death [26-36]. The complication rate has been reported to be in range of 0-6% [36]. It was recently reported that the number of renal biopsies have been increasing in the period from 1997-2008 [37], thereby increasing the potential number of patients with complications. Biopsies, by their inherent nature, are also prone to sampling errors because of the small amount of tissue that is extracted. For example, an 18 gauge needle with a 2 cm core, will only yield 0.011 cm3 of tissue, where normal kidney volume is approximately 160 cm3 [38], so the biopsy core only represents 1/14,500 of the total kidney.

1.3.3 Biomedical imaging methods Noninvasive imaging methods, such as magnetic resonance imaging (MRI), x- ray computed tomography (CT) and ultrasound (US) have been used to assess kidney structure and function. These modalities have different capabilities to assess both the structural morphology as well as the function of the kidney. CT can be used to find fluid collections or renal artery diseases [26, 39]. The cortical echogenicity on US images has been shown to correlate with the severity of kidney sclerosis [40]. US has been used in evaluating blood flow with and without microbubbles used as contrast agents in native and

4 transplanted kidneys [27, 28, 31-33, 41-45]. Doppler US measurements of blood flow have been used to determine the vascular resistance of the kidney as a surrogate for kidney health called resistive index. A high value of resistive index (RI) has been shown to correlate with renal failure or diminished allograft survival [46, 47]. However, the RI is a controversial metric that has not been widely adopted because of low sensitivity in assessing kidney state [48]. US is also the main modality used for image guidance of renal biopsy [35, 36, 45].

MRI techniques can be used to evaluate the anatomy of the kidney and can differentiate the cortex and medulla in normal kidneys [49], while the diminution of this ability has been indicated to correlate with interstitial fibrosis in the kidney [49]. Contrast agents such as gadolinium (Gd) chelates or ultrasmall superparamagnetic particles of iron oxide (USPIO) are often used in MRI to enhance certain anatomical features as well as evaluate function in kidney imaging [50-53]. Various MRI methods have been used to evaluate the function of the kidney. Perfusion and GFR have been measured using contrast agents and imaging their passage in and through the kidney [54-56]. For the transplanted kidney, studies using blood oxygen level dependent (BOLD) MRI, diffusion weighted (DW) MRI, and perfusion with Gd-based contrast agents have been reported [57-61]. An important limitation to using Gd-based contrast agents is the discovery of the causative effect these contrast agents have in occasionally initiating nephrogenic systemic fibrosis, a condition that can be extremely debilitating and has been shown to mainly affect patients with reduced renal function (GFR < 15 mL/min/1.73 m2 or stage 5 CKD) [62-65]. Furthermore, while MRI techniques can obtain three-dimensional (3D) structural and functional data of the kidney, scans are expensive and time- consuming.

1.4 Elasticity imaging Elasticity imaging is an emerging imaging approach that uses the elasticity of tissue as the contrast mechanism in images. Elasticity or stiffness is a physical property of a material that returns to its original shape after the stress (e.g. external force) that made it deform is removed. The mathematical description of such property is known as elastic modulus or modulus of elasticity. The most

5 common types of elastic modulus are: Young’s modulus (E) and shear modulus (G). It has been shown that the shear modulus (stress applied tangent to the surface) of tissues in the body can vary over 6 orders of magnitude, making the dynamic range of this contrast mechanism quite large [66].

The contrast arises among different types of tissue (e.g. liver versus muscle) and within the same tissue that has different compartments (e.g. kidney cortex versus kidney medulla) or when disease is present (normal and cirrhotic liver). Elasticity imaging combines developed imaging modalities such as MRI and US to measure deformation induced by an external or internal source. The kidney has been studied using several elasticity imaging techniques. Elastography, a method that utilizes compression and ultrasound-based strain imaging to obtain maps of relative stiffness [67] has been used in several ex vivo studies in kidneys [68-70] and some in vivo human studies of kidney transplant patients [71, 72]. Areas of lower strain correlated with fibrotic or scarred tissue, implying that this tissue is stiffer than normal tissue. An MRI-based method that utilized compression was also reported for studies of ex vivo kidneys [73]. A method that uses focused ultrasound to produce an acoustic radiation force to “push” tissue and measures the resulting deformation called acoustic radiation force impulse (ARFI) imaging has been used to image renal tumors [74, 75]. The elastic contrast between the tumor and the normal tissue was almost 11.5 times greater than the contrast observed using conventional ultrasound images. While elastography and ARFI are useful approaches, they do not provide a quantitative measure of tissue stiffness, but only a relative mapping.

Transient Elastography (TE) is a method that uses an external actuator to provide a single cycle of low-frequency (typically around 50 Hz) vibration and ultrasound methods to track the resulting motion [76, 77]. The technique has been developed commercially for measurement of stiffness in the liver in a product called FibroScanTM manufactured by Echosens [78]. Recent results showed that stiffness in renal allografts correlated significantly directly with the degree of fibrosis (Pearson r = 0.67, p = 0.002) and inversely with eGFR (Pearson r = -0.47, p = 0.003) but not with resistive index (Pearson r = 0.17, p = 0.23) [79].

6 A dynamic method called magnetic resonance elastography (MRE) uses an external mechanical actuator to create shear waves in soft tissues, and the 3D shear wave motion is measured using special motion-sensitized pulse sequences [80, 81]. In an elastic medium, the shear wave speed in tissue is proportional to tissue stiffness. This method has been applied to quantitatively evaluate the stiffness of renal cortex and medulla in ex vivo porcine kidneys and in vivo rat and swine models [81-85]. In the study in rats, comparisons were made between normal animals and animals that developed nephrocalcinosis due to exposure to ethylene glycol. The stiffness in the renal cortex was 3.87 ± 0.83 kPa in the control group and increased to 5.02 ± 1.06 kPa and 6.49 ± 1.33 kPa after 2 and 4 week exposures [82]. The serum creatinine levels in the animals exposed to ethylene glycol increased significantly, and calcium crystal deposits were detected by histology. In studies in swine, the renal artery was occluded in progressive steps, and the cortical and medullary stiffness decreased as a result of decreased perfusion [83- 85]{Warner, 2011 #502}. While MRE can obtain 3D elasticity data, it is not widely available and scans take considerable time. MRE has also been employed to assess myocardial stiffness [86] and shown to discriminate between moderate and severe fibrosis in chronic liver disease [87, 88]. Interestingly, patients with chronic liver disease, commonly associated with portal hypertension, also have elevated splenic stiffness compared to normal volunteers [90]. These studies demonstrate that stiffness of the kidney changes with disease state and changes enough to be detected. Moreover, the in vivo MRE studies in kidney [83-85]{Warner, 2011 #502} and liver [88] suggest that there is a potential hemodynamic contribution to tissue stiffness.

The kidney, like many other soft tissues can be modeled as a viscoelastic material, that is, the kidney has both elastic and viscous characteristics [89-93]. Viscoelastic materials exhibit time-dependent deformation when a stress is applied whereas elastic materials exhibit immediate deformation. Kidney mechanical properties have been studied with a variety of mechanical tests such as compression, tensile and shear tests [89, 92, 94]. Shear waves can also be used to investigate the viscoelastic properties of tissue, the shear modulus and viscosity. Shear waves of a certain frequency can be induced and

7 the speed can be measured, where the speed is related to the material properties. When shear wave speeds are measured at several frequencies in a viscoelastic medium, the shear wave speed will vary with frequency, a property called dispersion. Dispersion can be used to quantitatively characterize the viscoelasticity of the medium [95].

Viscosity is an understudied element in the viscoelastic properties of tissue. Measurements in the liver show that the shear modulus and viscosity increase as the degree of fibrosis increases [96-98]. In a report by Schmeling, et al., the authors found that the viscosity in the left ventricular wall of the heart during the diastolic phase of the cardiac cycle increased during occlusion of the left anterior descending coronary artery in animals that were reperfused and not reperfused [99]. During reperfusion, the viscosity returned to baseline in animals that recovered from the stunning while the increase in viscosity persisted throughout reperfusion in animals that did not recover. Viscosity was shown to increase in both ischemic and nonischemic regions of the ventricular wall. This is contrary to the passive elastance which only increased in the ischemic region. The authors postulated that the regional structural damage may cause more global changes in passive mechanical properties. Another study examining the creep of breast tissue with tumors present, showed that strain retardance time parameter, which describes the time-varying viscous response of tissue to a small deforming force, provides the best discrimination between malignant and benign tumors [100]. Therefore, measuring both shear modulus and viscosity would be important in identifying breast cancer. Another aspect of making measurements in viscoelastic materials is that if viscosity is not taken into account, measurements of shear modulus can be biased higher than their actual values [81]. If an elastic model is imposed on a viscoelastic material, then the shear modulus must account for the effects of both the elastic and viscous components, resulting in the higher bias of the shear modulus.

Shear wave measurement techniques have emerged over the last decade as a prominent way to assess the viscoelastic properties of tissue. Several methods have been developed using MRI and ultrasound to measure the shear wave propagation such as MRE, Shear Wave Elasticity Imaging (SWEI) [66, 101,

8 102], sonoelastography [103-105], TE [77, 106-108], Supersonic Shear Imaging (SSI) [109, 110], and Shearwave Dispersion Ultrasound Vibrometry (SDUV) [95, 111]. To fully characterize the kidney, measurements of the elastic and viscous components of the tissue need to be measured. Elastography and ARFI methods only provide a map of relative stiffness. In current practice, SWEI and TE only measure the elastic part and not the viscous part of the tissue response. TE as implemented for study of liver stiffness in the Fibroscan device by Echosens does not have image guidance, which would be essential for measurements in the kidney [78]. Sonoelastography and SSI can provide maps of shear modulus and viscosity, but specialized hardware is necessary to implement both methods.

1.5 Summary of chapters A brief summary of the contents of each of the following chapters is given below.

Chapter 2 consists of a conceptual introduction to the methods that are used in this thesis to estimate mechanical properties of viscoelastic materials. Linear viscoelastic theory and models are described as well as quasi-static indentation test, quasi-static creep test and shearwave dispersion ultrasound vibrometry. Lastly, a conversion method to compare time-base measurements to frequency-base measurements is discussed.

Chapter 3 presents a validation study, of linearity and phase velocity assumptions, of SDUV estimations of shear elastic modulus with quasi-static indentation measurements of shear elastic modulus on gelatin phantoms of differing stiffness. In addition, the indentation measurements are compared to estimates of shear elasticity derived from shear wave group velocities. SDUV feasibility is demonstrated using two transducers as well as one transducer. The content of this chapter is substantially similar to C. Amador, M. W. Urban, S. Chen, Q. Chen, K. An, and J. F. Greenleaf, "Shear Elastic Modulus Estimation From Indentation and SDUV on Gelatin Phantoms," Biomedical Engineering, IEEE Transactions on, vol. 58, pp. 1706-1714, 2011.

9 Chapter 4 presents a feasibility study of SDUV to estimate both shear elastic modulus and viscosity of renal cortex in vitro. A number of experimental variables are varied to evaluate measurement linearity, and repeatability. Viscoelastic renal properties versus tissue inhomogeneity, tissue anisotropicity, time variability after organ excision, and structural changes after immersion in a cross-linking agent are evaluated. The content of this chapter is substantially similar to C. Amador, M. W. Urban, Shigao Chen, and J. F. Greenleaf, "Shearwave Dispersion Ultrasound Vibrometry (SDUV) on swine kidney", IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, in press, 2011.

Chapter 5 consists in the application of SDUV to in vivo kidney to study renal tissue viscoelastic properties consequent to changes in renal blood flow. In this chapter, the feasibility of SDUV for in vivo measurements of viscoelasticity in healthy swine kidney is demonstrated. For this purpose, shearwave dispersion was studied by exciting shear waves in the renal cortex with a mechanical actuator and with acoustic radiation force.The content of this chapter is substantially similar to C. Amador, M. Urban, R. Kinnick, S. Chen, and J. Greenleaf, "Viscoelastic measurements on perfused and non-perfused swine renal cortex in vivo," presented at the IEEE International Ultrasonics Symposium, San Diego, CA, USA, 2010.

Chapter 6 presents a method to quantify viscoelastic properties in a model- independent way by estimating complex elastic modulus from time-dependant creep response induced by acoustic radiation force. Experimental data are obtained in homogeneous tissue mimicking phantoms.

Chapter 7 details the contribution of this work and its impact in elasticity imaging and kidney function evaluation. Directions for future work will also be explored and academic accomplishments of this thesis work will be listed.

10 Chapter 2

Estimating mechanical properties of viscoelastic materials: Theory

2.1 Introduction This chapter consists of a conceptual introduction to the methods that are used in this thesis to estimate mechanical properties of viscoelastic materials. Basic definitions in the field of linear viscoelastic are presented. Moreover, an overall summary of methods to study viscoelastic behavior is covered, including quasi- static indentation test, quasi-static creep test and Shearwave Dispersion Ultrasound Vibrometry. Lastly, a conversion method to compare time-base measurements to frequency-base measurements is discussed.

2.2 Behavior of solid materials Solid materials are characterized by their response to an applied stress [112]. An elastic material exhibits immediate strain upon loading, constant strain as long as the stress is fixed and no strain once the load is removed (Figure 2.1a). If the applied stress is excessively high, the material behavior is considered plastic and the strain does not totally disappear once the load is removed (Figure 2.1b). Materials that exhibit time dependant strain as a response to an applied stress are called viscoelastic (Figure 2.1c). Upon loading, viscoelastic materials exhibit an immediate elastic strain response followed by a slow and continuous increase of strain during constant loading and an initial elastic recovery followed by a slow and continuous decrease of strain once the load is removed.

Figure 2.1: Elastic, plastic and viscoelastic strain response to constant stress.

Elastic and plastic strains are defined as time independent; however some plastic materials exhibit time-dependant strain. On the other hand, viscoelastic behavior is significantly affected by the rate of straining or stressing, therefore, in addition to stress and strain, the time variable should be included when studying viscoelastic behavior.

It is established that soft biological tissue exhibits viscoelastic behavior [113]. The simplest approach to characterize tissue mechanical properties is to consider tissue as a homogeneous, isotropic, viscoelastic material. However, to better understand the mechanical response of tissue, the role of fluids must be considered. To do so, a material is often considered to be made of a porous solid skeleton through which the interstitial fluid can flow; this material model is known as multiphase media, porous media, poroelasticity or poroviscoelasticity [114]. Although a better approximation of material properties may be achieved by means of poroviscoelasticity, in this thesis, the studied tissue-mimicking phantoms and kidney are considered linear viscoelastic materials. The motivation for studying tissue mechanical properties relies on the fact that their mechanical properties vary by over several order of magnitude between various tissues and within the same tissue with different pathological states [66].

12 2.3 Viscoelastic behavior Most viscoelastic materials exhibit the following transient characteristics (Figure 2.2) [112]:

• Instantaneous elasticity upon loading • Creep, slow continuous deformation, under constant stress • Stress relaxation, slow continuous decrease in stress, under constant strain • Instantaneous recovery once the load is removed • Delayed recovery, slow continuous decrease is deformation once the load is removed

Figure 2.2: Characteristics of viscoelastic materials, creep recovery and stress relaxation.

Creep is a slow, progressive deformation of a material under constant stress.

The ratio between the strain response, ε(t), and the applied constant stress, σ0, is called the creep compliance, J(t). Stress relaxation is the gradual decrease of stress of a material under constant strain. The ratio between the stress response, σ(t), and the applied constant strain, ε0, is called the relaxation modulus, E(t).

Figure 2.3 illustrates the three regions that are observed in a creep curve: primary creep in which the curve is concave down, secondary creep in which the deformation is proportional to time, and tertiary creep in which the

13 deformation accelerates until creep rupture occurs [115]. Nonlinear viscoelasticity always occurs during tertiary creep and often in secondary creep [115]. Although secondary creep is usually a straight line in a plot of strain vs. time, that straight line does not represent linear viscoelasticity [115]. Under small stress levels, most viscoelastic materials exhibit linear behavior. The material is said to be linearly viscoelastic if stress is proportional to strain at a given time and the linear superposition principle holds [112].

Figure 2.3: Regions of creep behavior. Strain, ε, vs. time, t, for different load levels.

If the material is linearly viscoelastic and the input is an oscillatory stress (Equation 2.1), instead of a constant stress, the strain response (Equation 2.2), will be an oscillation at the same frequency at the stress but lagging behind by a phase angle δ, Figure 2.4.

()= (ωσσ )≈ ωti 2.1 t 0 sin et

()= (δωεε )≈− ()ti −δω 2.2 t 0 sin et

where σ0 and ε0 are the stress and strain amplitudes, ω is the frequency of the vibration and δ is the phase angles or loss angle [112].

Figure 2.4: Oscillating stress, σ, strain, ε, and phase lag δ.

As a result of the phase lag between stress and strain, the relation between these two variables is a complex number and it is called the complex modulus, E* (Equation 2.3).

* += 2.3 iEEE ls

where Es and El are the real and imaginary part of the complex modulus,

respectively. Es is associated with energy storage and release during periodic deformation, therefore called the elastic or storage modulus [112]. On the other

hand, El is associated with the dissipation of energy and its transformation into heat, therefore called the viscous or loss modulus [112]. The ratio between the loss modulus and the storage modulus is called tangent of the loss angle, loss tangent or tan(δ), it is associated with the damping capacity of viscoelastic

materials [112]. The dynamic variables Es, El and δ depend on frequency.

2.3.1 Linear viscoelastic models Linear viscoelastic models are made of different combination of linear springs and linear viscous dashpots [112]. The linear spring represent the pure elastic response, therefore it exhibits instantaneous elasticity and instantaneous recovery (Figure 2.5a). On the other hand, the dashpot element represents the pure viscous response, a linear increase in strain under constant stress (Figure 2.5b).

Figure 2.5: Behavior of a linear spring and linear dashpot.

Table 2-1 summarizes the properties of most common linear viscoelastic models [112]. Neither the Maxwell nor Kelvin-Voigt model accurately represents the behavior of most viscoelastic materials. However, they both are commonly used because of their simplicity. Most advanced models are often used to characterize viscoelastic material behavior such as the standard linear solid model [112].

2.4 Methods to study viscoelastic behavior Viscoelastic behavior is usually studied either by transient or dynamic tests. Transient tests are in time domain and study viscoelastic properties such as creep and relaxation. Time-dependent creep and relaxation tests are not capable of completely evaluating mechanical behavior of viscoelastic materials. There are situations where the response of materials to a loading for short times, usually below the resolving capability of the measurement device (approximated 0.01 seconds), is of practical importance [112]. To overcome this challenge, dynamic or oscillatory tests are used to study material response from about 10-8 seconds [112]. Dynamic experiments are in frequency domain and study viscoelastic properties such as complex modulus and loss tangent. The elastic behavior of viscoelastic materials, such as biological tissues, has been studied by means of indentation test, which is considered a transient or quasi-static approach.

16 Table 2-1: Properties of viscoelastic models when step-stress is applied.

Maxwell Kelvin-Voigt Standard linear solid

Model σ σ σ E1 E E η η η E2 σ σ σ

Creep 1 t 1 − η 11 − η + ()1− e Et / tJ )( ()1−+= e 2tE / compliance η E E EE 21 J(t) Relaxation −Et /η +ηδ Ee tE )( E − η tE )( = 1 ()+ eEE 2tE / Modulus + 12 EE 21 E(t) Complex 1 E 1 E J = J = J += 2 compliance s E s E + ωη 222 s E E + ωη 222 1 2 J*(ω) 1 ηω J = = ηω l J l J = ωη E + ωη 222 l + ωη 222 E2

Complex ωη 22 = EE 2 2 ++ EEEEE ωη 22 = E s = 21 12 2 Es Es Modulus + ωη 222 = ωη 2 22 E El ()EE ++ ωη * 21 E (ω) 2 E ηω 2ηω = E2 El = + ωη 222 El 2 E ()++ ωη 22 EE 21

Conventional methods such as indentation, creep and relaxation tests in both transient or quasi-static and dynamic form have been used to study tissue mechanical properties [113]. The main disadvantage of using these conventional methods to study tissue mechanical properties is that they are usually destructive and invasive. Alternatively, wave propagation methods has been proposed to study tissue mechanical properties non-invasively [66, 78, 80, 109, 111, 116]. In this thesis, indentation test, creep test and a wave method called Shearwave Dispersion Ultrasound Vibrometry (SDUV) are used to study elastic and viscoelastic behavior of tissue mimicking phantoms and pig kidneys in vitro and in vivo. Therefore, conventional relaxation and dynamic test are out of the scope of this thesis.

