Estimation of Spatiotemporal Isotropic and Anisotropic Myocardial Stiffness Using

Home , Competence (geology), Diffusion MRI, Horst (geology)

Estimation of Spatiotemporal Isotropic and Anisotropic Myocardial Stiffness using

Magnetic Resonance Elastography: A Study in Heart Failure

DISSERTATION

Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University

Ria Mazumder, M.S.

Graduate Program in Electrical and Computer Engineering

The Ohio State University

2016

Dissertation Committee:

Dr. Bradley Dean Clymer, Advisor

Dr. Arunark Kolipaka, Co-Advisor

Dr. Patrick Roblin

Dr. Richard D. White

Ria Mazumder

2016

Abstract

Heart failure (HF), a complex clinical syndrome that is characterized by abnormal cardiac structure and function; and has been identified as the new epidemic of the 21st century

[1]. Based on the left ventricular (LV) ejection fraction (EF), HF can be classified into two broad categories: HF with reduced EF (HFrEF) and HF with preserved EF (HFpEF).

Both HFrEF and HFpEF are associated with alteration in myocardial stiffness (MS), and there is an extensively rich literature to support this relation. However, t0 date, MS is not widely used in the clinics for the diagnosis of HF precisely because of the absence of a clinically efficient tool to estimate MS.

Current clinical techniques used to measure MS are invasive in nature, provide global stiffness measurements and cannot assess the true intrinsic properties of the myocardium.

Therefore, there is a need to non-invasively quantify MS for accurate diagnosis and prognosis of HF. In recent years, a non-invasive technique known as cardiac magnetic resonance elastography (cMRE) has been developed to estimate MS. However, most of the reported studies using cMRE have been performed on phantoms, animals and healthy volunteers and minimal literature recognizing the importance of cMRE in diagnosing disease conditions, especially with respect to HF is available.

Additionally the existing cMRE techniques assume that the waves are propagating in a ii uniform, infinite, homogenous, isotropic medium. However, such assumptions are violated in the heart since it bears a complex anisotropic (orthotropic) geometry; current cMRE techniques may not provide the true mechanical properties of the myocardium and instead provide only an effective estimate of MS.

The overall goal of this dissertation is to: i) implement the currently established cMRE technique in HF (both HFrEF and HFpEF) porcine models to validate MS as a diagnostic biomarker; ii) explore the scope of ex-vivo cardiac diffusion tensor imaging (DTI) in investigating myocardial architecture (required for anisotropic stiffness measurements) in a HF causing diseased model; iii) develop waveguide cMRE inversion (a tool to estimate anisotropic stiffness) and validate the algorithm using finite element (FE) simulations; and iv) implement waveguide cMRE inversion in a hypertensive heart model (that has the potential to trigger HFpEF) to demonstrate the feasibility of measuring anisotropic MS in

HF causing disease conditions.

From the results obtained it was observed that MS in a hypertensive heart (HFpEF causing condition) increased progressively with disease progression when compared to a normal heart; and this increase exhibited significant correlation with left ventricular pressure (increases due to hypertension) and thickness (increases secondary to hypertension). Additionally, MS demonstrated progressive focal increase in an infarcted myocardium (HFrEF causing condition) compared to non-infarcted remote myocardium with disease progression and the increase in MS exhibited significant correlation with i)

iii mechanical testing-derived MS, ii) circumferential end-diastolic strain, iii) T1 values and iv) extra-cellular volume fraction.

The next part of the dissertation investigates the change in cardiac geometry (essential for investigating anisotropic elastic properties) as a result of myocardial infarction (HFrEF causing condition) in formalin-fixed ex-vivo specimens using DTI. Since in-vivo DTI is very complex (due to cardiac and respiratory motion) and is still in its inception, formalin-fixed ex-vivo specimens were used for the preliminary investigation. Hence it was essential to ensure whether the alterations observed in cardiac geometry were related to pathology or if it was an effect of the fixation process. The results demonstrated that formalin-fixation did not alter the structural orientation of the fibers and that fibers in the infarcted myocardium were shorter and disarrayed. Additionally, a post processing filter was developed to reduce acquisition time in cardiac DTI, thereby assisting in faster imaging. The filter was implemented on formalin-fixed ex-vivo myocardial infarction

(HFrEF causing condition) induced porcine hearts to demonstrate that the technique preserved subtle pathological alterations in myocardial structure.

The last section of this dissertation validates the waveguide MRE inversion algorithm and demonstrates its feasibility in a hypertensive heart model. From the results it was observed that the inversion successfully resolved the anisotropic elastic properties of the materials in majority of the directions. The inversion failed in one shear direction because with the current actuation and geometric setting that particular mode was not being excited. Additionally, the anisotropic elastic coefficients estimated in the hypertensive

iv heart model that is prone to triggering HFpEF demonstrated significant increase in one compressional direction and all three shear directions.

In conclusion, this dissertation uses cMRE to demonstrate the potential of spatiotemporal isotropic and anisotropic myocardial stiffness as a diagnostic metric in heart failure porcine models.

Dedication

This dissertation is dedicated to Maa.

Acknowledgments

This dissertation was nothing short of an exciting and amazing roller-coaster ride, and would be incomplete if I don’t express my gratitude to all those people who made it possible. First and foremost I want to thank my advisors Dr. Kolipaka and Dr. Clymer for, the continuous guidance, time, knowledge and experience that shaped me to become an independent researcher. Their endless discussion, scribbles on the white board, their enthusiasm despite the multiple dead ends, their motivation and their belief that “there is light at the end of the tunnel” is what kept me going till the end.

I am grateful to the Department of Electrical and Computer Engineering, especially Dr.

Anderson for the three years of TA support, the Department of Radiology, especially Dr.

White for their funds (GRA), Hazel, Jennifer and Diane for offering me the GAA position, all of which kept me financially secured through the course of this PhD.

I would like to thank Dr. White for being on my dissertation committee and for his invaluable feedback during our meetings and through manuscript preparations; Dr.

Roblin for being on my candidacy and dissertation committee; Dr. Krishnamurthy for being on my qualifier and candidacy committee; Dr. Simonetti for his continuous feedback throughout the 3 years, Dr. Litsky for his help with mechanical testing and Dr.

vii

Potter and Dr. Raman for their insights during the weekly journal clubs.

Thanks are due for Dr. Young and his student Renee, our collaborators in Auckland, for their help in generating the finite element simulations.

I am grateful to Ding, Rizwan, Seongjin and Peter for their valuable perspectives whenever I was absorbed by an unsolvable mathematical/engineering abyss, Ning for her assistance with all scanner/pulse sequence related issues, Juliana for her insights as a radiologist and Molly for her help with statistics.

Next, I would like to thank all the members of the lab who have contributed in some way to this dissertation, Brian for his help with imaging, Matt for his help with preparing the animals, Anirudh for his help with the initial set-up, Sam for his help with the processing and Prateek for his hands-on help. That apart, all the other past and present members of the lab, Faisal, Priyanka, Shantanu, Ben, Huiming, Kovid, Will, Chethan and Sangmin for their insights during lab meetings.

Thanks are due to Debbie for being the motherly figure she is, Juliet for being an amazing friend and listener, for her help in everything, starting from course work to

MATLAB errors to simple formatting, David and Sam for their occasional valuable advices.

Beyond the boundaries of the lab, I would like to thank my network of friends both in US and India whose contributions may not have technical relevance but their support in the

viii last couple of years was very essential to this dissertation. My neighbors for helping me sprint through the last lap of this dissertation without any injury.

And last but not the least I am ever grateful to my family who forms an integral part of this dissertation. I sincerely thank my grandmother, aunts, uncles, cousins, nieces, nephews and in-laws and every other family member who believed in me. Without their constant support, encouragement and motivation that helped me stay sane; this dissertation would not have been possible.

Special mention is needed for my sister Neha, for pampering me, bearing with my tantrums and keeping me company every single day. My parents (maa and baba), for believing in me and supporting me through thick and thin. It is their innumerous sacrifices and unconditional love that has given me the strength to pursue this research.

Had it not been for maa’s trust in me, her passion for going beyond the ordinary and her willingness to put everything at stake for my dreams, I wouldn’t have come this long.

Finally, I would like to express my gratitude towards my loving husband Aritra. It was he who helped me remain calm and composed in the last few months, read and revised this dissertation, gave valuable comments, made sure I didn’t miss deadlines and whose constant support kept me going till the end.

Vita

2005...... Pratt Memorial School

2009...... B. Tech., Department of Electronics and

Communication Engineering, West Bengal

University of Technology

2013...... M.S., Department of Electrical and

Computer Engineering, The Ohio State

University

2013 to present ...... Graduate Teaching Associate, Department

of Electrical and Computer Engineering,

The Ohio State University

Publications

Journal Articles . Mazumder R, Clymer B, Mo, X. White RD, Kolipaka. Adaptive Anisotropic Gaussian Filtering to Reduce Acquisition Time in Cardiac Diffusion Tensor Imaging. The International Journal of Cardiovascular Imaging. 2016 Feb 2. (Epub ahead of print). . Mazumder R, Choi S, Clymer BD, White RD, Kolipaka A. Diffusion Tensor Imaging of Healthy and Infarcted Porcine Hearts: Study the Impact of Formalin-

Fixation. Journal of Medical Imaging and Radiation Sciences 2016. 47(1): p.74- 85. . Chamarthi S, Raterman B, Mazumder R, Michaels A, Oza V, Hanje J, Bolster B, Jin N, White RD, Kolipaka A. Rapid Acquisition Technique for MR Elastography of the Liver. Magnetic resonance imaging, 2014. 32(6): p. 679-83. . Mazumder R, Schroeder S, Mo X, Clymer BD, White RD, Kolipaka A. Quantification of Myocardial Stiffness in Hypertensive Porcine Model Using Magnetic Resonance Elastography, Journal of Magnetic Resonance Imaging (Under Review). . Mazumder R, Schroeder S, Mo X, Clymer BD, White RD, Kolipaka A. In-Vivo Magnetic Resonance Elastography: A Feasibility Study to Estimate Left Ventricular Stiffness in a Myocardial Infarction Porcine Model, Circulation: Cardiovascular Imaging (Under Review).

Journal Articles in Preparation . Mazumder R, Miller R, Jiang H, Clymer BD, White RD, Young A, Romano A, Kolipaka A. Validation of Waveguide Magnetic Resonance Elastography Using Finite Element Model Simulation.

Conference Proceedings . Mazumder R, Schroeder S, Clymer BD, White RD, Kolipaka A. In-Vivo Quantification of Myocardial Stiffness in Heart Failure with Preserved Ejection Fraction Using Magnetic Resonance Elastography: Assessment in a Porcine Model. 24th Annual Scientific Meeting ISMRM, Singapore, 2016. . Mazumder R, Schroeder S, Clymer BD, White RD, Kolipaka A. Quantification of Myocardial Stiffness in Heart Failure with Preserved Ejection Fraction Porcine Model Using Magnetic Resonance Elastography. 19th Annual Scientific Meeting SCMR, Los Angeles, USA 2016. . Illapani VSP, Flores JC, Mazumder R, White RD, Markl M, Kolipaka A. Quantification and Comparison of 4D PC-MRI Derived Wall Shear Stress and MRE Derived Wall Shear Stiffness Of Abdominal Aorta. 19th Annual Scientific Meeting SCMR, Los Angeles, USA 2016. . Miller R, Jiang H, Mazumder R, Cowan B, Nash, M, Kolipaka A, Young A. Determining Anisotropic Myocardial Stiffness from Magnetic Resonance Elastography: A Simulation Study. Functional Imaging and Modeling of the Heart, 2015. 9126: p. 346-354. . Mazumder R, Miller R, Jiang H, Clymer BD, White RD, Young A, Romano A, Kolipaka A. Validation of Waveguide Magnetic Resonance Elastography Using Finite Element Model Simulation. 23rd Annual Scientific Meeting ISMRM, Toronto, Canada 2015. . Mazumder R, Clymer BD, White RD, Romano A, Kolipaka A. In-vivo Waveguide Cardiac Magnetic Resonance Elastography. 18th Annual Scientific Meeting SCMR, Nice, France 2015. xi

. Mazumder R, Clymer BD, White RD, Kolipaka A. Waveguide Magnetic Resonance Elastography of the Left Ventricle in a Pressure Varying Model. 22nd Annual Scientific Meeting ISMRM, Milan, Italy 2014. . Mazumder R, Clymer BD, White RD, Kolipaka A. Cardiac Diffusion Tensor Imaging: Adaptive Anisotropic Gaussian Filtering to Reduce Acquisition Time. 22nd Annual Scientific Meeting ISMRM, Milan, Italy 2014. (Awarded suma cum laude). . Mazumder R, Clymer BD, White RD, Kolipaka A. Estimation of Helical Angle of the Left Ventricle Using Diffusion Tensor Imaging with Minimum Acquisition Time. 17th Annual Scientific Meeting SCMR, New Orleans, USA 2014. . Mazumder R, Choi S, Clymer B, White RD, Kolipaka A. Diffusion Tensor Imaging of Fresh and Formalin Fixed Porcine Hearts: A Comparison Study of Fiber Tracts. 21st Annual Scientific Meeting ISMRM, Salt Lake City, Utah USA 2013. . Mazumder R, Clymer B, White RD, Kolipaka A. MR Elastography as a Method to Determine the Mechanical Properties of Fresh and Formalin Fixed Porcine Hearts. 21st Annual Scientific Meeting ISMRM, Salt Lake City, Utah USA 2013. . Choi S, Mazumder R, Schmalbrock P, Knopp MV, White RD, Kolipaka A. Potential of Diffusion Tensor Imaging as a Virtual Dissection Tool for Cardiac Muscle Bundles: A Pilot Study. 21st Annual Scientific Meeting ISMRM, Salt Lake City, Utah USA 2013. . Romano A, Mazumder R, Cho S, Clymer B, White RD, Kolipaka A. Waveguide Magnetic Resonance Elastography of the Heart. 21st Annual Scientific Meeting ISMRM, Salt Lake City, Utah USA 2013. . Mazumder R, Choi S, Raterman B, Clymer B, White RD, Kolipaka A. Diffusion Tensor Imaging of Formalin Fixed Infarcted Porcine Hearts. 16th Annual Scientific Meeting SCMR, San Francisco, USA 2013. . Mazumder R, Choi S, Raterman B, Clymer B, White RD, Kolipaka A. Diffusion Tensor Imaging of Formalin Fixed Infarcted Porcine Hearts: A comparison between 3T and 1.5T. Joint SCMR and ISMRM New-Horizons in High Field Cardiovascular Imaging Workshop, San Francisco, USA 2013. . Mazumder R, Raterman B, Jin N, Bolster BD, White RD, Clymer B, Simonetti O, Kolipaka A. Rapid Acquisition Technique for MR Elastography of the Liver. 98th Scientific Assembly and Annual Meeting RSNA, Chicago, USA 2012.

Fields of Study

Major Field: Electrical and Computer Engineering

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Table of Contents

Abstract ...... ii

Dedication ...... vi

Acknowledgments...... vii

Vita ...... x

Publications ...... x

Fields of Study ...... xii

Table of Contents ...... xiii

List of Tables ...... xvii

List of Figures ...... xix

Chapter 1: Introduction ...... 1

1.1 Motivation and Significance ...... 1

1.2 Cardiovascular System ...... 3

1.3 Heart Failure - Overview ...... 16

1.4 Myocardial Stiffness – Its Significance in Heart Failure ...... 18

1.5 Invasive Techniques to Quantify Myocardial Stiffness – Its Inception and

Evolution ...... 25

xiii

1.6 Problem Statement ...... 29

1.7 Organization of this Dissertation ...... 29

Chapter 2: Non-Invasive Techniques to Estimate Myocardial Stiffness ...... 32

2.1 Ultrasound Imaging ...... 32

2.2 MRI Based Techniques ...... 34

2.3 Magnetic Resonance Elastography (MRE) ...... 38

2.4 Waveguide Magnetic Resonance Elastography ...... 54

2.5 Diffusion Tensor Imaging (DTI) ...... 59

2.6 Summary ...... 62

Chapter 3: Left Ventricular Myocardial Stiffness in Heart Failure with Preserved Ejection

Model ...... 63

3.1 Introduction ...... 64

3.2 Materials and Methods ...... 66

3.3 Results ...... 74

3.4 Discussion ...... 87

3.5 Conclusions ...... 93

Chapter 4: Left Ventricular Myocardial Stiffness in Heart Failure with Reduced Ejection

Model ...... 94

4.1 Introduction ...... 95

4.2 Methods ...... 96

4.3 Results ...... 103

4.4 Discussion ...... 112 xiv

4.5 Conclusions ...... 119

Chapter 5: Effect of Formalin Fixation on Diffusion Tensor Imaging ...... 120

5.1 Introduction ...... 121

5.2 Materials and Methods ...... 124

5.3 Results ...... 130

5.4 Discussion ...... 138

5.5 Conclusions ...... 144

Chapter 6: Adaptive Anisotropic Gaussian Filter to Reduce Acquisition Time in Cardiac

Diffusion Tensor Imaging ...... 146

6.1 Introduction ...... 147

6.2 Theory ...... 149

6.3 Materials and Methods ...... 153

6.4 Results ...... 159

6.5 Discussion ...... 172

6.6 Conclusions ...... 176

Chapter 7: Validation of Waveguide Magnetic Resonance Elastography Using Finite

Element Modeling ...... 178

7.1 Introduction ...... 179

7.2 Theory ...... 180

7.3 Materials and Methods ...... 182

7.4 Results ...... 191

7.5 Discussion ...... 199 xv

7.6 Conclusions ...... 201

Chapter 8: Anisotropic Myocardial Stiffness in Hypertensive Porcine Hearts: Initial

Feasibility ...... 203

8.1 Introduction ...... 204

8.2 Materials and Methods ...... 205

8.3 Results ...... 213

8.4 Discussion ...... 218

8.5 Conclusion ...... 221

Chapter 9: Summary and Future Work ...... 222

Appendix A: Waveguide Inversion Equation Derivation ...... 225

References ...... 229

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List of Tables

Table 1: Cardiac Functional Parameters...... 14

Table 2: Cardiac function and morphology measurements for all the animals at Bx, M1, and M2...... 75

Table 3: Cardiac function and morphology measurements for all the animals at Bx, D10 and D21...... 105

Table 4: Acquisition parameters and AAGF analysis results. DED-NEX combination, corresponding acquisition time and mean normalized RMSE for unfiltered and AAGF filtered maps...... 155

Table 5: Error Percentage Measurements. Mean and SD of the percentage error between

HAAAGF maps obtained from NEXF_C and corresponding HAUF reference maps for the 3

DED settings in the 3 different ROI measured in all the 3 MI-induced pigs...... 172

Table 6: Finite Element Geometry and Simulation Parameters...... 186

Table 7: Material Properties for Beam Models (M1-M5)...... 187

Table 8: Material Properties for Transversely Isotropic Heart Model (M6)...... 187

Table 9: Wavenumber Estimation and the Percentage Difference in its Estimation when

Compared to the Expected Values for the Beam Models...... 194

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Table 10: Wavenumber Estimation and the Percentage Difference in its Estimation when

Compared to the Expected Values for the Heart Model...... 194

Table 11: Stiffness Estimation and the Percentage Difference in the Estimation when

Compared to the Expected Values in all the Beam Models...... 197

Table 12: Stiffness Estimation and the Percentage Difference in the Estimation when

Compared to the Expected Values in the Heart Model...... 197

xviii

List of Figures

Figure 1: Cardiac Anatomy. Anatomy of the heart showing cardiac chambers, vessels, valves and muscle layers. [Adapted from musom.marshall.edu]...... 7

Figure 2: Cardiac Fiber Geometry and Structural Anisotropy. Top: Helical fiber geometry in epicardium (left-handed), mid-myocardium (circumferential) and endocardium (right- handed). Bottom: Cardiac anisotropy showing the three axes of symmetry namely, fiber, sheet and sheet normal [Adapted from Legrice et al. [121, 124]]...... 9

Figure 3: Cardiac Physiology. The seven different events occurring across the cardiac cycle. [Adapted from musom.marshall.edu]...... 11

Figure 4: Coronary Circulation. Arteries and veins supplying blood to the heart. [Adapted from Pearson Education Inc.]...... 15

Figure 5: Epidemiological Variation in Prevalence of HF. This study on 4910 patients shows that younger men are more prone to HFrEF while older women are prone to

HFpEF [Adapted from Borlaugh et al. [139]]...... 17

xix

Figure 6: Myocardial Ischemia. Ischemia can be caused by coronary artery disease, coronary thrombosis or coronary spasm. [Adapted from Mayo Foundation for Medical

Education and Research]...... 20

Figure 7: Pressure-Volume (P-V) Loops. Left: A P-V loop obtained from plotting instantaneous pressure vs. volume showing how the heart transitions from its end- diastolic state to the end-systolic state and back. Right: A family of PV loops obtained by varying the loading conditions. The end-systolic P-V points are connected to determine the end-systolic P-V relationship (ESPVR) which is a linear fit. The diastolic P-V points are connected to determine the end-diastolic P-V relationship (EDPVR) which is a nonlinear fit [Adapted from Burkhoff et al. [228]]...... 27

Figure 8: A Typical Stress–Strain Curve. The curve is obtained from a tension test, and shows various parameters measured from the test. [Adapted from pearsonhighered.com/samplechapter/0136081681.pdf]...... 28

Figure 9: The principle of MRE simulated in a phantom. Left: Magnitude image of the phantom with soft and stiff inclusions seen as the hyper-intense and hypo-intense regions, respectively. Middle: Wave image of a single phase offset obtained from MRE acquisitions performed at 100 Hz frequency. A red to blue region is a wavelength and stiff inclusions have longer wavelengths. Right: Stiffness map obtained from wave inversion indicating the soft and stiff inclusions [Adapted from Mariappan et al. [53]]. 36

Figure 10: MRE Driver Systems. Left: An electromagnetic driver system. Middle: A piezoelectric driver system. Right: A pneumatic driver system [Adapted from Mariappan et al. [53]]...... 39

Figure 11: MRE Pulse Sequence. Left: Gradient recall echo based MRE pulse sequence.

Right: Spin echo, echo planar imaging based MRE pulse sequence. ‘M’ shows the external motion. The alternating polarity of the MEGs is indicated by solid and dashed lines on the Gz axis along which motion encoding is performed [Adapted from Venkatesh et al. [252]]...... 45

Figure 12: cMRE Pulse Sequence. The cMRE pulse sequence encodes 4 cardiac phase- offsets and 8 cardiac phases in a single breathhold...... 46

Figure 13: Local Coordinate System. The primary eigenvector corresponds to the fiber direction (n3), and n1 and n2 corresponds to the sheet and sheet normal directions respectively [Adapted from Romano et al. [259]]...... 55

Figure 14: Experimental Set-Up. The animal is placed feet-first supine on the MR table.

A custom made plastic drum (passive driver) is positioned externally on the animal’s anterior chest wall right above the heart. A custom made active pneumatic driver that is placed outside the scanner room generates acoustic waves and transmits it to the passive driver via a plastic connecting tube...... 68

Figure 15: Left Ventricular Thickness as a Function of the Cardiac Cycle on a Mid-

Ventricular Slice from all the Animals. Each color on the marker indicates different

xxi animals and each shape correspond to the 3 different time points (circle-Bx, triangle-M1, and square-M2). The plot shows that mean LV thickness increased progressively from Bx

(green curve, R2=0.94) to M1 (blue curve, R2=0.92) to M2 (red curve, R2=0.81) indicating that the animals developed LV hypertrophy over time...... 77

Figure 16: cMRE Magnitude Images, Wave Images, and Shear Stiffness Maps. Baseline:

(a, g) Short-axis magnitude image of a mid-ventricular slice at ED and ES, respectively.

(b-e), (h-k) Snapshots of 4 phase offsets of the wave propagation in x-direction at ED and

ES, respectively. (f, l) Stiffness maps at ED and ES, respectively, demonstrating that ES stiffness is higher than ED stiffness. Two Months Post-Surgery: (m, s) Short-axis magnitude image of a mid-ventricular slice at ED and ES, respectively. The magnitude image at M2 for both ED and ES indicates LV hypertrophy when compared to the Bx images. (n-q), (t-w) Snapshots of 4 phase offsets of the wave propagation in x-direction at

ED and ES, respectively. (r, x) Stiffness maps at ED and ES, respectively, demonstrating that ES stiffness is higher than ED stiffness and both ED and ES stiffness is higher compared to Bx ED and ES stiffness, respectively...... 79

Figure 17: Mean Left Ventricular Myocardial Stiffness (all Slices) as a Function of the

Cardiac Cycle from all the Animals. Each color on the marker indicates different animals and each shape correspond to the 3 different time points (circle-Bx, triangle-M1, and square-M2). The plot shows that the mean LV shear stiffness by fitting a curve at Bx

(green curve, R2=0.99) is lower than the mean LV shear stiffness at M1 (blue curve,

R2=0.97) which is lower than the mean LV shear stiffness at M2 (red curve, R2=0.97)

xxii indicating that the LV compliance was compromised with the prolongation of hypertension...... 80

Figure 18: Box Plot for cMRE-Derived Shear Stiffness Measurements at ED and ES during Baseline, Month 1 and Month 2. The plot shows that the shear stiffness at ES was significantly higher than shear stiffness at ED for all the animals at all time points. The mean shear stiffness for ED at Bx, M1 and M2 was 3.84±0.4, 4.24±0.3, and 4.82±0.2, respectively, while the mean shear stiffness at Bx, M1 and M2 for ES was 4.94±0.5,

5.70±0.5, and 5.88±0.5, respectively. LV MS increased significantly from Bx to M2 both at ED (indicated *) and at ES (indicated #)...... 81

Figure 19: Spearman’s Correlation Plot between cMRE-Derived LV MS and Mean LV

Pressure and LV Thickness (ED and ES). a) Correlation analysis between ED LV MS and mean LV pressure demonstrated good correlation (휌≥0.5). b) Similarly correlation analysis between ES LV MS and mean LV pressure also demonstrated good correlation

(휌≥0.5). c) A strong correlation (휌>0.7) is observed between ED LV MS and ED LV thickness. d) Similarly a strong correlation (휌>0.7) is observed between ES LV MS and mean ES LV thickness...... 82

(indicated by *) from Bx to M2. Spearman’s correlation analysis between circumferential

xxiii strain and b) cMRE-derived ED MS and c) cMRE-derived ES MS demonstrated a moderate negative correlation (휌>0.3) but it was not significant (p>0.05)...... 83

M2, respectively, indicating absence of edema (c, g) T1pre maps at Bx and M2, respectively, and (d, h) T1post maps at Bx and M2, respectively shows lack of variation in image intensity in the LV indicating absence of distinct fibrosis...... 84

Figure 22: Spearman’s Correlation Analysis between cMRE-Derived ED and ES MS and

MRI Relaxometry Parameters. No correlation (|휌|<0.3) was observed between ED and ES

LV MS and any of the MRI relaxometry parameters: (a, e) T2, (b, f) T1pre, (c, g) T1post, and (d, h) ECV fraction, respectively...... 86

Figure 23: Schematic of the experimental set-up. The passive driver is placed on the animal’s anterior chest wall. Acoustic waves are generated using an active driver that’s placed outside the scan room. Waves from the acoustic driver are transmitted to the passive driver via the plastic tube...... 98

Figure 24: cMRE Images. Baseline: Magnitude image: (a) diastole (g) systole; Wave propagation (four phase offsets) in x-direction: (b-e) diastole (h-k) systole; Stiffness maps

(f) diastole (l) systole. Day 21: (m) DE image showing MIR (red) and RR (green);

Magnitude image delineating MIR the RR (n) diastole (t) systole; Wave propagation

xxiv

(four phase offsets) in x-direction: (o-r) diastole (u-x) systole; Stiffness maps (s) diastole

(y) systole...... 106

Figure 25: cMRE-Derived Stiffness. Box plots showing a) systolic and b) diastolic stiffness in MIR and RR at Bx, D10 and D21. Stiffness at MIR is higher than RR.

Stiffness increased significantly from Bx to D21 in MIR (*) but did not change in RR (#).

...... 107

Figure 26: Circumferential Strain. a) Box plot showing circumferential strain at Bx, D10 and D21. Strain decreased sigficantly in MIR compared to RR. From Bx to D21, RR did not change (#) but MIR decreased progressively (*). Correlation maps between circumferential strain and b) diastolic and c) systolic stiffness. Moderate negative correlation was observed with diastolic MS but systolic MS only demonstrated a negative trend...... 108

Figure 27: DE Image and Corresponding Relaxometry Maps. (a) Baseline DE image shows no enhancement; (d) D21 DE image shows hyper-enhancement (white arrow),

8mins after contrast injection. (b) Baseline T2 map with uniform intensity; (e) D21 T2 map shows patchy hyper-intensity (white arrow). (c) Baseline T1post (10 mins after contrast injection) map shows uniform intensity; (f) D21 T1post map shows reduced intensity (white arrow)...... 110

Figure 28: Relaxometry Analysis. Box plot shows relaxometry parameters in MIR and

RR at Bx, D10 and D21. a) T2 values increased significantly in MIR as compared to RR both at D10 and D21 b) T1post values decreased significant in the MIR as compared to RR xxv both at D10 and D21. c) ECV increased significantly in MIR compared to RR both at

D10 and D21...... 111

Figure 29: Correlation Analysis between cMRE-Derived MS and Relaxometry

Parameters. No significant correlation (r<0.5) was observed between T2 and a) diastolic

MS and d) systolic MS. Good inverse significant correlation was observed between (r<-

0.5) T1post and b) diastolic MS and e) systolic MS. Good positive significant correlation

(r>0.5) was observed between ECV and c) diastolic MS and f) systolic MS...... 113

Figure 30: Mechanical testing results and statistics. a) Box plot shows stiffness in infarcted and remote myocardium using uniaxial mechanical testing. b) Correlation map between mechanical testing-derived MS and both cMRE-derived systolic and diastolic stiffness demonstrated good significant correlation (r>0.8)...... 114

Figure 31: Myocardial Infarction. Coronary angiogram (a) pre-surgery and (b) post- surgery. The arrow in the left image shows blood flowing through the LAD while the arrow in the right image shows the absence of blood flow in the LAD. (c) T1-weighted image of one of the infarcted hearts. The location of the infarcted region (thinner myocardium) near the apex is illustrated with a black circle. (d) Short-axis image showing the infarcted (red contour) and remote (green contour) myocardium...... 125

Figure 32: Flow Chart for Image Analysis. Figure shows the sequence of steps followed for tracking parameter optimization and fiber tracking...... 127

xxvi

Figure 33: Mean and standard deviation of ADC and FA in all the 8 porcine hearts. a)

ADC in control group. The mean and SD of the ADC for the PrCtrl (green dashed line) and PoCtrl (blue dashed line) are 0.52x10-3 ± 0.026 x10-3 mm/s2 and 0.80x10-3 ± 0.072 x10-3 mm/s2 respectively. b) ADC in PoMI. The mean ADC across the infarcted (red dashed line) and remote regions (orange dashed line) are 0.95x10-3 ± 0.12 x10-3 mm/s2 and 0.63x10-3 ± 0.052 x10-3 mm/s2 respectively. c) FA in control group. The mean and

SD of the FA for the PrCtrl (green dashed line) and PoCtrl (blue dashed line) are 0.42 ±

0.028 and 0.26 ± 0.034 respectively. d) FA in PoMI. The mean FA across the infarcted

(red dashed line) and remote regions (orange dashed line) are 0.22 ± 0.023 and 0.25 ±

0.031 respectively...... 131

Figure 34: Determination of optimal FA range for fiber tracking. a) FA Histogram. The

FA histogram indicates a lower mode post-fixation (PoCtrl (dotted-blue) and PoMI

(dashed-red)) as compared to pre-fixation (PrCtrl (solid-green)). b) Mean and SD of FA mode. Mean and SD of the FA mode for PrCtrl (green), PoCtrl (blue) and PoMI (red) groups are 0.27±0.014, 0.17±0.010 and 0.16±0.011 respectively. c) Mean FA histogram

(controls) to estimate optimal FA range for fiber tracking. The peak of the normalized mean FA (normalization based on the total number of voxels) for the PrCtrl and PoCtrl group is 11.5 (corresponding to FA bin 0.15-0.175) and 8.4 (corresponding to FA bin

0.25-0.275), respectively. The lower limit of the FA range corresponding to 25% drop from the peak was determined to be 0.2 for the pre-fixation group and 0.1 for the post- fixation group...... 133

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Figure 35: TTA versus Normalized number of tracts. The figure shows the plot of TTA versus number of tracts. The x-axis corresponds to TTA increasing from 50 to 600. The y- axis corresponds to the number of tracts normalized with respect to the total number of masked voxels. A sharp change in slope is observed when transitioning from 50 - 100

TTA...... 134

Figure 36: Normalized mean length (in µm) versus normalized number of tracts in the control group with two different TTA’s a) 5o and b) 10o. The x-axis represents normalized number of tracts and the y-axis represents the normalized total mean length contributed by all the tracts in the entire heart. Normalization was based on the total number of masked voxels. Every point on the graph corresponds to fiber tracking with a specific fiber length range. As the lower limit (2, 10, 20, 30, 40, 50 mm) of the tracking range was increased (i.e., the markers on the plot shifts from right to left), the tracking conditions became conservative which increased the mean length but decreased the total number of fibers tracked. The normalized mean length was higher in PrCtrl (solid green) group as compared to PoCtrl (dotted blue) group...... 135

Figure 37: 3D fiber architecture in a healthy porcine myocardium. Figure shows fiber tracts passing through a defined region of interest (ROI). Tracking parameters include:

FA [0.1 1], TTA 45o and tracking length range [2 500] mm. TTA was set to 45o to mitigate its effect on the number of tracts identified (refer to Figure 36). Left Image: The planes denote the two long axes and the short axis of the principle eigenvector. The white circle shows the ROI drawn to track the fibers. Right Image: Tracts without the planes.

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The color on the fiber and planes denote the direction of fiber orientation; Green, red and blue corresponds to the x, y and z directions of the image, respectively...... 137

Figure 38: 3D fiber architecture in an infarcted porcine myocardium. Figure shows fiber tracts passing through a defined region of interest (ROI). Tracking parameters include:

Tracts without the planes. The color on the fiber and planes denote the direction of fiber orientation; Green, red and blue corresponds to the x, y and z directions of the image, respectively...... 138

Figure 39: Schematic of filter design and analysis. a) Local coordinate system for each voxel, defining the orientation of the Gaussian filter for that particular voxel. b) Rotated anisotropic Gaussian kernel G'. c) σz′ of the rotated Gaussian kernel G′ increases with increasing radial distance as shown by the Gaussian profiles. d) Sixteen radial transmural profiles were examined to investigate the HA line profiles. e) Location of MI on a long axis view with arrows indicating the location of the 2 short axis slices used to perform filter sensitivity analysis on 3 ROIs (red, purple and green)...... 151

xxix optimal window length. b) Unfiltered and filtered HA maps from a mid-ventricular 2

st rd nd mm slice for all 21 acquisitions (labelled below each image). 1 and 3 Row: HAUF. 2

th and 4 Row: HAAAGF...... 160

30 DED and c) 64 DED for the entire heart and for d) 12 DED e) 30 DED f) 64 DED for the center slices in 9 healthy animals. The different markers represent normalized RMSE from each animal. The mean normalized RMSE profile for each filtering technique

(AAGF (red), AVF (blue) and MF (green)) and the unfiltered maps (gray) is shown on the plot...... 162

Figure 42: Concordance-correlation and Bland-Altman’s Analysis. Plot of Concordance- correlation between gold standard and NEXF_C for a) 12 DED, b) 30 DED, c) 64 DED acquisition. The solid line corresponds to the reduced major axis and the dashed line corresponds to the line of perfect concordance. Bland-Altman’s analysis was performed between gold standard and NEXF_C generated maps for a) 12 DED, b) 30 DED, c) 64

DED acquisition. The solid lines show mean ± 1 SD...... 165

Figure 43: Three line profiles (the location of the profiles are shown in the cartoon of the

LV) showing HA transition on a slice from the apex, mid-ventricle and base of the LV comparing HA maps obtained from NEXF_C to the gold standard in a 12 DED acquisition. HA maps of the slice in the a) apex b) mid and c) base for which the profiles

xxx have been generated are shown in the top left hand corner of each image. Line profiles generated from filtered HA maps obtained from NEXF_C (4 NEX, solid line) show a smooth transition from the epicardium to the endocardium and are in agreement with the gold standard (20 NEX, dotted line)...... 166

Figure 44: Three line profiles (the location of the profiles are shown in the cartoon of the

LV) showing HA transition on a slice from the apex, mid-ventricle and base of the LV comparing HA maps obtained from NEXF_C for all the 3 DED settings (12, 30 and 64).