17 2.4.1 Quasi-static indentation Quasi-static methods are commonly used because of their simplicity compared to dynamic methods. For instance, the quasi-static indentation test is considered a gold standard test to assess elastic mechanical properties. Moreover, it has been applied both ex-vivo and in-vivo [113, 117-125]. Soft tissue indentation based on a Hayes model [126] is used in this thesis work. Figure 2.6 illustrates a lateral infinite isotropic elastic material with a finite thickness resting on a rigid half-space. The material deforms under the action of a rigid axisymmetric indenter pressed normal to the surface by an axial force F.

Figure 2.6: Soft tissue indentation based on a Hayes model. F is the indentation force, Δh is the indentation depth, a is the indenter radius, and h is the material thickness.

Shear tractions between indenter and material are assumed negligible and the material is assumed to adhere to the half-space rigid surface. For a flat-end cylindrical indenter, the effective shear elastic modulus G is:

()1−ν F G = ⋅ ()νκ ,4 haa Δh 2.4

where ν is the Poisson ratio, F is the indentation force, Δh is the indentation depth, a is the indenter radius, h is the material thickness and κ is a geometry factor. Values of κ for a range of a/h and ν have been estimated by Hayes, et al [126]. Figure 2.7 illustrates the non-dimensional geometric factor κ as a function of aspect ratio a/h for two different Poisson ratio ν. There is a relatively small

18 difference in geometric factor κ for Poisson ratio between 0.45 and 0.5 when the aspect ratio a/h is less than 0.5. However, when the aspect ratio a/h is more than 0.5, there is a relatively large difference in geometric factor κ for Poisson ratio between 0.45 and 0.5

Figure 2.7: Non-dimensional geometric factor κ as a function of aspect ratio a/h for two different Poisson ratio ν.

2.4.2 Quasi-static creep Creep tests are performed as either compression or indentation studies [113]. Mechanical properties of viscoelastic materials are usually estimated by fitting the experimental data (time-dependent creep strain or compliance) to a theoretical model such as those described in Table 2-1. The linear strain response at various step-stresses for Maxwell, Kelvin-Voigt and standard linear solid models is schematically illustrated in Figure 2.8.

Maxwell model does not show decreasing strain rate (primary creep) but a rather constant strain rate (secondary creep) under step-stress. On the other hand, Kelvin-Voigt exhibits both primary and secondary creep but not an instantaneous elastic response. Standard linear solid shows both the primary and secondary creep as well as an instantaneous elastic response. In all three

models, doubling the applied stress σ1 exactly doubles the strain ε(t) for any time t during creep (Figure 2.8 a, c, e). Because the linear relationship between

19 stress and strain at any time point, the creep compliance J(t) for this models is invariant with applied stress (Figure 2.8 b, d, f).

Figure 2.8: The linear strain and compliance response at various step-stresses for (a-b) Maxwell, (c-d) Kelvin-Voigt and (e-f) standard linear solid.

20 The majority of creep studies assume step-loading conditions, which are analytically convenient but experimentally impossible to implement. Table 2-2 shows the analytic solution of Maxwell, Kelvin-Voigt and standard linear solid model’s differential equation when a ramp and hold stress is applied (Figure 2.9).

Figure 2.9: Ramp and load stress.

Table 2-2: Analytic solution of viscoelastic model’s differential equation when a ramp and hold stress is applied.

Model Maxwell Kelvin-Voigt Standard linear solid Differential η σ ()ε ()+= ηε () + & ttEt EE 21 σ ()t &()=+ εησ & ()tt σ&()t + σ ()t = ... equation E η EE ε ()tE + 21 ε ()t 1 & η

Strain, ε(t) σ σ σ σ σ σ −Et /η − η 00 +− 0 tCF 0 ()1− CFe 0 0 ()1−+ CFe 2tE / η EE E 1 EE 2 η Et /η η 1Et = ()1 − tE /η CF = CF e 1 CF = ()e 12 −1 η Et1 2 tE 12

Correction factor (CF, Table 2-2) as a function of time ratios (t1/η/E, t1/η/E1 and t1/η/E2) of Maxwell, Kelvin-Voigt and standard linear solid is illustrates in Figure 2.10.

Figure 2.10: Correction factor as a function of time ratio. (a) Maxwell model, (b) Kelvin-Voigt and standard linear solid.

The correction factor is relatively small for time ratios (t1/η/E, t1/η/E1 and t1/η/E2) less than 0.5 and 10-3 for the Maxwell, Kelvin-Voigt and standard solid models. For instance, if the time constant of a material is 0.3 ms (η = 3 Pa·s, E = 9 kPa),

the rise time t1 should be less than 0.15 ms and 0.3 μs to accurately estimate material properties when fitting Maxwell, Kelvin-Voigt and standard solid models, respectively.

2.4.3 Wave propagation methods Viscoelastic properties can also be measured by studying shear wave propagation. Shear wave methods are usually non-invasive and are based on measured vertical particle motion from shear strain (angular deformation) that is involved in the passage of transverse waves. One-dimensional plane shear wave propagation in soft tissue is described by [127]:

∂ 2 (),txu 2 ()txuk =+ 0, ∂x 2 2.5

where u(x,t) is the displacement resulting from a shear wave propagating unidirectionallly along x-axis and k is the wave number. In the case of linear * viscoelastic medium the wave number k is complex, written as k = kr – iki [127]. A solution for Equation 2.5 in a linear viscoelastic medium is [127]:

22 ω − − 2.6 = r xkti )( i xk )( ),( 0 eeutxu

where ω is the angular frequency, kr and ki are the real and imaginary wave

number respectively. Shear wave phase velocity, cs, is defined as the ratio

between ω and kr. On the other hand, shear wave attenuation coefficient, αs, is * the imaginary wave number, ki. The complex wave number, k = kr – iki, and * complex shear modulus, G (ω)=Gs+iGl, are related by [128]:

− kk 22 G ()ω = ρω 2 ir s ()+ 22 2.7 kk ir

kk G ()ω −= 2ρω 2 ir l ()+ 22 2.8 kk ir

where ρ is density. Shear wave phase velocity, cs, and shear wave attenuation, * αs, written as a function of shear complex modulus, G (ω)=Gs+iGl, yield[129]:

2()+ GG 22 ()ω = ls cs ρ( ++ 22 ) 2.9 s GGG ls

ρω ( 222 −+ GGG ) ()ωα = sls s ()+ 22 2.10 2 GG ls

The wave speed in a given medium is defined by the velocity of a single frequency component (phase velocity) or the velocity of the wave packet (group velocity). The change in the phase velocity of a propagated wave with frequency is known as dispersion; therefore, phase velocity is not the same as group velocity in a dispersive medium. On the other hand, in a non-dispersive medium, phase velocity is the same as group velocity. Dispersion can be caused by both tissue geometry and material properties. Equation 2.6 assumes an infinite medium; therefore, geometric dispersion is negligible.

2.4.3.1 Shearwave dispersion ultrasound vibrometry Shearwave dispersion ultrasound Vibrometry (SDUV) is a method that quantifies both tissue shear elasticity and viscosity by evaluating dispersion of shear wave propagation speed over a certain bandwidth [95, 111]. For an

23 isotropic, viscoelastic, homogenous material the shear wave propagation

speed, cs, depends on the frequency of shear wave ω, Equation 2.9. The shear wave speed is estimated from its phase measured at least at two locations separated by Δr along its traveling path:

ωΔ ω()− r rr 12 c ()ω = = s Δφ −φφ 2.11 12

where Δφ is the phase change over the traveled distance Δr. Generally, a regression is made on the phase versus distance over an extended region in order to improve wave speed estimation. Shear wave speed is then estimated with Equation 2.11, and dispersion measurements at different frequencies, usually from 50 Hz to 500 Hz, are fit by a linear viscoelastic model (refer to Table 2-1) to solve for viscoelastic properties. The Kevin-Voigt model has been shown to be appropriate for describing viscoelastic properties of tissue in the low frequency range (50 – 500 Hz) [130, 131].

Figure 2.11 illustrates 4 different implementations of SDUV. Shear waves can be excited by external mechanical vibration or by acoustic radiation force. Harmonic external mechanical vibrations have been used to excite shear waves at different frequencies to study shear wave dispersion. The resulting motion is measured by pulse Doppler ultrasound with a single element transducer (Figure 2.11a) or an array transducer (Figure 2.11b). Because external mechanical excitation applies stress throughout the entire object of interest, boundary conditions may need to be considered in Equation 2.5; moreover dispersion measurements are made one frequency at a time.

Alternatively, localized shear waves are produced by using acoustic radiation force of ultrasound [74, 132]. SDUV applies a focused ultrasound beam to generate harmonic shear waves or impulse shear waves that propagate outward from the vibration center [95, 111]. SDUV was first implemented using two transducers: one push transducer to generate shear waves and one detection transducer to monitor shear wave propagation, Figure 2.11c. The SDUV implementations previously described limit its clinical application. To overcome this limitation, SDUV has been implemented on a Verasonics V-1

24 ultrasound system (Verasonics, Redmond, WA). Figure 2.11d illustrates the setup used to do SDUV with a curved linear array transducer. The Verasonics V-1 system (Verasonics, Redmond, WA) is a programmable ultrasound research platform that has 128 independent transmit channels and 64 receive channels. The system is integrated around a software-based beamforming algorithm that performs a pixel-oriented processing algorithm. This algorithm facilitates conventional (e.g. 2000 frames per second) and high frame rate imaging (e.g. 10000 frames per second). The high frame rate imaging, using plane wave transmissions, is attractive for shear wave imaging because the full shear wave propagation can be captured in a two-dimensional plane [133].

Chen et al. originally reported using modulated ultrasound to create harmonic shear waves to characterize the viscoelastic properties of gelatin phantoms using shear wave dispersion [95, 111]. A limitation of this method was that the modulation frequency had to be changed multiple times to evaluate the

25 dispersion over a significant bandwidth. This method was advanced to make faster measurements by transmitting repeated tonebursts of ultrasound [111]. Figure 2.12 illustrates the pulse sequence. A single toneburst could be used to generate shear wave dispersion but the signal-to-noise ratio (SNR) at high frequencies may be poor. Although repeated tonebursts require more acquisition time compared to a single toneburst, the advantage of using repeated tonebursts is that shear waves are created that have motion amplitudes with high SNR at harmonics of the repetition frequency [111, 134].

Figure 2.12: Push toneburst repeated at frequency PRFp produces shear wave at PRFp and its harmonics.

2.5 Time creep compliance conversion to complex modulus Several techniques have been proposed to study the mechanical properties of viscoelastic materials. As discussed in the previous section, both quasi-static indentation and quasi-static creep measurements are expressed as a function of time, on the other hand, shear wave dispersion measurements are expressed as a function of frequency. As long as these measurements are within the linear response region of a material, the same physical property is probed. However, to directly compare these measurements, the results should be in the same format. The most standard measure of viscoelastic properties is the complex moduli or frequency-dependent moduli, G*(ω) or E*(ω). A method to convert time-dependent compliance to complex modulus was proposed by Evans et al. [135]. In principle, the time-dependent creep compliance, J(t), is related to the complex modulus, G*(ω), by a convolution; therefore by deconvolution, using a transformation such as the Fourier transform, the complex modulus is a function of the Fourier transform compliance. The

26 conversion formula as a function of two parameters J(0) and η, and the N data points is described below:

iω G * ()ω = = :1, Nn − ω ()Nti ⎡ − ω () ()()− JJ (01 ) e ⎤ ω () ()10 −+ eJi ti 1 + ... ⎢ () η ⎥ ⎢ t 1 ⎥ N ⎢ ⎛ () (nJnJ −− 1 )⎞ ω ()−−− ω () ⎥ 2.12 + ⎜ ⎟()nti 1 − ee nti ⎢ ∑⎜ () (−− )⎟ ⎥ ⎣⎢ n=2 ⎝ ntnt 1 ⎠ ⎦⎥

where J(0) and η are the compliance at n = 0 and the steady-state viscosity. J(0) is estimated by extrapolation of the compliance function to t Æ 0. Similarly, η is estimated by extrapolation of compliance function to t Æ ∞. The frequency range depends on the resolution (the time of the first data point, t(1)) and duration (the time of the last data point, t(N)) of the data set.

The advantage of using Equation 2.12, to convert time-dependent compliance to complex modulus, is the fact that no fitting of theoretical models is required. Thus the moduli can be recovered for a range of frequencies without a model.

27 Chapter 3

Shear elastic modulus estimation from SDUV and quasi-static indentation on gelatin phantoms

The content of this chapter is substantially similar to C. Amador, M. W. Urban, S. Chen, Q. Chen, K. An, and J. F. Greenleaf, "Shear Elastic Modulus Estimation From Indentation and SDUV on Gelatin Phantoms," Biomedical Engineering, IEEE Transactions on, vol. 58, pp. 1706-1714, 2011.

3.1 Introduction Noninvasive measurement of tissue mechanical properties as an estimator for tissue pathology is an emerging field of medical imaging [66, 77, 78, 80, 101, 103, 104, 136]. In principle, all elasticity imaging methods introduce mechanical excitation to tissue and then monitor the tissue response with conventional imaging methods. The first proposed elasticity imaging methods either excite tissue externally, as in ultrasound elastography [137], or use focused ultrasound to produce acoustic radiation force to push tissue as in acoustic radiation force impulse (ARFI) imaging [101]. While elastography and ARFI are useful approaches, they do not provide a quantitative measure of tissue stiffness; both methods typically form a 2D image providing a relative map of tissue stiffness. Shear wave propagation speed methods, such as magnetic resonance elastography (MRE) [80], shear wave elasticity imaging (SWEI) [66], Transient elastography (TE) [78] and supersonic shear imaging (SSI) [109], have been proposed to quantify tissue mechanical properties. Most of these

28 methods consider a pure elastic medium to describe the tissue mechanical properties, therefore only tissue elasticity is quantified.

A few elasticity imaging methods take advantage of the dispersive nature of soft tissue and can quantitatively solve for both tissue elasticity and viscosity [81, 95, 109, 111, 138, 139]. Even though sonoelastography [104] and supersonic shear imaging (SSI) [109] can provide maps of shear modulus and viscosity, specialized hardware is necessary to implement both methods.

Shearwave Dispersion Ultrasound Vibrometry (SDUV) is a method that quantifies both tissue shear elasticity and viscosity by evaluating dispersion of shear wave propagation speed over a certain bandwidth [111, 116]. It is desirable to have an inexpensive, reproducible tool to validate SDUV measurements. Mechanical testing is usually regarded as the gold standard method, but mechanical testing devices are usually expensive.

Chen, et al., have reported a quantitative model for a sphere vibrated by two ultrasound beams in a homogeneous viscoelastic medium [116]. In this study, a Doppler laser vibrometer was used to measure the mechanical frequency response of a sphere. Although this method can estimate material properties in an independent manner, its main disadvantage is that the medium around the target must be optically clear. To overcome this problem, a single element ultrasound transducer is used to measure the sphere time-domain response [140, 141], which is then fit using a model to obtain estimates of the shear elasticity and viscosity. However, these methods are not suitable for tissue mechanical properties characterization since a sphere must be embedded within a homogeneous tissue. Therefore, a more comprehensive study is needed to validate SDUV.

Several methods to measure tissue mechanical properties such as stress- relaxation, quasi-static and dynamic test have been used on biological tissues [113]. Mechanical tests had been used to evaluate the accuracy of elasticity methods such as MRE, ARFI and TE. MRE measurements have been compared to compression tests and dynamic tests on tissue like gelatin phantoms of varying elasticity [142, 143]. An integrated indentation and ARFI

29 imaging has been used to characterize soft tissue stiffness [144]. TE measurements have been compared to tensile tests and dynamic test on a tissue like polymers [145, 146]. Cross-validation between MRE and ultrasound- based transient elastography had been made in homogeneous tissue mimicking phantoms [147, 148]. Dynamic tests allow estimation of the change in tissue property parameters versus frequency, but the material needs to be characterized one frequency at a time. Quasi-static methods include compression tests, tensile tests and indentation tests. Compared to the others, indentation tests have been widely used to assess the mechanical properties of tissues. Their main advantage is that they can be applied both ex vivo and in vivo [113, 117-125]. The indentation test is considered a gold standard test to assess elastic mechanical properties. Furthermore, it is attractive because of its widespread use and ease of implementation, with its only requirement being to have a surface for indenter contact application.

The purpose of this study is to validate linearity and phase velocity assumptions of SDUV estimations of shear elastic modulus with quasi-static indentation measurements of shear elastic modulus on gelatin phantoms of differing stiffness. In addition, the indentation measurements are compared to estimates of shear elasticity derived from shear wave group velocities. SDUV feasibility is demonstrated using two transducers as well as one transducer.

3.2 Methods and Experiments 3.2.1 Gelatin phantom characterization Three sets of gelatin phantoms were made to compare shear elastic modulus values from quasi-static indentation tests and SDUV implemented with two transducers. Gelatin phantoms were made using 300 Bloom gelatin (Sigma- Aldrich, St. Louis, MO) and glycerol (Sigma-Aldrich, St. Louis, MO) with a concentration of 7, 10, and 15% by volume to achieve different values of the shear elastic modulus. A preservative of potassium sorbate (Sigma-Aldrich, St. Louis, MO) was added with a concentration of 7, 10, and 15% by volume. Cellulose particles (Sigma-Aldrich, St. Louis, MO) with size 20 μm were also added with a concentration of 0.5% by volume to provide adequate ultrasonic scattering. To evaluate the impact of sample geometry, two different samples

30 (cylindrical shape) thicknesses were used. Similarly, three different sample diameters (four samples of each type) and two flat-end cylindrical indenter sizes, a 3 mm indenter diameter and a 2 mm indenter diameter were used. A block of gelatin (15 x 15 x 4 cm) was made from the same batch of each gelatin solution preparation for use in SDUV experiments. Table 3-1 summarizes the sample characterization.

To study SDUV feasibility with curved array transducer, an 8% gelatin phantom was used. A cylindrical shape sample with 19.75 mm thickness and 35 mm diameter was studied with 2 mm indenter diameter and a block of gelatin (15 x 15 x 4 cm) was made from the same batch for SDUV experiments with curved array transducer.

Table 3-1: Sample characterization for mechanical test.

Four samples of each type were made, except for 8%gelatin phantom.

7% gelatin phantom

Sample type Thickness (mm) Diameter (mm)

1 7.98 35.00

2 17.44 35.30

3 7.98 13.80

8% gelatin phantom

Sample type Thickness (mm) Diameter (mm)

1 19.75 35.00

10% gelatin phantom

Sample type Thickness (mm) Diameter (mm)

1 7.88 35.00

2 17.00 35.30

3 7.88 13.80

15% gelatin phantom

Sample type Thickness (mm) Diameter (mm)

1 7.30 35.00

2 19.00 35.30

3 7.30 13.80

3.2.2 Quasi-static indentation Quasi-static (low frequency) unconfined uniaxial indentation experiments were performed using a mechanical testing machine (Enduratec, ElectroForce®

31 3200). A 50 gram load cell was used to record force as the flat-end cylindrical indenter was moved at a rate of 0.1 mm/sec. The sampling frequency was 20 kHz. The noise floor of the system was about 0.15 mN. The linear region of the force-displacement curve was defined as described by Zhai, et al., [144]. The absolute difference from the raw data and the fit was calculated. A threshold equal to 3 times the system’s floor noise was set. A data window of approximately 20 samples (5% of indenter diameter) was linearly fit. The data window was increased until the absolute difference or error was just below the threshold. Each sample was compressed four times. Shear elastic modulus was estimated by Hayes’ model for soft tissue indentation [126].

For a flat-end cylindrical indenter, the effective quasi-static or transient shear elastic modulus G is:

()1−ν F G = ⋅ (),4 haa δνκ 3.1

where ν is the Poisson ratio, F is the indentation force, δ is the indentation depth, a is the indenter radius, h is the material thickness and κ is a geometry factor.

3.2.3 Shearwave dispersion ultrasound vibrometry SDUV was first implemented using two transducers: one push transducer to generate shear waves and one detection transducer to monitor shear wave propagation. Figure 3.1a illustrates the experimental setup. The ‘Push Transducer’ (custom made with piezo crystals from Boston Piezo-Optics, Inc., Bellingham, MA) has a diameter of 44 mm, a center frequency of 3 MHz and a focal length of 70 mm. Shear waves generated at the transducer focal point propagate through gelatin phantom and vibration was detected by a single element transducer (Harisonic 13-0508-R, Staveley Sensors Inc.) with a diameter of 12.7 mm, a center frequency of 5 MHz and a 50 mm focus length (‘Detect Transducer’). The ‘Push Transducer’ and ‘Detect Transducer’ were aligned confocally with a pulse echo technique using a small sphere as a point target. The acoustic radiation force was localized 5 mm deep into the gelatin phantom surface.

32 Push tonebursts of 300 μs duration were repeated at 50 Hz to improve signal- to-noise ratio of shear wave displacement at 50 Hz and its harmonics. The propagation of the shear wave was tracked by the single element transducer in pulse-echo mode over a lateral range of 10 mm. The pulse repetition frequency of the ‘Detect Transducer’ was 1.6 kHz for the 7% and 10% phantoms. Because the 15% gelatin phantom was expected to be stiffer, thus shear waves travel faster compared to the 7% and 10% gelatin phantoms, the pulse repetition frequency of the ‘Detect transducer’ for the 15% gelatin phantom was increased to 3.2 kHz.

The ultrasound echoes were digitized at 100 MHz and processed by the cross- spectrum analysis previously described [149] to estimate the shear phase gradient. The shear wave phase velocity from 50 Hz to 400 Hz was calculated by:

ωΔr ω()− rr c ()ω = = 12 s Δφ −φφ 3.2 12 where ω and Δφ are angular frequency and phase change over the traveled distance Δr, respectively.

Figure 3.1: (a) Illustration of the experimental set up to do SDUV with two transducers. (b) Implementation of SDUV with a curved array transducer. SDUV applies a localized force generated by a ‘Push Transducer’ (1) or by electronically focused push (Push beam) coupled to the phantom, transmitting repeated tonebursts of ultrasound. (a) A separate transducer acts as the detector, ‘Detect Transducer’ (2), and is moved to detect shear wave motion at several spatial locations or (b) same transducer is used to detect phantom response (Detection beams).

33 Shear wave dispersion measurements were fit to Kelvin-Voigt model to solve for viscoelastic properties. For an isotropic, viscoelastic, homogenous Kelvin-

Voigt material the shear wave propagation speed, cs, depends on the angular

frequency of shear wave, ωs

2()G + ηω 222 ()ω = s c ss ρ( ()++ ηω 222 ) 3.3 GG s

where ρ, G and η are the density, shear elastic modulus and viscosity of the medium, respectively [150].

Additionally, the group velocity for each phantom was calculated by evaluating the time shifts in the shear waves versus position and using

ΔΔ= 3.4 g trc

where cg is the group velocity, and Δt is the time shift of the shear wave peask measured over a distance Δr.

During each experiment, the single element transducer was moved by 1 mm intervals 11 times along the y-axis (refer to Figure 3.1a). This acquisition sequence was repeated 4 times in each of the regions of interest (ROI). Additionally, SDUV measurements were repeated at 4 different regions.

The SDUV setup illustrated in Figure 3.1a limits the clinical application of SDUV because it requires two transducers. To overcome this limitation, SDUV has been implemented on a Verasonics V-1 system (Verasonics, Redmond, WA). Figure 3.1b illustrates the setup used to do SDUV with a curved linear array transducer (C4-2, Philips Healthcare, Andover, MA). A 3 MHz, 331 μs push beam was transmitted and focused at 30 mm into the phantom to generate shear waves, and the mechanical response was measured with the same transducer with plane wave imaging techniques at 2000 frames per second (fps). The push occurs at the center element of transducer, and causes shear displacements across in the x-axis (refer to Figure 3.1b), the lateral resolution

34 was 0.5 mm. The push beam was repeated every 10 ms to get a pulse repetition frequency of 100 Hz.

3.3 Results 3.3.1 Quasi-static indentation The force-displacement raw data for one sample (Sample type 1, refer to Table 3-1) of 7%, 8%, 10% and 15% gel phantom with a 2 mm indenter diameter is shown in Figure 3.2. All four phantom samples showed a linear response up to approximately 1 mm compression. The maximum force for each linear region was 9 mN, 20 mN, 40 mN and 63 mN for 7, 8, 10 and 15% phantoms respectively.

Table 3-2 shows the influence of sample thickness and sample diameter on the Hayes model for the 7%, 10% and 15% gelatin phantoms. The sample thickness was approximately 5.3, 8, 11.3 and 17 times the indenter radii. Similarly, the sample diameter was approximately 9.2, 13.8, 23.3 and 35 times the indenter radii. Because the geometry factor κ is not very sensitive to Poisson’s ratio ν from 0.45 to 0.50 for a/h ratio range from 0.05 to 0.20 (refer to Chapter 2 for detailed analysis), the Poisson’s ratio ν was set to 0.475.

35 Table 3-2: Shear elastic modulus, kPa (mean ± SD, n = 4), for different sample diameter (d), indenter diameter (2a) and sample thickness.

2a = 2 mm 2a = 3 mm 2a = 2 mm 2a = 3 mm

Thickness (mm) d = 35 mm d = 35 mm d = 13.8 mm d = 13.8 mm

7% gelatin phantom

7.98 1.35 ± 0.06 1.36 ± 0.01 1.29 ± 0.19 1.22 ± 0.20

17.44 1.16 ± 0.01 1.29 ± 0.04 - -

8% gelatin phantom

19.75 1.75 ± 0.03 - - -

10% gelatin phantom

7.88 3.65 ± 0.21 3.63 ± 0.14 3.54 ± 0.09 3.51 ± 0.12

17 3.40 ± 0.05 3.28 ± 0.09 - -

15% gelatin phantom

7.3 4.68 ± 0.03 4.67 ± 0.10 4.76 ± 0.10 4.63 ± 0.05

19 5.60 ± 0.06 5.00 ± 0.01 - - 3.3.2 SDUV with two transducers The displacement amplitude estimates, as calculated by the cross-spectrum method [149], over 50 ms for 7% gelatin phantom are shown in Figure 3.3 and. The peak displacement amplitude was approximately 18 μm, 16 μm and 12 μm at 4, 6 and 8 mm away from the vibration center.

36 The displacement response of 15% gelatin phantom, which was stiffer than the other phantoms, was expected to be fast in time and small in amplitude. Therefore, to avoid errors in group velocity and phase velocity estimation, a higher pulse repetition frequency (PRF) was used. To illustrate this, the 15% gelatin phantom data were analyzed using a PRF of 1.6 kHz. Displacement amplitude estimates over 20 ms for the 15% phantom with PRF of 1.6 kHz and 3.2 kHz are shown in Figure 3.4. The three curves represent sets of the measured amplitude for 4, 6 and 8 mm away from the vibration center. As expected, the displacement is better reconstructed using PRF of 3.2 kHz.

The magnitude spectra of the velocity signal for the 7%, 10% and 15% gelatin phantoms over 200 ms are shown in Figure 3.5. The frequency at which the amplitude is highest, or the center frequency of broadband signal, is denoted as

ωp. The center frequencies of the SDUV response, from 0 ms to 200 ms, were 100 Hz for 7% phantom, 350 Hz for 10% phantom and 100 Hz for the 15% phantom. Group velocity, cg, is described by Morse and Ingard as the “velocity of progress of the ‘center of gravity’ of a group of waves that differ somewhat in frequency [151]”. The center of gravity, ωc, was calculated by [152]

37 ⋅= ()ωωω 2 ()ω 2 3.5 c V ∑∑ V

where V(ω) is the complex spectrum of the velocity signal and ω is the angular

frequency. The center of gravity, ωc, of the magnitude spectrum of the velocity signal for each gelatin phantom was 200, 350 and 250 Hz for the 7, 10 and 15% gelatin phantoms, respectively.

Figure 3.5: Magnitude spectra of the velocity signals over 200 ms. The three symbols (o, *, Δ) represent 7, 10 and 15% gelatin phantoms.

Figure 3.6 shows the distance from the vibration center, r, versus time shift for 7%, 10% and 15% gelatin phantoms over 5 mm. The time shifts were calculated by cross-correlation method [153]. The solid lines are linear regressions for the time shifts. The group velocity was calculated from (3.4).

Figure 3.6: Time shift estimates over 3 to 8 mm away from the vibration center. The three symbols (o, *, Δ) represent 7, 10 and 15% gelatin phantoms.

The group velocity, cg (slope of solid lines in Figure 3.6), for each gelatin phantom were 1.33, 2.35 and 3.15 m/s for 7, 10 and 15% respectively. By assuming a non-dispersive medium, in other words, by setting η = 0 in Equation

3.3, and also assuming a linear elastic material, where group velocity, cg, is same as the phase velocity, cs, for all frequencies, the shear elastic modulus for the 7, 10 and 15% gelatin phantoms were 1.77, 5.52 and 9.92 kPa respectively.

Phase of shear waves at frequencies 50 to 400 Hz was estimated by Kalman filter [154]. Figure 3.7 illustrates the phase of shear waves at frequencies 100 to 400 Hz for the 7% gel phantom. There is a linear relation between shear wave phase and propagation distance. The solid lines are linear regressions for the phase estimates.

The coefficients of determination, R2, of the linear regressions between phase estimates and distance, shown in Table 3-3, were greater than 0.95, 0.97 and 0.96 for the 7%, 10% and 15% gelatin phantoms respectively. These data supports the linear assumption of Equation 2.11.

Table 3-3: Coefficients of determination, R2, of the linear regressions between phase estimates and distance, for the 7%, 10% and 15% gelatin phantoms

Frequency, Hz 50 100 150 200 250 300 350 400

R2, 7% phantom 0.99 0.99 0.99 0.99 0.99 0.99 0.99 0.95

R2, 10% phantom 0.97 0.99 0.99 0.97 0.96 0.97 0.98 0.97

R2, 15% phantom 0.98 0.99 0.99 0.99 0.96 0.99 0.97 0.97

Figure 3.8 shows shear wave propagation speed, cs, as a function of frequency. The three symbols (o, *, Δ) represent the mean shear wave speed of four repeated measurements in the 7%, 10% and 15% gelatin phantoms. Error bars represent the standard deviation of the measured shear wave speed at each particular frequency four repeated times. The solid lines are the least

mean square (LMS) fits from Equation 3.3 that give shear elastic modulus, G, of 1.61, 3.30 and 5.37 kPa and viscosity, η, of 0.85, 1.43 and 2.14 Pa·s for 7%,

40 10% and 15% gelatin phantoms, respectively. The median absolute error, that is, the median of the absolute difference between the Kelvin-Voigt model fit and experimental data, were 0.09, 0.14 and 0.23 m/s for 7, 10 and 15% gelatin phantom respectively.

3.3.3 SDUV with one transducer Shear wave propagation profiles from SDUV using a linear curved array transducer are shown in Figure 3.9. The push occurs at x = 0 mm and causes shear waves displacements outward in the +x and –x directions.

Figure 3.9: Shear wave profiles (-,-·-·, -·-,···, --) from different time points (1.5 ms, 3.0 ms, 4.5 ms, 6.0 ms and 7.5 ms) after the transmission of the push pulse.

41 Magnitude spectra of the velocity signal over 20 ms and distance, x, as a function of time shift for the 8% gelatin phantom are shown in Figure 3.10.

Figure 3.10: (a) Magnitude spectra of the velocity signal over 20 ms. (b) Time shift estimates over 2 to 10 mm away from the vibration center.

The center frequency and the center of gravity were 100 Hz and 200 Hz respectively. The group velocity, slope of distance as a function of time shift, was 1.52 m/s. By assuming a non-dispersive medium, setting η = 0 in Equation 3.3, the shear elastic modulus for the 8% gelatin phantom was 2.31 kPa.

Phase of shear wave as a function of distance for 100, 200, 300 and 400 Hz and shear wave speed, cs, as a function of frequency for the 8% gelatin phantom is shown in Figure 3.11.

Coefficients of determination, R2, of the linear regression between phase estimates and distance, were less than 0.95. Shear elastic modulus, G, and viscosity, η, for 8% gelatin phantom were 1.77 kPa and 0.77 Pa.s. The error bars in Figure 3.11b represent the standard deviation of four repeated measurements; the solid line is the mean least square (LMS) fit from Equation 3.3. Median absolute error was 0.01 m/s.

3.4 Discussion The use of Hayes’ model is suitable for describing relatively small deformation indentation on lateral infinite isotropic elastic media. Even though this model takes the sample thickness into account, it is important to satisfy its assumed boundary conditions. Shear elastic modulus was slightly underestimated when the sample diameter was decreased, particularly on the softer phantom. This underestimation is caused by the violation of the assumption of lateral infinite geometry. Not surprisingly, there was not a significant variation of shear elastic moduli for different sample thickness (Refer to Table 3-2) for the 7% and 10% gelatin phantoms. However, shear elastic modulus was slightly different for the 15% gelatin phantom for different sample thickness.

Variability in quasi-static indentation results may be caused by an increase in material nonlinearity at large strain. However, the shear elastic modulus estimated at 10 % strain (that is, thicker samples with large indentation depth and thinner samples with smaller indentation depth), shown in Table 3-4, are not much different from those reported in Table 3-2, therefore the variability in indentation results may not be attributed to nonlinearity of materials.

43 Table 3-4: Shear elastic modulus, kPa (mean ± SD, n = 4), at 10% strain, for different sample diameter (d), indenter diameter (2a) and sample thickness.

2a = 2 mm 2a = 3 mm 2a = 2 mm 2a = 3 mm

Thickness (mm) d = 35 mm d = 35 mm d = 13.8 mm d = 13.8 mm

7% gelatin phantom

7.98 1.20 ± 0.01 1.35 ± 0.01 1.33 ± 0.01 1.26 ± 0.01

17.44 1.15 ± 0.01 1.29 ± 0.01 - -

8% gelatin phantom

19.75 1.72 ± 0.03 - - -

10% gelatin phantom

7.88 3.76 ± 0.13 3.82 ± 0.10 3.52 ± 0.08 3.46 ± 0.11

17 3.51 ± 0.10 3.41 ± 0.08 - -

15% gelatin phantom

7.3 4.77 ± 0.01 5.36 ± 0.40 4.84 ± 0.10 4.72 ± 0.01

19 5.49 ± 0.01 5.81 ± 0.05 - -

Zhai et al. [144] had reported similar variations in shear elastic modulus estimated by quasi-static indentation test. In this study, Finite Element Method (FEM) simulations suggest that a sample with Young’s modulus of 5 kPa is large enough when its thickness and diameter are over 15 times of the indenter radii. Therefore, the shear elastic modulus for the 7, 8, 10 and 15 gelatin phantoms were 1.16, 1.75, 3.40 and 5.60 kPa respectively (refer to Table 3-2, thicker samples and small indenter diameter). However, a more suitable model should include both sample thickness and sample diameter in consideration.

The peak displacement amplitude estimated by SDUV was approximately 18 μm when using two transducer and 5 μm when using linear curved array. Peak displacements were relatively small, therefore within a linear region of a force- displacement curve. Tissue response to a harmonic excitation using different voltage amplitudes on the ‘Push transducer’ has shown a fairly independent relationship between shear wave speed and excitation voltage, which is

44 equivalent to a linear relationship between force and displacement [155]. Similarly, the force-displacement curves from the indentation experiments were linear for up to 1 mm displacement. Although force-displacement curves of gelatin phantoms were nonlinear for large displacements (larger than 1 mm), indentation can be used to assess elastic components of mechanical properties of viscoelastic materials under small deformation.

The phase estimates at high frequencies showed more variation compared to lower frequencies (refer to Figure 3.7 and Figure 3.11a). This occurred in all 4 phantoms. Because the displacement amplitude is decreased at high frequencies, the error of the phase estimates is expected to increase at high frequencies [156]. However, the coefficients of determination, R2, of the linear regressions between phase estimates and distance, were higher than 0.95 in all 4 phantoms.

Table 3-5 shows a comparison between group velocity, cg, phase velocity

evaluated at center of gravity, cs(ωc), and phase velocity evaluated at center

frequency, cs(ωp). Both phase velocities calculations were close to group velocities for the 7, 8 and 10% gelatin phantoms. The magnitude spectrum of the velocity signal for the 15% phantom (Refer to Figure 3.5) was broader compared to the other phantoms. This could be a reason why the group velocity for the 15% gelatin phantom was rather different than the phase

velocities. In theory, the group velocity, cg, should be identical or close to the phase velocity, cs, evaluated at center of gravity, ωc.

Table 3-5: Group velocity, phase velocity evaluated at center of gravity and phase velocity evaluated at center frequency.

7% gelatin 8% gelatin 10% gelatin 15% gelatin

phantom phantom phantom phantom

Group Velocity, cg 1.33 m/s 1.52 m/s 2.35 m/s 3.15 m/s

Phase Velocity at ωc, 1.57 m/s 1.41 m/s 2.49 m/s 2.83 m/s

cs(ωc)

Phase Velocity at ωp, 1.32 m/s 1.37 m/s 2.49 m/s 2.38 m/s

cs(ωp)

45 The shear wave speed versus frequency results in Figure 3.8 and Figure 3.11b fits well with the Kelvin-Voigt model, particularly for the softer phantom. Stiffer phantoms seem to have peaks at certain frequencies that deviate from the ideal Kelvin-Voigt model, however the absolute error between the Kelvin-Voigt model fit and experimental data was relatively small. Shear wave estimation may be affected by tissue geometry depending on the type of wave that is being excited. For instance, mathematical models for shear wave dispersion of anti- symmetric Lamb and Rayleigh suggest that shear wave speed is affected by material thickness mostly at lower frequencies when the material thickness is larger than one to two wavelengths of the wave [157]. Although the largest wavelength, about 42 mm for the 15% gelatin phantom at 50 Hz, was approximately equal to the phantom thickness, substantial errors for measurement of the shear wave speed related to phantom thickness are not expected. SDUV assumes pure shear waves, that is, a shear wave propagating in an infinite medium; therefore there should be no reflections from boundaries. In addition, the phase gradient in Equation 2.11 assumes that there is only one wave traveling one direction. Figure 3.12 illustrates the two dimensional Fourier transform of displacement response for the 7%, 8%, 10% and 15% gelatin phantoms [158]. By inspection, there are no frequency components on the 2nd and 4th quadrant for each phantom, hence no reflected waves were traveling in the opposite direction to the generated shear waves, which suggest that there are no waves being reflected from the boundaries (bottom and sides). However, there may be reflections from the surface traveling in the same direction as the pure share wave that can not be distinguished in Fourier space and therefore may cause variations in the phase and cause errors in speed measurements.

kx is the spatial Fourier transform variable. Horizontal axis represents the one dimensional temporal Fourier space.