HA maps of the slice in the a) apex b) mid and c) base for which the profiles have been generated are shown in the top left hand corner of each image. Line profiles generated from filtered HA maps obtained from NEXF_C, for 12 (solid), 30 (dashed) and 64

(dashed-dotted) DED show a smooth transition from the epicardium to the endocardium and are in agreement with the each other...... 167

Figure 45: Regression analysis of normalized RMSE (both from AAGF filtered and unfiltered) vs normalized SNR for the entire heart and center slices. Plot of normalized

RMSE vs normalized SNR for HAUF maps and HAAAGF for a) 12 DED b) 30 DED and c)

64 DED for the entire heart and for d) 12 DED e) 30 DED f) 64 DED for the center slices in 9 healthy animals. The R2 values for each correlation for the exponential regression analysis is shown in each figure and the fit is denoted by a solid lines for both HAUF (red) and HAAAGF (black)...... 170

st Figure 46: HA maps and error profiles for infarcted myocardium. 1 Row: HAUF map

Left: From an infarcted region Right: From a basal slice, remote to the infarction site. 2nd

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Row: HAAAGF map Left: From an infarcted region Right: From a basal slice, remote to

rd the infarction site. 3 Row: Percentage difference between HAUF and HAAAGF Left: From an infarcted region Right: From a basal slice, remote to the infarction site. Error map is very uniform within the three different ROI under investigation...... 171

Figure 47: Specifications of the Beam and Cylindrical Models Simulated using Finite

Element Analysis. Geometric shape, methods of actuation, fiber orientation and the constraint condition is specified for a) M1; b) M2; c) M3; d) M4; and e) M5...... 183

Figure 48: Heart Model (M6 and M7) Simulated using Finite Element Analysis. a) MRI of the canine left ventricle based on which the heart model is constructed; b) Finite element model of the heart (based on canine geometry) showing compressional actuation throughout the epicardium (pink arrows); c) Fiber orientation in a long axis slice of the left ventricle post reconstruction in Matlab...... 184

Figure 49: Wave Propagation in all 6 Models. Single phase-offset for propagation in x direction (1st Row), 푦 direction (2nd Row) and 푧 direction (3rd Row)...... 193

Figure 50: Stiffness Maps for a Single Slice in all 5 Models. Each row indicates a beam model. Stiffness maps for compressional coefficients are shown in the first 3 columns. 1st

Column: 퐶11 map; 2nd Column: 퐶22 map; 3rd Column: 퐶33 map. Stiffness maps for shear coefficients are shown in the last 3 columns. 4th Column: 퐶44 map; 5th Column:

퐶55 map; 6th Column: 퐶66 map...... 195

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Figure 51: Stiffness Maps for a Single Slice in the Heart Model. The red box in the left image shows the mask of the LV. The first row shows the compressional coefficient maps, 퐶11, 퐶22, and 퐶33 map. The second row shows the shear coefficient maps, 퐶44,

퐶55 and 퐶66...... 196

Figure 52: Bland Altman’s Plot of the Compressional and Shear Stiffness Coefficients. a)

All 5 beam models pooled together; b) Heart model. The mean for the beams models is at

-1.8 kPa and the mean for the heart model is at -0.72kPa. All the parameters are within

±1.96 times the standard deviation...... 198

Figure 53: Schematic of the experimental set-up. The passive driver is placed on the animal’s anterior chest wall. Acoustic waves are generated using an active driver that’s placed outside the scan room. Waves from the acoustic driver are transmitted to the passive driver via the plastic tube...... 207

Figure 54: Cardiac Structural Anisotropy and Local Coordinate System. Top: Cardiac anisotropy showing the three axes of symmetry namely, fiber, sheet and sheet normal

[Adapted from Legrice et al. [121, 124]]. Bottom: The primary eigenvector corresponds to the fiber direction (n3), and n1 and n2 corresponds to the sheet and sheet normal directions respectively [Adapted from Romano et al. [259]]...... 212

Figure 55: Registration between cMRE Magnitude Image and DTI b0 Image at W8HTN. a) cMRE magnitude image b) unregistered DTI b0 image and c) registered DTI b0 image.

Green and red contours define the epicardial and endocardial borders respectively...... 213

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Figure 56: cMRE Magnitude Images and Wave Images. Baseline: a) Short-axis magnitude image of a mid-ventricular slice. (b-e) Snapshots of 4 phase offsets of the wave propagation in x-direction. Eight weeks post-surgery: f) Short-axis magnitude image of a mid-ventricular slice. (g-j) Snapshots of 4 phase offsets of the wave propagation in x-direction. (r, x). The images at week 8 indicate LV hypertrophy when compared to the baseline images...... 214

Figure 57: Box Plot of Anisotropic Stiffness Coefficients in all 6 Animals at BxHTN and

W8HTN. a) Compressional stiffness coefficients; b) Shear stiffness coefficients. C11

(p=0.05), C44 (p=0.03), C55 (p=0.04) and C66 (p=0.02) demonstrated significant increase at week 8 compared to baseline...... 215

Figure 58: Box Plot of Anisotropic Stiffness Coefficients in 5 Animals (Excluding the

Outlier) at BxHTN and W8HTN. a) Compressional stiffness coefficients; b) Shear stiffness coefficients. C11 (p=0.05), C44 (p=0.02), C55 (p=0.03) and C66 (p=0.01) demonstrated significant increase at week 8 compared to baseline...... 216

Figure 59: Helical Angle Map. Map showing feasibility of in-vivo cardiac DTI in a volunteer...... 224

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Chapter 1: Introduction

This chapter highlights the need for developing a non-invasive technique to diagnose heart failure which in turn provides the motivation for pursuing this research and emphasizes the overall significance of this dissertation.

1.1 Motivation and Significance

Heart failure (HF) is caused by abnormal cardiac function and has been identified as the epidemic of the 21st century [1]. Recent statistics by American Heart Association [2] reported that approximately 5.7 million (~2%) Americans suffer from HF and by 2030 the projected prevalence will increase by 46%. In 2012, the total cost for HF was estimated to be $30.7 billion, and by the end of 2030 the total cost has been predicted to increase by 127% [3]. According to the National Center for Health Statistics, one in nine deaths included HF as a contributing cause and 50% of the total HF incidences have mortality within the first 5 years of their diagnosis [2, 4]. These statistics show that HF is a serious clinical syndrome which, if unattended, will have severe global implications.

Although the importance of HF is well recognized and major advances in therapy have been made, accurate and timely diagnosis of HF continues to be a challenging problem, which prevents improvement in mortality and morbidity rates. Therefore, novel 1

diagnostic tools need to be developed to provide additional pathophysiological insights into HF that will facilitate early detection of the syndrome.

For over a century, myocardial stiffness (MS) has been recognized as the central determinant of cardiac function, particularly with respect to HF [5]. A global increase in

MS results in impaired ventricular relaxation, potentially leading to HF with preserved ejection fraction (HFpEF). A regional elevation of MS in myocardial infarction triggers

HF with reduced ejection fraction (HFrEF). Therefore, MS has the potential to be an important biomarker in the diagnosis and prognosis of HF [6-10].

Currently available techniques to measure MS, such as pressure-volume (P-V) loops and biomechanical testing provide global stiffness measurements and are invasive in nature, which makes them clinically challenging. In the last few decades, non-invasive imaging- based surrogates are being used to assess the mechanical properties of the myocardium.

However, the currently used non-invasive methods have several drawbacks. Doppler echocardiography (estimating MS from mitral inflow measurements) is operator dependent and has suboptimal predictive accuracy; although, ultrasound-based elasticity imaging although has shown promising results in animals, it is yet to be applied in-vivo in human hearts. MRI strain-based techniques (spatial modulation of magnetization tagging

[11], strain encoding [12, 13], and displacement encoding with stimulated echo [14]) measure myocardial deformation and do not consider the effects of variable loading conditions; hence they do not provide the true intrinsic stiffness estimates of the

myocardium. Therefore, there exists a need for developing a non-invasive diagnostic tool to spatially and temporally estimate MS.

With the advent of magnetic resonance elastography (MRE) [15-93], non-invasively quantifying the stiffness of the cardiac muscle has become possible [94-117]. Although the technique has been established by more than one research group, to the best of our knowledge, the utility of cardiac magnetic resonance elastography in the diagnosis of HF

(both HFpEF and HFrEF) has not been investigated extensively. In this dissertation, we explore the feasibility of using cardiac magnetic resonance elastography as a diagnostic tool to non-invasively estimate MS in HFpEF and HFrEF animal models.

To realize the importance and significance of MS in assessing HF models, it is first important to understand how the cardiovascular system functions under normal circumstances, which is introduced in the next section. In Section 1.3, a brief overview of

HF is given, followed by the importance of MS in diagnosing HF (Section 1.4) and a literature review of current invasive procedures used for quantifying MS (Section 1.5).

Section 1.6 states the problem being addressed in this dissertation and Section 1.7 provides an outline of the organization for the rest of the dissertation.

1.2 Cardiovascular System

The heart along with the circulatory body (arteries, veins, capillaries and blood) constitute the cardiovascular system. The cardiovascular system is responsible for transporting oxygen, nutrients, hormones and cellular waste products. To understand the

structure and function of the cardiovascular system this section briefly discusses cardiac anatomy, cardiac fiber geometry, cardiac physiology and coronary circulation. More details about cardiovascular system can be found in Pappano et al. reference book [118].

1.2.1 Cardiac Anatomy

The heart is a mechanical pump that supplies deoxygenated blood from the body to the lungs and oxygenated blood from the lungs to the body, thereby ensuring a steady continuous circulation.

Figure 1 shows the structure of the heart. It is a hollow cone-shaped organ divided into two halves (right and left side) by a muscular wall called the septum. The broad-end of the cone is called the base while the vertex of the cone is called the apex. The heart is composed of multiple chambers, vessels, valves and muscle layers briefly discussed below.

Chambers: The heart consists of four chambers, the right atrium, the right ventricle, the left atrium and the left ventricle. The right atrium receives deoxygenated blood from the body and sends it to the right ventricle, from where it is pumped to the lungs for oxygenation. The oxygenated blood from the lungs is received by the left atrium, which is then sent to left ventricle from where it is pumped back to the rest of the body. This transportation of oxygenated and deoxygenated blood is performed via the six major vessels.

Vessels: The six major vessels that carry blood to and from the heart are i) coronary sinus, ii) inferior vena cava, iii) superior vena cava, iv) pulmonary artery, v) pulmonary

vein, and vi) the aorta. Deoxygenated blood from the body is collected and brought to the right atrium by the coronary sinus (from the cardiac muscles), inferior vena cava (from the lower body) and superior vena cava (from the upper body). The right ventricle pumps this deoxygenated blood to the lungs via the pulmonary artery which post-oxygenation is sent to the left atrium via the pulmonary vein. The aorta is the largest artery in the body and is used to transport freshly oxygenated blood from the left ventricle to the different parts of the body. These major vessels are connected to the cardiac chambers by four valves that regulate the blood flow.

Valves: When the atriums contract, two atrioventricular valves, the tricuspid valve

(connecting the right atrium to the right ventricle), and the bicuspid mitral valve

(connecting the left atrium to the left ventricle) facilitates blood flow from the atrium to the ventricles and prevents backflow into the atrium. When the ventricles contract the two tricuspid semilunar valves, the pulmonary valve (connecting the right ventricle to the pulmonary artery), and the aortic valve (connecting the left ventricle to the aorta) prevents blood from flowing back into the ventricles from the pulmonary artery and the aorta respectively. Thus the primary responsibility of the valves is to regulate the direction of the blood flow (both oxygenated and deoxygenated). To ensure that the deoxygenated blood is sent for oxygenation and post-oxygenation the blood is transmitted back to the body, it is important for the heart muscles to contract, which is supported by the three layers of the cardiac muscle.

Muscle Layers: The heart wall is made up of three muscle layers. The outer wall known as the epicardium, the middle layer called the mid-myocardium and the inner wall known

as the endocardium. The epicardium is a thin layer of connective tissue and fat, and serves as the layer of protection for the heart. The mid-myocardium is composed of cardiomyocytes (cardiac muscle cells), which is primarily responsible for conduction of electricity (that coordinates the contraction) and contraction. The endocardium is composed of endothelial cells that line the chambers of the heart. The cells provide a smooth, non-adherent surface for blood collection and pumping and help regulate contractility. A set of self-generating electrical signals (as detailed below) initiates and regulates the autonomous pumping of the cardiac muscles.

Electrical Conduction and Mechanical Contraction: The mechanical activity of the heart is coupled with electrical signals that start at the sinoatrial node located near the wall of the right atrium. The signal from the sinoatrial node causes both the atriums to contract in unison. From there the electric signal travels to a second node, called the atrioventricular node, located between the right atrium and the right ventricle. At the atrioventricular node the signal pauses for a fraction of a second before spreading to the walls of the ventricles. The pause provides both the atriums just enough time to completely drain into the ventricles. From the atrioventricular node the electrical impulses enter the bundle of His (named after the inventor, Wilhelm His, Jr.) followed by the left and right branches extending through the inter-ventricular septum. Finally, the

Purkinjie fibers conduct the impulse from the apex of the heart to the ventricles, causing them to contract. These electrical impulses produced in the heart can be observed in an electrocardiogram (ECG) and is responsible for regulating the mechanical contraction of the cardiac muscles.

Figure 1: Cardiac Anatomy. Anatomy of the heart showing cardiac chambers, vessels, valves and muscle layers. [Adapted from musom.marshall.edu].

1.2.2 Cardiac Geometry and Structural Anisotropy

The fiber architecture, orientation, and anisotropy play a significant role in preserving the electrical and mechanical functions of the heart. While the myocardial fiber orientation influences the electrical conduction velocity and resistivity [119], the distribution of stresses in the left ventricular wall is a function of both the fiber tension and fiber

orientation [120]. Streeter et al., [120] showed using histology that the fibers inside the heart are oriented such that it bears a helical geometry. This helical geometry exhibits a smooth transition from a left-handed helix in the epicardium to a right-handed helix in the endocardium with the mid-myocardium being essentially circumferential in nature

(Figure 2). The counter-directional helical (left-handed in epicardium and right-handed in endocardium) pattern plays an important role in generating the left ventricular torsional motion during systole and diastole. Due to the double helix band at systole when the heart contracts, the apex of the left ventricle twists in an anticlockwise direction while the base twists in a clockwise direction (as viewed from the apex), while at diastole the opposite twisting motion occurs.

The afore-mentioned helical network of muscle fibers is also known to be structurally anisotropic [121]. The fiber bundles are organized to form sheets of fibers that are separated by a complex structure of cleavage planes giving rise to a laminar architecture.

The laminar fiber architecture is orthotropic in nature with three planes of symmetry. Of the three planes one is oriented along the fiber direction, one along the sheet, and the third along the sheet normal direction (Figure 2) [122-129].

This laminar structure of the heart along with its anisotropy is of utmost importance for understanding the mechanics (the orthotropic distribution of stress) associated with a normal beating heart [122, 126, 127, 130-132]. Furthermore, cardiac diseases such as myocardial infarction (MI) alter the myocardial fiber orientation which results in remodeling of the laminar structure [133-135]. This remodeling affects the mechanical

properties of the myocardium which plays an important role in identifying potential risks and therapy [122].

Figure 2: Cardiac Fiber Geometry and Structural Anisotropy. Top: Helical fiber geometry in epicardium (left-handed), mid-myocardium (circumferential) and endocardium (right-handed). Bottom: Cardiac anisotropy showing the three axes of symmetry namely, fiber, sheet and sheet normal [Adapted from Legrice et al. [121, 124]].

As shown by Streeter et al. histology can be used to analyze the myocardial fiber orientation. However, histological analysis has several limitations: i) it is an invasive procedure (requires myocardial tissue samples); ii) it is time consuming; and iii) it is

challenging to build three-dimensional fiber architecture from the two-dimensional myocardial fiber orientation information obtained using histology. Today, with advances in medical imaging, and the advent of diffusion tensor imaging (DTI), a MRI-based technique, it has become possible to non-invasively visualize the myocardial fiber architecture and quantify the helical geometry of the heart [136]. The details of DTI and its scope in diagnosing disease conditions are discussed in the next chapter.

1.2.3 Cardiac Physiology

The cardiac cycle consists of two primary phases: i) systole or ventricular contraction, and ii) diastole or ventricular relaxation. A series of electrical impulses (represented by the electrocardiogram or ECG) coordinates the cardiac cycle and causes change in chamber pressure and volume. Based on the pressure and volume in the chambers the two cardiac phases (systole and diastole) can further be sub-divided into seven cardiac events that are discussed below and illustrated in Figure 3.

Atrial Contraction: This cardiac event is initiated by an electrical impulse generated by the sino-atrial node (P wave on ECG representing atrial depolarization), which causes the atria to contract, thereby increasing the pressure within the atrial chamber. This forces the remaining blood (10%) in the atrium to flow into the ventricles (active filling) resulting in the final resting volume also known as the end-diastolic volume.

Isovolumetric Contraction: This phase begins with the appearance of the QRS complex on the ECG, which represents ventricular depolarization. Initially, as the ventricles contract, intra-ventricular pressure increases rapidly and the rate of pressure development 10

becomes maximal. However, ventricular volume does not change, hence termed

"isovolumetric" contraction.

Figure 3: Cardiac Physiology. The seven different events occurring across the cardiac cycle. [Adapted from musom.marshall.edu].

Rapid Ejection: In this phase, pressures in right ventricle and left ventricle exceed the pressure in the pulmonary artery and the aorta respectively thereby allowing rapid ejection of blood.

Reduced Ejection: This phase marks the beginning of ventricular repolarization as indicated by the T-wave on the ECG. Repolarization leads to a decline in ventricular

active tension and pressure generation reducing the rate of ejection. Left and right atrial pressures rise gradually due to continued venous return from the lungs and from the systemic circulation, respectively.

Isovolumetric Relaxation: When the intra-ventricular pressures fall below the threshold the aortic and pulmonic valves close spontaneously marking the beginning of the isovolumetric relaxation phase. Although ventricular pressures decrease, the volume remains constant since the valves remain closed. This ventricular volume is called the end-systolic volume.

Rapid Filling: When the intra-ventricular pressures fall below their respective atrial pressures, atrioventricular valves open rapidly and passive ventricular filling begins.

Once the ventricles are completely relaxed, and more blood enters from the atria, the pressure in the ventricles start rising gradually.

Reduced Filling: Finally, as the ventricles continue to fill with blood and expand, they become less compliant and the intra-ventricular pressures rises significantly. The increase in intra-ventricular pressure reduces the pressure gradient across the atrioventricular valves so that the rate of filling falls in late diastole. In normal resting hearts, since about

90% of ventricular filling occurs before atrial contraction, it is known as passive filling.

To ensure that the above mentioned cardiac events are executed efficiently it is important to ensure that the heart’s pumping action is regulated and adapts to changes in venous return (flow of blood back to the heart). This forms the basis for the Frank-Starling mechanism (also known as Starling’s law of the heart) which states that the heart’s

intrinsic ability to change its force of contraction ensures that the blood volume entering the heart matches the blood volume ejected from the heart across a wide range of venous return. The Frank-Starling mechanism is represented graphically by plotting an index of ventricular performance along the ordinate and an index of fiber length along the abscissa. The commonly used indexes of ventricular performance are cardiac output, stroke volume and stroke work while those for fiber length are ventricular end-diastolic volume, ventricular end-diastolic pressure, ventricular circumference and mean arterial pressure [137]. Thus, a family of curves represents the Frank-Starling mechanism which is also known as, Starling’s law of the heart. This intrinsic mechanism to adapt to venous changes is very important since a marginal mismatch between blood entering and leaving the ventricles can result in peripheral edema (backup of blood into systemic veins) or pulmonary edema (backup of blood into the pulmonary circulation). Furthermore, different disease conditions contribute to alterations in the Frank-Starling mechanism and hence the family of curves has diagnostic significance.

A number of hemodynamic parameters and indices of systolic and diastolic functions are measured to assess cardiac function and physiology. A glossary of the parameters that will be measured in different chapters of this dissertation, along with their acronyms, units, normal range, and definition, is provided in Table 1.

Table 1: Cardiac Functional Parameters.

Normal Parameter Acronym Unit Definition Range beats/min 60-100 bpm Heart Rate HR No. of cardiac cycles in a minute (bpm) End-Systolic 100-140 mmHg Pressure in left ventricle at ES ESP mmHg Pressure End-Diastolic 0-20 mmHg Pressure in left ventricle at ED EDP mmHg Pressure End-Systolic 16-143 ml Volume in the left ventricle at the end ESV Ml Volume of isovolumetric relaxation End-Diastolic 65-260 ml Volume in the left ventricle at the end EDV Ml Volume of atrial contraction 55-100 ml It is the amount of blood pumped by Stroke Volume SV Ml the left ventricle in one contraction measured by EDV – ESV 50-70 % Percentage of blood ejected from the Ejection EF % left ventricle in one contraction given Fraction by, (SV/EDV)*100 4.0-8.0 l/min Amount of blood pumped every Cardiac Output CO l/min minute given by, SV*HR

1.2.4 Coronary Circulation

While there is an enormous vascular network distributed throughout the body, those related to the heart are of interest from the perspective of this dissertation. As already mentioned, there are six major vessels that carry blood to and from the heart. Apart from those, the cardiac muscles require their own supply of blood which is provided by the coronary circulation (see Figure 4). Two major arteries that originate at the base of the aorta (from openings called coronary ostia) supply blood to the cardiac muscles, the left coronary artery (divides into left anterior descending and circumflex branches), and the 14

right coronary artery. Deoxygenated blood is carried away by the cardiac veins that drain into the coronary sinus and by the anterior and thebesian veins that directly drain into the cardiac chamber.

Figure 4: Coronary Circulation. Arteries and veins supplying blood to the heart. [Adapted from Pearson Education Inc.].

The cardiovascular anatomy, architecture and physiology discussed so far provide a condensed description of how the heart, along with the vascular system, functions as a mechanical pump. When this mechanical pump is compromised HF occurs. The next section gives an overview of HF related to its epidemiology, pathophysiology and etiology.

1.3 Heart Failure - Overview

Braunwald describes HF as ‘‘a pathophysiological state in which an abnormality of the cardiac function is responsible for the failure of the heart to pump blood at a rate commensurate with the requirements of the metabolizing tissues” [138]. This inability of the heart to pump blood to meet the body’s need can be either due to its inability to fill or eject. Hence, HF can be broadly classified into two distinct categories based on the left ventricular ejection fraction: HF with reduced EF (HFrEF) and HF with preserved EF

(HFpEF) [139]. Although there is some overlap between the two spectra of HF, in general they have distinguishing epidemiology, pathophysiology, and etiology which are discussed below.

Epidemiology of HF: Epidemiological studies show that among the 5.7 million

Americans who suffer from HF there is equal prevalence of both HFrEF and HFpEF

[140-143]. Despite the equal prevalence of both types of HF, the prevalence of HFpEF with respect to HFrEF is increasing at the rate of 1% per year [144]. Additionally, morbidity and mortality in HFpEF is usually driven by non-cardiac causes that trigger cardiac incidences, whereas in HFrEF, it is generally due to a direct cardiac condition

[145]. Furthermore, there is a distribution bias based on gender, age and race. As shown in Figure 5, a higher percentage of men suffer from HFrEF while a majority of HFpEF patients are women [139, 144, 146]. HFpEF is more common in older adults [147, 148] and studies based on races have shown that Caucasians are more prone to HFpEF than

African Americans [142, 149].

Figure 5: Epidemiological Variation in Prevalence of HF. This study on 4910 patients shows that younger men are more prone to HFrEF while older women are prone to HFpEF [Adapted from Borlaugh et al. [139]].

Pathophysiology of HF: Although the pathophysiology of HFrEF and HFpEF has some similarities in terms of left ventricular (LV) structure and function (as in increased LV mass and increased LV end-diastolic pressure [150, 151]), there are several distinct pathophysiological characteristics that are specific to each kind of HF. The primary pathophysiological difference between the two forms of HF is with respect to LV geometry and LV function. While HFrEF is characterized by LV dilation, eccentric LV hypertrophy, and systolic and diastolic dysfunction; HFpEF is associated with concentric

LV hypertrophy, and impaired diastolic function [151].

Etiology of HF: Both HFrEF and HFpEF can occur due to multiple disease conditions. 17

The most prominent of these diseases and their impact on myocardial stiffness (MS) are as follows: HFrEF is most commonly caused by ischemic heart disease and/or myocardial infarction (MI) that leads to regional elevation in myocardial stiffness (MS) which compromises the heart’s ability to eject efficiently [152]; on the other hand,

HFpEF is generally caused by hypertension, aging, diabetes, and other conditions that lead to LV hypertrophy, impaired LV relaxation and global increase in passive LV MS which compromises the heart’s ability to fill efficiently [9]. This indicates that both kinds of HF are related to changes in cardiac mechanical properties which are reflected in increased LV MS. In the next section we discuss different disease conditions and their association with increased LV stiffness in HF models.

1.4 Myocardial Stiffness – Its Significance in Heart Failure

Myocardial stiffness (MS) is the central parameter that is associated with abnormal cardiac function [6-9]. MS is elevated in both HFrEF and HFpEF. In order to emphasize the importance of MS as a potential universal metric to effectively diagnose HF this section highlights HF causing conditions that have an effect on MS.

1.4.1 HFrEF

As mentioned in the previous section, ischemia and infarction are the two major cardiac conditions that lead to HFrEF.

Myocardial Ischemia: When the blood flow is reduced through one or more of the coronaries (more common in the arteries but it can also occur in the veins), myocardial ischemia occurs (Figure 6). Conditions that can lead to myocardial ischemia are: i) Coronary Artery Disease (CAD): Coronary artery disease (CAD) is a disorder

wherein cholesterol-laden plaque starts to build up in the coronary arteries, resulting

in atherosclerosis [153]. In this condition, the arteries which were formerly smooth

and elastic, lose its compliance, become narrow and rigid, and therefore restrict the

blood flow to the heart [154]. ii) Coronary Thrombosis: The plaques that develop in atherosclerosis can rupture,

causing coronary thrombosis or blood clot. The clot when large enough to block an

artery can lead to severe myocardial ischemia [155, 156]. iii) Coronary artery spasm: Coronary artery spasm is a temporary stiffening and

tightening of the muscles in the artery wall, which leads to sudden narrowing of the

coronary arteries, thereby restricting the blood flow through the artery [157-159].

These ischemia causing conditions have a direct impact on the mechanical properties of the myocardium. Several studies have demonstrated that inadequate supply of oxygen during myocardial ischemia causes elevation of tissue stiffness both in the ischemic area and surrounding regions [8, 160-171]. Furthermore, other studies have shown that the increased MS in ischemic hearts recovers after reperfusion [172], indicating that reduced

MS is associated with recovery.

Figure 6: Myocardial Ischemia. Ischemia can be caused by coronary artery disease, coronary thrombosis or coronary spasm. [Adapted from Mayo Foundation for Medical Education and Research].

Myocardial Infarction (MI): Myocardial infarction or MI is a condition which generally arises from a state of prolonged ischemia and is caused by the complete occlusion of the coronary artery. The structural and mechanical properties of both the infarcted and non- infarcted myocardium undergo a series of progressive changes with the evolution of MI, which can be divided into 4 stages: i) Acute ischemia, ii) Necrosis, iii) Fibrosis, and iv)

Remodeling [10, 173, 174].

Acute ischemia occurs in the first few hours, where the mechanics of the infarcted region are dominated by the conversion of the affected myocardium from an active, force- generating material to a passive viscoelastic material. During this phase there is an 20

immediate loss of contractility in the infarcted region, a condition termed hypokenesis, and increased contractility in the viable myocardium, a process termed hyperkenesis.

Following the initial stages of ischemia the myocardium enters into a state of necrosis.

During necrosis, as cellular death sets in, the myocardium begins to undergo coagulation necrosis (cell swelling, organelle breakdown and protein denaturatization), followed by neutrophilic infiltration. Three to four days post-infarction, granulation tissue appears at the edges of the infarct zone which consists of macrophages and fibroblasts. When the number of fibroblasts and amount of new collagen begins to increase rapidly it marks the end of the necrotic stage (approximately 7 days in humans [175]). It has been shown that in the necrotic phase, both the circumferential and the longitudinal LV MS increase under multi-axial loading [176] but uniaxial tests did not reflect any change in LV MS either in the longitudinal or circumferential directions [177, 178].

Post necrosis the infarct enters into the fibrotic phase wherein the collagen content increases rapidly and the infarct stiffness roughly correlates with the collagen content. As collagen accumulation slows and mechanical properties of the myocardium decouple from the collagen content it marks the end of the fibrotic phase. The increase in LV MS peaks during the fibrotic phase and this increase in LV MS exhibits directional dependency. The deposition of large collagen fibers during fibrosis is predominant in the circumferential direction [179] which contributes to maximal increase in LV MS in the circumferential direction [176, 180]. Additionally, increased LV MS and hence reduced compliance over time decreases LV EF.

The last stage of infarct evolution is called the remodeling phase wherein the mechanical properties of the infarct decouple from the collagen content. Although collagen content may continue to rise for several weeks, LV MS in the infarcted region drops significantly during the remodeling phase [176].

Thus, from the above discussion it is evident that LV MS alters continuously during MI evolution. Therefore, quantifying LV MS can provide important information about the stage (acute ischemia, necrotic, fibrotic or remodeling) of MI progression, which can assist in stage specific treatment development.

1.4.2 HFpEF

Recently, HFpEF has been identified as a truly heterogeneous syndrome, influenced by a multitude of cardiac and non-cardiac comorbidities. It has been associated with increased passive MS that can occur either naturally (as in aging [181]), or indirectly (as a response to a primary abnormality like in diabetes [182]), or directly (due to some cardiovascular disease as in hypertension [183], diastolic dysfunction [184], cardiac amyloidosis [185]).

This section discusses in detail how these abnormalities affect the passive mechanical properties of the myocardium.

Aging: Aging is a naturally occurring evolutionary process that is characterized by a number of physiological, structural and functional changes over the life-span. In the cardiac muscles, aging leads to increased deposition of extracellular matrix components, primarily collagen with increased fibril diameter and collagen cross-linking, increased

ratio of type I to type III collagen and decreased elastin content all of which contribute to increased LV MS [186]. In a recent study on 788 subjects (mean age was 60 at first exam) examined twice within an interval of 4 years, it was observed that both end- systolic and end-diastolic elastance increased over the 4 year time period, especially in women [187], indicating that aging contributes to increase in LV MS. This increase in

LV MS causes impaired ventricular relaxation which may trigger HFpEF over time.

Aging is also associated with increase in arterial stiffness that induces hypertension and is a major contributing factor for HFpEF [188].

Hypertension: Hypertension (also known as high blood pressure) is a condition wherein the blood flows through the arteries with increased force. Hypertension is associated with a variety of cardiac structural and functional changes, such as LV hypertrophy, left atrial and aortic root enlargement, LV dysfunction and prolonged ventricular repolarization

[189, 190]. Among these different manifestations of hypertension, LV hypertrophy is most prevalent and is associated with an increased risk of cardiac morbidity and mortality

[191]. Hypertensive LV hypertrophy is affected primarily by two pathological processes, i) myocyte hypertrophy, and ii) progressive accumulation of fibrous tissue within the cardiac interstitium [192, 193]. This accumulation of fibrous tissue results in distortion of myocardial tissue structure, which in turn increases MS leading to diastolic dysfunction

[190]. Several studies on small animals (rats [194]), large animals (dogs [195]) and patients [196] have indicated that hypertension is associated with LV hypertrophy and an increase in LV MS and if uncontrolled may lead to severe diastolic dysfunction which in turn can trigger HFpEF. 23

Diastolic Dysfunction: As mentioned in section 1.2, diastole is that phase of the cardiac cycle wherein the ventricles relax and fill in with blood. Diastolic dysfunction occurs due to abnormal stiffening of the ventricular wall so that ventricular relaxation is compromised which in turn contributes to inadequate ventricular filling [197, 198]. To compensate for the impaired relaxation and abnormal filling, the pressures in the ventricles increase considerably, thereby affecting the Frank-Starling mechanism. If untreated, over time this increased pressure can lead to either pulmonary or systemic congestion and eventually trigger HFpEF [148, 199]. Previous studies have shown that by using pharmacological measures to normalize MS, researchers were able to improve ventricular filing and hence restore diastolic function [200, 201]. Therefore, quantifying

MS can assist in the diagnosis of diastolic dysfunction and timely treatment can prevent the dysfunction from progressing onto HFpEF.

Cardiac Amyloidosis: Cardiac amyloidosis is a condition where proteins called amyloids are deposited in the cardiac tissues. As the amyloid deposit increases, the heart gets increasingly stiff [202, 203] and is unable to relax completely, thereby leading to HFpEF

[185, 204, 205].

Diabetes: Diabetes is a condition characterized by high blood glucose levels that occur due to the body's inability to produce and/or use insulin. Although not a cardiac disease in itself, its occurrence leads to conditions that have an influence on the passive mechanical properties of the myocardium. Diabetes causes increase in arterial stiffness that can lead to hypertension, which, as already discussed, is a notable etiology for

HFpEF [206]. It has been shown that diabetes causes an increase in deposition of collagen in the myocardium and advanced glycation end-products which promote cross- linking contribute to increased MS [207]. An endomyocardial biopsy study involving

HFpEF patients both with and without diabetes, demonstrated that diabetic HFpEF patients had increased LV MS (assessed by radial LV stiffness) compared to the non- diabetic HFpEF patients [208].

Based on the discussion in this section it can be concluded that MS is indeed an important parameter that is associated with cardiac function in HF conditions. Therefore, it has the potential to be used as a diagnostic metric. The next section provides a literature review on the techniques currently used to measure MS.

1.5 Invasive Techniques to Quantify Myocardial Stiffness – Its Inception and

Evolution

In 1856, Carl Ludwig first defined the dependence of cardiac function on diastolic volume and established the importance of cardiac mechanics in assessing cardiac dysfunction. He described, “... a strong heart that is filled with blood empties itself more or less completely, in other words, filling of the heart with blood changes the extent of contractile power” [5, 209]. Post its inception in 1856, extensive work was performed by physiologists to understand and quantify the relationship between cardiac mechanics and cardiac function. The first diagnostic significance of cardiac compliance was recognized in 1918 when Otto Frank, using isolated frog hearts, demonstrated that the strength of the ventricular contraction increases with ventricular filling volume [210]. This observation 25

was extended by Ernest Starling and colleagues who found that increasing venous return to the heart increases the filling pressure of the ventricle leading to increased SV [211-

214]. Towards the middle and later half of the 20th century, biomechanical testing on ex- vivo strips was introduced to study the mechanical properties of cardiac muscle [215-

218]. A concise description of these two techniques that are currently used in the clinics to assess MS is provided below.

P-V Loop Analysis in MS: P-V loop analysis is practiced routinely to investigate the mechanical properties of the myocardium and to estimate MS [219-228]. It involves measuring the LV cavity pressure and the ventricular volume throughout the cardiac cycle by insertion of a catheter through the femoral artery into the LV. The pressure is then plotted against the volume to obtain the P-V loop. A family of such loops is obtained by varying the loading conditions (Figure 7) and then the loops are used to identify the end-systolic and end-diastolic pressure volume points. The slope of the line joining the end-systolic P-V points represents the end-systolic elastance (ratio of end-systolic pressure to end-systolic volume). The line joining the end-diastolic P-V points is nonlinear and it defines the passive ventricular stiffness of the myocardium. Being non-linear in nature a variety of curves that are fit to obtain the end-diastolic stiffness; however, no consensus regarding the best fit is available. Previous research using P-V loop analysis has shown an increase in LV MS in both HFrEF [229] and HFpEF [226] conditions.

Although P-V analysis is recognized as the gold standard for assessing LV mechanical properties [6, 227, 228, 230], it is invasive in nature, requires technical precision, provides a global stiffness measurement, and is therefore clinically challenging.

Biomechanical Testing: Excised strips from the myocardium are required to perform either uniaxial or biaxial mechanical testing [216-218, 231-233]. The excised samples are mounted on a mechanical testing system and a load (uniaxial or biaxial) is applied to it until failure. The load (stress) causes deformation of the specimen (strain) which is recorded continuously. This information is then used to obtain the stress vs strain graph which provides different mechanical parameters (such as Young’s modulus, ultimate tensile strength) of the material (Figure 8). Biomechanical testing has been used to study

the properties of the healthy and diseased myocardium [216]. [176].

Although, biomechanical testing provides stiffness estimates of the myocardial tissue, it is invasive in nature, provides global measurement, cannot account for physiological conditions, and cannot provide information of MS as a function of the cardiac cycle.

The preceding discussion suggests that the currently used diagnostic measures to quantify

MS are inefficient since they are invasive in nature. Therefore, there is a need to develop a technique that i) is non-invasive in nature and ii) can use MS as a metric to provide diagnostically relevant information to assess HF patients.

1.6 Problem Statement

The primary problem being addressed in this dissertation is the lack of an efficient diagnostic tool to non-invasively quantify MS in HF patients. To address this problem the overall goal of this dissertation is as follows:

1) Implement a novel technique called cardiac magnetic resonance elastography

(cMRE) to non-invasively quantify isotropic MS in HF animal models and

establish its diagnostic potential.