SDUV assumes shear waves propagating in a viscoelastic material, thus a material with complex shear elastic modulus. The compression rate for the indentation test was 0.1 mm/sec and each gelatin phantom showed a linear response up to 1 mm compression, therefore the excitation frequency for indentation test was approximately 0.1 Hz. Because the excitation frequency from the indentation test is close to zero, the shear elastic modulus estimation by indentation test should be the same or close to the real component of the shear complex modulus on the Kelvin-Voigt model, which is then the shear elastic modulus G.

47 Figure 3.13 provides a summary of the shear elastic moduli estimated from group velocity (linear elastic medium), phase velocity (viscoelastic medium, Kelvin-Voigt model) and indentation test. Error bars represent the standard deviation of the measured shear elastic modulus for each particular phantom at four different locations.

Figure 3.13: Shear elastic modulus comparison between phase velocity, indentation test and group velocity. Mean ± SD, n=4.

The shear elastic modulus estimated from group velocity measurements can definitively differentiate the three phantoms. However, these group velocity values do not agree well with either the indentation experiment results or phase velocity results, especially when the phantom is stiffer. This disagreement could be attributed to the fact that gelatin phantoms are dispersive [95, 131, 150]; therefore the wave speed is dependent on frequency. Shear elastic modulus estimation from the indentation test and phase velocity for the 7% phantom were slightly different. This could be due to inhomogeneities on gelatin samples. The cellulose component, introduced for ultrasound scattering, did tend to settle down in the sample molds while the gelatin was liquid. Because the 7% gelatin is less viscous, the cellulose distribution was probably different compared to the other phantoms.

A linear correlation comparing shear elastic modulus from indentation test with group velocity and SDUV phase velocity is shown in Figure 3.14. The correlation coefficients were 0.98 for the group velocity and 0.99 for the SDUV phase velocity method. Although the correlation coefficients are similar and larger than 0.98, most likely because the number of gelatin phantoms is small, the shear elastic modulus correlation between SDUV phase velocity method and indentation test is closer to the ideal correlation (continuous line on Figure 3.14). On the other hand, the shear elastic modulus correlation between group velocity and the indentation test seem considerably different from the ideal correlation, suggesting that shear elastic modulus estimation by group velocity will be biased when the medium being investigated is dispersive. Therefore a rheological model should be used to estimate mechanical properties of viscoelastic materials. Because tissues are more viscous than these phantoms [95, 111, 131], this would be the case for tissues as well.

This study shows acceptable agreement of shear elastic moduli estimates from SDUV phase velocity method and indentation test on gelatin phantoms. Moreover, feasibility of SDUV implementation in Verasonics systems is demonstrated and there is a good agreement between shear modulus

49 estimated by indentation, SDUV with two transducers and SDUV with linear curved array transducer. SDUV implementation with one transducer offers better lateral resolution and faster acquisition time, which allows studying shear wave dispersion in stiffer materials.

3.5 Conclusion In this paper, we presented an independent validation method of elastic modulus estimation by SDUV in gelatin phantoms. The shear elastic modulus, estimated from the SDUV phase velocity method, matched the elastic modulus measured by the indentation method. The shear elastic modulus estimated by group velocity did not agree with indentation test estimations. These results suggest that a rheological model for linear viscoelastic material must be used to estimate elastic modulus on dispersive gelatin phantoms and soft tissues.

50 Chapter 4

Shear wave dispersion ultrasound vibrometry in swine kidney: In vitro study

The content of this chapter is substantially similar to C. Amador, M. W. Urban, S. Chen, and J. F. Greenleaf, "Shearwave Dispersion Ultrasound Vibrometry (SDUV) on swine kidney," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, in press, 2011.

4.1 Introduction Renal fibrosis is a pathological process that alters the kidney structure and therefore its biomechanical properties. Renal fibrosis is a consequence of chronic kidney disease (CKD). Progressive CKD leads to renal failure, which is a condition that requires dialysis and kidney replacement [159]. Early detection of renal fibrosis could provide critical prognostic information required to guide therapy or alternatively to avoid invasive procedures. However, a major obstacle is the inability to detect fibrosis early and monitor it regularly with sufficient sensitivity and specificity.

Tissue pathology state such as fibrosis is linked to tissue mechanical properties [66]. Hence, several methods that noninvasively estimate tissue mechanical properties have been developed. For instance, kidney mechanical properties have been studied using several elasticity techniques. Elastography has been used in several ex vivo studies in kidneys [68-71] and some in vivo human studies of kidney transplant patients [72, 74]. Acoustic radiation force impulse (ARFI) imaging has been used to image renal tumors [74, 75]. Recent results

51 with transient elastography (TE) have shown that stiffness in renal allografts correlated significantly with the degree of fibrosis [79]. Magnetic resonance elastography (MRE) has been applied to quantitatively evaluate the stiffness of renal cortex and medulla in ex vivo porcine kidneys and in vivo rat and swine models [81-85, 160]. While elastography and ARFI are useful approaches, they do not provide a quantitative measure of tissue stiffness, but only a relative mapping. On the other hand, MRE can obtain 3D elasticity data, but is not widely available and scans take considerable time.

TE and MRE are capable of quantifying tissue stiffness; however, to fully characterize the kidney, measurements of the elastic and viscous components of the tissue need to be measured. If viscosity is not taken into account, measurements of shear stiffness can be biased higher than their actual values [81, 161]. Supersonic shear imaging (SSI) can provide maps of stiffness and viscosity, but specialized hardware is necessary to implement this method. Shearwave dispersion ultrasound vibrometry (SDUV) is capable of providing quantitative measurements of tissue viscosity, in addition to elasticity, and uses an intermittent pulse sequence that make SDUV compatible with current ultrasound scanners.

Mechanical testing is usually regarded as the gold standard method to evaluate mechanical properties of a material. Kidney mechanical properties have been studied with a variety of mechanical tests such as compression, tensile and shear tests [89, 92, 94]. In these studies, the general behavior of the kidney has been characterized as non-linear and viscous. The elastic modulus (E) for kidney samples was reported as 4.8 MPa [89] and 14.7-40 kPa [92, 94] for complete kidney. A series of rheological tests on pig kidney samples have been performed by Nasseri, et al., to characterize kidney non-linear viscoelastic behavior [91]. It was found that the limit of linear viscoelasticity is of the order of

0.2 % strain, where the shear storage (Gs) and loss modulus (Gl) were 2.5 kPa and 1.5 kPa, respectively, between 0.01 Hz and 20 Hz. Mechanical testing on kidney involves considerable technical difficulties as demonstrated by the wide range of values found in the literature. One of the major difficulties with testing kidney and other soft tissue is mounting the test specimens, because

52 inadequate or inappropriate mounting results in failure or slippage in the grips of the test equipment. Additionally, soft tissues undergo considerable extension or compression at loads below the resolving capability of the measuring device. Tissue mechanical testing is useful for the purposes of comparative testing, but the inherent variability in biological tissue and the technical problems discussed above limits the usefulness of these measurements. As a result, tissue mimicking phantoms have been used to evaluate the accuracy of elasticity methods by classical mechanical test [142-146], including SDUV [161].

The motivation of this study is to facilitate future in vivo SDUV studies in kidney because visual inspection of the cross section of kidney shows that kidney tissue is inhomogeneous and anisotropic. SDUV measures shear wave dispersion, that is, shear wave speed as a function of frequency. To resolve kidney elastic properties, a rheological model is required. The Kelvin-Voigt model has been shown to be appropriate for describing viscoelastic properties of soft tissue in the low frequency range (50 – 500 Hz) [130, 131, 150, 162]. In this study, shear wave dispersion measurements are fit to a Kelvin-Voigt model to solve for kidney viscoelastic properties. Then, the assumption of linear tissue response to a harmonic excitation is studied as well as repeatability of the method, tissue homogeneity and tissue anisotropy. Moreover, long-term variability of kidney viscoelastic properties is studied as well as differences caused by exposure to formaldehyde. SDUV feasibility is demonstrated using two transducers as well as one transducer.

4.2 Methods and experiments 4.2.1 Shearwave dispersion ultrasound vibrometry SDUV measurements were made by the initial SDUV implementation using two transducers and the latest implementation in the Verasonics V-1 system (Verasonics, Redmond, WA). Figure 4.1a illustrates the setup to do SDUV with two transducers. Shear waves are generated with ultrasound radiation force at the “Push Transducer” focal point. The ‘Push Transducer’ has a diameter of 44 mm, a center frequency of 3 MHz and a focal length of 70 mm. This transducer was driven by a signal generator and 40 dB power amplifier. Shear waves generated at the transducer focal point propagate through renal tissue and

53 vibration was detected by a single element transducer with a diameter of 12.5 mm, a center frequency of 5 MHz and a 50 mm focus length (‘Detection Transducer’). The ‘Push Transducer’ and ‘Detection Transducer’ were aligned confocally with a pulse-echo technique using a small sphere as a point of target. Acoustic radiation force was localized 5 mm deep into the kidney surface. The pulse repetition frequency of pushes was 50 Hz. Shear wave propagation was tracked by the ‘Detection Transducer’ in pulse-echo mode over a range of 5 mm along the x-axis. Ultrasound echoes were digitized at 100 MHz and processed by the previously described method [154] to estimate the shear wave phase.

Figure 4.1b illustrates the setup used to do SDUV with a curved linear array transducer (C4-2, Philips Healthcare, Andover, MA). A 3 MHz, 331 μs push beam was transmitted and focused in the renal cortex to generate shear waves in the medium. The push beam was repeated every 20 ms to get a pulse

54 repetition frequency of 50 Hz. Kidney mechanical response was measured with the same transducer with plane wave compounding imaging technique [133]. A set of 3 plane waves with different emission angles were transmitted at 6 kHz pulse repetition frequency (PRF). By coherently compounding each set of 3 plane waves, a compound image PRF of 2 kHz was produced. Local tissue displacement is estimated using 1-D autocorrelation between two compounded images [163].

For both SDUV implementations, shear wave phase velocity from 50 Hz to 500 Hz was calculated by:

ωΔr ω()− rr c ()ω = = 12 s Δφ −φφ 4.1 12 where ω and Δφ are angular frequency and phase change over the traveled distance Δr, respectively. Additionally, kidney viscoelastic properties were estimated by fitting shear wave phase velocity as a function of frequency to the Kelvin-Voigt model dispersion (Equation 4.2). For an isotropic, viscoelastic, homogenous Kelvin-Voigt material the shear wave propagation speed, cs, depends on the angular frequency of shear wave, ωs

2()G + ηω 222 ()ω = s c ss ρ( ()++ ηω 222 ) 4.2 GG s where ρ, G and η are the density, shear elastic modulus and viscosity of the medium, respectively [150].

4.2.2 Experiments A total of eight excised kidneys from female pigs were used in these in vitro experiments. All kidneys were removed immediately after sacrifice and placed in saline solution at room temperature. A series of different tests were performed to evaluate the use of SDUV for measurements of the viscoelasticity of the excised kidney (Table 4-1).

55 Table 4-1: Description of the tests that were used to study swine kidney viscoelasticity with SDUV.

Kidney 1 2 3 4 5 6 7 8

Experiments

Linearity Study x

SDUV repeatability x x x x x x x x

Organ homogeneity x x x x

Time influence x x

Formalin study x

Anisotropy study x

Transducers for SDUV 2 2 2 2 2 2 2 1

Time of experiment after 21 15 24 3 Every 3 hrs Every 3 hrs 3 3 animal sacrifice (hrs) for 24 hrs for 24 hrs

Shear wave direction*

Tangential x x x x x x x x

Radial x

* The tangential direction (y-axis) is where the shear wave propagate in a direction perpendicular to blood vessels and the radial direction (z-axis) is where the shear waves propagate in a direction parallel to blood vessel orientation

4.2.2.1 Linearity study Acoustic radiation force density applied to a tissue can be described as:

2αI F = c 4.3 where F is the acoustic radiation force, c is the speed of sound in the medium, α is the absorption coefficient of the medium and I is the in situ temporal average intensity at a given spatial resolution [164]. Given that the pressure is proportional to the voltage applied to the transducer and the ultrasound intensity is proportional to pressure squared, and the displacement is proportional to the force, then the tissue displacement is proportional to the square of the voltage applied to the “Push Transducer”. The assumption of linear tissue response to a harmonic excitation was studied by measuring shear wave dispersion at four different excitation voltage amplitudes (3.0 V, 2.6 V, 2.1

56 V and 1.5 V) on one excised kidney (Kidney #1, refer to Table 4-1). Shear elastic modulus and viscosity were measured in a 5 x 5 mm2 patch 5 repeated times.

4.2.2.2 SDUV repeatability SDUV repeatability was studied with both setups (SDUV with two transducers and SDUV with a curved linear array transducer). Figure 4.2a illustrates a B- mode image along zx-plane using the setup with two transducers. In this case, SDUV repeatability was evaluated by repeating SDUV measurement five times, in a 5 x 5 mm2 patch in the renal cortex (ROI1 in Figure 4.2a), of seven kidneys (Kidneys #1-7, refer to Table 4-1). Figure 4.2b illustrates a B-mode image along zx-plane using the setup with the curved linear array transducer. Similarly, the SDUV repeatability was evaluated by doing four repeated SDUV measurement in a 5 x 5 mm2 patch in the renal cortex (ROI1 in Figure 4.2b) of one kidney (Kidney #8, refer to Table 4-1).

Figure 4.2: (a) B-mode image along zx-plane. The beam was focused at 3 locations (white arrows). Tissue motion was tracked at 5 regions along x-axis (white squares) of 5 x 5 mm2. (b) Curved array B- mode image along zx-plane. Shear waves propagating perpendicular to blood vessels (tangential direction or x-direction in this figure) were generated by a push beam focused at x = 0 (ROI 1 and 2). Shear waves propagating parallel to blood vessels (radial direction or z-direction in this figure) were generated by a push beam focused at the edge of the kidney (ROI 3).

57 4.2.2.3 Organ homogeneity Visual inspection of the cross section of the kidney reveals that the kidney tissue is globally inhomogeneous. To study this feature, SDUV measurements were made at five different locations (Figure 4.2a, ROI1, ROI2, ROI3, ROI4 and ROI5), 5 x 5 mm2 patches in four kidneys (Kidneys #1-4, refer to Table 4-1). Furthermore, a 5 x 5 mm2 patch was studied every 1 mm on z-axis (ROI2 in Figure 4.2a) in one kidney (Kidneys #2, refer to Table 4-1).

4.2.2.4 Anisotropy study It is acknowledged that kidney tissue may not be isotropic, in other words, its properties are not the same for all orientations of the coordinate axes. To study this feature, SDUV measurements were made in 5 x 5 mm2 patches on zx- and zy-planes every 45º with respect to the z-axis (Figure 4.3a). Additionally, shear waves were generated in two different directions, shown in Figure 4.3b, in the tangential polarization the shear wave propagates in a direction perpendicular to blood vessels (y-axis in Figure 4.3b), and in the radial polarization the shear wave propagates in a direction parallel to blood vessel orientation (z-axis in Figure 4.3b). These SDUV measurements were made in one excised kidney (Kidney #8, refer to Table 4-1).

Figure 4.3: (a) Illustration of SDUV measurements every 45º respect to z-axis. (b) Illustration of shear wave propagation in two different directions. The blood vessels are running vertically (z-axis) in the kidney section shown. In the tangential direction (y-axis), the shear wave propagates in a direction perpendicular to blood vessels, and in the radial direction (z-axis) the shear wave propagates in a direction parallel to blood vessel orientation.

58 4.2.2.5 Time influence To evaluate the long-term variability of ex vivo kidney viscoelastic properties, five repeated shear wave dispersion measurements were made in a fixed 5 x 5 mm2 patch every 3 hours over 24 hours, starting 3 hours after sacrifice, in two kidneys (Kidney #5 and #6, refer to Table 4-1). During the course of the experiment, the kidneys were placed in saline solution at room temperature.

4.2.2.6 Formalin study Tissue stiffness can be increased by inducing collagen cross-links with aldehydes [165-169]. Changes in the material properties in the renal cortex when exposed to a chemical agent that changed the tissue structure and stiffness were explored. To test the level of contrast of SDUV for different tissue states, shear wave dispersion measurements were made in an excised kidney (Kidney #7, refer to Table 4-1) before and after immersion in 10% formaldehyde for 3 hours. Measurements were performed at 17 different locations, 5 x 5 mm2 patches in the renal cortex.

4.2.3 Statistical analysis Results are reported as mean ± standard deviation (SD). The number of samples, repetitions and size of regions of interest (ROI) were varied on the basis of the data and the degree of their scatter and reproducibility. Univariate analysis of variance (ANOVA) was used to test for statistically significant differences among variables for the different experiments. Because the kidney is modeled as a viscoelastic material, differences in shear wave speed between various excitation frequencies in one excised kidney (Kidney #1, refer to Table 4-1) were studied. To investigate renal cortex homogeneity, shear elastic modulus and viscosity among one region and between different regions in one kidney (Kidney #2, refer to Table 4-1) were compared. To study variations in both shear elastic modulus, G, and viscosity, η, as a function of time at room temperature two individual kidneys (Kidney #5 and #6, refer to Table 4-1) were studied for 24 hours. Additionally, shear elasticity of kidneys at specific time frames were compared. A paired t-test was used to investigate the level of contrast of SDUV for different tissue states in the formalin study. To study the anisotropy of the kidney, shear elastic modulus and viscosity of different angles

59 and different shear wave propagation directions were compared. Statistical significance for all tests was accepted for p ≤ 0.05.

Signal-to-noise ratio (SNR) was calculated to characterize how the real measurements were disturbed by noise. SNR was calculated as the ratio of mean to standard deviation of measurements.

4.3 Results 4.3.1 Linearity study Displacement amplitude estimates over 20 ms for four different excitation voltage amplitudes (3.0 V, 2.6 V, 2.1 V and 1.5 V) in one excised kidney (Kidney #1, refer to Table 4-1) were calculated by cross-spectrum methods [149] and are shown in Figure 4.4a. Tissue peak displacement as a function of voltage squared is shown in Figure 4.4b. The solid line is a linear fit to the experimental data. The coefficient of determination, R2, of the linear regression was 0.99.

The mean shear wave propagation speed in a 5 x 5 mm2 region as a function of frequency measured at four different excitation amplitudes is shown in Figure 4.5. The columns represent four different excitation voltage amplitudes (3.0 V, 2.6 V, 2.1 V and 1.5 V) in one excised kidney (Kidney #1, refer to Table 4-1).

4.3.2 SDUV repeatability Figure 4.6a shows SDUV repeatability when using two transducers. Shear wave propagation speed (mean ±SD) as a function of frequency was measured along the x-axis within the 5 x 5 mm2 ROI1 five repeated times (Kidney #1, refer to Table 4-1). Shear wave speed is significantly different at each frequency (p < 0.001). The solid line is the fit from Kelvin-Voigt model (Equation 3.3) that gives a shear elastic modulus G = 1.7 kPa and viscosity η = 1.8 Pa·s. The minimum SNR is 25 and 10 for the shear elastic modulus and viscosity, respectively. Shear wave speed dispersion fit had a Mean Square Error (MSE) of 0.004 m2/s2. Figure 4.6b illustrates SDUV repeatability when using the curved linear array transducer. Shear wave propagation speed (mean ±SD) as a function of frequency was measured along x-axis in 5 x 5 mm2 patch four repeated times (Kidney #8, refer to Table 4-1). Shear wave speed is significantly different at each frequency (p < 0.001). The solid line is the fit from Kelvin-Voigt model (Equation 3.3) that gives a shear elastic modulus G = 1.9 kPa and viscosity η = 1.1 Pa·s. The minimum SNR is 52 and 53 for both shear elastic modulus and viscosity, respectively. The shear wave speed dispersion fit had a MSE of 0.005 m2/s2.

Renal cortex shear elastic modulus and viscosity in a 5 x 5 mm2 patch from five repeated measurements of seven kidneys (Kidney #1-7, refer to Table 4-1) and four repeated measurements of one kidney (Kidney #8, refer to Table 4-1) are shown in Figure 4.7a and Figure 4.7b, respectively.

62 There is no statistically significant difference in shear elastic modulus among the 8 kidneys (p = 0.06). On the other hand, there is a statistically significant difference in viscosity among the 8 kidneys (p < 0.01). The minimum SNR is 6 and 8 for shear elastic modulus and viscosity, respectively.

4.3.3 Organ homogeneity Shear wave speed (mean ±SD) as a function of frequency of five ROI’s (5 x 5 mm2 patches) in one kidney (Kidney #2, refer to Table 4-1) is shown in Figure 4.8a. Shear wave speed is statistically different at each frequency regardless of the region (p < 0.001). The solid line is the fit from Kelvin-Voigt model (Equation 3.3) that gives G = 1.8 kPa and η = 1.9 Pa·s. The shear wave speed dispersion fit had a MSE of 0.003 m2/s2. Figure 4.8b and Figure 4.8c show shear elastic modulus and viscosity estimated by Kelvin-Voigt model (Equation 3.3) from five different regions and five repetitions, respectively. There is a statistically significant difference in shear elastic modulus and viscosity among the five regions (p < 0.001). The minimum SNR is 5 for shear elastic modulus and 6 for viscosity.

Figure 4.8: (a) Shear wave propagation speed (Mean ± SD) as a function of frequency, (b) shear elastic modulus and (c) viscosity box and whisker diagram of five ROI’s in one kidney (Kidney #2, refer to Table 4-1). The solid line is the fit from Kelvin-Voigt model (Equation 3.3). The box and whisker diagrams were made with five measurements on each individual region. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group.

Shear elastic modulus and viscosity (mean ±SD of four ROI’s) from four kidneys (Kidney #1-4, refer to Table 4-1) is summarized in Table 4-2. The minimum SNR is 5 for both the shear elastic modulus and viscosity, respectively.

64 Table 4-2: Shear elastic modulus and viscosity (Mean ± SD of four ROIs) from four kidneys.

Kidney 1 2 3 4

Shear elastic 1.80 ± 0.38 1.79 ± 0.14 2.09 ± 0.27 1.89 ± 0.06 modulus, kPa

Viscosity, Pa·s 1.87 ± 0.26 1.12 ± 0.22 2.08 ± 0.24 1.36 ± 0.22

Shear elastic modulus and viscosity estimated by Kelvin-Voigt model (Equation 3.3) from five repeated measurements in five small regions (five 1 x 5 mm2 regions of a 5 x 5 mm2 ROI along z-axis) of one kidney (Kidney #2, refer to Table 4-1) are shown in Figure 4.9a and Figure 4.9b, respectively. There is no statistically significant difference in shear elastic modulus (p = 0.3120) and viscosity (p = 0.7188) among the five small regions (p = 0.3120). The minimum SNR is 6 and 4 for shear elastic modulus and viscosity, respectively.

Figure 4.9: Box and whisker diagram for (a) shear elastic modulus and (b) viscosity in ROI2 every 1 x 5 mm2 along z-axis in one kidney (Kidney #2, refer to Table 4-1). The box and whisker diagrams were made with five repeated measurements on each individual region. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group.

4.3.4 Anisotropy study Shear elastic modulus and viscosity from four repeated measurements at eight different angles of scanning respect to z-axis (from 0º to 315º every 45º, refer to Figure 4.3a) are shown in Figure 4.10a and Figure 4.10b, respectively. There is

65 a statistically significant difference in shear elastic modulus and viscosity (p < 0.001) among the eight angles. The minimum SNR is 34 and 19 for shear elastic modulus and viscosity, respectively.

Figure 4.10: Box and whisker diagram for (a) shear elastic modulus and (b) viscosity in one kidney (Kidney #8, refer to Table 4-1) from 8 different angles of scanning respect to z-axis. The box and whisker diagrams were made with four repeated measurements at each individual angle. The bottom and top of each box represent the lower and upper quartiles, respectively. The horizontal line within the box is the median. The ends of the whiskers represent the minimum and maximum of each group.

Shear wave propagation speed (mean ± SD of four repeated measurements) as a function of frequency measured in a 5 x 5 mm2 patch for both tangential and radial excitation (Refer to Figure 4.3b) of one kidney (Kidney #8, refer to Table 4-1) is shown in Figure 4.11a. The shear wave speed dispersion fit had a MSE of 0.005 m2/s2 and 0.007 m2/s2, for tangential and radial excitation, respectively. Renal cortex shear elastic modulus and viscosity values measured in one kidney (Kidney #8, refer to Table 4-1) with shear waves propagating along the tangential direction and radial direction (refer to Figure 4.3b) are shown in Figure 4.11b and Figure 4.11c. Both shear elastic modulus and viscosity were relatively different when comparing tangential versus radial direction.

4.3.5 Time influence Shear elastic modulus and viscosity as a function of time after sacrifice from two kidneys (Kidneys #5-6, refer to Table 4-1) are shown in Figure 4.12a and Figure 4.12b. The different symbols represent mean ± standard deviation of four fixed 5 x 5 mm2 regions in each of the two kidneys. Continuous lines represent the trends of kidney #5 and trend of kidney #6 over time.

There is a statistically significant difference in shear elastic modulus in kidney #6 among the 9 time periods (p = 0.01). In contrast, there is no statistically

67 significant difference in shear elastic modulus on kidney #5 among the 8 time periods (p = 0.072). However, there is no significant difference in shear elastic modulus between kidneys #5, #6 after 3, 21 and 24 hours of sacrifice, (p = 0.405, p = 0.855, p = 0.243). Interestingly, there is a statistically significant difference in viscosity in kidneys #5 and #6 among the 8 and 9 time periods, respectively (p < 0.001).

Shear wave propagation speed (mean ± SD) as a function of frequency measured in 17 different locations (5 x 5 mm2 patches) before and after formalin immersion of one kidney (Kidney #7, refer to Table 4-1) is shown in Figure 4.13a. Shear elastic modulus and viscosity values in one kidney (Kidney #7, refer to Table 4-1) before and after formalin immersion are shown in Figure 4.13b and Figure 4.13c. Both shear elastic modulus and viscosity were significantly different when comparing normal versus formalin (p < 0.001) using a paired t-test.

Figure 4.13: (a) Shear wave propagation speed (mean ± SD) as a function of frequency measured in 17 different ROI’s (*) before and (Δ) after formalin immersion of one kidney (Kidney #7, refer to Table 4-1). (b) Shear elastic modulus and (c) viscosity values made in one kidney (Kidney #7, refer to Table 4-1) before and after formalin immersion. Both shear elastic modulus and viscosity were significantly different when comparing normal versus formalin (p < 0.001).

4.4 Discussion This study reports quantitative measurements of shear elastic modulus and viscosity in excised swine kidneys measured by SDUV over a number of different experimental variations. Figure 4.5 shows a rather constant shear wave speed as a function of frequency despite excitation amplitude variation. Moreover, the significant linear relationship between the tissue displacement and voltage squared in Figure 4.4a, agree with our assumption of proportionality between these variables.

69 Shear wave speeds shown in Figure 4.6a and Figure 4.6b are statistically significantly different at each frequency, which supports our assumption of viscoelasticity, which results in shear wave speed dispersion. Therefore, to estimate the viscoelastic properties of the kidney, a rheological model should be used. In this study, the dispersion data fit well with the use of the Kelvin- Voigt model over the studied frequency domain, mean square error (MSE) less than 0.007 m2/s2. Although Figure 4.6a shows higher variation of shear wave speed for high frequencies (350-500 Hz) compared to Figure 4.6b, the SNR using the two transducer setup was higher than 10 for both shear elastic modulus and viscosity. However, the error of the wave speed estimates is expected to increase at high frequencies because the displacement amplitude decreases [156]. Additionally, SNR was higher than 50 for both shear elastic modulus and viscosity measurements when using the curved array transducer, however, these measurements were made without any overlying tissue, so it is expected that when applied in vivo, acoustic radiation force and thereby shear wave motion will decrease leading to smaller values of SNR.

Kelvin-Voigt model (Equation 3.3) assumes a homogeneous material. Given that the kidney is inhomogeneous by visual inspection, this assumption may not be accurate. However, in this study, shear elastic modulus and viscosity were estimated in fairly small regions of interest, 5 x 5 mm2 regions. Furthermore, a detailed analysis of the 5 x 5 mm2 ROIs (refer to Figure 4.9) showed no statistically significant difference in shear elastic modulus and viscosity within the ROI, supporting the assumption of local homogeneity. The global inhomogeneity of kidney was studied by measuring SDUV in a single kidney in different ROIs. Not surprisingly, both shear elastic modulus and viscosity (refer to Figure 4.8) were statistically significantly different in five different regions on one kidney (Kidney #2, refer to Table 4-1), which suggests global inhomogeneity. The architecture of renal cortex blood vessels has been studied using microcomputed tomography (micro CT) in pig kidneys by Bentley, et al., the cortical microvasculature number and size vary among different regions in the renal cortex, which suggest that the renal cortex is inhomogeneous [170]. Similarly, our results suggest local homogeneity in 5 x 5 mm2 ROIs when using SDUV.

70 Another assumption of Kelvin-Voigt model (Equation 3.3) is tissue isotropy. The main function of the kidneys is to filter blood, therefore structures like blood vessels, tubules and collecting ducts are oriented in certain manner. These features bring the advantage of characterizing kidney anisotropic properties by measuring its diffusion properties with magnetic resonance diffusion weighted imaging (MR-DWI). Ries, et al., have studied human kidney diffusion isotropy, and there is fairly general anisotropic behavior in renal cortex [171]. Moreover, diffusion coefficients were highest in a superior-inferior direction compared to left-right direction respect to anatomical position. Tissue anisotropy has been studied with elasticity imaging mostly in skeletal and cardiac muscle [111, 162, 172], for instance, shear elastic modulus and viscosity of muscle is different across fibers and along fibers. Similarly, SDUV measurements of kidney mechanical properties by inducing shear waves with two directions indicate renal cortex anisotropy. Two values for shear elastic modulus and viscosity were found depending on shear wave propagation direction as shown in Figure 4.11. Interestingly, both shear elastic modulus and viscosity were relatively similar when the shear wave propagated along the x- and y-axes (Figure 4.10) but different along the z-axis (Figure 4.11).

When comparing renal cortex viscoelastic properties among 8 kidneys, shear elastic modulus was reasonably consistent (refer to Figure 4.7a), however, viscosity was rather different (refer to Figure 4.7b). This variability in viscosity may be attributed to the different times at which the experiments were done after the animal sacrifice (refer to Table 4-1). To test this hypothesis, the long- term time variability experiments showed a statistically significant difference in viscosity over 24 hours, which supports the previous hypothesis that viscosity may be sensitive to tissue changes over time after excision. Interestingly, there was a statistically significant difference in shear elastic modulus over 9 periods of time for one kidney, which could be attributed to the global inhomogeneities of renal cortex previously discussed.

Reactions of formaldehyde (FA) with proteins have been extensively studied. The most important of these is probably the formation of methylene bridges which cross-link polypeptides at reactive side groups [165]. It is well known that

71 aldehydes increase tissue stiffness. For instance, R. Van, et al., have studied how aldehydes affect the mechanical behavior of bovine pericardium [167]. Tensile tests were performed on fresh tissue, and after 0.5, 1, 2, 6, 24 h and 7 days of glutaraldehyde (GA) 0.5% treatment. The exposure to GA results in a significant increase in the stiffness of the tissue at low levels of stress. Moreover, the introduction of cross-links by GA causes resistance to the rearrangement of collagen in the direction of the applied load. A similar study by Sung, et al., in porcine pericardia, where free amino group content and tensile tests were performed after FA and GA exposure for 3 days, reported significant reductions in free amino groups content as compared to fresh ones [169]. This suggests that FA and GA were effective cross-linking agents. Tensile stresses of the FA and GA tissues were relatively grater than fresh ones, indicating that cross-linking of the amino groups within the biological tissue change the biological strength of tissues. Elasticity imaging techniques have been used to study aldehyde exposure effects in excised kidneys. Emelianov, et al., reported an increase in elasticity due to different tissue state was observed when GA was injected into an excised kidney [69]. Similarly, the level of contrast of SDUV for different tissue state was studied (Figure 4.13). Shear wave speed dispersion in kidney before and after immersion in 10% formalin clearly illustrate differences in both tissue moduli. Moreover, both shear elastic modulus and viscosity were statistically significantly different before and after immersion in 10% formalin, which agree with the literature.

Shear elastic modulus measurements presented in this study are rather similar to previous estimates in the literature. For instance, an MRE study in excised pig kidneys provided an estimate of approximately G = 2 kPa [ 81]. In vivo MRE and SDUV studies of kidney mechanical properties consequent to perfusion report a shear elastic modulus and viscosity of 3-4 kPa and of 3 Pa.s, respectively [84, 160, 173]. The in vitro shear elastic modulus, shown in Figures 1.7 through 1.10, are less than the MRE in vivo measurement at total occlusion. The renal tissue is comprised of residual blood volume at 100% occlusion, whereas the in vitro kidney is devoid of residual perfusion.

72 Finally, although this study demonstrates the feasibility of SDUV using a curved array transducer to study excised kidney, there may be some limitations when studying kidneys in vivo. For instance, endogenous motion in the kidney from pulsating blood vessels and gross patient motion may degrade results, however, in most cases these can be filtered out because they are low- frequency (< 10 Hz) and SDUV measurements are made quickly 0.1-0.2 seconds. Another limitation may be depth of kidney, the native kidney depth ranges from 45-75 mm [174], although shear waves from tangential excitation using a curved linear array can be excited and measured, optimization would have to be performed in terms of ultrasound frequency and signal processing techniques to obtain high quality echo data for motion tracking of the waves. Some of these aspects have been addressed in ongoing animal studies such as motion effects reported recently by Amador, et al. [173].

4.5 Conclusion Shearwave dispersion ultrasound vibrometry (SDUV) provides a fast, low cost, noninvasive tool to measure not only tissue shear elastic modulus but also tissue viscosity. This study shows the feasibility of SDUV to estimate both shear elastic modulus and viscosity of renal cortex in vitro with good precision using experimental configurations with two transducers and a curved linear array transducer. A number of experimental variables were varied to evaluate measurement linearity, and repeatability. Viscoelastic renal properties versus tissue inhomogeneity, tissue anisotropicity, time variability after organ excision, and structural changes after immersion in a cross-linking agent were evaluated. The measurement results of these tests provided insights that will be important for extending SDUV measurements of kidney to an in vivo setting.

73 Chapter 5

In vivo swine kidney viscoelasticity during acute gradual decrease in renal blood flow: pilot study

The content of this chapter is similar to C. Amador, M. Urban, R. Kinnick, S. Chen, and J. Greenleaf, "Viscoelastic measurements on perfused and non-perfused swine renal cortex in vivo," presented at the IEEE International Ultrasonics Symposium, San Diego, CA, USA, 2010.

5.1 Introduction Elasticity imaging is an emerging imaging modality that has the potential to assess kidney state in chronic kidney disease (CKD) by using the mechanical properties of kidney as the contrast mechanism in images. CKD encompasses a long-term decrease in renal function. Progressive CKD leads to the destruction of kidney parenchyma and ultimately to end-stage renal disease (renal failure), a condition that requires dialysis or kidney transplant [159].

Various functional measurements such as biomarkers, renal biopsies and noninvasive imaging methods are used to assess kidney function in management of CKD, however there is still a need for a fast, low cost noninvasive tool capable of assessing kidney function in the early stated of CKD. Several elasticity imaging methods, such as elastography, acoustic radiation force imaging (ARFI), transient elastography (TE), magnetic resonance elastography (MRE), supersonic shear imaging (SSI) and Shearwave dispersion ultrasound vibrometry (SDUV), have been used to study kidney mechanical properties and have demonstrated that elasticity of the

74 kidney changes with disease state and changes enough to be detected [68, 74, 79, 81, 82, 85, 175-177].

The kidney, like many other soft tissues has both elastic and viscous characteristics [113]. Measurements of the elastic component can be biased higher than the actual values if viscoelastic materials are treated as elastic materials [81, 161]. Therefore, to fully characterize the kidney, measurements of the elastic and viscous components of the tissue need to be measured. In current practice, elastography and ARFI are useful approaches, but do not provide a quantitative measure of tissue elastic moduli. TE and MRE are capable of quantifying tissue elastic moduli but not the viscous component. Supersonic shear imaging (SSI) can provide maps of elastic moduli and viscosity, but specialized hardware is necessary to implement this method. Shearwave dispersion ultrasound vibrometry (SDUV) is capable of providing quantitative measurements of tissue viscosity, in addition to elastic modulus. SDUV has been used to characterize swine kidney mechanical properties in vitro [155, 177].

The long-term goal of our research is early detection of renal fibrosis, which could provide critical prognostic information required to prevent progression to end-stage renal disease or the development of CKD. Although there are limited elasticity imaging studies regarding the mechanical properties of the healthy and diseased kidney, an in vivo MRE study suggests that healthy kidney shear elastic modulus decreases with acute decrease in renal blood flow and that in chronic renal arterial the decrease in renal blood flow offsets a likely increase in shear elastic modulus secondary to development of renal fibrosis [176]. SDUV potentially offers an in vivo tool to assess the physiological changes of the kidney and to monitor development of CKD.

The purpose of this study is therefore directed toward evaluating the feasibility of SDUV for in vivo measurements of viscoelasticity in healthy swine kidney. Moreover, in this study SDUV is used to measure kidney viscoelastic properties during acute gradual decrease of renal blood flow. For this purpose, shearwave dispersion was studied by exciting shear waves in the renal cortex with a mechanical actuator and with acoustic radiation force.

75 5.2 Materials and methods Animal experiments were reviewed and approved by the Mayo Clinic Institutional Animal Care and Use Committee. Five domestic female pigs were used in this study. For all studies, pigs were anesthetized (telazol 5mg/kg and xylazine 2mg/kg) and maintained with mechanical ventilation of 1-2% isoflurane in room air. An ear vein catheter was introduced for saline infusions (5mL/min). A catheter was placed in one carotid artery for monitoring mean arterial pressure (MAP). An ultrasonic Doppler flow meter (Transonic System, T206, probe 3RB429) was placed on the right renal artery for continuous monitoring of the renal blood flow (RBF). A pneumatic inflatable vascular occluder was placed on the right renal artery proximal to the Doppler flow meter.

5.2.1 Shearwave dispersion ultrasound vibrometry (SDUV) Shearwave Dispersion Ultrasound Vibrometry (SDUV) is a method that quantifies both tissue shear elasticity and viscosity by evaluating dispersion of shear wave propagation speed over a certain bandwidth [95, 111]. In this study, shear waves are excited by an external mechanical actuator and by acoustic radiation force.