2) Explore the potential of ex-vivo cardiac DTI (in-vivo cardiac DTI is beyond the

scope of this dissertation) in investigating fiber architecture in a HF model.

3) Use finite element simulations to validate waveguide cMRE (uses cMRE in

conjunction with DTI), a technique used to measure anisotropic stiffness.

4) Measure anisotropic MS using waveguide cMRE in a HF model to investigate if

anisotropic MS provides additional diagnostic information compared to isotropic

MS.

1.7 Organization of this Dissertation

To conceive, develop and validate solutions to the afore-mentioned problem, the rest of this dissertation has been organized as follows:

Chapter 2 introduces non-invasive techniques used for assessing MS and provides detailed description of the principles of two non-invasive techniques, cMRE and waveguide MRE.

Chapter 3: describes the implementation of cMRE in a HFpEF porcine model to demonstrate the potential of MS in identifying global changes in the mechanical properties of the myocardium. The cMRE-derived MS measurements are validated against in-vivo pressure measurements obtained via LV catheterization.

Chapter 4: describes the implementation of cMRE in a HFrEF porcine model to demonstrate the potential of MS in identifying regional changes in the mechanical properties of the myocardium. The cMRE-derived MS measurements are validated against mechanical testing-derived MS measurements.

Chapter 5: describes ex-vivo DTI to investigate the change in cardiac geometry as a result of HFrEF in formalin-fixed ex-vivo specimens and ensures that the alterations are caused due to pathology and not due to the fixation process.

Chapter 6: describes an adaptive anisotropic Gaussian filtering technique for cardiac DTI applications that has the potential to reduce acquisition time thereby assisting in faster imaging; tensor estimation from DTI is validated using helical angles.

Chapter 7: describes the implementation of waveguide MRE (that accounts for anisotropy of the material) using simulations of wave displacement generated from finite element modeling. The results obtained from waveguide MRE are validated against known mechanical properties of the simulated models.

Chapter 8: describes implementation of waveguide cMRE in a hypertensive porcine model (that has the potential to trigger HFpEF) to demonstrate feasibility of measuring

anisotropic MS in HF causing disease condition.

Chapter 9: provides concluding remarks and a direction for future work.

Chapter 2: Non-Invasive Techniques to Estimate Myocardial Stiffness

Chapter 1 summarized the importance of myocardial stiffness (MS) in the diagnosis of heart failure (HF). Specifically, it was noted that the currently available techniques to estimate MS are invasive in nature and there is a need for developing a non-invasive tool.

This chapter briefly explores current non-invasive surrogates used to quantify MS.

Additionally, we propose and discuss in detail two novel non-invasive diagnostic tools to quantify MS: cardiac magnetic resonance elastography and waveguide magnetic resonance elastography, which are the focus of the following chapters and the objective of this dissertation.

2.1 Ultrasound Imaging

Ultrasonography is a widely used medical imaging technique that is based on the propagation of high frequency acoustic waves to construct morphological images of the organs. Ultrasound in conjunction with elasticity imaging, known as ultrasound elastography, estimates tissue stiffness either from the analysis of the strain in the tissue under a stress (quasi-static methods), or by the imaging of mechanical waves (dynamic), whose propagation is governed by the tissue stiffness [234].

2.1.1 Quasi-static Ultrasound Elastography

In this type of imaging, a constant stress is applied to the tissue and the displacement generated by the stress is estimated using two-dimensional correlation of ultrasound images [234, 235]. Although the technique can be implemented easily since the applied stress is unknown and only the strain is imaged, the true stiffness of the material remains undetermined [234].

2.1.2 Dynamic Ultrasound Elastography

In this type of imaging a time-varying force, which can either be a short transient mechanical force or an oscillatory force with a fixed frequency, is applied to the tissue of interest. In biological tissues, this time-varying mechanical force propagates as either shear or compressional waves. The compressional waves are longer waves, also known as ultrasounds, which can be used to image the body. From the perspective of determining the mechanical property of the underlying tissue, it is the shear wave that is of interest.

They have shorter wavelengths and propagate with much reduced speed as compared to compressional waves. The speed of the shear wave (푐푠) is directly related to the elasticity of the medium and hence the shear modulus, 휇 can be determined using the following relationship [234],

2 휇 = 휌푐푠 . (1)

Although this technique is far more complex than quasi-static ultrasound elastography, different groups have implemented it to measure MS [236-238]. A novel dynamic ultrasound technique characterizing lamb wave and shear wave dispersion using ultrasound vibrometry has been applied to measure the stiffness of the myocardium. With 33

open and closed chest ultrasound in a healthy in-vivo porcine model, using the technique researchers have shown that the MS at systole is higher than that obtained at diastole

[238-240].

Despite the promising result in animals, to the best of our knowledge, dynamic ultrasound elastography has not yet been implemented on the human heart. Moreover, this technique does not have the capability to consider the total 3D displacement field in one scan.

2.2 MRI Based Techniques

Currently, cardiac cine MRI is the gold standard to assess cardiac function and morphology but not the intrinsic properties of the myocardium. Cine images acquired using MRI can be used to determine cardiac functional parameters such as stroke volume,

EF, cardiac output, and cardiac morphology such as end-systolic and end-diastolic thickness and LV mass.

2.2.1 Strain-Based MRI

Cine MRI can also be used to investigate cardiac deformation known as strain imaging.

There are several techniques to image cardiac strain such as myocardial tagging, strain encoding (SENC) [13], displacement encoding with stimulated echoes (DENSE) [14] and others. Myocardial tagging [241] uses modulation of the magnetization gradient to null the signal from the myocardium in a grid like pattern called tags. Cine images thus acquired display a dark grid like pattern on the myocardium which moves with the

cardiac cycle and is tracked to measure the displacement field. SENC imaging calculates cardiac strain from two images with different frequency modulation in the slice direction

[13]. DENSE is a phase-contrast MRI based technique that encodes myocardial deformation into the phase of a MRI signal [14]. Since the phase of DENSE images is proportional to the displacement, therefore, strain can be obtained by calculating the derivatives of the phase. These strain-based imaging techniques have been used to investigate cardiac mechanics in diseased conditions [242-244]. Although these techniques provide information about cardiac mechanics, they only measure tissue deformation and do not consider any loading conditions to estimate the modulus/stiffness of the myocardium.

2.2.2 Magnetic Resonance Elastography

Recently, with the advent of cardiac magnetic resonance elastography (cMRE) non- invasively quantifying MS has become possible. cMRE is an application of magnetic resonance elastogaphy (MRE), a phase-contrast (PC) MRI based technique that is used to estimate tissue stiffness non-invasively. The principle of MRE involves three different stages (Figure 9):

Stage 1: An external driver induces mechanical waves into the tissue of interest.

Stage 2: External waves are synchronized with motion encoding gradients to encode the waves in the phase of MRI image using PC technique.

Stage 3: Finally, a mathematical process called inversion is implemented on the wave images obtained from PC MRI to generate spatially varying quantitative stiffness maps.

Figure 9: The principle of MRE simulated in a phantom. Left: Magnitude image of the phantom with soft and stiff inclusions seen as the hyper-intense and hypo- intense regions, respectively. Middle: Wave image of a single phase offset obtained from MRE acquisitions performed at 100 Hz frequency. A red to blue region is a wavelength and stiff inclusions have longer wavelengths. Right: Stiffness map obtained from wave inversion indicating the soft and stiff inclusions [Adapted from Mariappan et al. [53]].

Previous studies have applied MRE in the cardiac muscles (both animals and human volunteers) and demonstrated very promising results [94-97, 99-104, 108, 110, 112, 116,

245, 246]. In an in-vivo study in a healthy animal model it was shown that cMRE-derived stiffness strongly correlates (푅2 = 0.84) with pressure measurements obtained via ventricular catheterization [97]. Another research group observed similar correlation between LV pressure and cMRE-derived shear wave amplitudes in a porcine model 36

(푅2 > 0.76) [116]. In an in-vivo animal study, by varying the loading conditions (by infusing dextran-40 to increase pre-load) and measuring MRE-derived end-diastolic stiffness and pressure simultaneously, researchers were able to obtain a stiffness versus volume plot which was in good agreement with the pressure versus volume plot [104].

By performing cMRE in healthy human volunteers a previous study established that end- systolic MS was higher than end-diastolic MS and that MS increases with increase in age

[96, 107, 247]. Another research group used shear wave amplitudes obtained from cMRE to demonstrate that the wave amplitudes in diastole were higher than that in systole [114].

They also demonstrated that the ratio of shear wave amplitudes inside the ventricle to the anterior chest wall in young volunteers was higher compared to that in older volunteers

[245]. cMRE has also been investigated in cardiac diseases (both animals and patients) that have the potential to trigger HF. In a MI induced porcine model researchers observed that in the same pig cMRE-derived MS in the infarcted region was significantly higher (p <

0.001) than the remote, non-infarcted region [100]. Using cMRE, an increased MS was observed in hypertrophic cardiomyopathy patients as compared to normal healthy volunteers [99]. Another research group used shear wave amplitudes obtained from cMRE to show that the wave amplitudes were significantly lower (푝 < 0.001) in patients with diastolic dysfunction [110, 245].

Although these studies demonstrate very promising results, to the best of our knowledge, no research groups have so far used cMRE to extensively investigate its application in the two different kinds of HF models, and this dissertation presents the first attempt in that

direction. In this dissertation we investigate the potential of cMRE for the diagnosis of

HF, develop a cMRE model to account for the heart’s complex anisotropic structure, and implement that model in HF inducing disease conditions. In the next section the principle of cMRE will be discussed, followed by a literature review of the model that will be used in this dissertation for estimating anisotropic stiffness (sections 2.4 and 2.5).

2.3 Magnetic Resonance Elastography (MRE)

As already mentioned, the principle of MRE involves three different stages which are detailed below:

2.3.1 Stage 1: Generation of Mechanical Waves by External Drivers

In general, MRE uses single frequency (although multiple frequencies can be used) vibrations generated by external driver devices to induce mechanical waves into the tissue of interest [53]. The frequency, amplitude, and design of the external mechanical actuation system required to generate mechanical waves into the tissue of interest plays an important role in determining the sensitivity of the encoded wave image.

Higher frequency waves are more sensitive to subtle deformations because of smaller wavelengths; however, higher the frequency, stronger is the attenuation, which restricts the depth of penetration. Typically wave frequency used in MRE ranges between 50-

500Hz. Low amplitude shear waves have decreased phase contrast sensitivity and signal to noise ratio. Amplitude of the propagating wave can be attenuated due to viscous losses of wave energy and geometric dispersion of wave fronts. Attenuation can also occur in

stiffer tissues, which in turn reduces the amplitude of the waves probing the tissue behind the stiff region, known as shadowing artifact [53, 54]. Therefore, an appropriate driver system to generate optimal displacement field for a given frequency should be chosen.

Hence, designing the actuation system is an integral part of MRE acquisitions. Currently, there are three primary driver systems (Figure 10) used for MRE imaging: i) electromechanical [79] ii) piezoelectric [248, 249], and iii) pneumatic [58]. Each has its own advantage and disadvantage as detailed below.

Figure 10: MRE Driver Systems. Left: An electromagnetic driver system. Middle: A piezoelectric driver system. Right: A pneumatic driver system [Adapted from Mariappan et al. [53]].

i) Electromagnetic Actuator: The electromechanical actuator consists of a coil with

several turns that utilizes the static magnetic field of the MR scanner to induce a

torque in the driver system (Lorentz force) when an alternating current is applied.

Although these drivers are relatively cheap and can generate a wide range of

vibrational frequencies, the control over the vibrational amplitude is minimal.

Moreover, when gradients are played and the magnetic field inside the scanner is not 39

constant, the currents generated in the driver coils can cause interference which can

manifest as image artifacts. ii) Piezoelectric Actuator: The piezoelectric actuator consists of a stack of piezoelectric

crystals that expands or bends when a voltage is applied. An alternating voltage,

when applied on a fixed stack of piezoelectric material (placed in between a spring

and a rigid wall), can generate longitudinal oscillations. Although piezoelectric

vibrations are independent of switching gradients, they require high voltage to

generate high amplitudes in order to penetrate deep into the body. However, these

piezoelectric drivers are fragile and may not have enough power to generate high

frequency waves with required amplitudes. Additionally,it is in close contact with the

subject and requires high voltages to operate, MR safety might be of concern. iii) Pneumatic Actuator: The pneumatic actuator is the most widely used driver setup. It

consists of two parts: an active driver that contains the electrical components and is

placed outside the MR room, and a passive drum-like driver that is positioned on the

subject’s body above the tissue of interest. The active driver contains a function

generator (that generates the sinusoidal motion), an amplifier (that amplifies the

signal from the function generator), and an acoustic speaker. The vibrations generated

by the active driver system are propagated to the passive driver via a pneumatic tube.

Pneumatic actuators are simple to assemble, cheap, and since the active and passive

components are separate, there is more flexibility to adapt the passive driver to

different tissues of interest. Very high frequency vibrations using pneumatic actuators

may not be feasible because of loss of energy due to compressibility of the medium. 40

2.3.2 Stage 2: Displacement Encoding Using PC-MRI

The principle of motion encoding (induced by an external driver) in cMRE is based on

PC MRI (first introduced for NMR application by Moran [250] in 1982), a technique that images moving magnetization by applying flow-encoding gradients to the standard MRI sequences [251]. To understand the fundamentals of how imaging is performed in cMRE, it is important to understand the mathematical basis of PC MRI.

Motion Encoding in PC-MRI:

In general, the angular frequency 휔 at a position 푥⃗(푡) produced by spins having a characteristic gyromagnetic ratio of 훾 when placed in a magnetic field 퐵푍 is given by

휔(푥⃗, 푡) = 훾퐵푧(푥⃗, 푡), (2)

where the magnetic field 퐵푍 can be expressed as

퐵푧(푥⃗, 푡) = 퐵0 + Δ퐵0 + 푥⃗(푡)퐺⃗(푡). (3)

In the above equation, 퐵0 is the main magnetic field, Δ퐵0 is the local field inhomogeneity and 퐺⃗(푡) is the magnetic field gradient at that location.

Since the angular frequency 휔 of the MR signal produced by the spins is the rate of change of their phase, the phase of the spin signals as a function of time is given by

휏 휙(푥⃗(푡), 푡) = ∫ 휔( 푥⃗(푡), 푡)푑푡 , (4) 푡0

where 푡0 is the instant when the RF pulse is applied to tip the magnetization into the transverse plane and 휏 is the time when the phase is being calculated.

The main magnetic field 퐵0 is considered to be zero in the rotating frame of reference. If the background phase due to the initial position of the spins at time 푡0 is 휙(푥⃗(푡), 푡0), then by substituting equation (3) and equation (2), in equation (4), the total phase accumulated by the MR signal at the end of time 휏 of can be expressed as

τ (5) 휙(푥⃗(푡), τ) = 휙(푥⃗(푡), 푡0) + 훾Δ퐵0(τ − 푡0) + ∫ 푥⃗(푡) 훾 퐺⃗(푡) 푑푡. 푡0

In equation (5) the sum of the first two terms is an unknown background phase which is constant, and therefore is independent of the motion of the spins. If this background phase is considered to be 휙0, then equation (5) can be re-written as

τ 휙(푥⃗(푡), τ) = 휙0 + ∫ 푥⃗(푡) 훾 퐺⃗(푡) 푑푡, 푡0 (6)

For simplicity, let us consider the initial time 푡0 = 0, then the position vector 푥⃗(푡) can be decomposed using Taylor series expansion such that

푡2 푥⃗(푡) = 푥⃗ + 푣⃗ 푡 + 푎⃗ …, (7) 0 0 0 2

where 푥⃗0, 푣⃗0 and 푎⃗0 are the zeroth, first and second derivative of the position vector 푥⃗(푡) at time 푡 = 0. Substituting equation (7) into equation (6) we get

τ 푡2 휙(푥⃗(푡), τ) = 휙 + ∫ (푥⃗ + 푣⃗ 푡 + 푎⃗ … ) 훾 퐺⃗(푡) 푑푡. (8) 0 0 0 0 2

Rearranging equation (8) we get

τ 휙(푥⃗(푡), τ) = 휙0 + 푥⃗0 훾 ∫ 퐺⃗(푡) 푑푡

(9) τ 1 τ + 푣⃗ 훾 ∫ 퐺⃗(푡)푡 푑푡 + 푎⃗ 훾 ∫ 퐺⃗(푡)푡2 푑푡 … 0 2 0

Replacing the integrals as moments, equation (9) can be re-written as

1 휙(푥⃗(푡), τ) = 휙 + 푥⃗ 훾 푚 (푡) + 푣⃗ 훾 푚 (푡) + 푎⃗ 훾 푚 (푡) + ⋯, (10) 0 0 0 0 1 2 0 2

where 푚0, 푚1, and 푚2 are the zeroth, first and second temporal moments of the gradient waveform, respectively. Thus, with an appropriate gradient waveform it is possible to sensitize the phase of the MR signal to individual components of the spin motion. That is, the zeroth moment 푚0 of a gradient waveform encodes the spatial position of the spins, the first moment 푚1encodes the velocity component of the spin, the second moment 푚2 encodes the acceleration component of the spin, and so on and so forth.

Motion Encoding in MRE:

In MRE a similar approach to the one described above is used for encoding externally induced harmonic motion [53]. A pair of bipolar motion encoding gradients (MEGs) whose frequency is matched to the frequency of the external mechanical vibration is placed in a conventional MRI pulse sequence along a specific direction. When a sinusoidal oscillating shear stress is applied to the tissue of interest, the spins of that tissue are displaced by an amount determined by its elastic property. If this stress is

applied in 푥 direction at an angular frequency of 휔, then the spin displacement is given by

⃗⃗ 푥⃗(푡) = 푥0 + 휓0 cos(푘 ⋅ 푟⃗ − 휔푡 + 휃), (11)

⃗⃗ where 푥0 is the initial displacement, 휓0 is the amplitude of the displacement, 푘 is the

2 휋 wave vector given by |푘⃗⃗| = , 푟⃗ is the position vector in 3D space, and 휃 is the phase 휆 offset between the mechanical oscillations and the MEGs.

The bipolarity of the MEGs ensures that the total area covered by the gradient is 0, so that no phase is accumulated by stationary spins and the gradients are sensitized to moving spins only. Additionally, a pair of bipolar MEGs with inverted polarity is used to remove the effect of the background phase. Then by substituting 푥⃗(푡) from equation (11) in equation (6), the net phase accumulated by the pair of bipolar MEG in 푥 direction is given by

τ=NT

where 푇퐸 is the echo time, 푁푇 is the total period of the gradient given that 푁 is the number of gradient cycles and 푇 is the gradient period.

Since the total area covered by the gradient is 0 the net phase accumulated by the stationary spins cancel out and equation (12) is reduced to:

τ=NT

Integrating the above equation and applying the limits of integration we get

2훾푁푇퐺 휓 2휋 휏 Δ휙 = 푥 0 sin (푘⃗⃗ ⋅ 푟⃗ + 휃 − ). (14) 휋 푇

Equation (14) shows that the phase shift in MRE is directly proportional to the amplitude of the displacement, 휓0, the phase offset, 휃, the number of cycles, 푁, and the magnitude of the MEG, 퐺푥. The phase offset defines the observed phase at an instant in time and by acquiring the phase for various values of 휃 a wave image of the oscillations can be observed. Phase sensitivity of the acquired wave image can be controlled by varying 푁 and 퐺푥.

Figure 11: MRE Pulse Sequence. Left: Gradient recall echo based MRE pulse sequence. Right: Spin echo, echo planar imaging based MRE pulse sequence. ‘M’ shows the external motion. The alternating polarity of the MEGs is indicated by solid and dashed lines on the Gz axis along which motion encoding is performed [Adapted from Venkatesh et al. [252]].

The MEGs can be placed along any direction in any conventional MRI pulse sequence

(spin-echo, gradient-echo (Figure 11)) to encode motion along that specific direction. For cardiac applications motion is encoded along all three directions (x, y and z).

Additionally, to acquire multiple cardiac cycles the MEGs for cMRE are placed on cine imaging sequences [95-97, 99, 100, 102, 104]. The MRELab at OSU has developed a retrospectively gated, multi-slice cine gradient echo based cMRE pulse sequence (Figure

12) that encodes external motion and acquires multiple cardiac phases in a single breathhold [107]. This cMRE pulse sequence will be used for all in-vivo applications in this dissertation.

Figure 12: cMRE Pulse Sequence. The cMRE pulse sequence encodes 4 cardiac phase-offsets and 8 cardiac phases in a single breathhold.

2.3.3 Stage 3: Wave Inversion Algorithms

The last stage in MRE involves implementing inversion algorithms to convert the wave images into quantitative stiffness maps. Since the displacements caused by the external vibrations in cMRE are on the order of microns, the tissue of interest is considered to be a linearly viscoelastic material. Using that assumption, according to Hooke’s Law [253,

254], the stiffness/elasticity tensor 푪 (fourth order tensor) in a continuous medium is a linear map between the stress (𝝈) and the strain (흐) tensor which is represented as

𝝈푖푗 = 푪푖푗푘푙흐푘푙. (15)

Due to the inherent symmetries of 𝝈, 흐, and 푪, the fourth order elasticity tensor containing 81 terms reduces to only 21 independent stiffness coefficients. Considering an isotropic medium, the tensor is further reduced to just two coefficients (known as the lame constants), the bulk modulus, 휆 and the shear modulus, 휇. Then, under the assumptions of local homogeneity, the lame constants become single unknowns, and the equation of harmonic motion becomes an algebraic expression that can be solved locally.

This algebraic expression [37, 93] is given by

휇∇2풖 + (휆 + µ)∇(∇. 풖) = −휌휔2풖, (16)

where u is the measured displacements, 휌 is the density of the material, and 휔 is the frequency of excitation. Since 휆 >> 휇 in soft tissues, the simultaneous estimation of both the parameters is very challenging. However, appropriate filtering could isolate the longitudinal and shear components in order to estimate the lame constants individually. A divergence operator would result in preservation of pure longitudinal waves that is solely 47

dependent on the parameter 휆, while a curl operator would result in the preservation of the pure shear waves that is solely dependent on the parameter 휇. Although this is true theoretically, the longitudinal wavelength is so long (on the order of tens of meters) in soft tissues that accurately estimating the longitudinal wavelength is very challenging.

Therefore, by assuming incompressibility (∇. 풖 = ퟎ), 휆 can be removed from consideration and equation (16) reduces to the Helmholtz wave equation [19, 37] given by

휇∇2풖 = −휌휔2풖. (17)

Essentially, this allows decoupling of the wave equation in each orthogonal direction, thereby allowing for estimation of shear elastic coefficients, individually in each sensitization direction.

A number of inversion techniques have been developed based on the above mentioned assumptions and the Helmholtz wave equation. Each inversion algorithm has its pros and cons. The most widely used wave inversion algorithms are discussed below: i) Local Frequency Estimation (LFE): Based on the estimation of instantaneous

frequency (as defined by Knutsson et al. [255]), LFE is one of the earliest inversion

algorithms that was developed to quantify shear stiffness. [19, 32-37] This method

employs lognormal quadrature filters (product of both radial (푅푖(푓)) and directional

(퐷푘(푢̂)) components) to obtain a local estimate of the instantaneous frequency over a

large number of scales. The radial component of the quadrature lognormal filter can

defined by

2 푓 −퐶퐵 푙푛 ( ⁄푓 ) (18) 푅푖(푓) = 푒 푖 , 48

where 퐶퐵 expresses the relative bandwidth, and 푓푖 is the central frequency. Along the orientation direction, the directional component of the quadrature lognormal filter is zero, and the filter profile corresponds to the radial components only.

It has been shown by Knutsson et al. that an isotropic estimate of signal strength, which is local both in the spatial and frequency domain, can be obtained by summing the magnitudes of the outputs of the orthogonally oriented quadrature filters [255]. By combining the outputs from two or more sets of filters which differ only in their central frequency 푓푖, a local frequency estimate can be obtained. This output 푞푖 is given by

2 푓 −퐶퐵 푙푛 ( ⁄푓 ) (19) 푞푖 = 퐴푒 푖 ,

where 퐴 is the local signal amplitude.

If the filters have the appropriate bandwidth relative to the ratio of the two central frequencies 푓푖, then in a particularly simple situation [32, 34-36, 255], the local frequency estimate is calculated as the ratio of the output of the two filters times the geometric mean of their central frequency, which is given by

푞푖 푓 = √푓푖푓푗. (20) 푞푗

This estimate of the local frequency works well only if the signal spectrum falls within the range of the filters, but a wide range of local frequency estimates can be obtained by using a bank of quadrature filters (푀) and performing a weighted summation over the different filter pairs (that differ only by their center frequency 푓푖) which is given by

푀−1 푞푖+1 ∑푖=1 푐푖 √푓푖푓푖+1 푞푖 (21) 푓 = 푀−1 , ∑푖=1 푐푖

where 푐푖 is the weighting factor corresponding to the amount of energy encountered

by each filter pair [34, 35, 255].

Once the instantaneous frequency is defined, shear stiffness 휇 can be calculated using

the following formula

2 푓푚푒푐ℎ 휇 = 2 , (22) 푓푖

where 푓푚푒푐ℎ is the frequency of the external vibration. The averaging operation

performed using the filter banks makes LFE insensitive to noise, however, local

frequency estimates at the edges become challenging due to the limited resolution at

the boundaries.

This inversion algorithm will be applied in Chapter 3 and Chapter 4 to estimate shear

stiffness in HFpEF and HFrEF induced porcine models. ii) Algebraic Inversion of Differential Equation (AIDE): The AIDE technique is based

on the assumptions of local homogeneity that, as already mentioned, assists in

reducing the equation of motion to a simple algebraic expression. In general, under

isotropic conditions the full AIDE inversion algorithm can estimate both the Lame’s

constants. However, for MRE applications assuming incompressibility, AIDE results

in the inversion of the Helmholtz equation described in equation (17). The shear

modulus 휇 is therefore given by

풖 휇 = −휌휔2 , (23) ∇2풖

where definition of terms is the same as in equation (16). This equation is solved at

each pixel by computing the local derivatives which is very sensitive to noise.

Accurate calculation of second derivatives from noisy data is performed by

convolving with Savitsky-Golay type filters. Alternatively, the data can also be fitted

to specific quadratic forms with analytic derivatives [19]. The AIDE technique

produces sharper edges between tissues of different elasticity when compared to the

LFE algorithm.

It is worth noting that both LFE and AIDE is not dependent on planar wave propagation and is therefore robust to complex interference patterns from reflection, diffraction and others. iii) Phase Gradient (PG): The harmonic component of the MRE displacement data has

both a magnitude and a phase (relative to an arbitrary zero) that characterizes the

harmonic oscillations at each pixel in the image. Assuming that the motion is a simple

shear wave, the PG inversion algorithm uses the gradient of the phase (change in

phase per pixel) obtained from the harmonic component and converts it to a local

frequency, post which the shear modulus 휇 is calculated as in LFE. Although PG

inversion provides very high resolution, it is very sensitive to noise and therefore

requires gradient averaging for better performance. Moreover, when two or more

waves are superimposed (for example reflected waves) or the motion is complex, PG

techniques provide inaccurate stiffness measurements as the phase values do not

represent a single propagating wave [19]. 51

iv) Principal Frequency Estimation (PFE): PFE is another inversion algorithm

introduced recently by McGee et al [55]. The inversion uses a defined region (could

be the entire image or a portion of it) on the first harmonic displacement data and

applies spatial Fourier transform to identify the peak frequency (zero padding may be

added prior to Fourier transform to improve the resolution of the peak) of that defined

region. A threshold (typically 50% of the peak power spectrum) is then applied on the

spatially transformed data to null out all frequency content below the threshold. Then

the weighted spectral peak (푓푐푒푛푡푟표푖푑) is calculated based on the radial spatial

frequency at each spectral location (푓푟푎푑) and the amplitude of that spatial frequency

(푀(푓)), and is expressed as:

∑ 푓 푀(푓)2 푓 = 푟푎푑 . (24) 푐푒푛푡푟표푖푑 ∑푀(푓)2

The wavelength 휆 of the propagating wave can be calculated from 푓푐푒푛푡푟표푖푑 (휆 is the

inverse of the weighted spectral peak), which is then used to estimate the shear wave

speed 푐 (푐 = 푓푚푒푐ℎ ∗ 휆, where 푓푚푒푐ℎ, as defined earlier, is the frequency of the

external vibration). The shear modulus 휇 can be measured from the shear wave speed

using the following equation:

휇 = 휌푐2. (25)

PFE is not so widely used because it only provides a global stiffness estimate and is

therefore, unable to resolve spatial variations in stiffness. However, the inversion

technique is important because it is not as sensitive to extremely low signal-to-noise

ratio (SNR) as the other inversions.

The algorithms mentioned above consider the tissue of interest to be an isotropic medium; however, as introduced in Chapter 1, section 1.2.2, cardiac muscle exhibits structural anisotropy [123, 126]. Furthermore, increase in stiffness in both HFpEF [256] and HFrEF [176] has been shown to be directionally dependent. Hence, to understand the true alteration in mechanical properties of healthy and diseased myocardium, it is important to quantify anisotropic MS. Recently, Romano et al. introduced an inversion algorithm called waveguide MRE to quantify anisotropic stiffness in-vivo in the calf muscles and in the brain [257-260]. v) Waveguide MRE: Waveguide MRE is based on the inherent anisotropic property of

biological tissues to act as waveguides for the propagation of acoustic waves which is

exploited to estimate anisotropic stiffness maps. The inversion algorithm requires a

prior knowledge of the fiber pathways along which the acoustic wave travels in a

particular volume surrounding these pathways. The orientation of the pathways can be

identified using diffusion tensor imaging (DTI). Provided with knowledge of the

position vectors of the pathways, a spatial-spectral filter is applied to the first

harmonic displacement data in order to isolate waves traveling in specific directions,

parallel and orthogonal to the fibers. Simultaneously, Helmholtz decomposition is

implemented to separate the total field into its longitudinal and transverse components.

Finally, to evaluate anisotropic stiffness, orthotropic inversion is performed on the

spatially and spectrally filtered displacement data.

This concept of waveguide elastography was first introduced in 2005 by implementing it on a stalk of celery [260]. It was later performed on a human volunteer to estimate anisotropic stiffness in the calf muscles [257]. In 2012, the technique was applied to measure in-vivo anisotropic stiffness of brain white matter tracts [259] and then later applied on amyotrophic lateral sclerosis patients [258]. However, to the best of our knowledge, this inversion has not been extensively validated and this is the first attempt to implement it in the heart [113]. The next section describes the inversion algorithm in details with respect to cardiac application.

2.4 Waveguide Magnetic Resonance Elastography

Knowledge about the fiber pathways along which acoustic waves travel is crucial to waveguide inversion. DTI provides the primary eigenvector (detailed in the next section), the orientation of which corresponds to the fiber direction as defined in Chapter 1, section

1.2.2. Once this information is obtained, a local coordinate system is defined for each imaging voxel (Figure 13) such that one of the axes (n3) of the local coordinate system aligns with the fiber direction (primary eigenvector). For cardiac applications, the other two axes orthogonal to this direction align with the sheet (n1) and sheet normal direction

(n2). Based on this local coordinate system, for a specific region of interest, a spatial spectral filter is defined to filter the first harmonic MRE wave data such that displacement components can be obtained only along the local coordinate system.

Spatial Spectral Filter: The spatial spectral filter consists of performing a three- dimensional spatial Fourier transform within a region of interest for a specific wave vector and spectrum. The forward Fourier transform is followed by a subsequent inverse

Fourier transform using the complex conjugate of the same forward kernel and spectrum which can be defined by the following two equations:

푼(풌) = ∫ 풖(풓)푒−푖푘⋅푟 푑푟, (26)

1 풖(풓) = ∫ 푒푖푘⋅푟푼(풌) 푑풌, (27) 2휋

where 풖 is the displacement data obtained from MRE, 풓 is a three-dimensional spatial vector, and 풌 is the wave vector. The wave vector 풌 depends on the unit vectors at each location 풓′ along a pathway and can be defined as:

풌 = 푘풏풊(풓′), (28)

where 풏풊 is the local coordinate system described earlier and 푘 is a scalar quantity also known as the wavenumber. From this, the equations (26) and (27) can be re-written to obtain the spatial spectral filter representation, 풖푆퐹(풓′) as follows:

′ ′ −푖푘풏푖(풓 )⋅풓 푼(푘풏푖(풓 )) = ∫ 풖(풓)푒 , (29)

1 ′ ′ ′ ′ 푖푘풏푖(풓 )⋅풓 풖푆퐹(풓 ) = ∫ 푼(푘풏푖(풓 )) 푒 푑푘, (30) 2휋 퐼푘

where 퐼푘 represents the interval of variation of 푘 (푘 = |풌|).

Helmholtz Decomposition: A simultaneous Helmholtz decomposition is performed on the forward spatial Fourier transform to decompose the total wavefield into longitudinal

(compressional, 푼퐿) and transverse (shear, 푼푇) components. The k-space Helmholtz decomposition to obtain 푼퐿 and 푼푇 is provided in Appendix A. Post-decomposition equation (30) has two components:

1 ′ ′ 퐿 ′ 푳 ′ 푖푘풏푖(풓 )⋅풓 풖푆퐹(풓 ) = ∫ 푼 (푘풏푖(풓 )) 푒 푑푘, (31) 2휋 퐼푘

1 ′ ′ 푇 ′ 푇 ′ 푖푘풏푖(풓 )⋅풓 풖푆퐹(풓 ) = ∫ 푼 (푘풏푖(풓 )) 푒 푑푘. (32) 2휋 퐼푘

퐿 ′ 푇 ′ Once the spatial spectral representation for 풖푆퐹(풓 ) and 풖푆퐹(풓 ) is obtained it can be

퐿 푇 used to define the longitudinal (풖풊 ) and transverse (풖풊 ) filtered displacements within the

퐿 local frame of reference (풏풊(풓′)). That is, 풖풊 is given by

퐿 퐿 퐿 퐿 풖ퟏ = 풏ퟏ,풙풖푺푭,풙 + 풏ퟏ,풚풖푺푭,풚 + 풏ퟏ,풛풖푺푭,풛, (33) 56

퐿 퐿 퐿 퐿 풖ퟐ = 풏ퟐ,풙풖푺푭,풙 + 풏ퟐ,풚풖푺푭,풚 + 풏ퟐ,풛풖푺푭,풛, (34)

퐿 퐿 퐿 퐿 풖ퟑ = 풏ퟑ,풙풖푺푭,풙 + 풏ퟑ,풚풖푺푭,풚 + 풏ퟑ,풛풖푺푭,풛, (35)

푇 and 풖풊 is given by

푇 푇 푇 푇 풖ퟏ = 풏ퟏ,풙풖푺푭,풙 + 풏ퟏ,풚풖푺푭,풚 + 풏ퟏ,풛풖푺푭,풛, (36)

푇 푇 푇 푇 (37) 풖ퟐ = 풏ퟐ,풙풖푺푭,풙 + 풏ퟐ,풚풖푺푭,풚 + 풏ퟐ,풛풖푺푭,풛,

푇 푇 푇 푇 (38) 풖ퟑ = 풏ퟑ,풙풖푺푭,풙 + 풏ퟑ,풚풖푺푭,풚 + 풏ퟑ,풛풖푺푭,풛.

The above equations are used to solve for the diagonals of the orthotropic tensor C, given by

퐶11 퐶12 퐶13 0 0 0 퐶 퐶 퐶 0 0 0 12 22 23 퐶 퐶 퐶 0 0 0 C = 13 23 33 , (39) 0 0 0 퐶44 0 0 0 0 0 0 퐶55 0 [ 0 0 0 0 0 퐶66]

where 푪ퟏퟏ, 푪ퟐퟐ, and, 푪ퟑퟑ are the compressional components and 푪ퟒퟒ, 푪ퟓퟓ, and, 푪ퟔퟔ are the shear components.