5.2.1.1 Shear wave excitation with mechanical actuator Three animals were studied with this SDUV implementation. The right kidney was exteriorized through a small flank incision. An electromechanical actuator (V203, Ling Dynamic Systems Limited, Hertfordshire, UK) was placed in contact with the surface of the kidney to vibrate the kidney and create propagating shear waves. The electromechanical actuator was driven by a single frequency signal in the range of 100 Hz to 400 Hz by 50 Hz increments. This signal was amplified and applied to the electromechanical actuator. The motion was measured using a high-frame rate mode that acquired 7 A-lines every 0.9 mm at a frame rate of about 2500 frames per second (fps) using a Sonix RP ultrasound scanner equipped with a L14-5/38 linear array transducer (Ultrasonix Medical Corp. Richmond, BC, Canada). The electromechanical actuator was placed near one end of the transducer, Figure 5.1a. Ultrasound echoes were processed by the previously described cross-correlation method to estimate displacement [149]. A temporal Fourier transform (FFT) was

76 performed to the displacement estimates and phase gradients were taken from the FFT signal at the frequency of interest.

The shear wave speed at different frequencies is estimated from its phase measured at least at 2 locations separated by Δr along its traveling path:

c ()ω ω r ΔΔ= φ 5.1 sss s

where φ φ −=Δ φ is the phase gradient over the traveled distance Δr. To s 21 estimate viscoelastic properties from shear wave dispersion, a rheological model is required. The most common rheological models are the Kelvin - Voigt and the Maxwell model. The Kelvin - Voigt model has been shown to be appropriate for describing viscoelastic properties of tissue in the low frequency range (50-500 Hz) [130, 131] and it has been used to characterized in vitro swine kidney mechanical properties with SDUV [155, 177]. For a viscoelastic, homogenous, isotropic material, the Kelvin - Voigt model relates the shear wave propagation speed, cs, and the frequency of shear wave, ωs by [150]

2()G + ηω 222 ()ω = s c ss 5.2 ρ( ()++ ηω 222 ) GG s

where ρ, G and η are the density, shear elastic modulus and viscosity of the medium, respectively. The shear wave speed was then estimated with Equation 5.1 and shear wave speeds over 100 Hz and 400 HZ were fit by Equation 5.2 to solve for the shear elastic modulus and viscosity. Shear wave phase velocity was estimated at each excitation frequency over a region of interest (ROI), approximate 7.2 mm along x-axis and 5 mm along z-axis, in the renal cortex at baseline renal blood flow, 25%, 50%, 75% and 100% decrease in baseline renal blood flow.

5.2.1.2 Shear wave excitation with acoustic radiation force External mechanical excitation creates single frequency shear waves to characterize viscoelastic behavior using shear wave dispersion. A limitation of this type of excitation is that the modulation frequency has to be changed multiple times to evaluate dispersion over a significant bandwidth. To overcome this limitation, acoustic radiation force is used to generate shear waves over a certain bandwidth with a single impulse excitation.

SDUV has been implemented on a Verasonics V-1 system. Two animals were studied with this SDUV implementation. Figure 5.1b illustrates the setup used to do SDUV with a curved linear array transducer (C4-2, Philips Healthcare, Andover, MA). The Verasonics V-1 ultrasound system (Verasonics, Redmond, WA) is a programmable ultrasound research platform that has 128 independent transmit channels and 64 receive channels. The system is integrated around a software-based beamforming algorithm that performs a pixel-oriented processing algorithm. This algorithm facilitates conventional and high frame rate imaging.

78 The curved linear array transducer was partially located in the abdominal cavity through a small flank incision. A 3 MHz, 331 μs duration push beam was transmitted and focused in the renal cortex to generate shear waves in the medium. The shear wave propagation was measured with the same transducer with 2 kHz flash imaging and plane wave compounding imaging technique [133]. A set of 3 plane waves with different emission angles were transmitted at 6 kHz pulse repetition frequency (PRF). By coherently compounding each set of 3 plane waves, a compound image PRF of 2 kHz was produced. The push causes shear displacements outward the focal region in the +x and –x directions. The spatial resolution in x-direction and z-direction were 0.25 mm and 0.5 mm respectively. The field of view (FOV) was 40 mm in x-direction and 60 mm in z-direction. Local tissue displacement is estimated using 1-D autocorrelation between two compounded images [163]. Shear wave phase velocity was estimated by previously described two – dimensional Fourier transform method [158, 178]. A two-dimensional (2D) Fourier transform is performed to the displacement estimates:

+∞ +∞ ()= ()2π ()+− fntkmxi , fkH ∑∑ z , etxu mn=−∞ =−∞ 5.3

where uz(x,t) is the estimated displacement in z-axis, which is a function of distance along x-axis and time, k is the wave number and f is the temporal frequency.

The 2D-FFT analysis were used to estimate shear wave phase velocities as a function of frequency at baseline renal blood flow, 25%, 50%, 75% and 100% decrease in baseline renal blood flow.

5.3 Results Table 5-1 shows the characteristics of the experimental animals. All five animals had similar body weight.

79 Table 5-1: Characteristics of the experimental animals.

Animal Animal Animal Animal Animal

1 2 3 4 5

Weight (kg) 50.2 48.0 47.7 47.1 47.7

Mean Arterial Pressure (mmHg)* 87.2 ± 4.3 104.7 ± 4.1 93.7 ± 5.3 99.7 ± 5.0 70.0 ± 1.3

Pulse (beats/min)* 117.0 ± 5.0 102.0 ± 3.0 110.8 ± 1.9 72.6 ± 0.9 90.0 ± 0.5 *Mean ± standard deviation of periodic measurements

A B-scan coronal plane image (cross-section) acquired with the Verasonics V1 ultrasound system equipped with a curved array transducer is illustrated in Figure 5.1.

Figure 5.2: B-scan coronal plane image (cross-section) of the kidney with Verasonics V1 system equipped with linear curved array transducer at baseline of renal blood flow.

The estimated tissue displacement from cross-correlation method [149] generated by 100 Hz harmonic excitation at baseline of renal blood flow is illustrated in Figure 5.3a. The magnitude of the temporal Fourier transform of the estimated displacement from Figure 5.3a is illustrated in Figure 5.3b. The estimated shear wave phase gradient estimated using Fourier transform analysis at 100 Hz, 200 Hz, 300 Hz and 400 Hz excitation for baseline renal blood flow is shown in Figure 5.3c. The mean shear wave phase velocity estimated from Equation 5.1 as a function of frequency for baseline renal blood flow is illustrated in Figure 5.3d.

Shear wave dispersion (shear wave phase velocity as a function of frequency) from three repeated measurements using mechanical excitation for animals 1, 2 and 3 is shown in Figure 5.4. The color bars represent baseline renal blood flow, 25, 50, 75 and 100% decrease in baseline renal blood flow respectively.

Figure 5.5a illustrates velocity estimates, from 1D autocorrelation method [163], generated by acoustic radiation force toneburst applied at baseline of renal blood flow. The push at x =0 causes shear motion outward the focal region in the +x and –x directions. Velocity estimates as a function of time over 7.4 mm to 9.5 mm in +x direction are shown in Figure 5.5b. The wave number – frequency diagram from 2D Fourier transform of tissue velocity estimates outward the focal region in the +x direction is shown in Figure 5.5c. Shear wave phase velocity as a function of frequency estimated by 2D-FFT method [178] for baseline renal blood flow is illustrated in Figure 5.5d.

One of the advantages of the 2D Fourier transform method is the high resolution in frequency as illustrated in Figure 5.5d. Shear wave phase velocity, for frequencies from 100 Hz and 400 Hz by 50 Hz increments, from three repeated measurements using acoustic radiation force toneburst excitation for animals 4 and 5 is shown in Figure 5.6. The color bars represent baseline renal blood flow, 25, 50, 75 and 100% decrease in baseline renal blood flow respectively.

Figure 5.6: Shear wave dispersion from three repeated measurements for (a) animal 4 and (b) animal 5. The color bars represent the baseline renal blood flow, 25, 50, 75 and 100% of baseline renal blood flow.

During acute renal blood flow reduction, a decrease in shear phase velocity at low frequency (100 Hz) was observed in the group of animals. On the other hand, no clear pattern was observed at high frequency (400 Hz), Figure 5.7.

Figure 5.7: Shear wave phase velocity (mean ± SEM of 5 animals) as a function of acute gradual decrease of renal blood flow at 100 Hz and 400 Hz excitation.

84 Shear elastic modulus and viscosity of the group of five animals (mean ± standard error of the mean) as a function of acute gradual decrease in renal blood flow is illustrated in Figure 5.8.

B-scan coronal plane images (cross-section) acquired with the Verasonics V1 ultrasound system equipped with a curved array transducer at base line renal blood flow and 100% decrease in baseline renal blood flow in one kidney is illustrated in Figure 5.9.

Figure 5.10a illustrate the cortical thickness (geometric distance between red lines shown in Figure 5.9) measured from B-scan images over 40 mm in x

85 direction. Cortical thickness as a function of acute gradual decrease in renal blood flow is illustrated in Figure 5.10b.

5.4 Discussion This study reports in vivo quantitative measurements of shear elastic modulus and viscosity of healthy swine kidneys measured by SDUV using two experimental configurations, a mechanical actuator and acoustic radiation force. Moreover, swine kidney shear elastic modulus and viscosity were measured during acute gradual decrease of renal blood flow. Currently, there is not gold standard for in vivo kidney viscoelasticity measurements. The in vivo kidney, shear elastic modulus as a function of decrease renal blood flow, results are similar to those reported in another in vivo study using MRE [176]: the shear elastic modulus is affected by renal blood flow. The kidney viscosity did not change as a function of renal blood flow. Because viscosity is a relatively unexplored parameter, there remains a question about how accurate the viscosity estimates are. In this study, we did not evaluate the precision of SDUV for in vivo measurements; therefore it is difficult to separate method variability to other parameter such as tissue heterogeneity, local blood pressure and blood volume, which unfortunately were also not measured.

86 This previous MRE study does not consider tissue viscosity. If viscosity is not taken into account, measurements of shear stiffness can be biased higher than their actual values [81, 161]. Tissue viscosity is an understudied quantity but it may provide important information about tissue state. For instance, shear wave phase velocity decreased as a function of gradual decrease of blood flow at low frequency (100 Hz). This decrease in shear wave velocity at low frequency (100Hz) was consistent among the group of 5 animals. On the other hand, there was a not a clear pattern in shear wave phase velocity as a function of decrease renal blood flow at high frequency (400 Hz), refer to Figure 5.4, Figure 5.5 and Figure 5.7. In a report by Schmeling, et al. the viscosity in the left ventricular wall of the heart during the diastolic phase of the cardiac cycle increased during occlusion of the left anterior descending coronary artery in animals that were reperfused and not reperfused [99]. During reperfusion, the viscosity returned to baseline in animals that recovered from the stunning while the increase in viscosity persisted throughout reperfusion in animals that did not recover. Viscosity was shown to increase in both ischemic and nonischemic regions of the ventricular wall. Viscosity may be an indicator of tissue damage (for instance, ischemia or acute kidney injury). A more comprehensive study is needed to evaluate such hypothesis specifically. The high variability in the viscosity estimates for this in vivo SDUV kidney study could be associated to errors in phase estimates at high frequencies, which are expected because displacement amplitude is decrease at high frequencies (shear wave attenuate faster). Urban et al. evaluated different parameters that affect the performance of SDUV [156]. Although the errors associated with phase estimate are expected to be small, these errors affect shear wave phase velocity estimates.

Shear wave dispersion (shear wave phase velocity as a function of frequency) shown in Figure 5.3d and Figure 5.5d was consistent between shear waves generated by mechanical actuator at a single frequency (pure-tone shear waves) and shear waves generated by acoustic radiation force with an impulse (multi-tone shear waves). Although shear wave phase velocities were consistent between the two approaches used for shear wave excitation, we did not directly compared the accuracy of the two approaches in this in vivo study. A comparison between multi-tone approach and single-tone approach in gelatin

87 phantoms was previously reported by Chen et al. [111] and there were not significant differences between shear elastic modulus and viscosity estimations.

To estimate viscoelastic properties, a model needs to be fit to the shear wave dispersion. In this study, the Kelvin-Voigt model was used to fit shear wave dispersion to estimate shear elastic modulus and viscosity. The Kelvin-Voigt model has been previously used to study in vitro kidney viscoelastic properties [155, 177].Although this rheological model assumes homogeneous and isotropic material, the in vitro study shows a fairly good fit to kidney shear wave dispersion. Moreover, the errors in shear elastic moduli and viscosity, estimated by Kelvin-Voigt model, associated with kidney heterogeneity and other parameters were reported. The variations in shear elastic modulus and viscosity at each renal blood flow period for the group of 5 animals (refer to Figure 5.8) could be attributed to the small number of shear wave phase velocity measurements for the mechanical actuator method (single-tone approach), refer to Figure 5.3d. To illustrate this, when fitting the Kelvin-Voigt model to 7 measurements of shear wave speed (e.g. 100 Hz to 400 Hz by 50 Hz increments in Figure 5.5), the shear elastic modulus is 3.47 kPa and viscosity is 1.79 Pa.s, compared to 3.83 kPa and 1.75 Pa.s from fitting 30 shear wave speed measuremenst. Because SDUV had been implemented in the Verasonics V1 ultrasound system, SDUV measurements are acquired with high temporal and spatial resolution, by means of shear wave detection, and as a consequence it allows the used of the two-dimensional Fourier transform method, which then estimates shear wave phase velocity over a large bandwidth with high resolution. Although the accuracy of shear wave phase velocity estimates from 2DFFT method was not evaluated in this study, the 2DFFT method is a robust method that is commonly used for seismic applications [178] and it has been used to study shear wave propagation modes in arteries [158].

The shear elastic modulus was highest at baseline renal blood flow, once the renal blood flow was decreased by 25% of baseline, the shear elastic moduli decreased by larger proportion when compared to 50, 75, and 100% decreased of baseline renal blood flow, refer to Figure 5.8a. It has been reported by

88 Rognant et al. [179] that a 25% decrease of renal blood flow from baseline is equivalent to approximately 70% acute renal artery stenosis, therefore the decrease in renal blood flow from 25% to 100% of baseline would be equivalent to relatively small increments in renal artery stenosis, which may be the reason why the shear elastic moduli did not change much during 25, 50, 75 and 100% decreased in baseline renal blood flow

Noninvasive measurements of kidney viscoelastic properties have the potential to significantly improve the management of acute and chronic kidney disease and limit the need for invasive procedures. However, since the kidney is a highly perfused organ, it is important to study the hemodynamic effects in renal viscoelasticity independent of renal disease. In this study, only renal blood flow was monitored, therefore, future studies should assess other parameters such as blood pressure, blood volume, urine volume, perfusion pressure, glomerular filtration rate, diuresis, etc.

A potential application for quantifying renal elasticity and viscosity using SDUV is to monitor kidney transplantation. Close monitoring of these patients after transplantation is needed to asses graft disfunction. In a study by Sadowski, et al. a significantly decreased renal blood flow in allografts suggests biopsy- proven acute rejection [59]. The B-mode images at baseline and 100% decrease of baseline renal blood flow illustrate a change in renal volume, refer to Figure 5.10a. Moreover, there is a relatively large difference between cortical thickness at baseline and at a 100% decrease of baseline renal blood flow, Figure 5.10b. These are images of just one section of the kidney; therefore, it is difficult to state that indeed the kidney volume is changing, especially if urine and blood volume were not measured. Nonetheless, the in vivo MRE studied reported statistically significant change in kidney volume from baseline compared to 100% decrease in baseline blood flow [176]. SDUV would have an ideal application as “virtual biopsy” of renal elastic modulus using ultrasound to monitor kidney transplantation.

5.5 Conclusion Shearwave dispersion ultrasound vibrometry provides a fast, low cost noninvasive tool to measure not only tissue elasticity but tissue viscosity. It has

89 the potential to monitor progression of disease with less risk, potential sampling error and cost inherent to biopsies. In this study we showed that shear elastic moduli is affected by renal blood flow. Moreover, the data from this study indicates that other variables such as local blood flow, pressure, and volume as well as method accuracy need to be measured to illustrate the relationship between shear elasticity and viscosity with acute and chronic kidney processes. Nonetheless, the ability of SDUV to detect changes in elastic moduli related to blood flow represent a novel method to measure kidney hypoperfusion.

90 Chapter 6

Tissue mimicking phantoms loss tangent and complex modulus estimated by acoustic radiation force creep

6.1 Introduction Tissue mechanical properties such as elasticity are linked to tissue pathology state [66, 77, 78, 80, 101, 103, 104, 136]. Shear wave propagation methods have been proposed to quantify tissue mechanical properties [66, 78, 80, 109]. In these methods, shear waves that result from a transient (impulsive or short tone burst) excitation of tissue propagate only a few millimeters, as a result of tissue absorption and attenuation, therefore boundary condition problems are overcome, allowing us to assume that the shear waves propagate as if in an infinite medium. Shear waves are usually generated by external mechanical vibration or by acoustic radiation force from a focused ultrasound beam [74, 80]. The advantage of using acoustic radiation force is the fact that anywhere an ultrasound system can focus; a pushing pulse of radiation force can be applied.

For a viscoelastic, homogenous, isotropic material, the shear wave speed, cs,

and shear wave attenuation, αs, are related to the complex shear modulus,

G*(ω) = Gs(ω) + iGl(ω), by [129]:

2()+ GG 22 ()ω = ls cs ρ( ++ 22 ) 6.1 s GGG ls

91 ()ωρ 2 ( 22 −+ GGG ) ()ωα = sls s ()+ 22 6.2 2 GG ls where ρ is the density of the medium, ω is the angular frequency (2πf, f is the frequency), Gs is the storage or elastic moduli and Gl is the loss or viscous moduli. Quantitative mechanical properties can be measured in a model independent manner if both shear wave speed and attenuation are known. However, measuring shear wave speed attenuation is challenging in the field of elasticity imaging. Currently, only shear wave speed is measured and rheological models, such as Kelvin-Voigt, Maxwell and Standard linear solid, are used to solve for shear viscoelastic complex modulus.

Acoustic radiation force has been used to study quasi-static viscoelastic properties of tissue during creep and relaxation conditions. Tissue creep response to an applied step-force by means of acoustic radiation force has been shown in several studies [74, 180-182]. Mauldin et al. have reported a method to estimate tissue viscoelastic properties by monitoring the steady-state excitation and recovery of tissues using acoustic radiation force imaging and shear wave elasticity imaging. This method, called monitored steady-state excitation and recovery (MSSER) imaging, is an noninvasive radiation force- based method that estimates viscoelastic parameters by fitting rheological models, Kelvin-Voigt and Standard liner solid model, to the experimental creep strain response. However, as in shear wave propagation methods, a rheological model needs to be fit to the MSSER experimental data to solve for viscoelastic parameters.

Current elasticity imaging techniques are useful to indentify tissue mechanical properties, however to quantify these properties a rheological model must be used. This chapter presents a method to quantify viscoelastic properties in a model-independent way by estimating complex elastic modulus from time- dependant creep response induced by acoustic radiation force. The creep response is generated as described in MSSER imaging method and the viscoelastic parameters, complex elastic modulus and loss tangent, are estimated by using a formula that converts time-domain creep compliance to frequency domain complex modulus developed by Evans et al. [135] then

92 shear wave dispersion ultrasound vibrometry is used to calibrate the complex modulus so that knowledge of the applied radiation force magnitude is not necessary. Experimental data are obtained in homogeneous tissue mimicking phantoms.

6.2 Theory 6.2.1 Complex modulus spectrum from creep compliance Transient characteristics of viscoelastic materials are known as creep and stress relaxation. Creep is a slow, progressive deformation of a material under constant stress. The ratio between the strain response, ε(t), and the applied

constant stress, σ0, is called the creep compliance, J(t). By using Boltzmann superposition principle, which states that the sum of the strain outputs resulting from each component of the stress input is the same as the strain output resulting from the combined stress input, the stress output under variable stress, σ(t), is [112]:

t ∂ ()ξσ ε () (tJt −= ξ ) dξ ∫ ∂ξ 6.3 0

where ε is strain, σ is stress, J is creep compliance and [] ∂⋅∂ ξ represents first derivative respect to the independent variable ξ . Equation 6.3 is known as the integral representation of viscoelastic constitutive equations [112] and illustrates how the complex modulus, E*(ω), is related to the time-domain creep compliance, J(t), by a convolution. This relationship becomes much clear (Equation 6.6) when using the Fourier transform convolution (Equation 6.4, refer to A1) and derivative (Equation 6.5, refer to A1) properties in Equation 6.3

∂σ () []ε ()= []() ⎡ t ⎤ FTtJFTtFT ⎥ ⎣⎢ ∂t ⎦ 6.4 []ε ()= ω []() []σ ()tFTtJFTitFT 6.5

[]σ ()tFT 1 E * ()ω = = []() ωε []()tJFTitFT 6.6

93 where FT[.] represents Fourier transform. Because creep compliance, J(t), is a function that grows with increasing time, its Fourier transform is not a convergent integral. Recently, Evans et al. have reported the analytic solution of Equation 6.6 by taking advantage of the properties of Fourier transform [135]. Briefly, the second derivative of the creep compliance vanishes with time, therefore its Fourier transform exists. The time-creep compliance to complex modulus conversion formula described by Evans et al. is [135]:

iω E * ()ω = = :1, Nn − ω ()Nti ⎡ − ω () ()()− JJ (01 ) e ⎤ 6.7 ω () ()10 −+ eJi ti 1 + ... ⎢ () η ⎥ ⎢ t 1 ⎥ N ⎢ ⎛ () (nJnJ −− 1 )⎞ ω ()−−− ω () ⎥ + ⎜ ⎟()nti 1 − ee nti ⎢ ∑⎜ () (−− )⎟ ⎥ ⎣⎢ n=2 ⎝ ntnt 1 ⎠ ⎦⎥ where J(0) and η are the compliance at n = 0 and the steady-state viscosity. J(0) is estimated by extrapolation of the compliance function to t Æ 0. Similarly, η is estimated by extrapolation of compliance function to t Æ ∞. The frequency range depends on the resolution (the time of the first data point, t(1)) and duration (the time of the last data point, t(N)) of the data set. The advantage of using Equation 6.6 to convert time-dependent compliance, J(t), to complex modulus, E*(ω), is the fact that no fitting of theoretical models is required. Thus the moduli can be recovered for a range of frequencies without a model.

6.2.2 Displacement and creep compliance relation

Acoustic radiation force can be used to apply a step-stress input, σ0, that causes creep in a viscoelastic material [74, 180-182]. However, the actual applied force is generally unknown; as a consequence, the magnitude of the applied stress is also unknown. In addition, ultrasound motion detection applications usually estimate displacement responses instead of strain response. Assuming that the material is linear, the creep compliance, J(t), is linearly proportional to displacement, u(t):

()β ⋅= ()tutJ 6.8

where β is a proportionality constant that relates the magnitude of the step-

stress, σ0, and the length of a infinitesimal cube, L. By combining Equation 6.6

94 and Equation 6.8, the complex modulus, E*(ω), can be extracted from the displacement, u(t), relative to the constant β:

1 E * ()ω = ωβ ()tuFTi ][ 6.9 If we called the extracted complex modulus, C*(ω), it can be written in a form where it is relative to the complex modulus, E*(ω), by the constant β:

* ()βω (+= ) 6.10 C iEE ls

where Es and El are the real and imaginary parts of the complex modulus E*(ω).

Es is associated with energy storage and release during periodic deformation,

therefore called the elastic or storage modulus [112]. On the other hand, El is associated with the dissipation of energy that is transformed into heat, and is therefore called the viscous or loss modulus [112].

Because the magnitude of the acoustic radiation force is proportional to absorption coefficient of the media, α, and the temporal average intensity of the acoustic beam at a given spatial location, I [164], in a homogenous material, the magnitude of the extracted complex modulus C*(ω) will vary as a function of material absorption and acoustic beam intensity, therefore, the extracted complex modulus C*(ω) would not be a very useful measure. To overcome this problem, a widely used property of viscoelastic materials called loss tangent or tan(δ), defined as the ratio between the loss modulus and the storage modulus, is used [112]:

C β ()E E tan()δ l l === l β () 6.11 Cs Es Es

where Cs and Cl are the real and imaginary part of the extracted complex modulus C*(ω). The loss tangent or tan(δ) is associated with the damping capacity of viscoelastic material [112].

6.2.3 Complex modulus calibration with shear wave dispersion The wavenumber, k, and the shear elastic modulus, G, are linked through the shear wave propagation equation. In an elastic medium, they are related by

95 ω 2 G = ρ k 2 6.12 where ρ is density of the medium and ω the angular frequency. In the case of linear viscoelastic medium the wave number, k, and shear elastic modulus, G, * * are complex, written as k = kr – iki and G (ω)=Gs+iGl [127]. Then for a viscoelastic medium Equation 6.12 can be written as [128]:

− kk 22 G ()ω = ρω 2 ir s ()+ 22 6.13 kk ir

kk G ()ω −= 2ρω 2 ir l ()+ 22 6.14 kk ir

where ρ is density, kr is the real part of the wave number (defined as kr = ω/cs, where cs is the shear wave speed), ki is the imaginary part of the wave number

(defined as ki = αs, where αs is shear wave attenuation), Gs is the storage shear modulus or shear elastic modulus and Gl is the loss shear modulus or shear viscous modulus. The loss tangent or tan(δ) written in terms of the complex wave number is [128]:

2 kk tan()δ = ir − 22 6.15 kk ir

If both tan(δ) and kr are known, the negative root for ki in Equation 6.15 is:

⎡ 2 ⎤ ⎛ 1 ⎞ ⎛ ⎛ 1 ⎞ ⎞ = ⎢ ⎜ −− ⎟⎥ 6.16 kk ri ⎜ ⎟ 1 ⎜ ⎟ ⎢⎝ tan()δ ⎠ ⎜ ⎝ tan()δ ⎠ ⎟⎥ ⎣ ⎝ ⎠⎦

Finally, by knowing kr and ki, the shear storage and loss moduli are obtained from Equation 6.13 and Equation 6.14.

6.3 Methods 6.3.1 Acoustic radiation force creep A Verasonics V-1 ultrasound system (Verasonics, Redmond, WA) equipped with a L7-4 linear array transducer was used in all experiments. Similar to monitored steady-state excitation and recovery (MSSER) radiation force

96 imaging previously described by Mauldin et al. [182], two types of ultrasound beams are used. High intensity pushing beams are interspersed with conventional intensity tracking beams during the creep period. The push- tracking beams mimic a temporal step-force while creep displacements are tracked through the creep period. Additionally, two reference tracking beams are used before the creep period and additional tracking beams followed force cessation. Figure 6.1 illustrates the beam sequence.

6.3.2 Shear wave dispersion ultrasound vibrometry Shearwave Dispersion Ultrasound Vibrometry (SDUV) is a method that quantifies both tissue shear elasticity and viscosity by evaluating dispersion of shear wave propagation speed over a certain bandwidth [95, 111]. The Verasonics V-1 ultrasound system (Verasonics, Redmond, WA) equipped with a L7-4 linear array transducer was used to generate shear waves with acoustic radiation force and capture shear wave propagation with flash imaging. For a complete description of the method, see [111] and [95].

6.4 Simulation and experiment 6.4.1 Simulation The purpose of the simulations was to evaluate the creep compliance to complex modulus conversion formula (Equation 6.7). Creep compliance data were simulated by using a combination of viscoelastic parameters in the Kelvin- Voigt and standard linear solid models, Figure 6.2.

Equation 6.17 and Equation 6.18 describe the Kelvin-Voigt model creep compliance, JKV(t), and Standard linear solid model creep compliance, JSLS(t), under step-stress input, σ0 [112]:

() 1 ()−= −Et /η KV tJ 1 e E 6.17

11 − η ()−+= 2tE / SLS tJ )( 1 e EE 21 6.18 where E, E1 and E2 are the elastic elements properties as Young Modulus and

η is viscous element property as viscosity. The complex modulus, E*(ω) = Es(ω)

+ iEl(ω), for the Kelvin-Voigt and Standard linear solid models are described in Equation 6.19, 6.20, 6.21 and 6.22, [112].

= 6.19 ,KVs EE

= ωη 6.20 E ,KVl

2 2 ++ EEEEE ωη 22 = 21 12 2 E ,SLSs ()2 ++ ωη 22 6.21 EE 21 E 2ηω = 2 E ,SLSl ()2 ++ ωη 22 6.22 EE 21

98 where ω is the angular frequency. For a given combination of E and η or E1, E2 and η, for the Kelvin-Voigt or Standard liner solid model, creep compliance and complex modulus were calculated.

Once the creep compliance response was generated, the conversion formula * ()ω (Equation 6.7) was used to estimate the complex modulus, Eestimated , from the simulated creep compliance (Equation 6.17 and Equation 6.18). The conversion formula results were compared to the theoretical complex modulus, * ()ω E ltheoretica , described in Equation 6.19, 6.20, 6.21 and 6.22, by calculating the

* ()ω += 22 magnitude of the complex modulus, EEE ls , and computing the

normalized mean absolute error (nMAE), between the magnitude of the * ()ω theoretical complex modulus, E ltheoretica , and the magnitude of the complex

* ()ω modulus recovered from the conversion formula, Eestimated . The normalized

mean absolute error is defined as:

⎛ * ()ω − * ()ω ⎞ ⎜ Eestimated E ltheoretica ⎟ nMAE = mean 6.23 ⎜ E * ()ω ⎟ ⎝ ltheoretica ⎠ Additionally, these simulations were used to illustrated the concept of tan(δ). Conversion formula was applied to both creep compliance and creep strain. All simulations were performed in MATLAB (The MathWorks, Inc., Natick, MA).

6.4.2 Experiment Two computerize imaging reference systems (CIRS) elasticity phantoms (CIRS 1 and CIRS 3, E1270, CIRS Norfolk, VA) were used in this study. The speed and attenuation of sound in both phantoms were similar, 1538.1 m/s and 0.42 dB/cm-MHz, 1539 m/s and 0.43 dB/cm-MHz, respectively.

6.4.2.1 Acoustic radiation force creep The pulse repetition frequency (PRF) for both pushing and tracking pulses was 6.25 kHz. The total duration of the creep period or pushing sequences, including the intermittent tracking beams, was 10 ms and the total acquisition time was 20 ms. The magnitude of the mimicked temporal step-force was

99 varied by increasing the length of the pushing beams. The pushing beam intensity was set at 8 cycles (1.6 μs) and 16 cycles (3.2 μs), the tracking beam intensity was set at 2 cycles (0.4 μs). Both pushing and tracking beams were focused at an axial distance of 20 mm with an F/1.0 focal configuration. The acoustic radiation force creep sequence was used in 5 different regions of the phantoms, and 5 repeated measurements were acquired at each region. The transducer was manually translated to the 5 different locations. These 5 different locations were randomly selected. A 2D autocorrelation method was used to calculate axial displacements.

6.4.2.2 Shearwave Dispersion Ultrasound Vibrometry A 5 MHz, 331 μs duration push beam was transmitted and focused at 20 mm to generate shear waves in the medium. The shear wave propagation was measured with the same transducer with plane wave compounding imaging technique [133]. A set of 5 plane waves with different emission angles were transmitted at 12.5 kHz pulse repetition frequency (PRF). By coherently compounding each set of 5 plane waves, a compound image PRF of 2.5 kHz was produced. The spatial resolution in x-direction and z-direction were 0.5 mm and 0.5 mm respectively. Displacement response is estimated using 2-D autocorrelation between two images [163]. Shear wave phase velocity was estimated by previously described two – dimensional Fourier transform method [158, 178]. The Kelvin-Voigt model is fit to shear wave dispersion to calculate shear complex modulus which then is compared to the independent-model complex modulus.

6.5 Results 6.5.1 Simulations The creep compliance responses from Kelvin-Voigt and standard linear solid models are shown in Figure 6.3. The elastic modulus, E, was fixed at 9 kPa, while viscosity, η, was set at 10 Pa.s (blue and continuous curve) and 100 Pa.s (green and continuous curve with *). Additionally, two different time vectors

were used to simulate creep compliance response, t1 = 0.001 s and 0.0001 s with 1 kHz (Figure 6.3a and Figure 6.3d) and 10 kHz (Figure 6.3b and Figure

6.3d) sampling frequency, Fs.

100

Figure 6.4 shows the estimated complex modulus computed from the conversion formula (Equation 6.7) to the simulated Kelvin-Voigt model creep compliance curves shown in Figure 6.3a and Figure 6.3b.

101

Figure 6.5 shows the estimated complex modulus by applying the conversion formula (Equation 6.7) to the simulated standard linear solid model creep compliance curves shown in Figure 6.3c and Figure 6.3d.

102

The viscoelastic parameters used to simulated the Kelvin-Voigt model creep compliance curves shown in Figure 6.3a and Figure 6.3b are summarize in Table 6-1 as well as the normalized mean absolute error (nMAE) calculated from the magnitude of the estimated complex modulus and the magnitude of the theoretical complex modulus shown in Figure 6.4, as described in Equation 6.23.

103 Table 6-1: Viscoelastic parameters used to simulate Kelvin-Voigt model creep compliance

E (Pa) η (Pa.s) t1 (s) tN (s) Fs (Hz) nMAE 9000 100 0.001 0.1 1000 0.0092 9000 10 0.001 0.1 1000 0.0313 9000 100 0.0001 0.1 10000 0.0003 9000 10 0.0001 0.1 10000 0.0001

The viscoelastic parameters used to simulated the standard linear solid model creep compliance curves shown in Figure 6.3c and Figure 6.3d are summarize in Table 6-2 as well as the normalized mean absolute error (nMAE) calculated from the magnitude of the estimated complex modulus and the magnitude of the theoretical complex modulus shown in Figure 6.5, as described in Equation 6.23.

Table 6-2: Viscoelastic parameters used to simulate Standard linear solid model creep compliance

E1 (Pa) E2 (Pa) η (Pa.s) t1 (s) tN (s) Fs (Hz) nMAE 9000 9000 100 0.001 0.1 1000 0.00006 9000 9000 10 0.001 0.1 1000 0.0058 9000 9000 100 0.0001 0.1 10000 0.00002 9000 9000 10 0.0001 0.1 10000 0.00001

Figure 6.6a and Figure 6.6b illustrates the Kelvin-Voigt model creep strain and compliance response to 1 kPa and 3 kPa step-stress input, the elastic modulus E and viscosity η were fixed at 9 kPa and 100 Pa.s. The conversion formula described in Equation 6.7, was used to estimate the complex modulus from creep strain response and creep compliance response, Figure 6.6c and Figure 6.6d. In this case, the extracted modulus from creep strain, C*(ω), is proportional to the extracted modulus from creep compliance, E*(ω), by a constant β which is related the applied step-stress magnitude. The tan(δ) or ratio between the storage modulus and loss modulus, from the extracted modulus C*(ω) and E*(ω) are shown in Figure 6.6e and Figure 6.6f.

104

Figure 6.6: Kelvin-Voigt model (a) creep strain response and (b) creep compliance response to 1 kPa (*) and 3 kPa (o) step-stress input. Estimated complex modulus (c) C*(ω), from creep strain, and (d) E*(ω), from creep compliance response to 1k Pa and 3 kPa step-stress input. Tan(δ) from estimated complex modulus using (e) creep strain and (f) creep compliance response to 1k Pa and 3 kPa step- stress input.

105 Kelvin-Voigt model tan(δ) for fixed elastic modulus and different viscosities and fixed viscosities and different elastic modulus are shown in Figure 6.7.

Figure 6.8a and Figure 6.8b illustrates the standard linear solid model creep strain and compliance response to 1 kPa and 3 kPa step-stress input, the

elastic modulus E1, E2 and viscosity η were fixed at 9 kPa and 100 Pa.s. The conversion formula described in Equation 6.7, was used to estimate the complex modulus from creep strain response and creep compliance response, Figure 6.8c and Figure 6.8d. In this case, the extracted modulus from creep strain, C*(ω), is proportional to the extracted modulus from creep compliance, E*(ω), by a constant β which is related the applied step-stress magnitude. The tan(δ) or ratio between the storage modulus and loss modulus, from the extracted modulus C*(ω) and E*(ω) are shown in Figure 6.8e and Figure 6.8f.

106

107 Standard linear solid model tan(δ) for fixed elastic modulus and different viscosities and fixed viscosities and different elastic modulus are shown in Figure 6.9.

Figure 6.9: Standard linear solid model tan(δ) for(a) fixed η = 100 Pa.s and elastic modulus of 6 kPa (- ), 9 kPa (*) and 12 kPa (o), (b) fixed E = 9 kPa and viscosity of 20 Pa.s (-), 40 Pa.s (*) and 60 Pa.s (o).

6.5.2 Experiments The mean (average of 5 repeated measurements) creep displacement

response, estimated storage (Cs), loss modulus (Cl) and loss tangent (tan(δ)) from a 1.6 μs and 3.2 μs push duration in CIRS 1 phantom are shown in Figure 6.10. The dashed lines represent the standard deviation of the five repeated measurements.

108

Figure 6.11 shows the mean (average of 5 repeated measurements) creep displacement response, estimated storage (Cs), loss modulus (Cl) and loss tangent (tan(δ)) from a 1.6 μs and 3.2 μs push duration in CIRS 3 phantom. The dashed lines represent the standard deviation of the five repeated measurements.

109

Figure 6.11: CIRS 3 phantom (a) mean creep displacement, (b) estimated storage moduli, (c) loss moduli and (d) loss tangent of a 1.6 μs (o) and 3.2 μs (*) push duration. Average of 5 repeated measurements over a window of 3 mm in axial direction and 1 mm in lateral direction. The dashed lines represent the standard deviation of 5 repeated measurements.

The mean loss tangent measured in five regions of CIRS 1 and CIRS 3 phantoms are shown in Figure 6.12. The dashed lined represent the standard deviation of 5 measured regions in each phantom.

110

Figure 6.13 illustrates the shear wave dispersion measured by SDUV, the shear wave attenuation estimated by acoustic radiation force and SDUV using Equation 6.16, the complex shear moduli calculated from shear wave speed and shear wave attenuation in Equation 6.13 and Equation 6.14, and complex moduli estimated by fitting a Kelvin-Voigt model to shear wave dispersion measured by SDUV in CIRS 1 phantom.

111

Shear wave dispersion measured by SDUV, the shear wave attenuation estimated by acoustic radiation force and SDUV using Equation 6.16, the complex shear moduli calculated from shear wave speed and shear wave attenuation in Equation 6.13 and Equation 6.14, and complex moduli estimated by fitting a Kelvin-Voigt model to shear wave dispersion measured by SDUV in CIRS 3 phantom are shown in Figure 6.14.

112

The shear elastic modulus G and η from the Kelvin-Voigt model fit to shear wave dispersion were 1.67 kPa and 1.68 Pa·s for CIRS 1 and 3.39 kPa and 4.01 Pa·s for CIRS 3. In the Kelvin-Voigt model, the storage modulus is not a function of frequency, therefore the average model-free storage modulus over 100 Hz to 500 Hz would be comparable to the storage modulus estimated from Kelvin-Voigt model fit to shear wave speed dispersion. The average model-free storage modulus over this frequency range was 1.33 kPa for CIRS 1 and 3.34 kPa for CIRS 3. On the other hand, in the Kelvin-Voigt model, the loss modulus is a function of frequency, therefore the slope of the model-free loss modulus would be comparable to the loss modulus estimated from Kelvin-Voigt model fit

113 to shear wave speed dispersion. The slope of the model-free loss modulus was 1.84 Pa·s for CIRS1 and 4.18 Pa·s for CIRS3. 6.6 Discussion Simulations showed that the new method of converting from time-compliance to complex modulus is robust when using a high sampling rate to study low viscosity materials. Both Kelvin-Voigt and Standard linear solid extracted complex moduli agreed with theoretical complex moduli; refer to Figure 6.4 and Figure 6.5. Moreover, the mean absolute error was relatively small even when poor sampling frequency was used. The error associated with too low sampling rate will affect the high frequency portions of the estimated complex modulus.