The wave equations for the longitudinal and shear components along the sheet direction

′ (풏ퟏ(풓 )), are given by the following equations:

2 퐿 휕 풖ퟏ(풏ퟏ) 2 퐿 푪ퟏퟏ 2 = −휌휔 풖ퟏ(풏ퟏ) (40) 휕푥1 57

2 푇 휕 풖ퟐ(풏ퟏ) 2 푇 푪ퟔퟔ 2 = −휌휔 풖ퟐ(풏ퟏ) (41) 휕푥1

2 푇 휕 풖ퟑ(풏ퟏ) 2 푇 푪ퟓퟓ 2 = −휌휔 풖ퟑ(풏ퟏ) (42) 휕푥1

The wave equations for the longitudinal and shear components along the sheet normal

′ direction (풏ퟐ(풓 )), are given by the following equations:

2 푇 휕 풖ퟏ(풏ퟐ) 2 푇 푪ퟔퟔ 2 = −휌휔 풖ퟏ(풏ퟐ) (43) 휕푥2

2 퐿 휕 풖ퟐ(풏ퟐ) 2 퐿 푪ퟐퟐ 2 = −휌휔 풖ퟐ(풏ퟐ) (44) 휕푥2

2 푇 휕 풖ퟑ(풏ퟐ) 2 푇 푪ퟒퟒ 2 = −휌휔 풖ퟑ(풏ퟐ) (45) 휕푥2

The wave equations for the longitudinal and shear components along the fiber direction

′ (풏ퟑ(풓 )), are given by the following equations:

2 푇 휕 풖ퟏ(풏ퟑ) 2 푇 푪ퟓퟓ 2 = −휌휔 풖ퟏ(풏ퟑ) (46) 휕푥3

2 푇 휕 풖ퟐ(풏ퟑ) 2 푇 푪ퟒퟒ 2 = −휌휔 풖ퟐ(풏ퟑ) (47) 휕푥3

2 퐿 휕 풖ퟑ(풏ퟑ) 2 푳 푪ퟑퟑ 2 = −휌휔 풖ퟑ(풏ퟑ) (48) 휕푥3

Equations 40 - 48 are solved to obtain complex elastic coefficients for 퐶11, 퐶22, 퐶33, 퐶44,

퐶55, and 퐶66 [40, 261].

Therefore, waveguide MRE allows estimation of anisotropic stiffness along the 3 axes of symmetry. Although, waveguide inversion has been implemented in different biological tissues, to date it has not been validated against any known ground truth. Therefore, in

Chapter 7 we use finite element modeling to validate the currently available waveguide inversion algorithm. Moreover, in Chapter 8 we also implement waveguide cMRE inversion to investigate the variations in anisotropic MS in hypertensive heart models.

In the next section we shall review DTI and discuss how it can be used to obtain information about the fiber pathways.

2.5 Diffusion Tensor Imaging (DTI)

DTI is a MRI based technique that measures the Brownian motion of water molecules and since this motion in biological tissues is guided by the tissue structure and orientation; it can provide information about the underlying tissue fiber architecture [262-

265]. If two gradients (known as diffusion encoding gradients) of opposite polarity but having the same amplitude (퐺) and duration (훿) are applied with a time interval Δ between them, then the diffusion (Brownian motion) exhibited by the water molecules causes an attenuation in the MR signal given by

−풃푫 푆 = 푆0 푒 (49)

where 푆 is the attenuated MR signal, 푆0 is the signal intensity in the absence of the diffusion gradients, 풃 is the gradient factor, and 푫 is the diffusion coefficient. The gradient factor 풃 for an arbitrary gradient waveform 퐺⃗(푡′) is given by [251]

푇퐸 ( )2 ⃗⃗( ) ⃗⃗( ) (50) 푏 = 2휋 ∫0 푘 푡 ∙ 푘 푡 푑푡,

where 푘⃗⃗(푡) is given by

훾 푡 푘⃗⃗(푡) = ∫ 퐺⃗(푡′) 푑푡′. (51) 2휋 0

In the presence of anisotropy the diffusion coefficient 푫 is a symmetric second order tensor given by

퐷푥푥 퐷푥푦 퐷푥푧 푫 = (퐷푦푥 퐷푦푦 퐷푦푧). (52) 퐷푧푥 퐷푧푦 퐷푧푧

Since the above tensor is symmetric, equation (49) can be rewritten as

푆 = 푆0 푒푥푝(−푏푥푥퐷푥푥 − 푏푦푦퐷푦푦 − 푏푧푧퐷푧푧 − 2푏푥푦퐷푥푦 − 2푏푥푧퐷푥푧 − 푏푦푧퐷푦푧). (53)

In order to solve for the 6 different components of the diffusion tensor 푫, at least six encoding directions (six different gradients) are required. Once the tensor is computed, diagonalization of 푫 provides the eigenvalues (휆1, 휆2, 휆3) and eigenvectors (휀1, 휀2, 휀3) of the tensor. The eigenvalues can be used to calculate different quantitative parameters defining the amount of diffusion (apparent diffusion coefficient, mean diffusivity, trace) and degree of anisotropy (fractional anisotropy). The eigenvectors provide information about the myocardial fiber architecture. The principal eigenvector (휀1) corresponds to the

direction of maximum diffusivity, which is aligned in the direction of the tissue fiber orientation; whereas the other two vectors (휀2, 휀3) relate to the direction of radial and circumferential diffusivity.

For cardiac applications other quantitative parameters which provide further information about the fiber orientation such as helical angle (HA) and transverse angle can be derived from the eigenvectors. For example, HA, which is defined as the measure of the angle between the short-axis imaging plane and the projection of the primary eigenvector onto the epicardial tangent plane [120], shows the orientation of the muscle fiber in the epicardium, mid-myocardium, and the endocardium. As already mentioned in Chapter 1, section 1.2.2, using ex-vivo cardiac DTI, Scollan et al. [136] showed smooth transition of

HA from a negative helix in the epicardium (-60o) to a positive helix (+60o) in the endocardium, a trend that was histologically shown by Streeter et al. [120] in the mid

1900s. Furthermore, previous studies using ex-vivo DTI in animal models have shown that the HA, and therefore the underlying fiber orientation, undergoes remodeling with the onset of MI [266-272].

Despite the encouraging results in ex-vivo applications, in-vivo cardiac DTI is still in its inception. This is because DTI is very sensitive to respiratory and cardiac motion which makes in-vivo implementation very challenging. However in the last decade, different research groups have shown promising results both in normal human volunteers [273-

278] and in patients with MI [279, 280].

2.6 Summary

The above sections discussed in details two potential tools (cMRE and waveguide MRE) that can non-invasively quantify MS which in turn can aid in the diagnosis of HF. The next two chapters use cMRE to exploit the potential of isotropic MS and understand its significance in diagnosing HFpEF and HFrEF.

Chapter 3: Left Ventricular Myocardial Stiffness in Heart Failure with Preserved

Ejection Model

In Chapter 1 it was mentioned that hypertension causes left ventricular (LV) hypertrophy which leads to increase in global passive myocardial stiffness (MS) and is a major contributing factor in the development of heart failure with preserved ejection fraction

(HFpEF). Hence it is important to investigate the alteration in MS induced by hypertension. In this chapter, we have used cMRE to follow the increase in MS with progression in hypertension and validated cMRE-derived MS measurements with mean

LV pressure and LV thickness. Furthermore, change in cMRE-derived MS is also compared with parameters obtained from routinely practiced clinical MRI protocol, i.e., cardiac strain measurements and MRI relaxometry parameters.

This material is previously published or presented as shown by the following citations.

 Mazumder R, Schroeder S, Mo X, Clymer BD, White RD, Kolipaka A.

Quantification of Myocardial Stiffness in Hypertensive Porcine Model Using

Magnetic Resonance Elastography, Journal of Magnetic Resonance Imaging (Under

Review).

 Mazumder R, Schroeder S, Clymer BD, White RD, Kolipaka A. In-Vivo

Quantification of Myocardial Stiffness in Heart Failure with Preserved Ejection

Fraction Using Magnetic Resonance Elastography: Assessment in a Porcine Model.

24th Annual Scientific Meeting ISMRM, Singapore, 2016.

 Mazumder R, Schroeder S, Clymer BD, White RD, Kolipaka A. Quantification of

Myocardial Stiffness in Heart Failure with Preserved Ejection Fraction Porcine

Model Using Magnetic Resonance Elastography. 19th Annual Scientific Meeting

SCMR, Los Angeles, USA 2016.

3.1 Introduction

Heart failure with preserved ejection fraction (HFpEF, EF≥45%) is caused primarily by increase in left ventricular (LV) myocardial stiffness (MS) that results in impaired LV relaxation [198]. HFpEF is of growing concern in the US; the average prevalence of

HFpEF hospitalization has increased from 38% to 54% over the past 15 years [144] with older women (>65 years) accounting for nearly 90% of HFpEF cases [281]. Although the importance of HFpEF is well-recognized, its complex pathophysiology is poorly understood and a standard diagnostic metric for HFpEF does not exist [148].

Recently, several researchers have shown that HFpEF is a heterogeneous disorder influenced by a wide range of cardiovascular and non-cardiac abnormalities [281].

Common cardiovascular abnormalities contributing to HFpEF include aging, LV

hypertrophy, concentric remodeling and ventricular-arterial stiffening [148, 282]. Major non-cardiac co-morbidities of high prevalence in HFpEF include obesity, hypertension, diabetes mellitus, chronic obstructive pulmonary disease and renal impairment [283]. The aforementioned cardiac and non-cardiac abnormalities are associated with global increase in LV MS [284]. Increased LV MS in turn causes impaired LV diastolic relaxation and filling which over time may trigger HFpEF [148, 151, 281]. Therefore, quantifying LV

MS may assist in the diagnosis, treatment planning, and monitoring of HFpEF patients.

Passive LV MS can be measured clinically using LV catheter-based pressure-volume loops [6, 223]. However, catheterization is an invasive procedure, provides only a global measurement of chamber stiffness and does not estimate the true intrinsic mechanical properties of the myocardium [9]. Currently, non-invasive surrogates such as tissue

Doppler-echocardiography based on mitral inflow velocity is used to evaluate HFpEF

[285, 286]. However, the predictive accuracy of tissue Doppler-echocardiography is suboptimal, rendering it to be poor index for assessing HFpEF [287]. In addition, it does not provide information about the true intrinsic properties of the underlying tissue.

Therefore, there is a need for an alternative non-invasive technique to estimate MS for the timely and reproducible assessment of HFpEF.

Recently, with the advent of cardiac magnetic resonance elastography (cMRE), a phase- contrast based MRI technique, non-invasive quantification of MS has become feasible

[95, 97, 104, 107, 110, 245]. Previously, this technique has been used in patients with diastolic dysfunction, to show that cMRE-derived shear wave amplitudes are

significantly lower in affected patients compared to normal healthy volunteers [110, 245].

However, to the best of our knowledge no cMRE studies have estimated temporal variation in MS during disease progression in a HFpEF model and compared it to invasive LV pressure measurements.

The aims of the study are to exploit cMRE in a well-established HFpEF [288] porcine model to: 1) estimate temporal variation in LV MS over a 2 month period; 2) validate LV

MS measurements against LV pressure measurements obtained from ventricular catheterization; and 3) compare alteration in LV MS measurements to changes in LV thickness, LV circumferential strain measurements and LV MRI relaxometry parameters with disease progression.

3.2 Materials and Methods

Eight juvenile Yorkshire pigs (serially studied at three time points, i.e. n=24) weighing

~70 lbs were used in this study. The study was performed in accordance with the university’s institutional animal care and use committee guidelines.

HFpEF Animal Procedure

The animals underwent renal wrapping surgery which is known to induce chronic systemic arterial hypertension, leading to LV hypertrophy potentially triggering HFpEF

[289, 290]. To that end, the animals were placed in supine position on the surgery table and pre-operative Bupivicaine (0.5%, dosage: 3-5 ml) was injected into the incision site.

HFpEF was induced using renal wrapping surgery via a midline abdominal incision. Both

the kidneys were cleared of perinephric fat and wrapped snugly with sterile umbilical tape without constricting the renal vessel [288]. The abdominal wall was then closed in multiple layers using absorbable sutures. Post-operative analgesia consisted of a dose of buprenorphine (0.3 mg/ml, dosage: 0.005-0.02 mg/kg) and a fentanyl transdermal patch

(100 mcg/hr/72hrs).

MR Imaging Timeline

MR imaging was performed on all the animals at baseline (Bx) prior to surgery, and then repeated approximately after one month (M1) and two months (M2) post-surgery with the imaging parameters (detailed later) remaining constant for all time points. These two post-operative time points were specifically selected since renal wrapping surgery of both the kidneys together induces rapid hypertension in a month [288], and hence while M1 would provide mechanical properties of the myocardium right after initial surge in blood pressure, M2 would provide information after a period of prolonged hypertension.

LV Pressure Measurements

Prior to each MRI scan LV catheterization was performed under fluoroscopy (GE OEC

9800, General Electric, USA) to record LV pressure. A 7Fr guide catheter (Boston

Scientific, Marlborough, MA) was advanced through the femoral artery into LV. Next a pressure catheter (Millar Mikro-Tip, MPC-500, Millar Instruments, Houston, TX, USA) was inserted into the LV through the guide catheter and LV pressures were recorded continuously using a single-channel bridge amplifier (FE221, ADInstruments, US) and a multi-channel Power Lab (PL3508 Power Lab 8/35, ADInstruments, US). At the same

time ECG was recorded using a single-channel Bio amplifier (FE136, ADInstruments,

US) and Power Lab.

Animal Preparation for MR Imaging

MR imaging was performed on animals under anesthesia, which was induced using ketamine (20 mg/kg) and acepromazine (0.5 mg/kg) and was maintained using isoflurane

(1-5%). The animals were positioned feet-first supine in the MR table and endotracheal intubation was performed to administer mechanical ventilation. A custom made passive driver was positioned on the anterior chest wall and secured in place using an elastic velcro strap. This passive driver was connected to a custom-made active driver (that generated the acoustic waves) via a rigid plastic tube as shown in Figure 14 to induce required vibrations into the heart for cMRE.

Figure 14: Experimental Set-Up. The animal is placed feet-first supine on the MR table. A custom made plastic drum (passive driver) is positioned externally on the animal’s anterior chest wall right above the heart. A custom made active pneumatic driver that is placed outside the scanner room generates acoustic waves and transmits it to the passive driver via a plastic connecting tube. 68

Image Acquisition

Images were acquired using a 1.5-Tesla clinical MRI scanner (Avanto, Siemens

Healthcare, Erlangen, Germany), with a 12-channel cardiac torso coil on the anterior side and a spine coil on the posterior end. Cardiac triggered balanced steady-state free precession cine sequence was implemented to acquire vertical, horizontal long-axis views and short-axis views covering the heart. The cine images were used to estimate cardiac function parameters. Imaging parameters for cine imaging included: echo time

(TE)/repetition time (TR)=1.49/27.36 ms; field of view=300x300 mm2; imaging matrix=256x256; slice thickness=6mm; flip angle=46◦; cardiac phases=30; GRAPPA acceleration factor=2.

Retrospective pulse-gated, segmented multi-phase gradient recalled echo cMRE sequence was used to obtain short-axis slices covering the entire LV [107]. Imaging parameters for cMRE included: TE/TR=9.71/12.5 ms; field of view=384x384 mm2; imaging matrix=128x128; slice thickness=8mm; flip angle=15◦; cardiac phases=8; GRAPPA acceleration factor =2; excitation frequency=80Hz; phase offsets=4; and 160Hz motion encoding gradients were applied separately in all three directions to encode the in plane and through plane external motion.

Spatial Modulation of Magnetization (SPAMM) tagging [291] was performed to analyze the change in myocardial circumferential strain with disease progression. A prospectively gated GRE based SPAMM tagging sequence was used to acquire the short-axis view of a mid-ventricular slice with the following imaging parameters: TE/TR=3.42/19.47 ms;

field of view=300x300 mm2; imaging matrix=224x168; slice thickness=8mm; flip angle=8◦; and cardiac phases=25;

MRI relaxometry maps were acquired on a short-axis mid-ventricular slice to analyze the change in T1, T2 and extracellular volume (ECV) fraction measurements with disease evolution. To identify the presence of myocardial injury (edema) short-axis T2 maps

[292] were acquired using the following imaging parameters: TE/TR=1.37/229.36 ms; field of view=360x270 mm2; imaging matrix=192x160; slice thickness=8mm; flip angle=35◦; cardiac phases=1; and GRAPPA acceleration factor=2. Short-axis T1 modified Look-Locker inversion recovery sequence was used to acquire pre-contrast

(T1pre) [292-294] and post-contrast (T1post) images to investigate the presence of fibrosis and change in ECV content. Imaging parameters for T1 maps were similar to T2 maps except TE = 1.01 ms and TR = 255.46 ms. T1post imaging was performed 10 minutes post-injection of contrast agent.

Additionally, delayed enhancement imaging (8 minutes post contrast) was performed to investigate the presence of any myocardial fibrosis [295]. Imaging was performed on three short-axis slices (base, mid, and apex) 8 minutes post-injection of contrast agent with the following acquisition parameters: TE/TR=4.34/662 ms; field of view=360x292 mm2; imaging matrix=192x160; slice thickness=8mm; and flip angle=25◦. Post-contrast imaging was performed after manual injection of a rapid bolus of Gadobenate

Dimeglumine (MultiHance, Bracco Diagnostics, Princeton, NJ) followed by a 20 mL saline flush. The dosage varied by weight at a rate of 0.2 ml/kg.

Image Analysis

In-vivo Pressure Measurements: LV pressures and ECG signal were continuously recorded as mentioned earlier. The ECG signal was used to identify the regions of end- systolic (ES) and end-diastolic (ED) phases of the cardiac cycle and their corresponding

LV pressures were obtained across three cardiac cycles. The mean ED LV pressure and the mean ES LV pressure were calculated from these three ED and ES pressure points.

The mean LV pressure was reported as shown in Eq 54.

2 × (푀푒푎푛 퐸퐷 퐿푉 푃푟푒푠푠푢푟푒) + 1 × (푀푒푎푛 퐸푆 퐿푉 푃푟푒푠푠푢푟푒) (54) 3

Cardiac Function and Morphology: Post-acquisition, cine images were contoured off- line, using a commercially available software package (Argus Ventricular Function,

Siemens Healthcare, Erlangen, Germany) to determine the ED volume, ES volume, EF, stoke volume, cardiac output and LV mass at Bx, M1 and M2.

LV Thickness Measurements: A mid-ventricular slice was selected from the cMRE magnitude images at Bx, M1, and M2, and epicardial and endocardial contours were dawn. Visual inspection was performed to ensure that the mid-ventricular slice was same across the three time points (Bx, M1 and M2). Based on the contours, epicardial and endocardial LV diameter were calculated in Matlab (Mathworks, Natick, MA, USA).

From the diameters the thickness of the LV slice at each individual cardiac phase was measured to investigate the change in LV thickness with disease progression. The phases corresponding to the minimum and maximum thickness were identified for ES and ED 71

thickness measurements, respectively. These same phases were selected to report ES stiffness and ED stiffness (detailed below). cMRE Analysis: MRELab (Mayo Clinic, Rochester, MN, USA) was used to process the wave images obtained from cMRE acquisitions to obtain stiffness maps. The wave images were masked to extract the LV and the reflected waves were removed using a directional-filter in 8 radial directions [18]. Next, a 4th order Butterworth band-pass filter with cutoffs 0.384 m/FOV to 0.0096 m/FOV was used to remove the longitudinal component of motion. The filtered wave data were then inverted using a 3D local frequency estimation algorithm [107] and stiffness maps were obtained for all the slices.

The stiffness maps were then loaded in Matlab and the 3D mean stiffness and standard deviation (SD) from all the slices across the 8 cardiac phases at Bx, M1 and M2 were reported. Before calculating the mean stiffness, regions with poor wave propagation were excluded from the stiffness maps based on visual inspection by an experienced observer.

The phases corresponding to the maximum and minimum thickness were selected to report the ES and ED stiffness measurements.

Circumferential Strain Measurements: Images obtained from SPAMM tagging were analyzed using the commercial HARP software (Diagnosoft, Palo Alto, California).

Epicardial and endocardial contours were drawn on the ES cardiac phase and circumferential Eulerian stain was automatically calculated for six different cardiac segments. The mean strain across the six different cardiac segments was calculated and reported for Bx, M1, and M2.

Delayed Enhancement and MRI Relaxometry Parameters: Delayed enhancement images were qualitatively assessed for the presence of hyper-intensity in all three slices. On the relaxometry maps ROIs were drawn in the center of the myocardium (avoiding both the epi- and the endocardium) in the mid-myocardial slice and the mean T1 and T2 values were reported. ECV was measured as the ratio of the myocardial and blood pool blood relaxation rates (∆R1). Blood T1 was estimated from the T1* maps [296]. ECV was calibrated by the blood hematocrit and calculated using the following equationss:

1 ∆푅1 = (55) 푇1 (푃표푠푡) − 푇1(푃푟푒)

∆푅1 퐸퐶푉 = (1 − ℎ푒푚푎푡표푐푟푖푡) × 푚푦표 (56) ∆푅1푏푙표표푑

Statistical Analysis

Statistical analysis was performed using SAS 9.4 software (SAS, Inc; Cary, NC). All measured parameters were compared against cMRE-derived ES and ED MS. Anderson-

Darling’s test was performed on each parameter (cardiac functional and morphological parameters, mean LV pressure, ED and ES thickness, ED and ES MS, circumferential strain and MRI relaxometry parameters) to check for normality. Since all the parameters were measured for each subject across three different time points (Bx, M1, and M2), those parameters that passed the normality test were analyzed using mixed effects models. A mixed effects model accounts for observational dependencies for each subject

and also allows for subject specific intercepts and slopes [297]. The time point for each measured parameter was included as a fixed-effects component with three levels corresponding to Bx, M1, and M2, and cMRE-derived MS (ES or ED) was added as a covariate. For parameters that did not pass the normality test, non-parametric Wilcoxon sign rank tests were performed to analyze alteration in parameter measurements across time. Spearman’s rank correlation coefficients were used to describe the association between LV MS (ES, ED) and i) mean LV pressure, ii) LV thickness (ED and ES), iii) circumferential strain, iv) MRI relaxometry parameters.

3.3 Results

LV Pressure Measurements: The range and mean LV pressure Eq 54 from all the animals at Bx, M1, and M2 were ([21.8 – 43.6], 33.5) mmHg, ([22.0 – 53.5], 40) mmHg and

([34.6 – 61.3], 49.9) mmHg, respectively. The mean LV pressure demonstrated non- significant increase from Bx to M1 (slope=6.5, p=0.1734), while the mean LV pressure increased significantly from M1 to M2 (slope=10.0, p=0.05). Overall, from Bx to M2 the significant positive slope in mean LV pressure (slope=16.5, p=0.0027) confirmed the development of hypertension.

Cardiac Function and Morphology: Cardiac functional and morphological parameters obtained from cine images are detailed in Table 2. EF, stroke volume, and cardiac output demonstrated no significant differences over the 3 MR imaging studies. On the other hand, the range and mean LV mass from Bx ([49.4 – 82.8], 59.0) gm to M2 ([75.0 –

124.1], 96.6) gm increased significantly (slope=37.6, p<0.0001), with significant increase 74

each at M1 ([62.8 – 105.4], 75.0) gm, (from Bx to M1, slope=16.06, p=0.04) and at M2

(from M1 to M2, slope=21.55, p=0.0083). Increase in LV mass indicates that the animals developed LV hypertrophy.

Table 2: Cardiac function and morphology measurements for all the animals at Bx, M1, and M2.

LV ED ES Stroke Cardiac Animal Time EF Mass Volume Volume Volume Output Identifier Point (%) @ ED (ml) (ml) (ml) (l/min) (g) Bx 43.3 57.9 32.8 25.1 1.88 52.9 P1 M1 65.8 67.5 23.1 44.4 3.91 66.9 M2 42 58.8 34.1 24.7 1.71 101.3 Bx 42.8 71.5 40.9 30.6 2.94 82.8 P2 M1 47.2 92.8 49 43.8 4.25 105.4 M2 33.8 110.1 75.1 35.1 4.18 124.1 Bx 46.4 58.9 31.6 27.3 2.4 54.8 P3 M1 51.7 81.6 39.4 42.2 3.55 79.3 M2 46.7 90.9 48.4 42.5 3.61 103.5 Bx 44.7 50.5 27.9 22.5 2.64 53.7 P4 M1 40.8 67.2 39.8 27.4 2.6 62.8 M2 40.5 100.2 59.6 40.5 4.09 98.2 Bx 49.7 64.2 32.3 31.9 3.09 63.6 P5 M1 47.6 76.2 39.9 36.3 3.74 80.3 M2 51.1 101.8 49.8 52 4.84 109.8 Bx 21.5 47.4 37.2 10.2 1.12 54.6 P6 M1 35.8 55 35.3 19.7 2.03 65.9 M2 33.3 50 33.3 16.6 1.63 77.1 Bx 68.9 40.6 12.6 28 2.68 49.4 P7 M1 48.5 65.3 33.6 31.6 3.16 68 M2 41.7 59.1 34.5 24.6 1.9 83.6 Bx 24.1 57.5 43.7 13.9 1.64 59.9 P8 M1 29.9 62.8 44 18.8 1.76 71.6 M2 63.5 47.5 17.2 29.9 2.55 75 Bx 42.7 56.1 32.4 23.7 2.3 59.0 Mean M1 45.9 71.1 38.0 33.0 3.1 75.0 M2 44.1 77.3 44.0 33.2 3.1 96.6 75

LV Thickness Measurements: Figure 15 shows variation in LV thickness as a function of the phase of the cardiac cycle with disease progression. A quadratic function was used to fit the mean variation in thickness (by pooling all the 8 animals) across the cardiac cycle.

The R2 values (for the quadratic fit) at Bx (R2=0.94), M1 (R2=0.92), and M2 (R2=0.81) indicate that the mean curves are well fitted. Based on the mean curves at Bx, M1 and

M2, it can be concluded that LV thickness increases from Bx to M1 to M2 further affirming that the animals developed LV hypertrophy.

The mean and standard deviation (SD) of the ED thickness at Bx, M1, and M2 were

9.1±0.6 mm, 10.4±0.8 mm, and 12.3±1.3 mm, respectively. The mean±SD of the ES thickness at Bx, M1, and M2 were 13.7±1.8 mm, 16.0±1.5 mm, and 17.8±1.2 mm, respectively. In general there was a significant increase in LV thickness at both ED thickness (slope=3.24, p<0.0001) and ES thickness (slope=4.14, p=0.0001) from Bx to

M2. Moreover, comparison at each time point with its prior time point showed similar results, both the ED and ES thickness increased significantly from Bx to M1

(p(ED)=0.02, p(ES)=0.01) and from M1 to M2 (p(ED)=0.002, p(ES)=0.03).

Figure 15: Left Ventricular Thickness as a Function of the Cardiac Cycle on a Mid- Ventricular Slice from all the Animals. Each color on the marker indicates different animals and each shape correspond to the 3 different time points (circle-Bx, triangle-M1, and square-M2). The plot shows that mean LV thickness increased progressively from Bx (green curve, R2=0.94) to M1 (blue curve, R2=0.92) to M2 (red curve, R2=0.81) indicating that the animals developed LV hypertrophy over time.

cMRE Analysis: Figure 16 shows ES and ED magnitude image, the four snap shots of the propagating wave encoded in the x-direction, and the corresponding stiffness maps at Bx and M2. From the stiffness maps it can be observed that the both the ED and ES LV MS is higher at M2 when compared to Bx. 77

Figure 17 shows the variation of LV MS as a function of the phase of the cardiac cycle with disease progression. A quadratic was used to fit the mean variation (from all the 8 animals) in LV stiffness. The R2 values for the quadratic fit at Bx (R2=0.99), M1

(R2=0.97), and M2 (R2=0.97) demonstrated an excellent fit. Based on the mean curves at

Bx, M1, and M2, it can be concluded that the mean LV MS increases progressively from

Bx to M1 to M2 in all the cardiac phases, indicating that hypertension induced increased

LV MS in the animals.

LV ED and ES MS: The mean±SD for ED MS at Bx, M1, and M2 were 3.84±0.4 kPa,

4.24±0.3 kPa and, 4.82±0.2 kPa, respectively. The mean±SD for ES MS at Bx, M1, and

M2 were 4.94±0.5 kPa, 5.70±0.5 kPa and, 5.88±0.5 kPa, respectively (Figure 18). Slope analysis from Bx to M2 indicated that as the disease progressed the mean LV MS increased significantly for both ED (slope=0.98, p<0.0001) and ES (slope=0.94, p=0.002). However, while ED MS demonstrated a significant increase both from Bx to

M1 (difference=0.40, p=0.02) and M1 to M2 (difference=0.58, p=0.002), ES MS did not.

ES MS only showed a significant increase from Bx to M1 (difference=0.76, p=0.007) but a non-significant increase from M1 to M2 (difference=0.12, p=0.47).

Figure 16: cMRE Magnitude Images, Wave Images, and Shear Stiffness Maps. Baseline: (a, g) Short-axis magnitude image of a mid-ventricular slice at ED and ES, respectively. (b-e), (h-k) Snapshots of 4 phase offsets of the wave propagation in x- direction at ED and ES, respectively. (f, l) Stiffness maps at ED and ES, respectively, demonstrating that ES stiffness is higher than ED stiffness. Two Months Post- Surgery: (m, s) Short-axis magnitude image of a mid-ventricular slice at ED and ES, respectively. The magnitude image at M2 for both ED and ES indicates LV hypertrophy when compared to the Bx images. (n-q), (t-w) Snapshots of 4 phase offsets of the wave propagation in x-direction at ED and ES, respectively. (r, x) Stiffness maps at ED and ES, respectively, demonstrating that ES stiffness is higher than ED stiffness and both ED and ES stiffness is higher compared to Bx ED and ES stiffness, respectively.

Figure 17: Mean Left Ventricular Myocardial Stiffness (all Slices) as a Function of the Cardiac Cycle from all the Animals. Each color on the marker indicates different animals and each shape correspond to the 3 different time points (circle- Bx, triangle-M1, and square-M2). The plot shows that the mean LV shear stiffness by fitting a curve at Bx (green curve, R2=0.99) is lower than the mean LV shear stiffness at M1 (blue curve, R2=0.97) which is lower than the mean LV shear stiffness at M2 (red curve, R2=0.97) indicating that the LV compliance was compromised with the prolongation of hypertension.

Correlation Between cMRE-Derived LV MS and LV Pressure and Thickness: Figure

19(a, b) shows the correlation between ED, ES MS and mean LV pressure, respectively.

Similarly, Figure 19(c, d) shows correlation between ED MS and ED thickness, ES MS and ES thickness, respectively. A significant positive correlation was observed between mean LV pressure and LV ED MS (휌=0.56, p=0.005) and ES MS (휌=0.45, p=0.03).

Additionally, both LV ED and ES MS had significant strong positive correlation with ED thickness (휌=0.73, p<0.0001) and ES thickness (휌=0.84, p<0.0001). 81

Figure 19: Spearman’s Correlation Plot between cMRE-Derived LV MS and Mean LV Pressure and LV Thickness (ED and ES). a) Correlation analysis between ED LV MS and mean LV pressure demonstrated good correlation (𝝆≥0.5). b) Similarly correlation analysis between ES LV MS and mean LV pressure also demonstrated good correlation (𝝆≥0.5). c) A strong correlation (𝝆>0.7) is observed between ED LV MS and ED LV thickness. d) Similarly a strong correlation (𝝆>0.7) is observed between ES LV MS and mean ES LV thickness.

Circumferential Strain: The mean and SD of the LV Eulerian circumferential strain at

Bx, M1, and M2 were -7.49±1.61, -7.26±1.16, and -5.21±2.36, respectively (Figure 20a).

Circumferential LV strain decreased significantly (slope=2.28, p=0.03) from Bx to M2, while the decrease from Bx to M1, and M1 to M2 were not significant. The Spearman’s correlation between circumferential LV strain and LV ED and ES MS demonstrated that

circumferential strain had a moderate negative correlation with both ED (휌=0.31) and ES

(휌=0.37) LV MS, however the correlation was not significant (p(ED)=0.15 and p(ES)=

0.08) (Figure 20b and Figure 20c).

Figure 20: LV Circumferential Strain Analysis. a) Box plot showing circumferential LV strain at Bx, M1, and M2. Although, LV strain did not change significantly from one time point to the other (Bx to M1, and M1 to M2) there was a significantly decreasing trend (indicated by *) from Bx to M2. Spearman’s correlation analysis between circumferential strain and b) cMRE-derived ED MS and c) cMRE-derived ES MS demonstrated a moderate negative correlation (𝝆>0.3) but it was not significant (p>0.05).

Delayed Enhancement and MRI Relaxometry Parameters: Figure 21 shows delayed enhancement images and relaxometry maps from a mid-ventricular slice at Bx and M2.

From the delayed enhancement image at M2 it can be observed that there is no presence of regional or diffused hyper-intensity, indicating absence of focal or diffused fibrosis.

Additionally, within the LV myocardium no distinct change in image intensity is observed in the MRI relaxometry maps from Bx to M2.

Figure 21: Delayed Enhancement and MRI Relaxometry Maps. (a, e) Delayed enhancement image shows uniform intensity both at Bx and M2, respectively indicating that fibrosis is not present. (b, f) T2 maps show absence of hyper intensity both at Bx and M2, respectively, indicating absence of edema (c, g) T1pre maps at Bx and M2, respectively, and (d, h) T1post maps at Bx and M2, respectively shows lack of variation in image intensity in the LV indicating absence of distinct fibrosis.

T2 Measurements: The mean T2 estimate (by pooling all animals) at Bx, M1 and M2 were 45.4±1.1 ms, 45.2±2.3 ms, and 45.6±2.1 ms, respectively. No significant change 84

was observed from Bx to M1 (p=0.84) and from M1 to M2 (p=0.73) indicating that hypertension did not affect T2 values from Bx to M2 (slope=0.14, p=0.9).

T1 Measurements: The mean (from all the animals) T1pre values at Bx, M1 and M2 were

970.6±21.2 ms, 982.4±20.9 ms, and 978.6±19.9 ms, respectively, while the mean (from all the animals) T1post values at Bx, M1 and M2 were 506.5±23.4 ms, 520.2±19.6 ms, and

490.5±49.7 ms, respectively. In general, no significant change was observed from Bx to

M2 either in T1pre (p=0.73) or in T1post (p=0.29). Furthermore, when individual time points were compared (Bx to M1 and M1 to M2) no significant change was observed either in T1pre or in T1post measurements.

ECV Measurements: The mean ECV measure (from the 8 animals) at Bx, M1 and M2 were 25.7±1.8 ms, 24.4±1.5 ms, and 24.2±2.9 ms, respectively. In general, from Bx to

M2 ECV measurements did not show any significant change (p=0.2).

Correlation between cMRE-Derived MS and MRI Relaxometry Parameters: Figure 22 shows Spearman’s correlation between ED and ES MS and MRI relaxometry parameters: a) ED MS vs T2; b) ED MS vs T1pre; c) ED MS vs T1post; d) ED MS vs ECV fraction; and e) ES MS vs T2; f) ES MS vs T1pre; g) ES MS vs T1post; h) ES MS vs ECV fraction.

No significant correlation was observed between ED MS and a) T2 map (휌=-0.13, p=0.53); b) T1pre map (휌=-0.08, p=0.70); c) T1post map (휌=-0.18, p=0.41); d) ECV fraction (휌=-0.27, p=0.2). Similarly, no significant correlation was observed between ES

MS and e) T2 map (휌=-0.26, p=0.22); f) T1pre map (휌=0.05, p=0.81); g) T1post map

(휌=0.11, p=0.62); h) ECV fraction (휌=-0.27, p=0.20).

Figure 22: Spearman’s Correlation Analysis between cMRE-Derived ED and ES MS and MRI Relaxometry Parameters. No correlation (|𝝆|<0.3) was observed between ED and ES LV MS and any of the MRI relaxometry parameters: (a, e) T2, (b, f) T1pre, (c, g) T1post, and (d, h) ECV fraction, respectively.

3.4 Discussion

This study demonstrated the feasibility of using cMRE to determine the changes in MS in an established HFpEF porcine model. Our findings indicated that mean LV pressure, LV thickness and cMRE-derived MS increased significantly with disease progression.

Furthermore, both mean LV pressure and LV thickness had good correlation with ED and

ES cMRE-derived LV MS, indicating that LV hypertrophy secondary to hypertension caused increase in MS. Circumferential LV strain decreased only at M2 and showed a moderate negative correlation when compared to cMRE-derived MS. MRI relaxometry parameters did not demonstrate any significant change with disease progression and none of the parameters (T2, T1, and ECV measurements) showed any correlation with cMRE- derived MS. Therefore, this study demonstrates the potential of using cMRE as a non- invasive tool for the assessment of disease conditions that are potential predecessors to

HFpEF.

LV Pressure Measurements: Previous cMRE studies in porcine models have shown that pressure measurements obtained via ventricular catheterization strongly correlates with cMRE-derived MS [97] and cMRE-derived shear wave amplitudes [116]. Similar correlation of cMRE-derived MS with increasing mean LV pressure was observed confirming that change in pressure is indeed related to change in LV MS. Although this trend was consistent in most of the animals, in one animal despite increase in stiffness from Bx to M1 to M2, mean LV pressure decreased from Bx (ED=20.6 mmHg, ES=89.5 mmHg) to M1 (ED=3.2 mmHg, ES=59.6 mmHg) and then increased at M2 (ED=26.8 mmHg, ES=130.2 mmHg). Nevertheless, we suspect that the drop in pressure could be 87

physiological response of the animal to anesthesia during the pressure measurements or it can be associated with any calibration error in pressure measurements at M1. However, an increase in pressure was observed in the same animal from Bx to M2. Overall, this study validated cMRE-derived stiffness against change in invasive pressure measurements during disease progression in a HFpEF porcine model.