As expected, the complex modulus estimated from simulated time-strain response is a factor of the complex modulus estimated from simulated time- compliance response. Moreover, the loss tangent estimated from simulated time-compliance or time-strain to complex modulus conversion were very similar, which agree with the theory for linear viscoelastic materials, refer to Figure 6.6 and Figure 6.7. The loss tangent interpretation was studied by varying viscoelastic parameters in both Kelvin-Voigt and Standard linear solid, as shown in Figure 6.7 and Figure 6.9. In summary, varying either storage or loss modulus is represented as a shift in frequency. More specifically, increasing the storage modulus for a fixed value of loss modulus shifted the loss tangent curve to the right, toward high frequencies; on the other hand, increasing the loss modulus for a fixed value of storage modulus shifted the loss tangent curve to the left or low frequencies. A potential limitation of the proposed method, measuring loss tangent of tissues to differentiate healthy tissue from disease tissue, is the case when both storage and loss modulus increase or decrease with the same proportion, in that case, the loss tangent does not change, but the magnitude of the complex modulus is different. Figure 6.15 shows a vector diagram with the relationship between complex modulus, storage modulus, loss modulus and loss angle.

114

The complex modulus can be represented as a vector resultant of the storage

modulus, Gs, and loss modulus, Gl, and their ratio is represented as tan(δ). The

complex modulus is independent of tan(δ) when Gs and Gl change

independently, for instance changing Gs and Gl in opposite direction cause G*

to be the same and tan(δ) to change, Figure 6.15a, or changing Gs and Gl in the same direction and magnitude causes G* to change but tan(δ) remains the same, Figure 6.15b.

Representative creep displacement response shown in Figure 6.10 and Figure 6.11 were obtained in the tissue-mimicking phantoms. When the magnitude of the radiation force was increased by a factor of 2, a proportional increase in displacement was observed in both phantoms, which is expected for linear viscoelastic materials. Moreover, the extracted complex modulus was also proportional to the acoustic radiation force magnitude. Most importantly, the estimated loss tangent was independent of force magnitude and geometry, as shown theoretically and in simulations. The tissue mimicking phantoms were expected to have different storage modulus and similar loss modulus, as reported by the manufacturer, this was illustrated in Figure 6.12, where the loss tangent is relatively less for the CIRS 1 phantom when compared to CIRS 3

115 phantom, therefore CIRS 1 phantom is softer than CIRS 3 phantom. Because there may be a case where loss tangent is the same for materials with different storage and loss modulus, as discussed in the previous paragraph, Shearwave Dispersion Ultrasound Vibrometry (SDUV) was used in combination with acoustic radiation force creep to estimate the true complex modulus, refer to Figure 6.13 and Figure 6.14. The calibrated complex modulus for both phantoms provides a more complete characterization of viscoelastic properties, and still in a model-free manner. A difference in both storage and loss modulus was seen for both phantoms, however, because the difference in storage modulus was higher compared to difference in loss modulus between the two phantoms, the loss tangent was still different for both phantoms. Shear wave elasticity methods usually fit a rheological model to shear wave speed to solve for viscoelastic parameters. The complex modulus estimated by fitting a Kelvin- Voigt model to the shear wave dispersion measured by SDUV was similar to the estimated model-free complex modulus, for the CIRS phantoms.

In this chapter, we described and validated a method to fully quantify viscoelastic parameters in a manner independent of models by acoustic radiation force creep and Shearwave Dispersion Ultrasound Vibrometry. Previous work in this area involved the use of rheological models, but the need for such models affects the viscoelastic parameter estimation as well as the fitting process. The described acoustic radiation force – creep method, uses a conversion formula that is the analytic solution of a constitutive equation. This conversion formula is shown to be sensitive to sampling frequency, the first reliable measure in time and the long term viscosity approximation. A more comprehensive study is needed to evaluate such parameters in biological tissue applications. Future work will focus in both in vitro and in vivo tissue viscoelastic properties estimation by acoustic radiation force creep and SDUV.

6.7 Conclusion Very few methods have been proposed to characterize tissue mechanical properties in a model independent manner. The method presented in this chapter is a novel approach to overcome difficulties encountered with rheological model and fitting approaches. Acoustic radiation force creep in

116 combination with a creep-compliance to complex modulus conversion formula provides a non-invasive, fast, robust and local measure of tissue viscoelasticity. Clinical applications of this novel method are highly supported because it only requires pushing beams similar to the acoustic radiation force imaging (ARFI) method, which is currently implemented on commercial ultrasound scanning machines, therefore tissue heating is expected to be below FDA limits.

117 Chapter 7

Conclusions and future directions

7.1 Conclusions The main innovations presented on this thesis are:

• Independent validation method of elastic modulus estimation by SDUV in gelatin phantoms • Quantitative characterization of the shear elasticity and viscosity of the in vitro and in vivo kidney using Shearwave dispersion ultrasound vibrometry • Quantitative characterization of the shear elasticity and viscosity of the in vivo kidney during acute decrease of renal blood flow • A novel method to fully quantify viscoelastic parameters independently of models using acoustic radiation force creep and shear wave dispersion ultrasound vibrometry

7.2 SDUV validation In this thesis two different approaches to validate SDUV were presented. One of the approaches is a gold standard test to assess mechanical properties. This was the indentation test, which is commonly used to asses the elastic behavior of materials, rather than viscoelastic behavior. It has been used in both in vitro and in vivo conditions and it provides a useful quantitative measure of tissue elasticity. The indentation test is an attractive method because of its widespread use and ease of implementation, its only requirement being to have

118 a surface for indenter contact application. The purpose of this thesis was to measure kidney viscoelastic properties; however one of the major difficulties with testing kidney and other soft tissue with indentation tests is mounting the test specimens, because inadequate or inappropriate mounting results in failure or slippage in the grips of the test equipment. Additionally, soft tissues undergo considerable expansion or compression at loads below the resolving capability of the measuring device. Tissue mechanical testing is useful for the purposes of comparative testing, but the inherent variability in biological tissue and the technical problems discussed above limits the usefulness of these measurements. As a result, tissue mimicking phantoms are used instead for validation purposes. In this thesis, the experimental data showed acceptable agreement of shear elastic moduli estimates from SDUV phase velocity method and indentation tests on gelatin phantoms. On the other hand, the shear elastic modulus estimated by group velocity did not agree with the indentation test estimations. These results suggest that a rheological model for linear viscoelastic material must be used to estimate elastic modulus on dispersive gelatin phantoms and soft tissues.

The other method presented in this thesis is a novel approach that overcomes difficulties encountered with rheological models and their required fitting approaches. This method has the potential to fully quantify viscoelastic parameters in an independent model manner by acoustic radiation force creep and shear wave dispersion ultrasound vibrometry. The described acoustic radiation force – SDUV method, uses a conversion formula which is the analytic solution of a constitutive equation. The acoustic radiation force creep in combination with the time-compliance to complex modulus conversion formula provides a non-invasive, fast, robust and local measure of tissue viscoelasticity. Clinical applications of this novel method are highly supported because it uses similar number of pushing beams compared to acoustic radiation force imaging (ARFI); therefore tissue heating is expected to be below FDA limits. Because this new method was developed close to the end of the thesis work, only tissue mimicking phantoms were studied, however, preliminary data will be presented in the future direction section.

119 7.3 Kidney viscoelasticity A noninvasive, reproducible and quantitative technique that uses ultrasound radiation force to generate a local shear wave was used to study kidney viscoelasticity in vitro and in vivo. The measurement of the shear wave propagation speed in combination with rheological models helped estimate kidney viscoelastic properties over several experimental and physiological conditions. The main advances of this part of this thesis have been contributions to evaluating kidney viscoelastic properties in a novel manner. Additionally, the measurement of viscosity is something that has been ignored by many elasticity imaging modalities, and viscosity may be an important indicator for kidney health. In the in vitro experiments, a number of kidney properties and structure characteristics were reported, including local and global in-homogeneity, time-dependent viscoelasticity, kidney anisotropy and relatively large difference in viscoelastic properties between different tissue states. The majority of this reported information is well known in the literature and is important in the field of elasticity imaging. On the other hand, the main finding in the in vivo studies is that acute changes in renal blood flow affect kidney viscoelastic properties. Moreover, the clinical significance of this work is that the successful development of a non-invasive, fast, ultrasound-based elasticity imaging technique can be an alternative to renal biopsy for frequent assessment and follow-up of patients and specific treatment regimens. SDUV measurements can be made in less than a second, which allows for multiple measurements in the kidney in a single visit. SDUV can provide a “virtual biopsy” of the viscoelastic properties of the kidney to provide physicians with a valuable tool for diagnosis and prognosis of kidney health.

7.4 Future directions Shearwave dispersion ultrasound vibrometry method is being optimized to be use for in vivo transcutaneous applications. The main applications would be to use SDUV as a virtual biopsy to monitor development of chronic kidney disease and transplanted kidneys in conjunction with renal biopsy. Figure 7.1a illustrates the set up used in preliminary experiments in pigs. The measurements will be positioned on a previously designed grid such as shown in Figure 7.1b. This grid will be used for several planes of the kidney.

120

Figure 7.1: (a) In vivo pig kidney transcoutaneos set up for SDUV measurements. (b) B-scan image with sample grid of points (yellow circles) for SDUV measurements.

The main problem encountered with transcutaneous measurement, is that most of the ultrasound energy is absorbed by the muscle and fat layers surrounding the kidney, therefore there is not a strong shear wave generated in the kidney. Figure 7.2 illustrates the displacement response of a transient acoustic radiation force impulse transcoutaneously and the time-to-peak estimation. By inspection, Figure 7.2a shows shear wave propagation but its amplitude is in the order of few microns. Figure 7.2b illustrates the displacement as a function of time for three locations along the lateral direction. Figure 7.2c shows the time-to-peak calculations, the slope of the linear fit is the shear wave group velocity, for this preliminary experiment, the shear wave group velocity was 3.05 m/s at about 200 Hz of center of gravity or 85 Hz center frequency impulse. Unfortunately, because of the poor shear wave displacement signal, the shear wave dispersion could not be evaluated. At this point, only group velocity estimations are possible. By assuming that the kidney is elastic, the shear elastic modulus calculated from the measured group velocity is 9.3 kPa, which is slightly higher compared to the baseline shear elastic modulus estimated by Kelvin-Voigt model fit to shear wave dispersion. In this thesis, it has been shown in Chapter 3 how the shear modulus is overestimated when assuming a elastic material.

121

Once the transcutaneous measurements are optimized, the next step will be to study the development of chronic kidney disease. For this purpose, an animal study has been designed and it is described below.

7.4.1 SDUV measurements of the viscoelastic properties of healthy pig kidneys and fibrotic pig kidneys The working hypothesis in this study is that changes in kidney viscoelastic properties may not only be due to renal blood flow and renal blood pressure changes but is also due to fibrosis. Studies will be performed in domestic pigs. Pigs were selected because they comprise a well-established model for chronic

122 kidney disease such as renal artery stenosis (RAS). A swine model of unilateral RAS will be used to study the viscoelastic properties of disease kidney [183]. Several studies have shown that this swine model of unilateral RAS exhibit renal fibrosis after 10-12 weeks as detected by trichrome staining [183-187]. Moreover, the relationship between the degree of stenosis and severity of individual kidney hemodynamics, function and tubular functions have been studied by Urbieta-Caceres et al [188], where a fairly linear relationship between the degree of stenosis and renal fibrosis as detected by trichrome staining is shown. RAS will be induced in a group of animals and transcutaneous SDUV measurements will be acquired every 2 weeks up to the week 8. A summary of the planned experiments is illustrated below:

Animal RAS or Doppler SDUV Animal preparation sham flow/pressure measurements sacrifice operation wire (every 2 weeks) (week 1) (every 2 weeks) (every 2 weeks) (week 8)

In each SDUV measurement, both renal blood flow (RBF) and renal perfusion pressure (RPP) will be measured by a doppler flow/pressure wire (FloWire, Cardiometrics, Mountain View, CA) of 0.014 in. in diameter (cross-sectional area of 0.099 mm2). At the end of week 8, tissue will be collected for histological analysis. The incidence and levels of fibrosis, inflammation, and other tissue abnormalities will be analyzed with the elasticity and viscosity to find associations of changes in tissue morphology and their effects on the viscoelastic properties of the tissue.

Potential difficulties of this study include additional factor that affect kidney viscoelasticity, such as glomerular filtration rate (GFR) and fluid excretion, however, as a first step we would like to focus on main hemodynamic variables such as RBF and RPP; Doppler flow/pressure wire size may affect the RBF and RPP measurements, the Doppler flow/pressure wire has an outer diameter of 0.014 in (0.356 mm). The diameter of the renal artery will be different for each animal, for instance, if the renal artery diameter is 4 mm, the Doppler flow/pressure wire will represent 0.8% of the renal artery cross-sectional area. Although renal blood flow will be reduced to 90%, which is equivalent to about 97% of stenosis or 97% of the renal artery cross-sectional area [189],

123 significant interference of Doppler flow/pressure wire at 90% reduction of RBF is not expected.

The acoustic radiation force creep method presented in this thesis is very promising. Future studies regarding this method include a feasibility study for in vitro and in vivo measurements of kidney and other tissues viscoelastic properties. Figure 7.3a and Figure 7.3b show the mean (average of 5 repeated measurements) creep displacement response and loss tangent (tan(δ)) from a 5 locations in an excised swine kidney. The dashed lines represent the standard deviation of the five repeated measurements. Figure 7.3c and Figure 7.3d shows the average displacement and loss tangent of the 5 different locations.

Figure 7.3: Excised swine kidney (a) mean creep displacement, (b) estimated loss tangent of 5 repeated measurements in 4 locations, the dashed lines represent the standard deviation of 5 repeated measurements. (c) Mean creep displacement and (d) loss tangent of 5 locations, dashed lines represent the standard deviation of 4 locations.

124 Shear wave dispersion measured by SDUV, the shear wave attenuation estimated by acoustic radiation force and SDUV, the complex shear moduli calculated from shear wave speed and shear wave attenuation, and complex moduli estimated by fitting a Kelvin-Voigt model to shear wave dispersion measured by SDUV in one excised swine kidney are shown in Figure 7.4.

The excised swine kidney loss tangent for different points in a renal cortex was expected to be different because the kidney is highly inhomogeneous. This preliminary data does not show significant different in loss tangent for different locations in the kidney. The calibrated complex modulus with SDUV illustrate a

125 fairly linear loss modulus, as in the case of a Kelvin-Voigt model, but the storage modulus is rather variant. When fitting the Kelvin-Voigt model to the shear wave dispersion, the loss modulus is slightly different between the calibrated loss modulus and Kelvin-Voigt loss modulus. However, for a preliminary study, the results are promising. More comprehensive studies need to be done to optimize the method. For instance, finite element method will be used to simulate the acoustic radiation force creep experiment and to understand both the stress and strain fields that are involved.

7.5 Significant academic achievements This thesis work has produced significant academic achievements including two published peer-reviewed paper, one accepted peer-reviewed paper, four conference proceeding papers on which I am an author, one conference abstract on which I am an author, and a student award.

7.5.1 Peer-reviewed papers The peer reviewed papers encompass the material presented in Chapter 3 and 4 and an application related to this thesis work.

Amador, Carolina; Urban, Matthew W.; Chen, Shigao; Chen, Qingshan; Kai- Nan, An; Greenleaf, James F - Shear elastic modulus estimation from indentation and SDUV on gelatin phantoms. IEEE Transactions on Biomedical Engineering, 58(6): 1706-1714, June 2011.

Warner. Lizette; Yin, Meng; Glaser, Kevin J.; Woollard, John A.; Amador, Carolina; Korsmo, Michael J.; Ehman, Richard L.; Lerman, Lilach O. - Noninvasive in vivo assessment of renal tissue elasticity using MR Elastography: Preliminary findings. Investigative Radiology, 46(8): 509-514, August 2011.

Amador, Carolina; Urban, Matthew W.; Chen, Shigao; Greenleaf, James F. - Shearwave Dispersion Ultrasound Vibrometry (SDUV) on swine kidney. IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 2011 (in press)

126 7.5.2 Conference proceedings Amador, Carolina; Urban, Matthew W.; Chen, Shigao; Greenleaf, James F. - In vivo assessment of renal tissue viscoelasticity during acute and gradual renal ischemia. Conference proceedings of IEEE International Ultrasonics Symposium, Orlando, FL, USA, 2011.

Amador, Carolina; Urban, Matthew W.; Kinnick, Randall; Chen, Shigao; Greenleaf, James F. - Viscoelastic measurements on perfused and non- perfused swine renal cortex in vivo. Conference proceedings of IEEE International Ultrasonics Symposium, San Diego, CA, USA, 2010.

Amador, Carolina; Urban, Matthew W.; Warner Lizette V.; Greenleaf, James F.- In vitro renal cortex elasticity and viscosity measurements with Shearwave Dispersion Ultrasound Vibrometry (SDUV) on swine Kidney. Conference proceedings of IEEE Engineering in Medicine and Biology Society. p. 4428- 4431. 2009.

Amador, Carolina; Urban, Matthew W.; Warner Lizette V.; Greenleaf, James F - Measurements of swine renal cortex shear elasticity and viscosity with Shearwave Dispersion Ultrasound Vibrometry (SDUV). Conference proceedings of IEEE International Ultrasonics Symposium. p. 491-494. 2009.

7.5.3 Conference abstracts Urban, Matthew W; Chen, Shigao; Amador, Carolina; Greenleaf, James F - Kramers-Kronig relationships applied to shear wave propagation in soft tissues. 159th Meeting of the Acoustical Society of America. April 19-23, 2010. Baltimore, MD.

7.5.4 Academic awards In conjunction with presenting portions of this thesis, I was awarded a student travel award and was a student paper competition participant at the 2010 IEEE International Ultrasonic Symposium. The paper was on in vivo kidney viscoelasticity during decrease of renal blood flow as it is reference in Chapter 6.

127

APPENDIX A

Discrete Fourier Transform

The discrete Fourier transform (DFT) of a sequence, x(n), is defined as [152]:

∞ ()= )( enxvX −2πnvi ∑ A.1 n=−∞

Some common DFT pairs are:

δ ()n ⇔ 1 A.2

⎛ a ⎞ − δ ⎜n − ⎟ ⇔ e avi ⎝ 2π ⎠ A.3

⎛ a ⎞ ian δ ⎜ve −⇔ ⎟ ⎝ 2π ⎠ A.4

− 1 an ()nue ⇔ + 2πvia A.5

There are a number of DFT properties that are used to simplify the evaluation of DFT. Some of these properties are [152]:

Shift property

⎛ a ⎞ − ⎜nx − ⎟ ⇔ iav ()vXe ⎝ 2π ⎠

− ⎛ a ⎞ ian )( ⎜vXnxe +⇔ ⎟ A.6 ⎝ 2π ⎠

Convolution property

128 () ()⇔∗ ()()vYvXnynx

()() ()∗⇔ ()vYvXnynx A.7

Derivative property

m ()nxd ⇔ ()()2π m vXvi dn m A.8

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