Cardiac Function and Morphology: Cardiac functional parameters (EF, stroke volume, cardiac output) did not demonstrate any significant change. The mean EF for all the animals (considering all 3 time points) was in the range of 40-45. Typically an EF ≥ 45 is considered normal and is expected in HFpEF conditions. However, in this study, the mean EF was marginally lower than expected because 2 animals started off (Bx) with very low EF (< 25). The EF in these animals improved over time but in general it was still lower than the normal range, which reduced the total mean. The low EF observed in these 2 animals can be attributed to the fact that juvenile pigs used in this study were still growing and hence their cardiac functions were still developing. Our results demonstrated an initial increase in stroke volume and cardiac output from Bx to M1 for all animals and then in some animals from M1 to M2 both stroke volume and cardiac output decreased.

Typically, hemodynamics of hypertension suggests that both stroke volume and cardiac output should decrease. Especially in severe diastolic dysfunction (which this porcine model should eventually develop), when ventricular filling and LV ED volume is significantly reduced, a low stoke volume and in turn reduced cardiac output is expected

[298]. From the decreasing trend observed in a few animals at M2 it can be concluded that to observe a significant decrease in stroke volume and cardiac output, prolonged 88

hypertension is required and imaging at two months is not sufficient to notice that change. LV mass estimated in this study increased significantly with hypertension that is consistent with previously obtained results in HFpEF patients (n=4128) [299].

LV Thickness Measurements: Our results demonstrated that LV thickness increased throughout the cardiac cycle with disease progression, indicating that all animals developed hypertrophy. It is well known that hypertrophy secondary to hypertension reduces LV compliance, leading to diastolic dysfunction [300]. This association between hypertrophy (induced by hypertension) and LV compliance was reflected with an increase in MS that had a strong positive correlation with LV thickness. It is important to note that not all kinds of LV hypertrophy are related to increase in LV MS. LV hypertrophy can be induced either due to physiological remodeling or pathological remodeling. Physiological remodeling occurs as a physiological adaptation to an increased workload of the heart following intense physical training [301]; on the other hand, pathological remodeling occurs as a response to a pathophysiological condition such as hypertension or valvular disease [301]. While pathophysiological remodeling causes increase in LV MS as seen in this study, it is not true for physiological remodeling

[301] and hence just increase in LV thickness cannot be used as a diagnostic metric in

HFpEF. cMRE-Derived MS Measurements: The cyclic variation in LV MS across the cardiac cycle observed in this study is consistent with previous work [107]. Furthermore, as observed in previous work, LV ES MS was significantly higher compared to LV ED MS

in all animals at each time point (Bx, M1, and M2). Additionally, change in LV ED and

ES MS over time displayed characteristics related to HFpEF conditions. It is well understood that HFpEF is primarily associated with diastolic dysfunction wherein the systolic function may or may not be preserved. The significant increase in LV ED MS that was observed both at M1 and M2, could contribute to impaired LV relaxation indicating the possibility of developing diastolic dysfunction. Moreover, although LV ES

MS initially increased significantly (Bx to M1), over time i.e. from M1 to M2 the increase became insignificant, indicating that after the initial surge systolic function was being preserved. This is further exemplified from the correlation plots (Figure 19) between LV ED and ES MS and mean LV pressure which demonstrated higher correlation at ED (휌=0.56) compared to ES (휌=0.45).

Circumferential LV Strain: Hypertension induced LV hypertrophy is associated with preserved EF and reduced circumferential shortening, which is reflected as decreased circumferential strain measurements (lower negative strain values). This was demonstrated in a previous study where reduced circumferential strain was observed in hypertensive patients (n=67) as compared to healthy controls (n=45) [302]. The results obtained in this study showed significant reduction in LV circumferential strain at M2 when compared to Bx, which is consistent with the previously obtained results.

Furthermore, the negative linear correlation observed between LV circumferential strain and LV ED and ES MS indicates that increased stiffness in this hypertensive model causing LV hypertrophy is associated with decreased myocardial deformation.

Additionally, from the trend observed in circumferential strain measurements from Bx to 90

M1 and from M1 to M2 it can be concluded that prolonged hypertension is required to observe severe reduction in LV strain measurements.

Delayed Enhancement and MRI Relaxometry Parameters: The absence of focal hyper- intensity in delayed enhancement images indicated that although hypertension has the potential to induce myocardial fibrosis it was not observed in this study. From the unchanged T2 values from Bx to M1 to M2, it can be concluded that hypertension did not induce acute myocardial injury (with edema) during disease progression. The absence of correlation between MS and T2 values and no change in T2 values at different time points can be attributed to the fact that T2 values may not have been obtained at a time interval during the inflammatory stage (edema) during disease progression.

LV hypertrophy secondary to hypertension contributes to a progressive accumulation of fibrous tissue within the cardiac interstitium. However, from the T1 measurements (both pre- and post-contrast) and qualitative analysis of delayed enhancement images, no obvious signs of localized or diffused fibrosis could be identified. Moreover, ECV measurements, which should have altered with increased collagen deposition, remained unchanged within the two-month period. This indicates that two months was not enough to reflect myocardial fibrosis and to see an effect in T1 and ECV measurements, a longer wait period is required. The correlation plots between LV MS and i) T1post and ii) ECV measurements demonstrated an insignificant negative trend which was counter-intuitive.

From the plots, we observed that one data point (possible outlier) on both T1post and ECV fraction contributed to the negative trend, and excluding this point would demonstrate no

correlation between MS and ECV or T1 measurements. On closer inspection it was observed that one animal at M2 had a variable heart rate that was not accounted for in the

T1 protocol and which resulted in very low values for T1 (both for the myocardium and the blood). This animal contributed to the outlier in the data, which was the cause of the negative trend between MS and T1post and ECV measurements. However, from the initial results of this study it can be understood that cMRE-derived MS can provide additional information compared to T1, T2 and ECV measurements, which can be used for early diagnosis of HFpEF.

Limitations: There are some limitations in our study. First, the local frequency estimation algorithm used to measure MS considers the myocardium to be an isotropic, homogenous, and infinite medium, which is not true. Hence the MS estimates obtained in this study using cMRE are termed to be “effective” measurements [97, 107]. Second, due to limited temporal resolution, it is difficult to capture the precise ED and ES cardiac phases. However, minimum and maximum mid-ventricular thickness was used as a measure to select the best approximate ED and ES cardiac phases respectively. Third, some animals had poor wave propagation in the posterior myocardial wall that was farther from the driver. To account for this, regions with poor wave propagation were masked out before reporting the stiffness measurements. Fourth, in one of the animals at

M1, the tags obtained for cardiac strain analysis were very noisy which in turn corrupted the tracking across the different cardiac phases resulting in erroneous strain measurements. This was resolved by excluding this animal from all strain measurement analysis. Finally, the two-month time point was not sufficient to study the effect of 92

prolonged hypertension and a longer wait period would provide better understanding of the association of MS with cardiac functional parameters, strain measurements and MRI relaxometry parameters. This two-month time period was chosen based on the earlier studies [288, 303, 304]. Despite these limitations this study has demonstrated that cMRE- derived MS measurements can potentially be used for timely (at M1) diagnosis of HFpEF inducing disease conditions when other routine clinical parameters (cardiac function, strain, relaxometry) remained nondeterministic.

3.5 Conclusions cMRE-derived MS is validated in an established HFpEF model against LV pressure and

LV thickness. cMRE-derived MS increases temporally with disease progression, and has a positive correlation with mean LV pressure and LV thickness. Additionally, this study shows that cMRE-derived MS has weak correlation with LV circumferential strain and no correlation with MRI relaxometry parameters.

This chapter demonstrated the potential of using cMRE as a diagnostic tool to estimate temporal variation in MS with disease progression in a HFpEF porcine model. In the next chapter, to demonstrate the diagnostic relevance of cMRE in HFrEF conditions, variation in LV MS with disease progression is estimated in myocardial infarction (HFrEF causing disease condition) induced porcine hearts.

Chapter 4: Left Ventricular Myocardial Stiffness in Heart Failure with Reduced

Ejection Model

It was introduced in Chapter 1 that myocardial infarction (MI) results in regional alteration of myocardial stiffness (MS) and is a major contributing factor in the development of heart failure with reduced ejection fraction (HFrEF). This chapter assesses the diagnostic potential of cMRE by using it to estimate spatially resolved MS on a MI porcine model. The cMRE-derived estimates of MS obtained from the MI affected region are compared against the estimates of the remote myocardium to investigate whether cMRE-derived MS can be used as a metric to differentiate between infarcted and viable myocardium. Furthermore, cMRE-derived MS measurements are validated against ex-vivo mechanical testing and compared to other established MRI- based diagnostic metrics used to assess MI such as i) cardiac strain and ii) MRI relaxometry parameters (T1 T2 and extracellular volume fraction (ECV)).

This material is previously published or presented as shown by the following citations.

 Mazumder R, Schroeder S, Mo X, Clymer BD, White RD, Kolipaka A. In-Vivo

Magnetic Resonance Elastography: A Feasibility Study to Estimate Left Ventricular

Stiffness in a Myocardial Infarction Porcine Model, Circulation: Cardiovascular

Imaging (Under Review). 94

4.1 Introduction

Myocardial Infarction (MI), which results from occlusion of a coronary artery, accounts for 1.5 million incidences in the US annually [305]. Coronary artery occlusions result in an inadequate supply of oxygenated blood to the myocardium leading to myocardial necrosis. This affects cardiac mechanics by causing regional myocardial dysfunction

[306] and increase in myocardial stiffness (MS) [176, 229], which may eventually trigger heart failure with reduced ejection fraction (HFrEF) [307]. Therefore, understanding and quantifying cardiac mechanics (related to myocardial stiffness) associated with the onset, progression, and remodeling of MI [308] is important for developing effective treatment to prevent HFrEF.

Currently, pressure-volume analysis (P-V) and biomechanical testing are used to quantify mechanical properties of the myocardium. Previous studies using P-V analysis have shown that the left ventricular (LV) compliance decreased following MI [229].

Furthermore, studies using biomechanical testing have shown a regional elevation of MS at the site of the MI [176]. Although, these techniques have successfully shown the change in mechanical properties of the myocardium post-MI, both these techniques are invasive in nature and hence clinically challenging. Therefore, a non-invasive tool to quantify regional MS may provide an alternative to the currently used techniques.

Strain-based cardiac MRI techniques (spatial modulation of magnetization tagging [309], displacement encoding with stimulated echo [310], strain encoding [311]) used for quantitative evaluation of regional myocardial contractile performance do not account for

the effects of variable loading conditions. As a result, these techniques provide relative strain measurements that do not reveal the true intrinsic mechanical properties of the myocardium.

Recently, with the advent of cardiac magnetic resonance elastography (cMRE), a phase- contrast-based MRI technique to non-invasively quantify MS, has become feasible [94,

97, 100, 107-112]. However, to best of our knowledge, no cMRE studies have estimated regional MS in MI regions and compared it with corresponding myocardial tissue properties as defined by MRI relaxometry properties.

This study creates a MI induced porcine model and aims to 1) use cMRE to estimate MS in both infarcted and remote normal regions during disease progression; 2) validate cMRE measurements against results from ex-vivo mechanical testing; and 3) measure circumferential strain, T1, T2 and extracellular volume fraction (ECV) in both infarcted and remote non-infarcted regions and compare the measurements to cMRE-derived MS.

4.2 Methods

All animal procedures were performed in accordance with the university’s institutional animal care and use committee guidelines. Seven juvenile Yorkshire pigs (serially studied at three time-points, i.e. n=21) weighing ~70 lbs were used for this study.

MI Induction Procedure

Under fluoroscopy (GE OEC 9800, General Electric, USA) a 7Fr catheter (AL1 ST SH guide catheter (Boston Scientific, Marlborough, MA)) was advanced through the femoral 96

artery, descending aorta and all the way into the left anterior descending artery (LAD).

Pre-surgical baseline coronary angiogram was obtained using Omniplaque contrast (350 mg/ml) to select an infusion site. A Maverick over-the-wire coronary angioplasty balloon catheter (Boston Scientific, Marlborough, MA) sized according to the target vessel was positioned in the LAD distal to the first diagonal branch. The balloon was inflated to nominal pressure preventing blood flow to the distal LAD. After 5 mins of ischemia, 2 ml of absolute ethanol was infused through the balloon catheter guide wire lumen into the distal LAD territory over 3 mins followed by a 1 ml saline flush. The balloon was left inflated for an additional 3 mins to prevent retrograde flow of the ethanol back up into the proximal LAD. Total occlusion of the coronary artery was verified by another angiogram and then the balloon was deflated and removed from the vessel. A follow up angiogram was performed to document lack of blood flow to the target area [312].

MR Imaging Timeline:

MRI was performed on all the animals prior to coronary occlusion for baseline (Bx) measurements, and then 10 days (D10) and 21 days (D21) post-MI with the imaging parameters (given below) remaining same for all time points. These two post-MI time points were specifically selected to monitor the mechanical properties of the myocardium as the non-reperfused MI evolved from the acute/early reparative state (necrosis with edema, neutrophilic infiltration, myocyte fragmentation, peripheral phagocytosis, granulation with loose collagen deposition) during weeks 1-2 to the sub-acute/early fibrotic phases (progressively dense collagen deposition) from weeks 3-8 [10, 173, 174].

Animal Preparation for MRI

Imaging was performed in animals under anesthesia, which was induced using ketamine

(20 mg/kg) and acepromazine (0.5 mg/kg) and was maintained using isoflurane (1-5%) inhalation. The animals were placed supine on the MRI table and endotracheal intubation was performed to administer mechanical ventilation. External vibration for cMRE was induced into the myocardium using an acoustic speaker placed outside the scan room and connected via plastic tube to a passive driver as shown in Figure 23. This passive driver was positioned on the anterior chest wall and secured tightly using an elastic velcro strap.

Image Acquisition

Image acquisition was performed using a clinical 1.5-Tesla MRI scanner (Avanto,

Siemens Healthcare, Erlangen, Germany), with a body coil placed on the anterior side and a spine coil on the posterior end. Cardiac triggered segmented balanced steady-state free precession (b-SSFP) cine sequence was implemented to acquire vertical, horizontal long-axis views and short-axis views covering the heart. The cine images were used to estimate cardiac functional parameters. Imaging parameters for cine imaging included: echo time (TE)/ repetition time (TR)=1.49/27.36 ms; field of view (FOV)=300x300 mm2; imaging matrix (IM)=256x256; slice thickness (ST)=6mm; flip angle (FA)=46◦; cardiac phases (CP)=30; GRAPPA acceleration factor (AF)=2.

Retrospective pulse-gated, segmented cine gradient recalled echo (GRE) cMRE sequence was used to obtain short-axis slices covering the entire LV [107]. Imaging parameters for cMRE included: TE/TR=9.71/12.5 ms; FOV=384x384 mm2; IM=128x128; ST=8mm;

FA=15◦; CP=8; GRAPPA AF=2; excitation frequency=80Hz; encoding frequency=160Hz; phase offsets=4.

A prospectively gated GRE based cardiac tagging sequence was used to acquire short- axis slices covering the entire heart. Imaging parameters included: TE/TR=3.42/19.47 ms; FOV=300x300 mm2; IM=224x168; ST=8mm; FA=8◦; CP=25;

Quantitative imaging was performed to analyze the change in T1, T2 properties and ECV fraction at different stages of the disease progression. Blood samples were drawn to measure the hematocrit fraction for ECV calculations. Short-axis T2 maps [292] were acquired to identify the presence of any myocardial edema as a result of MI. Imaging parameters included: TE/TR=1.37/229.36 ms; FOV=360x270 mm2; IM=192x160;

ST=8mm; FA=35◦; CP=1; GRAPPA AF=2. Short-axis T1 modified Look-Locker 99

inversion recovery sequence was acquired pre-contrast (T1pre) [292-294] and then re- acquired post-contrast (T1post), 10 mins after injection of contrast agent to investigate fibrosis and estimate ECV. Imaging parameters for T1 maps were similar to T2 maps except TE = 1.01 ms and TR = 255.46 ms.

Short-axis delayed enhancement imaging was performed using a T1- weighted phase- sensitive IR (PSIR) sequence across the entire heart, 8 minutes post-injection of contrast agent in order to confirm the region of MI. Imaging parameters for PSIR included:

TE/TR=4.34/662 ms; FOV=360x292 mm2; IM=192x160; ST=8mm; FA=25◦; CP=1;

Post-contrast images (i.e. delayed enhancement and T1post) were acquired after manual injection of a rapid bolus of Gadobenate Dimeglumine (MultiHance, Bracco Diagnostics,

Princeton, NJ) followed by a 20 mL saline flush. The dosage varied by the animal’s weight at a rate of 0.2 mL/kg.

Image Processing

Cardiac Function and Morphology: The LV was manually contoured on the cine images to determine the end-diastolic volume (EDV), end-systolic volume (ESV), ejection fraction (EF), cardiac output (CO) and LV mass using a commercially available software package (Argus Ventricular Function, Siemens Healthcare, Erlangen, Germany). The papillary muscles and trabeculae were not included in the endocardial contours. Heart rates were also determined and all functional parameters were measured at each time point (i.e. Bx, D10, and D21).

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cMRE Analysis: cMRE images were analyzed using MRELab (Mayo Clinic, USA) to estimate systolic and diastolic MS by applying a 3D local frequency estimation algorithm

(LFE). Using DE images as reference, the MI (hyper-intense) regions (MIR) and the non- infarcted (unenhanced region opposite to MIR) remote regions (RR) were identified on the stiffness maps and MS at D10 and D21 in MIR and RR was reported. For Bx measurements regions were identified on the stiffness maps that corresponded to MIR and RR on the D10/D21 DE images and an average from both these regions were reported as the Bx MS to be consistent with other time points.

Cardiac Strain Analysis: Tagged images were analyzed using commercial HARP software (Diagnosoft, Palo Alto, California). The slice with the strongest infarct was selected and endocardial and epicardial contours were drawn on the end-systolic phase.

Circumferential Eulerian strain was automatically calculated for the different segments of the heart. For Bx measurements the average from all the segments was reported as the cardiac strain. For D10 and D21, segments corresponding to the RR and MIR were selected to report the strain in the infarct and remote zones.

Quantitative Mapping (MRI Relaxation Parameters): Regions on the relaxometry maps both for Bx and post-MI (D10 and D21) were defined based on the DE images (as described for the cMRE analysis) and the mean values were reported. Mean ECV was calculated as the ratio of the myocardial and blood pool (blood T1 was estimated from

T1* maps) relaxation rates (∆R1) calibrated by blood hematocrit using the following equation:

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1 ∆푅1 = (57) 푇1 (푃표푠푡) − 푇1(푃푟푒)

∆푅1 퐸퐶푉 = (1 − ℎ푒푚푎푡표푐푟푖푡) × 푚푦표 (58) ∆푅1푏푙표표푑

Mechanical Testing

After the imaging on D21 the animals were sacrificed using Euthasol to arrest the heart in systole. Post-sacrifice on D21 the hearts were extracted and prepared for biomechanical testing. First, uniform 3 mm thick short axis slices were cut from the base to the apex.

Next, slices containing the infarct were identified and approximately 35x10 mm2 transmural cuts were made on the infarcted region (wall thinning in the infarcted region made it difficult to keep the width constant). Then similar size cuts were performed on a remote region and thus multiple infarcted and remote samples were obtained for repeated measurements. These samples were then stored in a hypotonic cardioplegic or lactated ringers solution [176] until the availability of the material testing system. A servohydraulic material testing system (Bionix 858, MTS System Corp, Eden Prairie,

MN) was used to determine the stiffness of the infarcted and remote specimens. Each specimen was secured in cryogrips. No preload was used for this study to avoid damage to the specimens. A ramped load in uniaxial tension under displacement control at 10 mm/min was applied until failure with continuous recording of load and displacement.

Peak load to failure and structural stiffness was determined for each sample from the

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load-displacement curve by measuring the maximum load and linear slope of the curve respectively.

Statistical Analysis

Data analyses were performed by using SAS 9.4 software (SAS, Inc; Cary, NC).

Longitudinal measures of stiffness were analyzed by mixed effect models, accounting for the association of the same measure at different time points from the same animal [297].

These models included location (MIR or RR) as a covariate and days post-surgery as independent variable of interest and allow subject specific intercepts and slopes. The slopes, means and standard errors were estimated and compared by using these models.

Correlations between both systolic and diastolic MS and circumferential strain, T2, T1post,

ECV, and mechanical testing were assessed by Pearson’s correlation method. P≤0.05 was considered statistically significant.

4.3 Results

Out of 7 animals scanned, one died on D10 and since no complete post-surgical time point was collected on this animal, this animal was excluded from any analysis. Out of the remaining 6 animals analyzed for this study, one animal died after the D10 scan, and therefore, results for D21 were unavailable. These animals died due to surgical complications.

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Cardiac Function and Morphology: Cardiac functional and morphological analysis measurements are detailed in Table 3. The range and mean heart rate for all 6 animals at

Bx, D10, and D21 were ([87–125], 102) bpm, ([83–122], 101) bpm, and ([90–115], 102) bpm, respectively. The range and mean EF for all 6 animals at Bx, D10, and D21 were

([34.4–59.6], 42.08)%, ([31.2–63.1], 41.13)%, and ([25.7–43], 35.98)%, respectively.

Although, individual animals demonstrated no specific trend in EF with disease progression, mean EF from all animals pooled together exhibited a reducing trend from

Bx to D10 to D21. The range and mean CO from all animals at Bx, D10, and D21 were

([1.88–3.12], 2.43)L/min, ([2.26–3.37], 2.71)L/min, and ([1.92–4.48], 2.88)L/min respectively. Again, although, no discernable trend was observed when individual animals were compared, mean CO increased with disease progression. The range and mean LV mass at Bx, D10 and D21 were ([46.3–93.8], 65.3)gm, ([57.6–99.3], 74.38)gm, and ([66.2–125], 83.38)gm, respectively. In general, LV mass indicated an increasing slope with disease progression in 5 out of 6 animals. cMRE Stiffness Estimates: Figure 24 shows the diastolic and systolic magnitude image, wave propagation, and stiffness maps at Bx and D21. Mean (from all animals) diastolic

MS at Bx was 3.87±0.4kPa. At D10, and D21 mean diastolic MS was 5.09±0.6kPa and,

5.45±0.7kPa, respectively in MIR and 3.97±0.4kPa, and, 4.12±0.2kPa, respectively in RR

(Figure 25a). Mean (from all animals) systolic MS at Bx was 4.98±0.7kPa. At D10, and

D21 mean systolic MS was 5.72±0.8kPa and, 6.34±1.0kPa, respectively in MIR and

5.08±0.6kPa, and, 5.16±0.6kPa, respectively in RR (Figure 25b). The results demonstrate that MS was significantly higher in MIR as compared to RR both at D10 (diastole: 104

p=0.0003; systole: p=0.0318) and D21 (diastole: p=0.0002; systole: p=0.0018). Slope analyses indicated that as the MIs evolved, both diastolic and systolic MS increased in

MIR (diastolic: slope=1.58, p<0.0001; systolic: slope=1.43, p=0.0025) but it did not show any significant change in RR.

Table 3: Cardiac function and morphology measurements for all the animals at Bx, D10 and D21.

LV Animal Time Heart EF EDV ESV SV CO Mass Identifier Point Rate (%) (mL) (mL) (mL) (L/min) @ ED (bpm) (gm) Bx 93 59.6 55.4 22.4 33.0 2.9 68.2 P1 D10 83 63.1 50.6 18.7 32.0 2.7 58 Bx 122 35.0 55.6 36.2 19.4 2.4 59.9 P2 D10 103 42.3 67.8 39.1 28.7 3.0 72.7 D21 102 43.0 64.8 37.0 27.9 3.0 71.4 Bx 87 35.9 75.8 48.6 27.3 2.3 66.3 P3 D10 91 31.2 82.6 56.8 25.8 2.3 77.3 D21 90 35.1 77.1 50.0 27.1 2.5 76.3 Bx 125 34.4 74.4 48.8 25.6 3.1 93.8 P4 D10 112 39.6 76.5 46.2 30.3 3.4 99.3 D21 106 42.9 98.6 56.3 42.3 4.5 125 Bx 95 47.1 42.5 22.5 20.0 1.9 46.3 P5 D10 122 34.0 55.0 36.3 18.7 2.3 57.6 D21 97 33.2 58.4 39.0 19.4 1.9 66.2 Bx 92 40.5 56.3 33.5 22.8 2.1 57.5 P6 D10 96 36.6 74.7 47.3 27.3 2.6 81.4 D21 115 25.7 84.5 62.8 21.7 2.5 78.0 Bx 102 42.1 60.0 35.3 24.7 2.4 65.3 Mean D10 101 41.1 67.9 40.7 27.1 2.7 74.4 D21 102 36.0 76.7 49.0 27.7 2.9 83.4

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Figure 24: cMRE Images. Baseline: Magnitude image: (a) diastole (g) systole; Wave propagation (four phase offsets) in x- direction: (b-e) diastole (h-k) systole; Stiffness maps (f) diastole (l) systole. Day 21: (m) DE image showing MIR (red) and RR (green); Magnitude image delineating MIR the RR (n) diastole (t) systole; Wave propagation (four phase offsets) in x- direction: (o-r) diastole (u-x) systole; Stiffness maps (s) diastole (y) systole. 106

Figure 25: cMRE-Derived Stiffness. Box plots showing a) systolic and b) diastolic stiffness in MIR and RR at Bx, D10 and D21. Stiffness at MIR is higher than RR. Stiffness increased significantly from Bx to D21 in MIR (*) but did not change in RR (#).

Cardiac Strain Analysis: Figure 26a shows the box plot for circumferential strain in MIR and RR at different time points (Bx, D10, and D21). The mean circumferential Eulerian strain at Bx was -7.41. Strain measurements in MIR at D10 and D21 were -1.10, and -

0.18, respectively, while that in RR at D10, and D21 were -8.26, and -9.50, respectively.

The mean strain in RR was significantly higher than the mean in MIR both at D10

(p<0.0001) and D21 (p<0.0001). Additionally, slope analysis indicated no significant change in strain from Bx to D21 in RR (slope=-2.09, p=0.0765) but significant decrease in strain from Bx to D21 in MIR (slope=7.23, p=0.0002). Figure 26b and Figure 26c show correlation of circumferential Eulerian strain in the MIR with diastolic MS, and systolic MS, respectively. While circumferential Eulerian strain exhibits a significant negative correlation with diastolic MS (r=0.53, p=0.044), it demonstrates only a negative trend with systolic MS (r=0.31, p=0.254).

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Quantitative Mapping (MRI Relaxation Parameters): Figure 27 shows the DE image, T2, and T1post maps in an animal both at Bx and D21 (in a slice containing the infarct). As shown, at Bx uniform intensity was observed in the DE image (Figure 27a), T2 (Figure

27b) and T1post (Figure 27c) map. However, on D21 hyper-enhancement was present in

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MIR for both DE image (Figure 27d) and T2 map (Figure 27e) while reduced intensity was observed in T1post (Figure 27f) map.

T2 Map Measurements: Mean (from all animals) T2 estimate at Bx was 44.6±2.1ms. At

D10, and D21 T2 values were 59.8±5.4ms and, 68.4±9.7ms, respectively in MIR and

45.1±1.4ms, and, 47.2±1.6ms, respectively in RR (Figure 28a). The results show that the

T2 values in RR was significantly lower than MIR both at D10 (p=0.0003) and D21

(p<0.0001). Additionally, slope analyses indicated that as the disease progressed from Bx to D21 the mean T2 measure increased significantly (slope=23.62, p<0.0001) in the MIR, however, no change (p=0.31) was observed in the RR.

T1 Map Measurements: Mean (pooling all animals) T1post measurement at Bx was

525.9±37.3ms. At D10, and D21 T1 values were 390.0±15.2ms, and, 361.7±22.9ms, respectively in MIR and 543.7±32.6ms, and, 527.1±29.1ms, respectively in RR (Figure

28b). The results demonstrate that T1post values in MIR was significantly lower compared to RR both at D10 (p<0.0001) and D21 (p<0.0001). Furthermore, as the disease progressed from Bx to D21, the T1post values reduced significantly in MIR (slope=-158.9, p<0.0001) but not in RR (p=0.6).

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Figure 27: DE Image and Corresponding Relaxometry Maps. (a) Baseline DE image shows no enhancement; (d) D21 DE image shows hyper-enhancement (white arrow), 8mins after contrast injection. (b) Baseline T2 map with uniform intensity; (e) D21 T2 map shows patchy hyper-intensity (white arrow). (c) Baseline T1post (10 mins after contrast injection) map shows uniform intensity; (f) D21 T1post map shows reduced intensity (white arrow).

ECV Measurements: Mean ECV from all animals at Bx was 25.6±1.1%. At D10 and D21

ECV estimates were 48.1±6.3%, and 52.5±6.6%, respectively, in MIR and, 25.2±2.4%, and 26.6±3.0%, respectively, in RR (Figure 28c). An intra-time point comparison indicated that the ECV measures in MIR were significantly (p<0.0001) higher than RR both at D10 and D21. Additionally, the results also revealed that while there was no change in ECV with disease progression in RR (p=0.6409, slope analysis), in MIR ECV increased significantly (slope=26.95, p<0.0001) with time.

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Figure 28: Relaxometry Analysis. Box plot shows relaxometry parameters in MIR and RR at Bx, D10 and D21. a) T2 values increased significantly in MIR as compared to RR both at D10 and D21 b) T1post values decreased significant in the MIR as compared to RR both at D10 and D21. c) ECV increased significantly in MIR compared to RR both at D10 and D21.

Quantitative Mapping Correlation Analysis: Figure 29 shows the MIR correlation maps between cMRE-derived stiffness (both systolic and diastolic) and MRI relaxometry parameters. Although there is a positive trend no significant correlation was observed between T2 and either diastolic (Figure 29a) or systolic MS (Figure 29d). Significant inverse correlation was observed between T1post and both diastolic (r=-0.549, p=0.022)

(Figure 29b) and systolic (r=-0.741, p=0.0007) (Figure 29e) MS. A significant good

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positive correlation was observed between ECV and both diastolic (r=0.548, p=0.023)

(Figure 29c) and systolic (r=0.703, p=0.0016) (Figure 29f) MS.

Mechanical Testing: Figure 30a demonstrates that the mechanical testing-derived stiffness from the excised MIR samples is higher compared to RR samples. Mean stiffness across all animals in MIR is 1.698 N/mm, which is nearly twice as much as RR

(0.868 N/mm) (p=0.005). Correlation maps (Figure 30b) indicate that there was a strong positive correlation between mechanical testing-derived stiffness and both cMRE-derived diastolic (r=0.86, p<0.0001) and systolic (r=0.89, p<0.0001) MS.

4.4 Discussion

Overall Summary: This study demonstrates that cMRE can non-invasively quantify alteration in MS in a MI induced porcine model. The results indicate that over a 3week period, the infarcted region undergoes a steady increase in MS both at diastole and systole, as opposed to the remote region where MS remains preserved. This increase in cMRE-derived stiffness is validated by uniaxial ex-vivo mechanical testing, indicating that cMRE has the potential to be used as a diagnostic tool to investigate the mechanical alterations triggered by MI. Additionally, multi-parametric analysis indicated that cMRE- derived stiffness has i) negative trend with strain measurements; ii) positive trend with T2 measurements; ii) significant inverse correlation to T1post measurements; and iii) strong positive correlation to ECV measurements.

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Figure 29: Correlation Analysis between cMRE-Derived MS and Relaxometry Parameters. No significant correlation (r<0.5) was observed between T2 and a) diastolic MS and d) systolic MS. Good inverse significant correlation was observed between (r<-0.5) T1post and b) diastolic MS and e) systolic MS. Good positive significant correlation (r>0.5) was observed between ECV and c) diastolic MS and f) systolic MS. 113

Cardiac Function and Morphology: Cardiac MRI functional parameters (EF, SV and

CO) did not establish any dominant characteristic trend with MI evolution. Previous studies on cardiac functional parameters in porcine models for MI reported both increase

[313] and decrease [314] in EF and CO. The inconsistencies observed in the animals’ cardiac functional response could be caused by several factors. First, juvenile porcine model was used for the study, which implied that the animals were still growing and had undeveloped cardiac function [313]. Second, the site and size of the MI and the extent of the myocardial injury were not constant in all the animals. Third, pathological response to

MI could vary from one animal to another, which in turn could affect the cardiac functional measurements. Finally, post-MI alteration in EF is generally long-term, and thus may not be visible in the first few weeks but continue to decrease late, thereby

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triggering heart failure; and a 21-day time point may not be sufficient enough to observe the drop in EF. cMRE-Derived Stiffness: The diastolic and systolic phases of the wave-images were processed using a 3D LFE inversion algorithm and as the MI progressed from Bx to D21 an increase in MS was observed in MIR. To the best of our knowledge, there is only one other study that uses cMRE (implements phase gradient inversion of the radial component of motion on 1D linear line profiles) to quantify MS in a MI model [100].

Since our study uses 3D LFE that incorporates complete 3D wave propagation information as opposed to the previous study that uses 1D wave profiles, a direct comparison of stiffness values is not possible. However, it is important to note that both the studies observed increased MS in MIR when compared to RR at D21. Since the previous study estimates MS post 3 weeks of inducing MI, Bx and D10 measurements are unavailable for comparison. Our findings also demonstrate that throughout systolic

MS is higher compared to diastolic MS, an outcome that is consistent with previously reported findings [107].

Cardiac Strain Analysis: Circumferential strain measurements were significantly reduced in MIR as compared to RR both at D10 and D21, which is consistent with results obtained by another research group [315]. Since, circumferential strain is a measure of circumferential shortening the value is negative during systole in the normal myocardium, and higher negative strain values indicate better compliance. In an infarcted myocardium since the myocardium’s ability to contract is compromised due to increased

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stiffness, the amount of deformation in the infarcted myocardium is reduced which in turn reduces the strain measurements. This implies that a negative correlation should be expected between MS and strain. Although we observed a significant negative correlation between diastolic MS and strain, only a negative trend was observed with systolic MS. It is important to note that diastolic MS reports the true intrinsic passive stiffness of the myocardium (i.e. without active contraction and ~zero LV pressure), whereas, systolic

MS contains effects from active contraction and pressure. Isolating pressure effects from the systolic MS measurements is very challenging, and this could potentially contribute to the insignificant association between circumferential strain and systolic MS.

Quantitative Mapping (MRI Relaxometry Parameters): The significant increase in the T2 value from Bx to D10 and D21 in MIR and the hyper-intensity noticed in the T2 map images confirm presence of myocardial edema which is consistent with results reported in previous studies [316]. Despite increase in T2 values no significant correlation was observed with cMRE- derived MS. This can be attributed to the fact that physiological response of MI is different from one animal to the other and each animal could be at a very different inflammatory stage. The accurate time point to investigate the change in T2 estimate would be within the first week from the onset of MI when the myocardium is at its peak inflammatory stage with maximum edema. Since the inflammatory stage subsides after fibrosis starts, the increase in MS observed in this study could be a result of fibrosis and not inflammation which is further confirmed by the T1 and ECV correlation maps. Due to fibrosis caused by MI, the contrast agent was trapped in the infarcted myocardium which was reflected as reduced T1 values in the T1post maps also observed 116

by other groups [317, 318]. This correlated well (inverse correlation) with cMRE-derived

MS justifying that fibrosis and mechanical properties are interdependent. The increase in the ECV with disease progression observed in MIR is consistent with fibrosis as stated in previous works [319, 320]. The positive correlation between both systolic and diastolic

MS and ECV indicates that change in mechanical properties of the myocardium is directly dependent on the alteration of the extracellular matrix content.

Mechanical Testing: A significant increase in stiffness was observed in MIR compared to

RR which is consistent with previously reported study [176]. A strong positive correlation was observed between mechanical testing-derived stiffness and cMRE- derived stiffness. Since mechanical testing is invasive in nature, requires technical precision and is therefore clinically inefficient; the strong correlation between cMRE and mechanical stiffness indicates that cMRE can be potentially used as a non-invasively alternative to estimate MS in MI.

Limitations: There are some limitations in our study. First, the time period between sacrifice and mechanical testing varied from 1 day to 2 weeks based on the availability of the mechanical testing system. This limitation was addressed by freezing (-20◦C) the specimens in Ringer’s solution so that the mechanical properties remained preserved.

Second, the loading frequencies of cMRE and mechanical testing are very different.

Third, due to oblique cuts in the excised specimen and wall thinning due to pathology, the width of the samples might not have been uniform throughout, and the geometric measurements such as widths and lengths used to estimate stiffness might not be very

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precise. Fourth, failure often occurred at regions other than the narrowest location and these factors could affect the peak stress values, which could eventually affect the stiffness measurements. Despite these factors a significantly strong positive correlation coefficient was observed between mechanical testing-derived stiffness and cMRE- derived stiffness. Fifth, from the DE images it was observed that some of the infarcts had regions of dark myocardium that could be a result of microvascular obstruction.

Therefore, while estimating the MRI relaxometry parameters these regions were excluded from the ROI. Sixth, systolic and diastolic phases were investigated instead of end- diastole and end-systole due to following reasons: a) the temporal resolution was not high enough to capture the precise end-systolic or end-diastolic phase [107]; and b) due to ST segment elevation and arrhythmia noticed post-infarction, motion artifacts prevailed in the end-systolic and end-diastolic phases due to miss-triggering. Therefore, systolic and the diastolic cardiac phases were selected, since those images were collected from a more stable section of the cardiac cycle. Finally, the wave propagation in the heart is known to be guided by the myocardial fiber orientation. Hence, to estimate the true stiffness of the myocardium a 3D anisotropic inversion that accounts for the fiber orientation and as well as the geometry is needed, but for this particular animal model it is currently outside the scope of this dissertation (however, anisotropic inversion will be explored for other models in later chapters). Therefore the reported MS measurement in this chapter is not an absolute measure and is termed to be an “effective” estimate. Despite these limitations this study showed significant increase in stiffness in MIR compared to RR both at systole and diastole.

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4.5 Conclusions

This study demonstrated that the effective cMRE-derived MS in MIR is higher than RR, an inference that was validated using mechanical testing-derived stiffness. Significant negative correlation was observed between cMRE-derived diastolic MS and circumferential strain measurements in MIR. Additionally, significant correlation was also observed in MIR between cMRE-derived MS (diastolic and systolic), and T1post, and

ECV confirming that cMRE can be used as a potential alternative to mechanical testing.

This chapter used cMRE to demonstrate the alteration in isotropic mechanical properties of the myocardium during MI. In addition to altering the mechanical properties of the myocardium, MI also influences myocardial structure and orientation. Therefore, in the next chapter, the effect of MI on myocardial fiber architecture is investigated in ex-vivo porcine hearts using diffusion tensor imaging.

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Chapter 5: Effect of Formalin Fixation on Diffusion Tensor Imaging

It was stated in Chapter 2 that fiber orientation information plays a significant role in determining anisotropic cardiac mechanics and that the fiber orientation is altered under the influence of pathology. This chapter investigates the alteration in fiber architecture due to myocardial infarction in ex-vivo formalin-fixed porcine hearts. Since cardiac DTI is still under development due to difficulties associated with in-vivo imaging caused by sensitivity of DTI imaging parameters to cardiac and respiratory motion, ex-vivo formalin-fixed specimens are used. Specimens are generally fixed in formalin in order to preserve and maintain the tissue integrity and therefore, before investigating the diseased hearts, healthy (freshly and formalin-fixed) hearts are examined to see if formal fixation preserved the ability for DTI to observe myocardial fiber orientation.

This material is previously published or presented as shown by the following citations.

 Mazumder R, Choi S, Clymer BD, White RD, Kolipaka A. Diffusion Tensor

Imaging of Healthy and Infarcted Porcine Hearts: Study the Impact of Formalin-

Fixation. Journal of Medical Imaging and Radiation Sciences2016. 47(1): p.74-85.

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 Mazumder R, Choi S, Raterman B, Clymer B, White RD, Kolipaka A. Diffusion

Tensor Imaging of Formalin Fixed Infarcted Porcine Hearts. 16th Annual Scientific

Meeting SCMR, San Francisco, USA 2013.

 Mazumder R, Choi S, Raterman B, Clymer B, White RD, Kolipaka A. Diffusion

Tensor Imaging of Formalin Fixed Infarcted Porcine Hearts: A comparison between

3T and 1.5T. Joint SCMR and ISMRM New-Horizons in High Field Cardiovascular

Imaging Workshop, San Francisco, USA 2013.

 Choi S, Mazumder R, Schmalbrock P, Knopp MV, White RD, Kolipaka A. Potential

of Diffusion Tensor Imaging as a Virtual Dissection Tool for Cardiac Muscle

Bundles: A Pilot Study. 21st Annual Scientific Meeting ISMRM, Salt Lake City, Utah

USA 2013.

 Mazumder R, Choi S, Clymer B, White RD, Kolipaka A. Diffusion Tensor Imaging

of Fresh and Formalin Fixed Porcine Hearts: A Comparison Study of Fiber Tracts.

21st Annual Scientific Meeting ISMRM, Salt Lake City, Utah USA 2013.

5.1 Introduction

Myocardial infarction (MI) causes remodeling (change in shape, size and function) of the left ventricular (LV) myocardium [10, 321, 322] and, if untreated, eventually leads to heart failure [323, 324]. An understanding of the effect of MI on LV remodeling especially that associated with the changes in the fiber structure and orientation could

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potentially facilitate the development of novel treatments for MI. With the advent of cardiac diffusion tensor imaging (DTI) [269, 273-277, 325-327], a MRI-based technique, researchers have been able to non-invasively investigate the three dimensional (3D) myocardial fiber architecture in a MI model.

DTI is based on the Brownian motion exhibited by water molecules in biological tissues which is known to be impeded or facilitated based on the tissue structure and its orientation [328]. This inherent property of diffusion demonstrated by water molecules causes an exponential decay of the received MR signal which can be characterized using a 3x3 diffusion tensor D [265]. Diagonalization of D provides the eigenvalues (λ1, λ2, λ3) and eigenvectors (ε1, ε2, ε3) of the tensor. These eigenvalues and vectors completely define the anisotropic diffusion occurring at each imaging voxel. The principal eigenvector (ε1) corresponds to the direction of maximum diffusivity which is aligned in the direction of the fiber; whereas the other two vectors (ε2, ε3) relate to the direction of radial diffusivity. D can be used to analyze the myocardial fiber architecture [263] and provide quantitative structural information using parameters such as fractional anisotropy

(FA), trace values, apparent diffusion coefficient (ADC) [265] and helical angles [136].

The myocardial fiber architecture thus established with DTI has been validated against previously established histological models [136, 329].

Recently, in-vivo cardiac DTI has been implemented in healthy humans [273] and in patients [279, 280, 327] to study normal and pathological fiber architecture. However, high resolution cardiac DTI is still under development due to cardiac and respiratory

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motion difficulties associated with in-vivo imaging. Therefore, to date, the majority of the studies performed to establish myocardial architecture using cardiac DTI, have been implemented on ex-vivo animal specimens. These ex-vivo specimens are generally fixed in formalin after extraction in order to preserve and maintain the tissue. Therefore, there is a need to understand the impact of formalin-fixation on the diffusion properties of the myocardium so as not to misinterpret the findings as being related to the pathology of concern.

In addition, ex-vivo cardiac DTI has been explored by various groups to study remodeling following MI. FA, trace values, ADC and helical angles have been examined across the myocardial wall in regions remote from, adjacent to, and within the infarcted area in different animal models [134, 266-268, 270, 272, 330, 331]. However, different study groups have reported contradictory results with respect to the effect on DTI parameters as a result of MI [267, 268, 272]. The underlying ground truth behind how the actual pathology alters the DTI parameters and how much of it is a result of the fixation process remains arguable and needs to be verified before any substantial claim is made. We hypothesize that the conflicting results in terms of how diffusion parameters are affected due to MI can be attributed to the process of fixation and its effect on the diffusion properties of water molecules. The aim of the study is to investigate the effect of myocardial tissue fixation on DTI parameters (ADC, FA, tract termination angle (TTA) and fiber length) by comparing healthy ex-vivo pre-fixed (PrCtrl) hearts to post-fixed

(PoCtrl) hearts in a porcine model. Furthermore, the study also investigates remodeling of the fiber architecture, with respect to fiber length, in fixed infarcted (PoMI) porcine 123

model, by employing optimized DTI tracking parameters obtained from comparison of the control groups pre and post fixation.

5.2 Materials and Methods

Eight juvenile Yorkshire pigs (90-110 lbs) were used in this study in compliance with

The Ohio State University’s Institutional Animal Care and Use Committee. Four pigs were used as controls (PrCtrl and PoCtrl) to study the effect of formalin-fixation on the diffusion parameters and fiber architecture. MI was induced in the other four pigs (PoMI) to study the remodeling of fiber architecture.

Animal Preparation

Control Group: In the control group, the animals were euthanized and the hearts were extracted and stored in ice. A balloon was inserted through the aortic opening into the LV chamber and inflated with air using a syringe in order to prevent the LV from collapsing.

Then, MRI was performed on these specimens (PrCtrl) within 5 to 48 hours of extraction

(depending on the availability of the scanner). Post scanning, the hearts were placed in a

10% neutral buffered formalin solution (4% formaldehyde solution) and stored at room temperature for approximately two weeks (a window of 12 – 18 days) and then they

(PoCtrl) were re-scanned.

MI Group: The animals were anesthetized by using ketamine and acepromazine and anesthesia was maintained using isoflurane (1-2%). A 50 mg bolus of amiodarone was administered as an anti-arrhythmic. A 7 french guiding catheter was advanced through

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the descending aorta into the left coronary ostia and a pre-surgical baseline coronary angiogram was recorded to identify the size of the vessel, location of diagonal branches, and to select an infusion site (Figure 31(a)).

Figure 31: Myocardial Infarction. Coronary angiogram (a) pre-surgery and (b) post-surgery. The arrow in the left image shows blood flowing through the LAD while the arrow in the right image shows the absence of blood flow in the LAD. (c) T1-weighted image of one of the infarcted hearts. The location of the infarcted region (thinner myocardium) near the apex is illustrated with a black circle. (d) Short-axis image showing the infarcted (red contour) and remote (green contour) myocardium. 125

A 0.014” guide wire was advanced through the guide catheter and into the distal portion of the left anterior descending artery (LAD). An appropriately sized over-the wire balloon catheter (Maverick, Boston Scientific, Natick, MA) was advanced over the wire, and the balloon was inflated to occlude blood flow through the LAD. Complete occlusion was confirmed by a post-surgical coronary angiogram (Figure 31(b)). After 5 minutes of ischemia the guide wire was removed from the balloon catheter and 2 mL of absolute ethanol was injected through the guide wire lumen of the balloon catheter over 1 minute, followed by a 2 mL saline flush. The balloon was left inflated for an additional 3 minutes to prevent retrograde flow of the ethanol back up into the proximal LAD. The balloon was deflated and complete occlusion of the targeted portion of the LAD was confirmed with another coronary angiogram. The animals were monitored for three weeks to allow for maximum fibrosis and remodeling in the infarcted region [10] as indicated by T1- weighted MRI (Figure 31(c)). After 22 days, the animals were euthanized and the hearts were removed, flushed with saline and stained using tetrazolium chloride to delineate the area of the infarction. Then they were placed in a 10% neutral buffered formalin solution and stored at room temperature for six months. The PoMI group was obtained from another study which caused the difference in the fixation period between the PoCtrl (a window of 12 – 18 days) group and the PoMI group (6 months).

Image Acquisition

Ex-vivo cardiac DTI was performed on the eight porcine hearts in a 3T MRI scanner (Tim

Trio, Siemens Healthcare, Erlangen, Germany). A bipolar 2 dimensional diffusion- weighted single shot spin-echo echo-planar imaging sequence was used to acquire multi- 126

slice short axis views of the heart covering the entire LV. Imaging parameters included: diffusion encoding directions = 256; TE = 90 ms; TR=7000; slice thickness = 2 mm; matrix = 128x128; FOV = 256x256mm2; b values = 0,1000 s/mm2; acquisition voxel =

2x2x2mm3; number of averages = 1; acquisition time for 40 slices ~ 30 mins; GRAPPA acceleration factor of 2. Additionally, for the PoMI group, high resolution T1-weighted scout images were obtained to delineate the infarcted region from the rest of the myocardium (Figure 31(c) and Figure 31(d)).

Figure 32: Flow Chart for Image Analysis. Figure shows the sequence of steps followed for tracking parameter optimization and fiber tracking.

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Image Analysis

The acquired images were corrected using FSL 4.1.6 (FMRIB Software Library, Oxford,

UK) for eddy current induced artifacts [262] that are caused by rapid switching of the diffusion gradients. The eddy current corrected images were then masked to segment the

LV myocardium (papillary muscles were included in the mask). The masked myocardium was processed to generate the diffusion tensors for the entire heart which were then used to estimate eigenvalues, eigenvectors and generate ADC and FA maps for the PrCtrl,

PoCtrl and PoMI groups. Based on wall-thinning observed on the high resolution T1- weighted scout images in the PoMI group, regions of interests (ROI) were drawn to segment the infarcted region from the remote region (Figure 31(d)). A comparison of mean ADC and FA was performed between the infarcted and remote regions in the PoMI group to analyze any discernible changes in the DTI parameter values caused due to MI.

Next, tracking parameters were optimized to generate fiber tracts to assess the change in fiber architecture as a result of formalin-fixation and MI remodeling. A flow chart demonstrating the steps involved in fiber tracking following optimization of the tracking parameters is provided in Figure 32.

Histograms of the FA maps were created to determine the optimal FA range to be used for fiber-tracking based on the bins that corresponded to the highest voxel density. Once the optimal FA range was fixed, ExploreDTI v4.8.2 [332], was used to perform tractography across the entire heart, using a deterministic streamlined approach [263].

TTA (the maximum angle between the principle eigenvectors (ε 1) in two successive voxels) was varied and the corresponding total number of fiber tracts was recorded to 128

analyze the effect of formalin-fixation on these angles. Based on our initial experience,

TTA was varied from 5o to 60o in increments of 5o and the corresponding total number of tracts for each TTA value was recorded. For this analysis, the length range parameter used for tractography was kept constant fixed (2 - 500 mm) so that the total number of tracts identified was independent of the effect of fiber length.

From the results obtained, critical TTA (see results) values were selected to investigate the effect of formalin-fixation on fiber lengths. Fiber tracking (across the entire heart) was performed by employing the optimal FA range and critical TTA. The length range used for tracking was varied by altering the lower limit (2, 10, 20, 30, 40 and 50 mm) and fixing the upper limit (500mm). For each iteration (altering the lower limit of fiber length), the total number of tracts obtained and the mean total length of the tracts were recorded. Mean total length was defined as the average of the total length contributed by all the tracts per tracking condition.

Finally, a qualitative analysis of the fiber architecture in the PoCtrl and PoMI was implemented to investigate the remodeling of fiber tracts based on fiber length and visual orientation. The analysis was performed by employing the optimal FA and critical TTA obtained from the control group to obtain whole heart tractography. Following tractography, small regions of interest (ROI) were defined in the infarcted region of the

PoMI group and approximately in the same region of the PoCtrl group to qualitatively analyze fibers passing through the defined ROI.

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Statistical Analysis

Differences in mean ADC, mean FA and the mode of FA between the PrCtrl and PoCtrl groups were tested for significance (p<0.05) using a 2-tailed paired student’s t-test.

Additionally, a significant difference (p<0.05) of the mean ADC and FA values between the remote and infarcted region in the PoMI group was also determined with a 2-tailed paired student’s t-test. Furthermore, the mean ADC and FA values between the 4 groups

(PrCtrl, PoCtrl, infarcted region in PoMI, remote region in PoMI) were tested with a one- way analysis of variance (ANOVA). A 2-tailed unpaired student’s t-test was performed to determine the significant difference (p<0.05) in the modes of the FA between the

PoCtrl and PoMI groups.

5.3 Results

ADC and FA

Mean ADC and FA were estimated for the entire heart in the PrCtrl and PoCtrl groups and in the infarcted and remote myocardium in the PoMI group as shown in Figure 33.

Both ADC and FA showed a significant difference between pre and post formalin- fixation. Fixation increased (p-value = 0.0018) the mean ADC (Figure 33 (a)) from

0.52x10-3 ± 0.026 x10-3 mm/s2 in PrCtrl to 0.80x10-3 ± 0.072 x10-3 mm/s2 in PoCtrl.

Whereas, fixation decreased (p-value=0.0090) mean FA (Figure 33 (c)) from 0.42 ±

0.028 in PrCtrl to 0.26 ± 0.034 in PoCtrl. A comparison between the infarcted and remote regions in the PoMI group indicated that the mean ADC (Figure 33 (b)) in the infarcted region (0.95x10-3 ± 0.12 x10-3 mm/s2) was significantly (p-value = 0.0006) higher than

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the remote region (0.63x10-3 ± 0.052 x10-3 mm/s2).

Figure 33: Mean and standard deviation of ADC and FA in all the 8 porcine hearts. a) ADC in control group. The mean and SD of the ADC for the PrCtrl (green dashed line) and PoCtrl (blue dashed line) are 0.52x10-3 ± 0.026 x10-3 mm/s2 and 0.80x10-3 ± 0.072 x10-3 mm/s2 respectively. b) ADC in PoMI. The mean ADC across the infarcted (red dashed line) and remote regions (orange dashed line) are 0.95x10-3 ± 0.12 x10-3 mm/s2 and 0.63x10-3 ± 0.052 x10-3 mm/s2 respectively. c) FA in control group. The mean and SD of the FA for the PrCtrl (green dashed line) and PoCtrl (blue dashed line) are 0.42 ± 0.028 and 0.26 ± 0.034 respectively. d) FA in PoMI. The mean FA across the infarcted (red dashed line) and remote regions (orange dashed line) are 0.22 ± 0.023 and 0.25 ± 0.031 respectively. 131

Although, the mean FA (Figure 33 (d)) in the infarcted region (0.22 ± 0.023) was lower compared to the remote region (0.25 ± 0.031), the decrease in FA value was not significant (p-value = 0.0557). A one-way ANOVA showed significant difference in both the ADC (p-value < 0.00001) and the FA (p-value <0.00001) between the 4 groups

(PrCtrl, PoCtrl, infarcted region in PoMI, remote region in PoMI).

Optimal FA

Next, optimal FA range to be used for fiber tracking was determined for all the three groups. A distribution of the histogram showed that the mode of FA value was lower in post-fixation (PoCtrl and PoMI) group as compared to pre-fixation (PrCtrl) (Figure 34

(a)). The mean and the SD of the mode of the FA values within the PrCtrl, PoCtrl and the

PoMI groups were 0.27±0.014, 0.17±0.010 and 0.16±0.011 respectively (Figure 34 (b)).

A significant difference in the mode of the FA value was observed between the PrCtrl and PoCtrl group (p-value = 0.0013); and between the PrCtrl and PoMI group (p-value =

0.0007). However, no significant difference (p-value = 0.2) in the mode of the FA value was observed between the PoCtrl and PoMI group. Based on this observation, the same optimal FA range was used for fiber tracking in the PoCtrl and PoMI group and a different range was determined for the PrCtrl group. The upper limit of the range was fixed at 1 and the lower limit of the FA range was calculated based on a 25% drop from the peak value (refer to the lines on Figure 34 (c)). This optimal FA range was determined to be [0.2 1] for PrCtrl and [0.1 1] for PoCtrl and PoMI for all further processing. 132

Figure 34: Determination of optimal FA range for fiber tracking. a) FA Histogram. The FA histogram indicates a lower mode post-fixation (PoCtrl (dotted-blue) and PoMI (dashed-red)) as compared to pre-fixation (PrCtrl (solid-green)). b) Mean and SD of FA mode. Mean and SD of the FA mode for PrCtrl (green), PoCtrl (blue) and PoMI (red) groups are 0.27±0.014, 0.17±0.010 and 0.16±0.011 respectively. c) Mean FA histogram (controls) to estimate optimal FA range for fiber tracking. The peak of the normalized mean FA (normalization based on the total number of voxels) for the PrCtrl and PoCtrl group is 11.5 (corresponding to FA bin 0.15-0.175) and 8.4 (corresponding to FA bin 0.25-0.275), respectively. The lower limit of the FA range corresponding to 25% drop from the peak was determined to be 0.2 for the pre- fixation group and 0.1 for the post-fixation group.

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Figure 35: TTA versus Normalized number of tracts. The figure shows the plot of TTA versus number of tracts. The x-axis corresponds to TTA increasing from 50 to 600. The y-axis corresponds to the number of tracts normalized with respect to the total number of masked voxels. A sharp change in slope is observed when transitioning from 50 - 100 TTA.

TTA

Critical TTA was determined by employing the optimal FA values in the fiber tracking algorithm (Figure 35). The plot of number of tracts (normalized by the total number of voxels in the LV mask) versus the TTA (maximum allowable turn angle between two successive voxels in degrees) showed a sharp increase in the slope from 5o to 10o, which gradually decreased after 10o and flattened after 25o. This trend was consistent for all the three groups (PrCtrl, PoCtrl and PoMI). The plot provided two critical TTA (5o and 10o) to be examined for our next optimization of fiber length. 134

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Fiber Length

The normalized mean fiber length decreased in the PoCtrl group when compared to the

PrCtrl group (Figure 36). In the both groups (PrCtrl and PoCtrl), for both the angles (5o and 10o) as the lower limit of the length range increased from 2 mm to 50 mm (tracking conditions became more conservative) the mean length of the fibers increased and the total number of fiber tracts decreased. This is because shorter fibers were excluded from the tracking conditions which increased the mean fiber length measurements.

MI Fiber Orientation

Qualitative differences were observed between the PoCtrl (Figure 37) and PoMI (Figure

38) groups with respect to orientation and length of fibers. Fiber tracts in the infarcted region of a heart from the PoMI group (shown in Figure 38) demonstrate that the tracts were shorter in length, less dense and disarrayed as compared to healthy heart from the

PoCtrl group. Similar patterns were observed in all the other hearts.

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Figure 37: 3D fiber architecture in a healthy porcine myocardium. Figure shows fiber tracts passing through a defined region of interest (ROI). Tracking parameters include: FA [0.1 1], TTA 45o and tracking length range [2 500] mm. TTA was set to 45o to mitigate its effect on the number of tracts identified (refer to Figure 36). Left Image: The planes denote the two long axes and the short axis of the principle eigenvector. The white circle shows the ROI drawn to track the fibers. Right Image: Tracts without the planes. The color on the fiber and planes denote the direction of fiber orientation; Green, red and blue corresponds to the x, y and z directions of the image, respectively.

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Figure 38: 3D fiber architecture in an infarcted porcine myocardium. Figure shows fiber tracts passing through a defined region of interest (ROI). Tracking parameters include: FA [0.1 1], TTA 45o and tracking length range [2 500] mm. TTA was set to 45o to mitigate its effect on the number of tracts identified (refer to Figure 36). Left Image: The planes denote the two long axes and the short axis of the principle eigenvector. The white circle shows the ROI drawn to track the fibers through the infarcted region. Right Image: Tracts without the planes. The color on the fiber and planes denote the direction of fiber orientation; Green, red and blue corresponds to the x, y and z directions of the image, respectively.

5.4 Discussion

Our study demonstrated that formalin-fixation alters the diffusion properties of cardiac muscle fibers. Post-fixed hearts had higher ADC values, lower FA and reduced total mean length as compared to pre- fixed hearts. However, the trend in TTA was consistent in both the control groups and the diseased myocardium. PoMI hearts had significantly higher ADC in infarcted region as compared to the remote regions. FA showed an 138

insignificant decrease in the infarcted zone compared to the remote normal tissue.

Additionally, fibers in the infarcted region were short and disarrayed when compared to the PoCtrl group.

The results from our study and other previous studies [134, 266-268, 270, 272, 330, 331] demonstrate that cardiac DTI can be used to study fiber architecture remodeling as a result of MI. Therefore, cardiac DTI can potentially be used as a diagnostic tool for patients having contraindications to Gadolinium based contrast agents (since delayed enhancement based MRI is not feasible in such patients). However, in-vivo cardiac DTI

[273, 279, 280, 325, 327] is still under investigation due to the challenges associated with cardiac motion, respiratory motion and long breathhold times. Hence, majority of the current research for technique establishment and optimization is based on experiments performed on formalin-fixed ex-vivo specimens. It is evident from our results that the fixation process affects diffusivity of water molecules. Therefore, when standardizing quantitative measurements (FA, ADC) for in-vivo applications based on information from formalin-fixed ex-vivo hearts, in either healthy or diseased myocardium, the effects of fixation on the measurements should be considered.

Fixation caused an increase in the ADC values in the controls which was consistent with a study performed on the nervous tissues of rat brains [333]. Formalin-fixation prevents degeneration of tissues by reacting with primary amines on proteins and nucleic acids to form partially-reversible methylene bridges. During this process the cells tend to undergo i) a period of shrinkage followed by ii) a prolonged period of swelling followed by iii) a

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period of secondary shrinkage. It has been shown that when the concentration of formaldehyde is below 5% (4 % in this study) the initial shrinkage is very low and it is followed by a period of extensive swelling [334]. This extreme swelling in cellular structures impacts the diffusion properties and could be reflected with increased ADC estimates. Since the PoCtrl hearts were fixed for approximately 2 weeks, the hearts could be in the stage of cellular swelling which led to the observation of higher ADC values in

PoCtrl hearts when compared to the PrCtrl hearts.

Furthermore, a decrease in ADC values was observed in the remote normal tissue in the

PoMI model when compared to the PoCtrl model. We speculate that because the PoMI specimens were fixed for nearly 6 months before being scanned it provided the tissues enough time to migrate to the final stage of the fixation process which involves a period of cellular shrinkage. This hypothesis is further supported by another study where 4 weeks of formalin-fixation with a 10% neutral buffered solution resulted in decreased diffusivity in mouse brains [335].

However, there are other studies which have observed contradictory results [336, 337].

Since there isn’t much literature on the effect of diffusion properties of the heart as a result of fixation our comparison with earlier work is based mainly on brain studies, and the type of tissue being investigated can play a role in the contradictions observed.

Additionally, inconsistencies and contradictions with previous studies can be associated with the fixation process in general [338]. The type of fixation (perfusion fixation, immersion fixation or both), thickness of tissue, preparation of the fixing agent, time

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interval between tissue extraction and fixation, the ratio of the volume of the specimen to the amount of formalin solution, extent of fixation, temperature of fixation and temperature during imaging all play a role in the fixation process which can eventually affect the diffusion properties of the heart differently. Therefore for any substantial standardization of diffusion parameters in normal tissues, and comparison between different studies using ex-vivo formalin-fixed specimens, a standard protocol for the fixation procedure should be followed.

In the PoMI model ADC in the infarcted region was significantly higher compared to the remote regions. This observation of higher ADC in the infarcted zone is consistent with results obtained from other small animals (rats [330]) large animals (pigs [268, 339]) and humans ([268, 280]). It is well-known that in the infarcted myocardium the ruptured cell membranes cause an increase in the extra-cellular space thereby assisting unrestricted diffusion. This is well-reflected by the significant increase in the ADC values in the infarcted myocardium as opposed to the remote normal myocardium.

Fixation caused a reduction in the FA value, which was consistent with results obtained from studies performed in the brain [340] and spinal cord [341]. This can be attributed to the observation of reduced total mean fiber length in the post-fixed specimens. Shorter fibers in the PoCtrl group imply reduced available length for unidirectional channelized diffusion resulting in lower FA values. Furthermore, as mentioned earlier, fixation results in a stage of extensive swelling and a subsequent increase in water diffusion which allows increased random movement of water molecules. Increased unguided random

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motion contributes to reduced anisotropy and hence decreased FA in the PoCtrl model as compared to the PrCtrl model.

Our results did not demonstrate a significant difference in the FA value within the PoMI group when comparing the infarcted region to the remote normal tissue which is consistent with results obtained by Wu Y. et al. (post-infarct porcine models) [271, 272].

However, as mentioned earlier, there are contradictory conclusions about FA values in

MI induced hearts. Researchers have shown that a marked decrease in FA occurred in infarcted hearts in humans [280], rats [330] and pigs [268] when compared to the controls. In contrast, another study in rat models [267] showed increased FA due to infarction. Therefore, it might not be sufficient to diagnose infarction in fixed ex-vivo hearts based only on FA values because the integrity of the results might be affected by the fixation process. Additionally since the infarcted region demonstrated extreme wall thinning, partial volume effects could be a cause for insignificant difference in FA values between the infarcted and normal myocardium.

TTA did not show a noticeable discrepancy in the trend of the slope followed by the three groups (PrCtrl, PoCtrl and PoMI). Limited literature is available on TTA and its variation as a result of infarction. To the best of our knowledge, only one group has reported change in propagation angle (the average angle between adjacent eigenvectors along myofiber tracts) with MI [342, 343]. However, they have not mentioned any change in

TTA with MI and therefore, we cannot directly compare our results to theirs.

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Our results showed a reduction in the total mean length per tracking condition (where the tracking condition was dependent on the lower limit of the fiber length range) in the

PoCtrl group when compared to the PrCtrl group. As mentioned earlier, the process of fixation reduces FA, and due to the reduced FA the tracking algorithm considers lesser number of pixels as part of the same fiber. As a result, a single long fiber pre-fixation appeared to be composed of multiple short fibers post-fixation thereby reducing the total mean length. Additionally, the interval between euthanizing the animal and fixing the specimen resulted in partial autolysis of the fibers as suggested by D'Arceuil et al. [340], thereby further reducing the total mean length.

Finally, a qualitative analysis of the fiber architecture demonstrated that the number of fibers passing through a defined ROI in the PoMI group was less dense compared to the

PoCtrl group proving that the infarcted region had undergone structural changes.

Histological evidence shows that immediately post-infarction the infarcted region undergoes necrosis which progresses to a stage of fibrosis followed by remodeling [10].

In porcine models, three weeks post-infarction the animal is towards the end of the fibrotic stage which is classified by deposition of collagen and shrinkage of the myocardium at the site of the infarction [10, 135, 321]. The loss of the muscle mass along with the deposition of collagen reduces molecular diffusivity and results in fewer fiber tracts being identified in the infarcted region. Additionally, fibers passing through the infarcted region were disarrayed and not as smoothly oriented as the control group.

Our study includes several limitations. First, there was a gap (5 to 48 hours) between euthanizing the animal and data acquisition due to unavailability of the scanner 143

immediately post-sacrifice. Nonetheless, the tissue was stored in an ice bath during this period to prevent decomposition. Second, in PrCtrl group, the hearts were inflated to an arbitrary pressure to prevent the LV from collapsing and to ensure proper imaging. The pressure variation might have an effect on the DTI parameters. However, we did not observe any major variations in the DTI parameters within the PrCtrl group. Third, since the PoMI hearts were from a different study it induced a discrepancy of the fixation period between the controls and the diseased myocardium. Finally, the image resolution

(2x2x2 mm3) may have an influence on the DTI parameters. Despite of these limitations, our results were consistent with previously reported results.

5.5 Conclusions

In conclusion, we have demonstrated that formalin-fixation affects molecular diffusivity by reducing FA and mean fiber length and increasing ADC. Therefore, the fixation process and its influence on the diffusion parameters need to be taken into account when interpreting impact of diseases on these parameters. Further, when extrapolating the changes observed in diffusion parameters in fixed ex-vivo specimens with in-vivo studies inconsistencies might be observed due to the fixation process. However, fixation does not alter the structural orientation of the fibers which was evident from the TTA graphs.

Therefore, structural remodeling of the fiber architecture needs to be considered when investigating the effect of MI on the fixed myocardium. This is established by the distinct sparse disarrayed short fibers observed near the infarcted myocardium which is absent in the control group.

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This chapter uses 256 diffusion encoding directions with 1 average to acquire the DTI data. It has been shown in the literature that either a large number of diffusion encoding directions or a number of averages is required to accurately calculate the diffusion tensor which is vital for estimating the fiber architecture. However, an increase in either diffusion encoding directions or the number of averages increases acquisition time.

Therefore, in the next chapter we develop a novel adaptive anisotropic Gaussian filtering technique to reduce acquisition time in cardiac DTI.

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Chapter 6: Adaptive Anisotropic Gaussian Filter to Reduce Acquisition Time in

Cardiac Diffusion Tensor Imaging

In the previous chapter it was demonstrated that the fixation process does not alter the structural orientation of the fibers. Therefore, in this chapter we use helical angles (a metric derived from structural orientation) in an ex-vivo porcine model to investigate if it is possible to reduce acquisition time in cardiac diffusion tensor imaging by implementing a novel filtering technique. Additionally, this chapter also estimates helical angles in ex-vivo formalin-fixed diseased hearts to explore whether the filtering technique can potentially preserve the structural alterations introduced by pathology.

This material is previously published or presented as shown by the following citations.

 Mazumder R, Clymer B, Mo, X. White RD, Kolipaka. Adaptive Anisotropic

Gaussian Filtering to Reduce Acquisition Time in Cardiac Diffusion Tensor Imaging.

International Journal of Cardiovascular Imaging 2016 Feb 2. (Epub ahead of print).

 Mazumder R, Clymer BD, White RD, Kolipaka A. Cardiac Diffusion Tensor

Imaging: Adaptive Anisotropic Gaussian Filtering to Reduce Acquisition Time. 22nd

Annual Scientific Meeting ISMRM, Milan, Italy 2014. (Awarded summa cum

laude).

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 Mazumder R, Clymer BD, White RD, Kolipaka A. Estimation of Helical Angle of

the Left Ventricle Using Diffusion Tensor Imaging with Minimum Acquisition Time.

17th Annual Scientific Meeting SCMR, New Orleans, USA 2014.

6.1 Introduction

Myocardial fiber orientation governs electrical conduction and mechanical activation of the left ventricle (LV) [344]. The propagation of electrical impulses responsible for rhythmic contraction of the LV exhibits anisotropy, and occurs predominantly along the longitudinal axis of the myocardial fibers [345, 346]. Furthermore, the counter- directional helical organization of the myocardial fibers influences the torsional motion of the LV and assists in regulating stress and strain during systole and diastole [121, 347].

Remodeling of fiber orientation can result from either functional (arrhythmia [348]) or structural (myocardial infarction [349] and ventricular hypertrophy [350]) abnormalities.

Therefore, a quantitative estimate of fiber orientation is important in order to investigate the influence of the orientation on the electromechanical properties of the heart.

In recent years, diffusion tensor imaging (DTI) has emerged as a non-invasive quantitative tool to characterize the orientation of myocardial fibers using helical angle

(HA) measurement [136]. HA is defined as the measure of the angle between the short- axis imaging plane and the projection of the primary eigenvector onto the epicardial tangent plane [120]. It has been observed that a variety of pathological conditions, such

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as myocardial infarction (MI) and hypertrophic cardiomyopathy, effect myocardial fiber orientation [280, 351] rendering HA to be a potentially relevant quantitative diagnostic parameter.

The accuracy of HA measurements depends on the estimate of the diffusion tensor 푫, which is very sensitive to noise. This sensitivity arises because the diffusion-weighted magnitude images (DWI) are degraded by Rician noise which leads to distorted estimate of the diffusion ellipsoids. Noise effects are further amplified as spatial resolution of the

DWI is increased. D can be improved by i) acquiring more measurement directions for the anisotropic ellipsoid and ii) improving signal to noise ratio (SNR) of the DWI. The former can be achieved by increasing the number of diffusion-encoding directions (DED) while the latter can be achieved by averaging the DWI over a number of excitations

(NEX). However, an increase in either DED or NEX is directly proportional to an increase in acquisition time (TA).

A potential solution to improve tensor estimation is to implement post-acquisition filters during different stages of data processing. Various regularization and filtering techniques have been implemented in the past to improve image quality and to reduce noise primarily with respect to brain applications. These include sequential anisotropic Wiener filtering [352], bilateral filtering [353], Perona-Malik based filtering [354], wavelet based filtering [355], non-linear diffusion filtering [356, 357] and Riemannian based approach to anisotropic filtering [358]. Based on the implementation stage of these filters, filtering can be broadly categorized into three groups. In the first category, the filter is applied

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directly on raw DWI data prior to tensor estimation [352, 354, 356, 359]. In the second category, filtering is performed in conjunction with tensor estimation [360, 361], while in the last category, the filter is implemented directly on the diffusion tensors [362, 363].

In our investigation, we extend the concept of anisotropic filtering and develop a three- dimensional (3D) adaptive anisotropic Gaussian filter (AAGF) to smooth the eigenvectors of 푫 specifically for myocardial applications. The filter is designed to preserve the structural information of myocardial fibers by taking into consideration the inherent curvature of the myocardium (caused by the transmurally rotating fibers) and smoothing primarily along the direction of the principle eigenvector. This specific adaptive anisotropic nature of the filter preserves the integrity of the underlying microstructure and prevents blurring which could potentially mask pathological changes.

We hypothesize that the eigenvectors obtained from rapidly acquired DWI data with fewer NEX and DED, when filtered with our proposed technique, will generate HA with similar accuracy as that achieved from longer DWI acquisitions obtained with increased

NEX and DED. Additionally, the competence of the filtering technique in identifying microstructural alterations in a diseased myocardium needed to be investigated

(performed using a MI model).

6.2 Theory

The general 3D Gaussian filtering uses a 3D spatially varying window with weights defined as:

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2 2 2 (푥−푥0) (푦−푦0) (푧 −푧0) 1 − [ 2 + 2 + 2 ] 휎푥 휎푦 휎푧 (59) 퐺 = 3/2 푒 , (2휋) (휎푥)(휎푦)(휎푧)

where 휎푥, 휎푦, and 휎푧 represent the spread of the Gaussian function in 푥, 푦 and 푧 directions, respectively. 퐺 demonstrates anisotropic characteristics when the spread in one of the three directions is greater than the others. To preserve the structural information of the diffusion tensor, it needs to be ensured that the direction with the largest spread coincides with the direction of the primary eigenvector 푽ퟏ. Therefore, for each imaging voxel an orthonormal local rotated coordinate system (풙′, 풚′, 풛′) is defined, such that the rotated axis (풛′) on which the maximum spread will be assigned aligns with the primary eigenvector 푽ퟏ (Figure 39a.).

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Based on this rotated coordinate system for each imaging voxel a rotated Gaussian window 퐺′ is defined. As stated, the spread (휎푧′) of 퐺′ in the 풛′ direction (designed to align with V1) is greater than the spread (휎푥′, 휎푦′) in the other two directions (Figure

39b.). 퐺′ can be mathematically described by the following relation:

퐺′(푥′, 푦′, 푧′) = 푹G(x, y, z), (60)

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where R is the rotation matrix given by:

′ ′ ′ 푥푥 푥푦 푥푧 0 푦′ 푦′ 푦′ 0 푅 = 푥 푦 푧 (61) ′ ′ ′ 푧푥 푧푦 푧푧 0 ( 0 0 0 1)

Since G′ is the Gaussian window with respect to the rotated frame, it is defined as:

′ ′ 2 ′ ′ 2 ′ ′ 2 (푥 −푥0) (푦 −푦0) (푧 −푧0) 1 − [ 2 + 2 + 2 ] 휎푥′ 휎푦′ 휎푧′ (62) 퐺′ = 3/2 푒 (2휋) (휎푥′)(휎푦′)(휎푧′)

′ ′ ′ where (푥0, 푦0, 푧0) = (푥0, 푦0, 푧0) is the centroid of the window and the point of rotation.

Furthermore, in order to account for the transmurally rotating fibers along the LV, 휎푧′ is defined as a function of the radial distance (as shown in the short axis imaging plane in

Figure 39c.). That is, as the Gaussian window moves away from the centroid of the lumen the spread in the V1 direction increases with increasing radius. This is done to approximate the curvature of the heart (i.e. arc of a fiber) with a straight line (Figure

39c.).

′ Finally, the filtered eigenvector is obtained by applying the rotated kernel 퐺푖 on the eigenvector V1i over a specific window length. The subscript 풊 corresponds to a specific window occurrence as the window is scanned through the image space. To accommodate

′ changes in V1i, 퐺푖 is redefined each time the window is relocated, making the filter spatially variant.

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6.3 Materials and Methods

Animal Preparation

Preparation of Healthy Myocardium to Determine Optimal DED-NEX Combination

Required to Generate Optimum HA Maps in Minimum TA: Nine ex-vivo porcine hearts were used to determine the optimal NEX and DED combination needed to estimate HA.

The animals were euthanized and the hearts were extracted, flushed with saline and immersed in a 10% neutral buffered formalin solution at room temperature. Prior to scanning, the hearts were washed under running cold water and then immersed in water bath for 15 minutes to hydrate the myocardium.

Preparation of MI-Induced Myocardium to Evaluate Sensitivity of Filter: Three ex-vivo porcine hearts were used to evaluate the effectiveness of the filtering technique in preserving abnormal myocardial fiber orientation in MI-induced hearts. Infarction was created using ethanol injection in the left anterior descending artery (LAD) [312]. Post- infarction the animals were monitored for three weeks to allow maximum fibrosis and remodeling in the infarcted region [10]. After 22 days, the animals were euthanized and the hearts were removed, flushed with saline, stained using tetrazolium chloride to delineate the area of infarction and finally placed in a 10% neutral buffered formalin solution at room temperature. Prior to scanning, the same hydration procedure performed in the healthy hearts was followed in the MI-induced hearts.

Image Acquisition

Ex-vivo DTI was performed in 12 hearts (9 healthy, 3 MI) in a 3T MRI scanner (Tim

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Trio, Siemens Healthcare, Erlangen, Germany). A two-dimensional bipolar diffusion- weighted echo planar imaging sequence was used to acquire multi-slice short-axis views of the heart. Twenty one scans were performed with different combinations of NEX and

DED as detailed in Table 4. The maximum NEX acquired in each DED (12, 30, and 64) group was determined on the basis of a constant TA (~ 30 mins). Other imaging parameters included: repetition time (TR)=7000 ms; echo time (TE)=90 ms; echo train length=128; echo spacing=0.7ms; bandwidth=1628 Hz/pixel; slice thickness=2 mm; imaging matrix=128128; field of view (FOV)=256256 mm2; isotropic voxel

3 2 resolution=222 mm and b0/b1 value for diffusion encoding=0/1000 s/mm . Number of slices acquired ranged anywhere between 32 and 42, based on the individual heart size.

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Table 4: Acquisition parameters and AAGF analysis results. DED-NEX combination, corresponding acquisition time and mean normalized RMSE for unfiltered and AAGF filtered maps.

Mean Diff from gold Mean RMSE Mean RMSE Concordance standard TA from all 9 from all 9 correlation- DED NEX ( 1SD) (in ms) animals animals coefficients 95% Confidence (HA ) (HA ) (ρ for 95% CI) UF AAGF c Limits of Agreement 1 2,329 19.11 ± 1.9 16.68 ± 2.5 0.66 (0.64, 0.68) 0.82 (-24.57, 26.14) 2 4,643 16.52 ± 1.8 14.30± 2.0 0.75 (0.74, 0.76) 1.29 (-19.8, 22.4) 3 6,971 15.36 ± 1.7 13.52 ± 1.53 0.80 (0.79, 0.81) 1.2 (-17.6, 20.0) 4 9,300 14.19 ± 1.8 12.57 ± 1.6 0.83 (0.82, 0.84) 1.47 (-15.4, 18.35) 12 6 13,943 12.95 ± 1.7 11.97 ± 1.5 0.85 (0.84, 0.86) 1.65 (-14.19, 17.49) 8 18,600 11.60 ± 1.7 11.26 ± 1.2 0.87 (0.86, 0.873) 1.71 (-13.27, 16.68) 12 27,886 10.14 ± 1.4 10.71 ± 1.1 0.88 (0.87. 0.884) 1.79 (-12.33, 15.91) 16 37,186 8.91 ± 1.3 10.19 ± 1.0 0.89 (0.88, 0.894) 1.8 (-11.64, 15.24) 20 46,486 NA NA 0.906 (0.9, 0.911) 1.81 (-10.37, 14) 1 5,586 16.05 ± 2.4 14.22 ± 2.5 0.76 (0.75, 0.77) 1.4 (-18.9, 21.72) 2 11,157 13.70 ± 2.1 12.44 ± 2.1 0.817(0.81, 0.83) 1.15 (-16.81, 19.1) 3 16,743 12.00 ± 2.0 11.76 ± 2.2 0.87 (0.86, 0.88) 1.64 (-13.18, 16.47) 4 22,314 10.83 ± 2.2 11.02 ± 1.9 0.88 (0.876, 0.89) 1.48 (-12.47, 15.44) 30 5 27,900 9.56 ± 1.6 10.30 ± 1.3 0.89 (0.887, 0.9) 1.53 (-11.73, 14.8) 6 33,471 8.96 ± 2.2 10.25 ± 1.7 0.90 (0.89, 0.904) 1.54 (-11.36, 14.44) 7 39,057 8.19 ± 1.7 9.98 ± 1.5 0.90 (0.89, 0.904) 1.71 (-11.05, 14.46) 8 44,629 NA NA 0.92 (0.91, 0.924) 1.66 (-9.7, 13)

1 11,629 13.92 ± 2.7 12.93 ± 2.8 0.82 (0.81, 0.83) 1.32 (-16.26, 18.9) 2 23,243 10.61 ± 2.0 10.73 ± 1.7 0.88 (0.87, 0.884) 1.62 (-12.57, 15.81) 64 3 34,871 8.81 ± 1.6 9.96 ± 1.4 0.89 (0.88, 0.92) 1.84 (-11.36, 15.04) 4 46,486 NA NA 0.92 (0.91, 0.921) 1.69 (-9.76, 13.13) 64 4 46,486 NA NA

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Image Analysis

The acquired images were masked to segment the LV. A pixel from the edge was left out of the mask from both the epicardium and endocardium to avoid boundary effects caused due to air-tissue interface. Custom-built software written in Matlab (Mathworks, Natick,

MA) was used to process the masked images. Diffusion tensors were generated for all 21 acquisitions shown in Table 4 and subsequently diagonalized to determine the eigenvalues and eigenvectors. These eigenvectors were used to estimate unfiltered HA

(HAUF) maps.

Gold Standard: Due to the lack of direct histopathological correlation the maximum acquired NEX (20, 8 and 4 for DED 12, 30 and 64 respectively) in each group was used for the reference HA value.

Optimization of Filter Parameters and Analysis of Filter Performance using Healthy

Myocardium (Comparison with Isotropic Filters): The performance of AAGF was compared to 2 different 3D isotropic filters, a mean or averaging filter (AVF) and a median filter (MF). The primary eigenvectors were filtered using AAGF, AVF and MF, and these filtered eigenvectors were used to estimate HA maps (HAAAGF, HAAVF and

HAMF respectively) for every NEX in each DED group. AAGF filter specifications were as follows: Radial thickness of the myocardium was divided into 4 segments and the

spread in the direction of maximum anisotropy (휎푧′) was incremented from 1.5

(endocardium) in steps of 0.5 for each segment to 3.0 (epicardium). The spreads in the

other two directions (휎푥′ and 휎푦′) were kept constant at 1. All units were defined based on

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pixel length. Several 3D filter window-lengths were explored on a randomly selected heart to find the optimal filter length. This optimal length was selected based on minimum normalized root mean square error (RMSE) in HA between the reference (i.e. highest acquired NEX in each DED) to that of each NEX for all DEDs. The same optimal window length was used for the isotropic filters. A normalized RMSE estimation of unfiltered and filtered HA from all 9 healthy hearts was plotted using SAS 9.4 software

(SAS, Inc, Cary, NC). The mean normalized RMSE for unfiltered and filtered maps for each DED-NEX setting was estimated and plotted in the same figure to compare the performance of our proposed filtering technique.

Determining Acquisition Parameters (DED, NEX) for Minimum TA: To determine acquisition parameters for measuring minimum TA, in each of the 3 DED settings (12, 30 and 64) a cut-off NEX (NEXF_C) was established. This cut-off was based on the minimum NEX required by AAGF filter to produce robust HAAAGF maps. Robustness of the filtered maps was determined by simultaneously considering normalized RMSE,

concordance correlation-coefficient (휌푐) [364] and Bland-Altman’s limits of agreement

[365]. Based on generated plots (mean RMSE from the 9 hearts) normalized RMSE from

HAAAGF map was regarded acceptable if it was within 5% of the minimum normalized

RMSE obtained for that particular DED setting. Concordance coefficients and Bland-

Altman’s analysis (pooling the mid-ventricular slices from all the animals) with a 95% confidence interval (CI) was generated using STATA 13 (StataCorp LP, College Station,

Texas) by comparing HAAAGF maps to the gold standard (in each DED group). To evaluate the minimum required NEX in each DED group a ρc greater than 0.8 was 157

considered permissible. Additionally, narrow limits of agreement from the Bland

Altman’s plot were taken into account to assess agreement between HAAAGF and gold standard maps.

Once NEXF_C was established, HA line profiles were generated in three different slices of the LV (apex, mid and base), along 16 equally spaced (11.25o apart) transmural regions on the free wall (Figure 39d.) for both NEXF_C based and reference HA maps. A comparison was performed to verify if the linear variation of HA line profiles from the epicardium to endocardium in the reference maps were comparable to the line profiles from the NEXF_C maps. Finally, an inter-DED group assessment of the entire myocardium was performed to estimate the optimal combination of DED and NEX that generated the best HAAAGF maps in the least possible TA.

SNR Analysis

SNR (ratio of mean signal to the standard deviation (SD) of noise in the b0 image) was investigated in order to understand the relationship between reductions in normalized

RMSE versus normalized SNR. The SNR from the reference image (gold standard in each DED group) was used for normalization in each DED-NEX combination.

Additionally, we investigated the response of the filter at NEXF_C in terms of available normalized SNR and reduction in normalized RMSE.

Analysis of Sensitivity of Filter in Diseased Myocardium (MI-Induced Hearts): Once

NEXF_C was determined in the normal porcine hearts this value was used to generate

HAAAGF maps for each DED setting in the MI-induced porcine hearts. A pixel-wise

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comparison was performed (between the HAAAGF maps and HAUF maps generated from the gold standard) by estimating the percentage difference between the two HA measurements. Three ROIs were investigated in the diseased myocardium; one corresponded to the infarcted area (ROI 1), the second corresponded to a remote region on the same slice as the infarct (ROI 2), and the third (ROI 3) corresponded to a slice remote from the site of the infarct (Figure 39e.). Mean and SD for error in HA was determined in the 3 ROIs from the percentage difference maps and the result was used to evaluate the sensitivity of the filter to pathology influenced remodeling.

6.4 Results

Optimizing Filter Length: Optimization of filter length was performed by randomly selecting one porcine heart for all DED-NEX combinations, which was then used as a sample representation for further analysis in all the other hearts. AAGF was applied on the eigenvectors and HA maps were generated using 3 different window sizes, 3x3x3,

5x5x5 and 7x7x7. The normalized RMSE between the control and HAAAGF (filtered using the 3 different window sizes) for each NEX is plotted in Figure 40a. We observed that in all 3 DED groups the window length 3x3x3 led to the minimal normalized RMSE.

Hence, the filter window 3x3x3 was used for all further processing. A representation of

HA maps from a mid-ventricular slice of the myocardium in the same animal using the

st rd optimal window size (3x3x3) is shown in Figure 40b. The 1 and 3 rows show HAUF

nd th maps and the corresponding HAAAGF maps are shown in the 2 and 4 rows. The maps indicate that at each NEX, the HAAAGF map obtained is a smoothed version of the

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corresponding HAUF map. These maps represent the trend observed in all the other hearts.

Figure 40: AAGF window length optimization in the entire heart and HA map of a single slice for all 21 acquisitions. a) Plot of NEX vs normalized RMSE of HA maps obtained with three filter windows 3x3x3, 5x5x5 and 7x7x7 for all the 21 acquisition to determine optimal window length. b) Unfiltered and filtered HA maps from a mid-ventricular 2 mm slice for all 21 acquisitions (labelled below each image). 1st rd nd th and 3 Row: HAUF. 2 and 4 Row: HAAAGF.

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Analyzing Filter Performance using Healthy Myocardium (Comparison with Isotropic

Filters): Eigenvectors were filtered with 3D 3x3x3 AAGF, AVF and MF and subsequently filtered HA maps were generated. For comparing the performance of each filter a NEX vs normalized RMSE graph for the entire heart in 9 animals was plotted

(Figure 41 (a-c)) and the mean (shown as colored lines on the plot) from all animals for each NEX was connected. A further assessment was performed on the central slices of the myocardium where transition in HA both in plane and through plane was subtle and less critical compared to the apex. Normalized RMSE estimation was performed for only

5 mid-ventricular slices and again the mean was generated for all 9 animals (Figure 41

(d-f)). We observed that the normalized RMSE for all NEX in the five mid-ventricular slices was lower than the normalized RMSE from the entire heart suggesting that the filter functioned better in the mid-ventricular slices. In both sets of plots between the 3 filters (red (AAGF), green (MF) and blue (AVF)), AAGF had lower normalized RMSE throughout when compared to the isotropic filters indicating that AAGF filtering technique is superior to a regular mean or median filter.

Determining Acquisition Parameters (DED, NEX) for Minimum TA: To determine the best acquisition parameters that provided the least TA we first needed to establish

NEXF_C. From Table 4 we see that the minimum normalized RMSE for the HAUF maps for 12, 30 and 64 DED were 8.9%, 8.2% and 8.8% respectively.

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Figure 41: Normalized RMSE vs NEX for the entire heart and 5 center slices for all the 9 healthy hearts. Plot of normalized RMSE vs NEX for unfiltered HA maps and HA maps filtered using the 3 different filtering techniques (AAGF, AVF and MF) for a) 12 DED b) 30 DED and c) 64 DED for the entire heart and for d) 12 DED e) 30 DED f) 64 DED for the center slices in 9 healthy animals. The different markers represent normalized RMSE from each animal. The mean normalized RMSE profile for each filtering technique (AAGF (red), AVF (blue) and MF (green)) and the unfiltered maps (gray) is shown on the plot.

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Therefore, the acceptable range of RMSE (<5% from the minimum) for 12, 30 and 64

DED would be 13.9%, 13.2% and 13.8% respectively. From the RMSE of the HAAAGF maps, we observed that for 12 DED, any NEX above 3 (RMSE=13.5%) falls under the acceptable range (<13.9%) but going above 8 NEX does not provide any advantage

(above 8 NEX normalized RMSE of the unfiltered maps is equal to or lower than the filtered maps).

Furthermore, any NEX above 3 has a ρc (0.80 (95% CI: [0.79, 0.81]) which is within the permissible threshold (>0.8). Hence, any NEX from 3 to 8 can be defined as NEXF_C, since they meet the set criterion. Now each of these NEX (3, 4, 6 and 8) reduced RMSE by 1.9%, 2.4%, 0.9% and 0.3% respectively, when compared to their unfiltered counterparts. We observe that increasing the NEX to 6 or 8 increases TA considerably

(TANEX=6: 13.9s, TANEX=8:18.6s) while causing a marginal reduction (<1%) in RMSE.

Additionally, between 3 and 4 NEX although both the reduction in RMSE and ρc is almost comparable, NEX=4 (1.47[-15.4, 18.35]) has much narrower Bland-Altman’s limits of agreement as compared to NEX=3 (1.2 [-17.6, 20.0]). Therefore, after simultaneously considering reduced normalized RMSE, good ρc and narrow limits of agreement NEXF_C for a 12 DED acquisition was set to 4. The concordance plot and

Bland-Altman’s plot for NEXF_C=4 shown in Figure 42(a, d) demonstrate that there is good agreement between HAAAGF and the gold standard. A similar analysis was performed for 30 and 64 DED and the cut-offs were defined as NEXF_C=2

(RMSE=12.41% (Figure 41b), ρc=0.82[0.81, 0.83] (Figure 42b) and limits of agreement:

1.15[-16.81, 19.1] (Figure 42e)) and NEXF_C=1 (RMSE=12.9% (Figure 41c), 163

ρc=0.82[0.81, 0.83] (Figure 42c) and limits of agreement: 1.32[-16.26, 18.9] (Figure 42f))

NEX, respectively. This reduced TA by factors of 5, 4 and 4 times for 12, 30 and 64

DED, respectively.

Once NEXF_C was established, slices each from the apex, mid-ventricle and base were selected and line profiles were generated for HAAAGF maps obtained from the cut-offs and

HAUF maps obtained from the gold standard. Three line profiles from a slice of the apex, mid and base sections of the LV with 12 DED acquisitions in an animal are shown in

Figure 43. The line profiles in the apex, mid-ventricle and base show smooth transition from the epicardium to the endocardium. From the figure we also observe that the filtered profiles in all the cases are good approximations of the unfiltered counterparts obtained from the gold standard. Similar trends were observed in the other animals. Therefore, we can conclude that the structural information of the LV obtained with higher NEX can be approximated by filtering the lower NEX principal eigenvectors with our proposed technique, thereby causing a reduction in TA.

Finally, an inter-DED group comparison was performed to establish the best DED-NEX combination that provided the least TA. Figure 44(a-c) compares different line profiles in the apex, mid-ventricle and base of a myocardium for the 3 DED settings (12, 30 and 64) with their respective NEXF_C (4, 2 and 1). The comparison establishes that HAAAGF maps from the different encoding groups agree well with each other. However, TA for HAAAGF with 12 DED and 4 NEX was minimum (9.3s for a single slice) indicating that this combination of DED-NEX generates the best HAAAGF maps in the least possible time.

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Figure 42: Concordance-correlation and Bland-Altman’s Analysis. Plot of Concordance-correlation between gold standard and NEXF_C for a) 12 DED, b) 30 DED, c) 64 DED acquisition. The solid line corresponds to the reduced major axis and the dashed line corresponds to the line of perfect concordance. Bland-Altman’s analysis was performed between gold standard and NEXF_C generated maps for a) 12 DED, b) 30 DED, c) 64 DED acquisition. The solid lines show mean ± 1 SD. 165

Figure 43: Three line profiles (the location of the profiles are shown in the cartoon of the LV) showing HA transition on a slice from the apex, mid-ventricle and base of the LV comparing HA maps obtained from NEXF_C to the gold standard in a 12 DED acquisition. HA maps of the slice in the a) apex b) mid and c) base for which the profiles have been generated are shown in the top left hand corner of each image. Line profiles generated from filtered HA maps obtained from NEXF_C (4 NEX, solid line) show a smooth transition from the epicardium to the endocardium and are in agreement with the gold standard (20 NEX, dotted line).

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Figure 44: Three line profiles (the location of the profiles are shown in the cartoon of the LV) showing HA transition on a slice from the apex, mid-ventricle and base of the LV comparing HA maps obtained from NEXF_C for all the 3 DED settings (12, 30 and 64). HA maps of the slice in the a) apex b) mid and c) base for which the profiles have been generated are shown in the top left hand corner of each image. Line profiles generated from filtered HA maps obtained from NEXF_C, for 12 (solid), 30 (dashed) and 64 (dashed-dotted) DED show a smooth transition from the epicardium to the endocardium and are in agreement with the each other.

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SNR Analysis: We next evaluated the association between RMSE and SNR. Figure 45 shows a plot of normalized RMSE (HAAAGF and HAUF) versus normalized SNR in all the 3 DED settings both for the entire heart and the 5 center slices. It was observed that with increasing normalized SNR (increasing NEX) the normalized RMSE exhibited an exponential decrease for both the AAGF filtered and unfiltered maps. An exponential regression analysis demonstrated that R2 values in all the cases was greater than 0.93 (as shown in the Figure 45) displaying a strong inverse correlation between increasing SNR and RMSE (i.e., RMSE decreased with increasing SNR). A further assessment showed that at NEXF_C the available SNR for all 3 DED groups is less than 50% of the gold standard. As mentioned earlier, it was observed that HAAAGF provides reduced normalized RMSE compared to HA¬UF at this SNR (less than 50%) indicating that at low SNR AAGF provides better estimates of DTI. This shows that AAGF allows lower

SNR acquisitions to produce better vector estimates thereby assisting in decreasing TA.

Analyzing Sensitivity of Filter in Diseased Myocardium (MI-Induced Hearts): Figure 46 shows HA maps obtained from 12 DED AAGF data with NEX=4 (top row) and from the gold standard (NEX=20, 2nd row) in a porcine myocardium induced with MI. The percentage difference between the AAGF data and the gold standard is shown in the 3rd row of the figure. This animal had a prominent infarct in the septal wall of the apex, which extended into the mid-ventricular region. As mentioned earlier, 3 distinct ROIs were investigated. Since the infarct was observed in the septal wall (area approximated in

TTC staining, confirmed by myocardial wall thinning in MRI scout images), ROI 1 corresponds to the infarct region on the septal wall as shown by the red contour. On the 168

same slice a region ROI 2 was selected on the free-wall far from the infarct denoted by the purple contour. A third region remote to the site of the infarct was defined in a basal slice as indicated by the green contour. From ROI 1 we can conclude that the infarcted region demonstrated a distinct loss in endocardial layer and mid-myocardial layer, as majority of the myocardium within the red contour (infarcted region) has HA values corresponding to the epicardial layer. ROI 2 had the usual trend of a smooth transition of

HA from the endocardium to the epicardium indicating that this region was not affected by the remodeling process caused due to MI. HA transition in ROI 3 was consistent with that from a healthy heart suggesting that the basal slices were unaffected by the pathological changes. The error maps demonstrated uniformity throughout the LV except for a few pixels near the epicardium and endocardium mostly due to air/tissue interface causing susceptibility artifact. These few pixels in the error maps have been deliberately left out of the contour while calculating the mean percentage error in each ROI since it appears primarily to be an edge/susceptibility artifact. The mean percentage error and the

SD in ROI 1, ROI 2 and ROI 3 for the 3 DED setting in the 3 MI-induced pigs is shown in Table 5. A mean error percentage less than 10% suggests that there was good agreement between the filtered and reference maps, thereby indicating that the filtering technique is sensitive to disease conditions and can successfully preserve pathological anomalies caused on the micro-structure of the myocardium.

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Figure 45: Regression analysis of normalized RMSE (both from AAGF filtered and unfiltered) vs normalized SNR for the entire heart and center slices. Plot of normalized RMSE vs normalized SNR for HAUF maps and HAAAGF for a) 12 DED b) 30 DED and c) 64 DED for the entire heart and for d) 12 DED e) 30 DED f) 64 DED for the center slices in 9 healthy animals. The R2 values for each correlation for the exponential regression analysis is shown in each figure and the fit is denoted by a solid lines for both HAUF (red) and HAAAGF (black).

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st Figure 46: HA maps and error profiles for infarcted myocardium. 1 Row: HAUF map Left: From an infarcted region Right: From a basal slice, remote to the nd infarction site. 2 Row: HAAAGF map Left: From an infarcted region Right: From a basal slice, remote to the infarction site. 3rd Row: Percentage difference between HAUF and HAAAGF Left: From an infarcted region Right: From a basal slice, remote to the infarction site. Error map is very uniform within the three different ROI under investigation.

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Table 5: Error Percentage Measurements. Mean and SD of the percentage error between HAAAGF maps obtained from NEXF_C and corresponding HAUF reference maps for the 3 DED settings in the 3 different ROI measured in all the 3 MI-induced pigs.

ERROR PERCENTAGE

DED MI Pig 1 MI Pig 2 MI Pig 3

ROI 1 ROI 2 ROI 3 ROI 1 ROI 2 ROI 3 ROI 1 ROI 2 ROI 3

12 1.85±1.5 5.18±5.4 4.03±5.2 2.68±5.6 7.01±9.7 5.10±7.6 3.03±2.9 3.2±3.7 4.4±6.7

30 2.48±2.3 4.60±4.8 3.71±7.2 6.39±6.3 6.93±6.8 6.47±8.1 3.82±3.3 3.05±3.0 4.2±6.5

64 2.38±1.9 5.62±7.6 2.44±2.7 6.79±7.7 7.88±10.6 6.83±9.3 5.09±7.6 3.10±3.5 4.5±6.9

6.5 Discussion

Our results demonstrate that a potential alternative approach towards improving LV HA estimation from diffusion tensor imaging is to apply post-processing AAGF on the principal eigenvectors. This allows a significant reduction in scan time by making additional image acquisition unnecessary. The locally modified anisotropy of the AAGF is an important improvement over isotropic mean or median filtering because it reduces transmural blurring. This conservative smoothing scheme preserves pathological anomalies as demonstrated by the feasibility study in a MI model.

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We observed that the RMSE estimate was higher for the entire heart as compared to the central slices. This higher error can be attributed to the characteristic spiral geometry that forms a partial loop-8 structure at the apex [366, 367]. Due to this sharp turn in the helical angles at the tip of the apex, and a low image resolution (voxel dimensions: 2x2x2 mm3), voxels near the apex had mixed tissue types which contributed to partial volume effects, thereby corrupting the tensor estimation. Furthermore, the number of pixels available in the apical slices was fewer compared to the mid-ventricular slices and hence the same straight line approximation of the Gaussian function that works in the mid- ventricular regions may fail for the apical slices. This can be partially resolved by modifying AAGF, and making it adaptive such that the filter specifications are varied as a function of the axial length. That is, the window size would increase with increasing distance from the apex to the base of the heart and the radial variation of the Gaussian function would also be dependent on location of the window on the long axis. However, this investigation is beyond the scope of this dissertation.

Most of the anisotropic DTI filters in the literature have been developed for brain applications. Since white matter tracts are long and relatively straight fibrous structures, these filters are not suited to encounter the curved myocardial anatomy. The AAGF approach uses the curvature of the myocardium and the organization of fibers to implement a spatially dependent filter shape that adapts to the orientation and curvature of the fiber.

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Currently, AAGF is implemented directly on the primary eigenvectors to estimate HA.

However, its application is not restricted to HA estimation, but can potentially be extended to all myocardial DTI metrics derived from the primary eigenvectors. For example, the filtered eigenvectors could be used for myocardial fiber tracking applications.

To the best of our knowledge, there is no gold standard for the ideal DED-NEX combination in literature and all protocols are built on individual applications restricted by TA. In our current study, we observed that if AAGF is applied, 12DED-4NEX is sufficient to generate robust HA maps. This conclusion was drawn from the mean of 9 ex-vivo porcine hearts. Individual analysis of the heart yielded the same results ensuring that the conclusions were not biased by the effect of a single myocardium. However, since a previous study has shown that at least 30DED is necessary for fiber tracking applications [368], if the application of AAGF is further extended for fiber tracking, additional investigation is necessary to analyze the effect of the filtering technique on fiber tracts.

The cut-off DED-NEX combination established in this dissertation may not directly relate to in-vivo imaging since imaging parameters would be completely different (TE,

TR, spatial resolution) and presence of ECG trigger and cardiac motion would generate a very different SNR response. However, with respect to in-vivo cardiac DTI sequences available in literature [273, 277, 369, 370], we can analyze the potential impact of the filtering technique on improving DTI vector estimates and scan time. The stimulated

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echo acquisition mode (STEAM) sequence [369, 371] used 6DED-1NEX acquisition to estimate eigenvectors. Although 6 DED was not investigated in this study but 1NEX acquisition was explored for all the 3 DED settings. Based on that we can conclude that in each case HA estimated from AAGF for 1 NEX had a lower RMSE compared to unfiltered HA indicating that filtering in-vivo images could potentially improve eigenvector estimation and in turn improve HA measurements and fiber tracking. The motion compensated spin echo approach [277] used 6DED-30NEX which takes 7 mins at an average heart rate of 60 bpm. Considering the results from 12DED-20NEX data, we can conclude that improvement in tensor estimation with increasing averages plateaus

(marginal improvement with increasing averages) after a certain NEX (Figure 41) and

12DED-4NEX was sufficient to estimate HA when the eigenvectors were filtered using

AAGF. Therefore, assuming that the same trend prevails for in-vivo imaging, acquiring so many averages may not be necessary thereby decreasing the scan time considerably.

Literature reports contradictory effect on HA transitions as a result of MI. One group reported a distinct shift towards negative helix [268, 272] in regions both adjacent and remote to the infarction, while another group reported a noticeable rightward/positive shift [266]. We have not noticed any specific trend as such in the three MI models we investigated; exploring further on the trend of HA due to MI remodeling is beyond the scope of this work. However, this study ensured that the filtering technique proposed could well preserve the abnormal fiber orientation observed in a diseased myocardium. In the 3 MI-induced myocardia examined here, anomalies noticed in pre-filtered reference

HA maps existed in post-filtered maps. 175

There are a few limitations in our study. First, using histology as the gold standard to validate HA was not feasible since the hearts were borrowed from another study.

However, the range of HA observed in our study and the trend of HA transition from epicardium (left-handed helix) to endocardium (right-handed helix) is consistent with the literature [266, 372] which has been previously validated histologically [136].Second, higher NEX at higher DED was not performed in order to limit maximum scan time to be

~30 minutes for each encoding direction. Third, lower spatial resolution which was limited by our maximum acquisition time might have compromised the true estimation of

HA at the apex due to sharp turn angles. Fourth, it is known that formalin-fixation causes de-hydration in tissues, which was mitigated by soaking the hearts in a water-bath for 15 minutes prior to each scan [334]. Finally, since all acquisitions were performed in one scan session, signal obtained from later acquisitions can vary due to loss of moisture content in the sample, however it was compensated by repeatedly spraying saline water on the tissue. Despite of these limitations we have demonstrated that AAGF is superior to the isotropic filters thereby reducing TA.

6.6 Conclusions

In this study, an AAGF was implemented to smooth the eigenvectors generated from

DTI. The subsequent effect of filtering the primary eigenvectors obtained both by fewer

NEX and DED produced robust HA similar to that derived from primary eigenvectors of higher NEX with increased DED, thereby reducing TA considerably. The filtering technique could also successfully preserve pathological differences.

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As mentioned in Chapter 2, information acquired from cMRE and DTI can be combined to investigate anisotropic mechanical properties of the myocardium using an anisotropic inversion algorithm called waveguide magnetic resonance elastography. This anisotropic inversion algorithm is validated in the next chapter using finite element simulations.

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Chapter 7: Validation of Waveguide Magnetic Resonance Elastography Using Finite

Element Modeling

It was mentioned earlier in the introductory chapters that the mechanical properties of the heart exhibit structural anisotropy which is altered in different disease conditions and could potentially be estimated using waveguide magnetic resonance elastography. In this chapter we validate waveguide magnetic resonance elastography inversion technique in models against known anisotropic material properties simulated using finite element analysis.

This material is previously published or presented as shown by the following citations.

 Mazumder R, Miller R, Jiang H, Clymer BD, White RD, Young A, Romano A,

Kolipaka A. Validation of Waveguide Magnetic Resonance Elastography Using

Finite Element Model Simulation. 23rd Annual Scientific Meeting ISMRM, Toronto,

Canada 2015.

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7.1 Introduction

Passive mechanical property of the left ventricular (LV) myocardium is known to exhibit structural anisotropy dictated by the myocardial fiber structure and orientation [120].

Myocardial fibers are arranged in a counter-directional helical network which is further organized to form layers of myocardial sheets separated by a complex structure of cleavage planes [125, 126]. The mechanical property of this laminar architecture is directionally varying which assists in the distribution of stress in a normal beating myocardium. Researchers have shown that the stiffness of the myocardium is different in the direction of the myocardial fiber compared to the directions orthogonal to it [123,

126, 344, 373]. Additionally, different cardiovascular diseases have been associated with alteration in the anisotropic mechanical properties (stiffness) of the myocardium [10, 176,

180, 256]. Hence it is important to estimate the anisotropic stiffness of the myocardium to understand its role in normal and abnormal cardiac mechanics.

Although the need for quantifying anisotropic myocardial stiffness is well recognized, a clinically efficient non-invasive technique to perform this quantification is not widely available. In the last decade an emerging technique known as waveguide magnetic resonance elastography (MRE) is being used to estimate anisotropic stiffness of biological tissues [113, 257, 258, 260, 374]. The technique uses MRE (a phase-contrast

MRI technique that measures tissue displacements caused by external vibrations [16]) in conjunction with fiber orientation information (usually obtained using diffusion tensor imaging (DTI)) to estimate compressional and shear stiffness along the direction of the fiber and in directions orthogonal to it. Waveguide MRE has been implemented to 179

evaluate the anisotropic elastic properties of calf muscles [257] and cortico-spinal tracts of healthy volunteers [259]. Additionally, it has also been used to detect anisotropic pathological changes in patients with amyotrophic lateral sclerosis [258].

Despite the promising results in healthy volunteers and in patients, this technique lacks validation against a known ground truth. Hence, before this technique can be implemented in the cardiac muscles to investigate the anisotropic elastic properties of the healthy and diseased myocardium, the accuracy of the parameters estimated using this technique needs to be established. Therefore, the aim of this study is to validate the waveguide MRE inversion algorithm by first simulating MRE mimicking displacement fields in different anisotropic geometric models with known material parameters using finite element (FE) analysis; and then implementing the inversion on the displacement fields to estimate the anisotropic elastic parameters of the geometric models and compare them with the known material parameters.

7.2 Theory

Waveguide Elastography

Waveguide elastography [259] is based on the inherent anisotropic property of biological tissue fibers, which act as waveguides for the anisotropic propagation of acoustic waves.

These acoustic waves induced by external vibration cause directionally dependent tissue displacement, which is exploited by the waveguide inversion algorithm to estimate anisotropic elastic coefficients of the underlying tissue. The inversion algorithm requires a prior knowledge of the fiber pathways along which acoustic waves travel within the 180

tissues. Based on the knowledge of the direction of the pathways, a local coordinate system is defined with three axes of symmetry orthogonal to each other.

Additionally, the algorithm also requires information about the amount of displacement caused in a tissue when excited with acoustic vibrations at a particular mechanical frequency. The first harmonics of these wave displacements are then filtered using a spatial-spectral filter defined by the local coordinate system (<푛1, 푛2, 푛3>). The spatial- spectral filter is a complex filter that isolates wave propagation along specific directions at every individual location along a pathway, in a particular volume surrounding that pathway. In general, the filtering consists of a forward three-dimensional (3-D) spatial

Fourier transform within a volume for a specific wave vector and spectrum, followed by a subsequent inverse Fourier transform using the complex conjugate of the same forward kernel and spectrum. Simultaneously, Helmholtz decomposition is performed in k-space in order to separate the wavefield into its longitudinal (compressional) and transverse

(shear) components.

Post filtering the spatially spectrally filtered displacement is used to solve for the diagonals of an orthotropic elastic tensor to evaluate the compressional (퐶11, 퐶22, and

퐶33) and the shear (퐶44, 퐶55, and 퐶66) stiffness measurements along each of the 3 axes of symmetry defined by the local coordinate system (<푛1, 푛2, 푛3>). In general, the equation to solve for the stiffness coefficient (퐶푖푖) is represented as follows:

2 푘 휕 푢푗 (푛푙) 2 푘 퐶푖푖 2 = 휌휔 푢푗 (푛푙), (63) 휕푥푙

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푘 where 푢푗 (푛푙) (푗 can be 1, 2 or 3) represent the directionally filtered displacements along the local axes (<푛1, 푛2, 푛3>). The superscript 푘 can be either 퐿 or 푇 corresponding to the longitudinal and transverse components provided by the Helmholtz decomposition. 휔 is the frequency of excitation, and 휌 is the density of the material. A ratio of the right hand side to the 1D Laplacians from the left hand side solves for the complex elastic coefficients 퐶푖푖 (i = 1, 2, ....,6). Further details of the equations and derivation are provided in Chapter 2 and Appendix A.

7.3 Materials and Methods

FE Models

Abaqus 6.13 (Dassault Systèmes Simulia Corp., Providence, RI, USA) was used to generate 3 rectangular beam models (Figure 47a – Figure 47c), 2 cylindrical beam models (Figure 47d Figure 47e), and a canine LV heart model (Figure 48). The details of the models (geometric shape, method of actuation, excitation frequency, fiber orientation, number of nodes, number of elements and degrees of freedom) are provided in Table 6.

The fiber orientation for the heart model was obtained by performing DTI in an ex-vivo canine heart. The density of all the models was fixed at 1000 kgm-3. A linearly elastic and transversely isotropic material was used to define the passive mechanical properties of all the models (M1-M6).

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Figure 47: Specifications of the Beam and Cylindrical Models Simulated using Finite Element Analysis. Geometric shape, methods of actuation, fiber orientation and the constraint condition is specified for a) M1; b) M2; c) M3; d) M4; and e) M5.

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Anisotropic material properties were assigned such that the direction of the fiber corresponded to the direction of maximum stiffness (along 푬ퟑퟑ) and transverse isotropy was assigned to the other two orthogonal directions (along 푬ퟏퟏ and 푬ퟐퟐ). Shear modulus

퐺푖푗 was estimated based on the compressional parameters, using the following equation:

퐸푖푖 퐸푗푗 퐺 = ; 퐺 = , (64) 푖푗 2(1 + 휈 ) 푗푖 2(1 + 휈 ) 푖푗 푗푖

where 퐺푖푗 = 퐺푗푖, 퐸푖푖 and 퐸푗푗 are the longitudinal stiffness along the 푖푖 and 푗푗 directions, respectively, and 휈푖푗 or 휈푗푖 are the Poisson’s ratio which are not generally equal. Since tissue is considered to be a nearly incompressible material Poisson’s ratio was set to be

0.49 in ν12, ν31 and ν32; Poisson’s ratio in the other directions was estimated from the relation:

휈푖푗 휈푗푖 = . (65) 퐸푖푖 퐸푗푗

Expected Wavenumber Estimation

The geometry (shape and size) of the material which acts as a waveguide for the acoustic wave propagation induces an effective wave velocity that is indirectly dependent on the intrinsic property of the material. For a thin rod approximation, the effective velocity (ce) is given by √(E∕ρ), where E is the Young’s modulus and ρ is the density of the material

[253]. For a particular material, with specific mechanical properties, the effective velocity provides an estimate of the effective wavelength (ce = fλe, where, f is the excitation frequency and λe is the effective wavelength) which can then be used to estimate the

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expected effective wavenumbers (ke = 2π/λe) in each of the longitudinal and transverse directions. These expected effective parameters according to the simulated material properties for all compressional and shear components are provided in Table 7 for the beam models (M1-M5) and in Table 8 (M6) for the heart.

Table 6: Finite Element Geometry and Simulation Parameters.

Excitation Degrees Model Geometry Dimension Frequency Nodes Elements of (Hz) Freedom

Rectangular 40x40x200mm3 M 23409 20480 181414 2 Beam

M3 100

M4 Cylindrical Diameter=40mm 12699 11300 98794 Beam Length=200mm M5

Left M NA 80 5485 4320 41550 6 Ventricle

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Table 7: Material Properties for the Beam Models (M1-M5).

Expected Input Expected Wavenumbers at 100Hz Stiffness Velocity Direction Excitation Frequency Parameters ce ke (in kPa) (in ms) (rad/m) Compressional (ퟏퟏ 18 4.24 148.08 and ퟐퟐ) Compressional (33) 60 7.75 81.11 Shear (ퟐퟑ / ퟑퟐ and 7.85 2.80 224.24 13 / ퟑퟏ) Shear (12 / 21) 6.04 2.46 255.62

Table 8: Material Properties for the Heart Model (M6).

Expected Input Expected Wavenumbers at 80Hz Stiffness Velocity Direction Excitation Frequency Parameters ce ke (in kPa) (in ms) (rad/m) Compressional (ퟏퟏ 5 2.24 224.79 and ퟐퟐ) Compressional (33) 10 3.16 158.95 Shear (ퟐퟑ / ퟑퟐ and 2 1.41 355.43 13 / ퟑퟏ) Shear (12 / 21) 1.67 1.29 388.97

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FE Frequency Response Analysis

In Abaqus, the steady-state response due to harmonic loading is solved using the harmonic equation of motion given by:

−휔2푀푢∗ + 푖휔퐷푢∗ + 퐾푢∗ = 푃∗, (66)

where 푃∗ is the forcing term, 푢∗ is the complex displacement, 푀 is the mass matrix, 퐷 is the damping matrix and 퐾 is the stiffness matrix.

To prevent unrealistic large oscillations, structural damping was applied to all the models.

Structural damping forces are proportional to the forces generated by stressing the structure and opposing the velocity. It is common to represent structural damping as a

∗ complex stiffness (퐾 ) which has a real component (퐾푆) and an imaginary component

∗ (퐾퐿 = 휔퐷); the latter acts as a loss modulus which accounts for the damping. Hence, 퐾 is given by:

∗ 퐾 = 푖퐾퐿 + 퐾푆 (67)

∗ 퐾 = 퐾푆 (푖푠 + 1) (68)

where 푠 is the structural damping coefficient, which relates the real and imaginary components of stiffness to one another. Substituting Equation (68) in Equation (66) we get:

2 ∗ ∗ ∗ −휔 푀푢 + (푖푠 + 1)퐾푆푢 = 푃 (69)

This above equation is used to solve the steady-state response. 188

Image Analysis

The displacement data acquired from FE simulations on each node was reconstructed onto a matric grid using linear interpolation in MATLAB (Mathworks, Natick, MA). The beam models were reconstructed at an isotropic imaging resolution of 2x2x2 mm3 (FOV:

256x256x256 mm3, imaging matrix: 128x128x128). Since the all fibers were aligned along the length of the geometric structure the local coordinate system (<푛1, 푛2, 푛3>) for each imaging voxel was constant and corresponded to (<0,0,1>). The heart model was reconstructed at an anisotropic imaging resolution of 0.47x0.47x2.4 mm3 (FOV:

120x120x120 mm3, imaging matrix: 256x256x50). The fiber orientation acquired from

DTI of the canine left ventricle was used to define 푛3 of the local coordinate system. The other two directions (푛1, 푛2) were defined based on orthogonality. For the heart model, since compressional actuators were placed throughout the epicardial surface to avoid bulk motion from the point of contact of the actuators, a couple of pixels from the epicardial wall were masked out. Additionally, to avoid issues associated with convergence of wave propagation at the tip of the apex, the apex was also masked out.

Wavenumber Estimation: First a broadband spatial spectral filter (as defined earlier) was implemented on the first harmonic displacements of the wave data to isolate the propagating wave in each of the longitudinal (<푛1, 푛2, 푛3>) and transverse (푛12/푛21,

푛23/푛32, and 푛13/푛31) directions. Filter parameters for the beam model were fixed at: longitudinal filter length=1 rad/m to 200 rad/m, transverse filter length=100 rad/m to 400 rad/m, and a spectral window voxel=13x13x13. Filter parameters for the heart model were fixed at: longitudinal filter length=100 rad/m to 300 rad/m, transverse filter 189

length=300 rad/m to 450 rad/m, and a spectral window voxel=11x11x11. Once the wavefield was separated into the longitudinal and transverse components, a 3D centroid based principal frequency estimation technique (PFE) [55] was implemented. PFE performs a 3D spatial Fourier transform on the filtered and separated first harmonic displacements data. Next, a threshold (50% of the peak amplitude) was applied to discard the power spectrum that is less than the threshold value (this allows the power spectrum to be focused on the peak). Finally, a weighted average was performed on the remaining spectrum, such that the weighting was based on the square of the amplitude of the power spectrum [55]. The weighted spectral peak was then used to estimate the dominant wavenumber (푘푒푠푡) in each of the longitudinal and transverse directions. Based on transverse isotropy, an average of the isotropic directions was performed to obtain 푘푒푠푡.

This 푘푒푠푡 was then compared to the expected wavenumbers (푘푒) calculated from the material properties of the model to investigate their agreement.

Stiffness Estimation: Based on the dominant 푘푒푠푡 obtained using PFE, a narrowband spatial spectral filter with window widths of +/- 20 rad/m centered on 푘푒푠푡 was defined for the same volume of interogation (13x13x13 for beam models and 11x11x11 for heart model). Again, Helmholtz decomposition was performed to obtain the directionally filtered longitudinal and transverse displacements. These displacements were then used to evaluate the compressional (퐶11, 퐶22, and 퐶33) and shear (퐶44, 퐶55, and 퐶66) anisotropic elastic coefficients along the diagonals of the orthotropic tensor using Equation (63). The compressional (퐶11, 퐶22, and 퐶33) and shear (퐶44, 퐶55, and 퐶66) anisotropic elastic coefficients are related to the Abaqus elastic coefficients as follows: 190

Compressional coefficients:

퐶11 = 퐸11, 퐶22 = 퐸22 푎푛푑 퐶33 = 퐸33 (70)

Shear coefficients:

퐶44 = 퐺23/퐺32, 퐶55 = 퐺31/퐺13 푎푛푑 퐶66 = 퐺12/퐺21 (71)

Statistical Analysis: To compute the mismatch in estimating the wavenumbers a percentage difference between 푘푒 and 푘푒푠푡 was calculated. Additionally, to analyze the effect of 푘푒푠푡 on the stiffness coefficients (퐶푖푖) a percentage difference between the expected (퐶푖푖_푒) and the estimated (퐶푖푖_푒푠푡) was also calculated. Finally, Bland Altman’s analysis was performed between 퐶푖푖_푒 and 퐶푖푖_푒푠푡 to investigate the agreement between the expected and the estimated stiffness parameters.

7.4 Results

The wave propagation from all the 6 models generated using FE analysis and reconstructed using MATLAB is shown in Figure 49. The first, second and third rows demonstrate wave propagation in the x, y, and z directions, respectively for a single slice.

From the wave images in the beam models it can be observed that the addition of shear actuators increases the complexity of the wave propagation pattern especially in the x and y directions. The 푘푒 and 푘푒푠푡 post broadband filtering for the beam models is provided in

Table 9 and for the heart model is provided in Table 10. The tables show that except for 191

푘12/푘21 all the other estimated wavenumbers agree well with the expected wavenumbers.

Additionally, the tables also demonstrate the percentage difference between 푘푒푠푡 and 푘푒.

Figure 50 and Figure 51 shows the compressional and shear stiffness maps of a single slice for all the five beam models and the heart model respectively. The images indicate uniform stiffness with little or no variation. Similar maps were obtained in all the other slices.

The 퐶푖푖_푒 and the mean 퐶푖푖_푒푠푡 and its standard deviation after narrowband filtering for all the 5 models, and the heart model, are provided in Table 11, and Table 12, respectively.

The tables show that except for 퐶66 all the other stiffness estimates are in agreement with the expected stiffness values. Additionally the tables also include the percentage difference between 퐶푖푖_푒푠푡 and 퐶푖푖_푒.

Figure 52a, and Figure 52b, shows the Bland-Altman’s plot for both the compressional and shear coefficients for all the 5 beam models and the heart model, respectively. From the plots it can be observed that the stiffness estimates are within the limits of agreement

(±1.96 times the standard deviation). The mean for the beams models is at -1.8 kPa and the mean for the heart model is at -0.72kPa.

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Figure 49: Wave Propagation in all 6 Models. Single phase-offset for propagation in x direction (1st Row), 풚 direction (2nd Row) and 풛 direction (3rd Row).

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Table 9: Wavenumber Estimation and the Percentage Difference in its Estimation when Compared to the Expected Values for the Beam Models.

k Directions e M M M M M (rad/m) 1 2 3 4 5 k Difference k Difference k Difference k Difference k Difference est est est est est (rad/m) (%) (rad/m) (%) (rad/m) (%) (rad/m) (%) (rad/m) (%)

풏ퟏퟏ, 풏ퟐퟐ 148 135 9.2 135 9.0 137 8.0 156 8.0 133 10.4

풏ퟑퟑ 81 85 5.2 87 7.2 85 4.6 76 5.7 76 6.2 풏 / 풏 , ퟐퟑ ퟑퟐ 224 238 6.3 245 9.5 246 10.0 220 2.0 215 4.1

풏ퟏퟑ / 풏ퟑퟏ 194

풏ퟏퟐ / 풏ퟐퟏ 256 179 30.1 159 37.9 153 40.2 228 11.1 227 11.2

Table 10: Wavenumber Estimation and the Percentage Difference in its Estimation when Compared to the Expected Values for the Heart Model.

k k Difference Directions e e (rad/m) (rad/m) (%)

풏ퟏퟏ, 풏ퟐퟐ 225 231 2.7 풏ퟑퟑ 159 155 3.1 풏 / 풏 , ퟐퟑ ퟑퟐ 355 307 13.6 풏ퟏퟑ / 풏ퟑퟏ 풏ퟏퟐ / 풏ퟐퟏ 389 235 39.5 194

Figure 50: Stiffness Maps for a Single Slice in all 5 Models. Each row indicates a beam model. Stiffness maps for compressional coefficients are shown in the first 3 st nd rd columns. 1 Column: 푪ퟏퟏ map; 2 Column: 푪ퟐퟐ map; 3 Column: 푪ퟑퟑ map. Stiffness maps for shear coefficients are shown in the last 3 columns. 4th Column: th th 푪ퟒퟒ map; 5 Column: 푪ퟓퟓ map; 6 Column: 푪ퟔퟔ map.

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Figure 51: Stiffness Maps for a Single Slice in the Heart Model. The red box in the left image shows the mask of the LV. The first row shows the compressional coefficient maps, 푪ퟏퟏ, 푪ퟐퟐ, and 푪ퟑퟑ map. The second row shows the shear coefficient maps, 푪ퟒퟒ, 푪ퟓퟓ and 푪ퟔퟔ.

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Table 11: Stiffness Estimation and the Percentage Difference in the Estimation when Compared to the Expected Values in all the Beam Models.

Stiffness 푪 풊풊_풆 M M M M M Coefficient (kPa) 1 2 3 4 5 푪 Difference 푪 Difference 푪 Difference 푪 Difference 푪 Difference 풊풊_풆풔풕 풊풊_풆풔풕 풊풊_풆풔풕 풊풊_풆풔풕 풊풊_풆풔풕 (kPa) (%) (kPa) (%) (kPa) (%) (kPa) (%) (kPa) (%)

푪ퟏퟏ, 푪ퟐퟐ 18 21.7±0.1 20.6 21.6±0.5 20.1 21.6±0.5 20.2 16.5±0.3 8.3 21.7±0.5 20.7

푪ퟑퟑ 60 54.7±2.4 8.9 54.5±2.5 9.1 54.4±3.3 9.4 69.7±2.2 16.2 69.7±2.8 16.2

푪ퟒퟒ, 푪ퟓퟓ 7.85 6.9±0.1 12.6 6.9±0.1 12.6 6.6±0.1 16.2 8.2±0.2 4.2 8.6±0.4 9.0

푪ퟔퟔ 6.04 12.2±0.1 101.4 15.4±0.2 154.7 16.4±0.2 171.3 7.5±0.1 23.9 7.8±0.2 29.4

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Table 12: Stiffness Estimation and the Percentage Difference in the Estimation when Compared to the Expected Values in the Heart Model.

푪 푪 Difference Stiffness Coefficient 풊풊_풆 풊풊_풆 (kPa) (kPa) (%)

푪ퟏퟏ, 푪ퟐퟐ 5 4.77±0.01 4.6

푪ퟑퟑ 10 10.46±0.12 4.6

푪ퟒퟒ, 푪ퟓퟓ 2 2.72±0.02 36.0

푪ퟔퟔ 1.67 4.57±0.01 173.7

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Figure 52: Bland Altman’s Plot of the Compressional and Shear Stiffness Coefficients. a) All 5 beam models pooled together; b) Heart model. The mean for the beams models is at -1.8 kPa and the mean for the heart model is at -0.72kPa. All the parameters are within ±1.96 times the standard deviation.

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7.5 Discussion

This study validates the anisotropic elastic coefficients obtained from waveguide MRE against known material parameters of models simulated using finite element analysis.

Our findings indicate that all the estimated stiffness coefficients were within the Bland

Altman’s limits of agreement (1.96 times standard deviation) and the percentage difference when compared to the expected values was within 20% in most of the cases

(except for 퐶66). From the percentage difference between estimated and expected parameters it was observed that at most a ±10% difference in wavenumber can be allowed if the estimated coefficients need to be within a ±20% difference.

This study investigated a beam model initially because to validate the algorithm it was necessary to establish the technique in a very simple geometric model before investigating a complex tissue structure like the heart. Additionally, fibers in many biological tissues at a microscopic level would share the same geometry as a rod or a cylindrical beam which further justifies the necessity of using this geometry.

The heart model investigated in this study extracted the fiber direction information from

DTI and a transversely isotropic model was constructed based on this orientation. Since, the model assumed transverse isotropy the information from the other two directions would be on an isotropic plane and the average from both the directions would be sufficient to indicate the material properties of the plane. Explicit information about the other two cardiac muscle directions may not be necessary as long as transverse isotropy is maintained. However, since it is known that the heart exhibits orthotropy with different

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material properties in three different directions it would be interesting to construct an orthotropic simulation model that accounts for the cardiac muscle orientation from the primary, secondary and tertiary diffusion directions obtained using DTI. Such an orthotropic model is very intricate and is currently beyond the scope of this study.

Our results demonstrate that in all the models (beams and heart) the wavenumber was over estimated for 퐶66 by more than 10%. This can be attributed to the fact that this particular mode was not being excited by the type of actuation being performed. The geometry of the object could also play a role since when the rectangular beam was replaced by a cylindrical beam and the waves were uniformly reflected back from the entire circumference a substantial improvement in wavenumber estimation was observed.

This indicates that the waveguide inversion algorithm requires a multi-aspect excitation to completely resolve the wave propagation in all the compressional and shear directions and in this current study with the model setting and excitation performed, 퐶66 remained unresolved.

Limitations: There are some limitations in this study. First, the actual FE simulations are generated on a nodal basis at a very high resolution, and the images reconstructed in

MATLAB are laid on a uniform grid at a coarse resolution (2x2x2 mm3). Since the image reconstruction involves significant interpolation the wave propagation includes some approximation errors from the interpolation technique. Second, the k-space resolution is such that a shift in the frequency peak by just a single voxel causes a difference of approximately ±42.5 rad/m in the wavenumber estimation in the beam models and

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±249.3 rad/m in the heart model, which represents substantial difference in the stiffness estimate. The object dimensions and time constraints of the inversion algorithm restricts from pursuing a finer k-space resolution. However, to take care of any small shift in the peak, the wavenumber estimation is performed using weighted average (weighting based on square of energy) so that the estimate is not biased on the location of just one peak.

Third, since the models M4 and M5 were cylindrical in nature, and the volume of interrogation was rectangular the edge pixels of the cylindrical model encountered windowing effect. Hence, to estimate the wavenumbers a couple of pixels from the edges were excluded from the mask. Finally, as already discussed the actuation methods investigated in this study could not excite the mode for 퐶66. There are different ways to generate multi-aspect excitations. Either multiple actuators need to be placed in orthogonal directions to provide the excitation along all the wave propagation directions, or a single actuator placed in a reverberant environment can provide sufficient excitation to excite all the individual modes. It is interesting to note, that in an in-vivo situation the wave propagating within the tissue is reflected from the edges, nearby tissues and bones, which may provide multi-aspect excitation to resolve all directions accurately. Despite these limitations, the waveguide inversion algorithm could resolve the anisotropic stiffness coefficients of the simulated models in most of the cases.

7.6 Conclusions

The results from this study demonstrate that under multi-excitation conditions waveguide elastography can successfully estimate anisotropic (longitudinal and transverse) stiffness in a transversely isotropic model. 201

In the next chapter this waveguide inversion algorithm will be implemented in a heart failure model to demonstrate its in-vivo feasibility.

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Chapter 8: Anisotropic Myocardial Stiffness in Hypertensive Porcine Hearts: Initial

Feasibility

In Chapter 1 it was mentioned that the alteration in mechanical properties of the diseased heart exhibits directional dependency. We hypothesize that if the directions associated with maximal change in elastic properties can be identified it can assist in developing direction specific treatment that may be a more effective therapy. Therefore, in this chapter we demonstrate an initial feasibility of performing waveguide magnetic resonance elastography in-vivo in hypertensive porcine hearts in order to investigate the alteration in the anisotropic elastic properties of the myocardium.

This material is previously published or presented as shown by the following citations.

 Mazumder R, Clymer BD, White RD, Romano A, Kolipaka A. In-vivo Waveguide

Cardiac Magnetic Resonance Elastography. 18th Annual Scientific Meeting SCMR,

Nice, France 2015.

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8.1 Introduction

Myocardial stiffness (MS) [6-9] is the central determinant of cardiac function. MS is elevated in cardiovascular diseases such as ischemia[375], myocardial infarction [321], hypertension (HTN) [183], diastolic dysfunction [184], and hypertrophic cardiomyopathy

[376]. These diseases over time can eventually trigger heart failure (HF) either with reduced or with preserved ejection fraction (HFpEF) [377]. Although epidemiological studies have confirmed equal prevalence of both kinds of HF [140], clinical therapies for

HFpEF have not been established yet [378], precisely because the pathophysiological mechanisms underlying HFpEF are poorly understood [199, 379, 380]. Furthermore, previous researchers have shown that alteration in MS related to HFpEF inducing disease conditions exhibit directional dependencies [381, 382]. Studies investigating electromechanical alterations in aging (a major contributing factor in the development of

HFpEF [186-188]) hearts (dogs [381], rabbits [382]) have demonstrated that age contributes to reduction in transverse conduction velocity. This reduction in conduction velocity is associated with increased fibrosis (causes an increase in stiffness) indicating that MS in aging hearts is more pronounced in transverse directions as oppose to longitudinal directions. From this discussion we hypothesize that quantifying anisotropic

MS will provide valuable insights into the pathophysiology of HFpEF causing disease conditions which might aid in developing directionally biased and effective treatment.

Currently, anisotropic MS can be measured using bi-axial mechanical testing (that too only in two directions with compressional components) on ex-vivo myocardial strips.

However, the process is invasive in nature and provides only a global stiffness estimate. 204

Furthermore, the technique requires extraction of tissue sample and hence MS measured using this technique does not account for the physiological changes occurring in the myocardium. Another technique to measure anisotropic MS uses finite element simulations in conjunction with imaging (ultrasound, CT, MRI), and hemodynamic measurements to characterize cardiac geometry and reconstruct models of the heart [123,

125]. These models are then processed and used to investigate anisotropic MS in HF causing disease conditions [383, 384]. However, this technique is complex and computationally intensive and is hence clinically inefficient. Therefore, there is a need for a non-invasive clinically efficient diagnostic tool to estimate anisotropic MS.

Recently, with the advent of waveguide magnetic resonance elastography (MRE) [113,

258-260] non-invasively estimating anisotropic stiffness has become feasible. Waveguide

MRE combines MRE (a phase contrast MRI technique to estimate tissue stiffness), diffusion tensor imaging (DTI) and anisotropic inversion to determine the anisotropic elastic coefficients of the tissue of interest. In this study we implement waveguide cardiac

MRE and estimate anisotropic MS in HTN induced porcine hearts (that has the potential to trigger HFpEF) to investigate the alteration in anisotropic elastic properties of the myocardium.

8.2 Materials and Methods

All animal procedures were performed in accordance with the university’s institutional animal care and use committee guidelines. Six juvenile Yorkshire pigs weighing ~70 lbs were induced with HTN. 205

Animal Model Preparation

The animals underwent renal-wrapping surgery which is known to induce chronic systemic arterial hypertension, leading to LV hypertrophy potentially triggering HFpEF

[289, 290]. The animals were placed in supine position on the surgery table and pre- operative Bupivicaine (0.5%, dosage: 3-5 ml) was injected into the incision site. Renal- wrapping surgery was performed via a midline abdominal incision. Both the kidneys were cleared of perinephric fat and wrapped snugly with sterile umbilical tape without constricting the renal vessel [288]. The abdominal wall was then closed in multiple layers using absorbable sutures. Post-operative analgesia consisted of a dose of buprenorphine (0.3 mg/ml, dosage: 0.005-0.02 mg/kg) and a fentanyl transdermal patch

(100 mcg/hr/72hrs).

MR Imaging Timeline

Previous studies in large animals have shown that approximately an eight week period is required for systemic HTN (induced by renal-wrapping procedure) to trigger LV hypertrophy, myocardial fibrosis and impaired diastolic function [303, 304]. Therefore, the HTN animals were scanned 8 weeks (W8HTN) post renal-wrapping procedure. Since

HTN induces global elevation in MS, to analyze the changes in the mechanical properties of the myocardium post W8HTN, a baseline image (BxHTN) was acquired before inducing

HTN.

Animal Preparation for MR Imaging

MR imaging was performed on animals under anesthesia, which was induced using

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ketamine (20 mg/kg) and acepromazine (0.5 mg/kg) and was maintained using isoflurane

(1-5%). The animals were positioned feet-first supine on the MR table and endotracheal intubation was performed to administer mechanical ventilation. A custom made passive driver was positioned on the anterior chest wall and secured in place using an elastic velcro strap. This passive driver was connected to a custom-made active driver (that generated the acoustic waves) via a rigid plastic tube as shown in Figure 53 to induce required vibrations into the heart for performing cMRE.

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Image Acquisition

Images were acquired using a 1.5-Tesla clinical MRI scanner (Avanto, Siemens

Healthcare, Erlangen, Germany). cMRE Acquisition: Retrospective pulse-gated, segmented multi-phase gradient recalled echo cMRE sequence was used to obtain short-axis slices covering the entire LV [107].

Imaging parameters for cMRE included: TE/TR=9.71/12.5 ms; field of view=384x384 mm2; imaging matrix=128x128; slice thickness=8mm; flip angle=15◦; cardiac phases=8;

GRAPPA acceleration factor =2; excitation frequency=80Hz; phase offsets=4; and

160Hz motion encoding gradients were applied separately in all three directions to encode the in plane and through plane external motion.

DTI Acquisition: Waveguide MRE algorithm requires information about the fiber pathways along which acoustic waves propagate. Thus the fiber orientation information required for anisotropic inversion was obtained using DTI. Since, in-vivo DTI is still in its inception because of the complexities associated with cardiac and respiratory motions,

DTI was performed in-vitro post sacrifice. The animals were euthanized on the MR table by injecting potassium chloride (KCl, 125 mg/ml, dosage: 70 mg/kg) to arrest the heart in diastole. Five minutes prior to injecting KCl, heparin (1000 u/ml, dosage: 10,000 units) was injected into the animals followed by a 20 ml saline flush to prevent the blood from clotting immediately post sacrifice. A 2D spin-echo, echo planar imaging-based DTI sequence was used with the following imaging parameters: TE/TR=70/2000 ms; field of view=384x384 mm2; imaging matrix=128x128; slice thickness=8mm; flip angle=90◦;

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b0/b1=0/1000 s/mm2; number of directions=12; and averages=20; The resolution of DTI data was maintained similar to the in-vivo cMRE sequence, so that co-registration of DTI and cMRE data can be performed (explained in image analysis).

Image Analysis

DTI Processing: The DTI images were averaged and then corrected for eddy current induced artifacts [262] using FSL 4.1.6 (FMRIB Software Library, Oxford, UK). Eddy current corrected images were processed to generate diffusion tensors for the entire heart, which were then used to estimate the eigenvalues (휆1, 휆2, 휆3) and eigenvectors (푉1, 푉2,

푉3). Based on the primary (휆1) secondary (휆2) and tertiary (휆3) diffusion directions, the eigenvectors provided the orientation of the cardiac muscles.

Image Registration: A two-dimensional (2D) non-rigid (deformable) image registration algorithm (Demon registration) [385-391] was implemented to register both cMRE and

DTI data using Matlab (Mathworks, Natick, MA) [391]. The DTI b0 images were qualitatively compared to the cMRE magnitude images and the cMRE cardiac phase that best resembled the phase at which the heart was arrested was selected. Prior to image registration both DTI (b0 and the eigenvectors) and cMRE images were masked. The mask consisted of the LV, the papillary muscles, the LV blood pool. In the basal and mid-ventricular slices small portions of the right ventricular insertion points were left intact for automatic anatomical identification. cMRE magnitude images were considered as the basis on which the DTI b0 images were registered. The transformation matrix obtained from performing the registration on the magnitude images was then applied on

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the eigenvectors (푉1, 푉2, 푉3) to register it to the cMRE data. Post-registration the registered eigenvectors and the cMRE wave images in x, y and z directions were masked to segment the LV. Any unregistered (a small portion) segment was discarded from the mask. The DTI obtained at W8HTN was also registered to the cMRE wave images acquired at BxHTN using the same procedure described above to determine the directional information at BxHTN. These registered DTI images and the cMRE wave images were used to solve the anisotropic inversion algorithm.

Waveguide cMRE Inversion: As mentioned in earlier chapters waveguide cMRE inversion algorithm requires prior knowledge of the pathways along which acoustic waves may travel within the myocardium which is obtained from the registered eigenvectors (푉1, 푉2, 푉3). These eigenvectors were used to define the mutually orthogonal local coordinate system (<푛1, 푛2, 푛3>) for each imaging voxel such that 푛3 corresponded to the primary diffusion direction (푉1), 푛1 corresponded to the secondary diffusion direction (푉2) and 푛2 corresponded to the tertiary diffusion direction (푉3)

(Figure 54). Based on this local coordinate system a broadband spatial spectral filter

(longitudinal filter length = 1 rad/m to 200 rad/m, transverse filter length 100 rad/m to

400 rad/m) was defined and applied on the first harmonic cMRE displacements at each imaging voxel in a restricted volume of interrogation (5x5x5) [113, 258, 259].

Simultaneously, Helmholtz decomposition was performed to separate the total field into its longitudinal and transverse components. Next the principal frequency of the spatially- spectrally filtered first harmonic displacement data was estimated for both the longitudinal (푛1, 푛2, and 푛3), and the transverse (푛12/푛21, 푛23/푛32, and 푛13/푛31) 210

components [55] after a 50% threshold was applied on the power spectrum. From the principal frequency, the wavenumber in each individual direction was calculated (푘푖푖 where i = 1, 2, 3 corresponded to the longitudinal wavenumbers and i = 4, 5, 6 corresponded to the transverse wavenumbers) [55].

Once the approximate wavenumbers (푘푖푖) in each direction were obtained, narrowband spatial spectral filters with window widths of +/- 20 rad/m centered on these wavenumbers were defined for the same volume (5x5x5). Again, Helmholtz decomposition was performed and the narrowband spatially-spectrally filtered and separated data were used to evaluate the anisotropic elastic coefficients. Since the heart exhibits an orthotropic anisotropic behavior (3 axes of symmetry, Figure 54), the diagonals of the orthotropic tensor is solved using the following general anisotropic equation of motion:

휕2푢푘(푛 ) 푗 푙 2 푘 퐶푖푖 2 = 휌휔 푢푗 (푛푙) (72) 휕푥푙

푘 where 푢푗 (푛푙) (푗 can be 1, 2 or 3) represents the directionally filtered displacements along the local axes (<푛1, 푛2, 푛3>). The superscript 푘 can be either 퐿 or 푇 corresponding to the longitudinal and transverse components provided by the Helmholtz decomposition. 휔 is the frequency of excitation, and 휌 is the density of the material (1000kg/m3). A ratio of the right hand side to the 1D Laplacians from the left hand side solves for the complex elastic coefficients 퐶푖푖 (i = 1, 2, ....,6). Further details of the equations and derivation are provided in Chapter 2 and Appendix A.

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Figure 54: Cardiac Structural Anisotropy and Local Coordinate System. Top: Cardiac anisotropy showing the three axes of symmetry namely, fiber, sheet and sheet normal [Adapted from Legrice et al. [121, 124]]. Bottom: The primary eigenvector corresponds to the fiber direction (n3), and n1 and n2 corresponds to the sheet and sheet normal directions respectively [Adapted from Romano et al. [259]].

Statistical Analysis

Differences in the mean anisotropic compressional and shear stiffness coefficients between BxHTN and W8HTN were tested for significance (p≤0.05) using a one-tailed paired student’s t-test.

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8.3 Results

Figure 55 shows an example of registering a W8HTN in-vitro DTI b0 image to a W8HTN in-vivo cMRE magnitude image. From the figure it can be observed that the septal wall in the unregistered DTI b0 image is collapsed. This structural change (septal wall collapse) was observed in all the hearts post-sacrifice. A comparison between cMRE magnitude image and the registered DTI b0 image demonstrated marginal mismatch in some regions. As mentioned earlier, these regions were left out from the mask prior to performing the anisotropic inversion.

Figure 55: Registration between cMRE Magnitude Image and DTI b0 Image at W8HTN. a) cMRE magnitude image b) unregistered DTI b0 image and c) registered DTI b0 image. Green and red contours define the epicardial and endocardial borders respectively.

Figure 56a and Figure 56f shows the cMRE magnitude image of a single slice in the same animal with epicardial (green) and endocardial (red) contours at BxHTN and W8HTN.

Figure 56(b-e) and Figure 56(g-j) displays four masked snap shots of the propagating wave encoded in the x-direction. The figure demonstrates that as the disease progressed

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from BxHTN to W8HTN it caused an increase in the LV thickness. This indicates that hypertension induced LV hypertrophy in the animals.

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Figure 57: Box Plot of Anisotropic Stiffness Coefficients in all 6 Animals at BxHTN and W8HTN. a) Compressional stiffness coefficients; b) Shear stiffness coefficients. C11 (p=0.05), C44 (p=0.03), C55 (p=0.04) and C66 (p=0.02) demonstrated significant increase at week 8 compared to baseline.

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Figure 58: Box Plot of Anisotropic Stiffness Coefficients in 5 Animals (Excluding the Outlier) at BxHTN and W8HTN. a) Compressional stiffness coefficients; b) Shear stiffness coefficients. C11 (p=0.05), C44 (p=0.02), C55 (p=0.03) and C66 (p=0.01) demonstrated significant increase at week 8 compared to baseline. 216

Figure 57 shows the box plots for the compressional and shear elastic coefficients at

BxHTN and W8HTN for all the animals. The mean and standard deviation (SD) of the compressional coefficients, C11, C22, and C33 at BxHTN were 4.71±1.7 kPa, 7.19±3.4 kPa, and 6.58±2.8 kPa, respectively, and at W8HTN were 10.94±6.7 kPa, 9.48±4.5 kPa, and

12.77±14.2 kPa, respectively. The mean±SD of the shear coefficients, C44, C55, and C66 at

BxHTN were 4.87±1.8 kPa, 2.96±0.6 kPa, and 4.55±1.3 kPa, respectively, and at W8HTN were 7.50±3.3 kPa, 10.68±7.4 kPa, and 8.31±3.4 kPa, respectively. C22 and C33 did not demonstrate any significant trend with disease progression. However, C11 (p=0.05), C44

(p=0.03), C55 (p=0.04), and C66 (p=0.02) demonstrated a significant increase in stiffness from BxHTN to W8HTN in all the animals. It was observed that one animal demonstrated the reverse trend at W8HTN in all the directions (except for C11). This animal was an outlier which and has been discussed in details in the next section.

Figure 58 shows the box plots for the compressional and shear elastic coefficients at

BxHTN and W8HTN excluding the outlier. The mean and standard deviation (SD) of the compressional coefficients, C11, C22, and C33 at BxHTN were 5.16±1.5 kPa, 7.71±3.5 kPa, and 7.12±2.7 kPa, respectively, and at W8HTN were 12.56±6.1 kPa, 10.6±4.1 kPa, and

14.6±14.9 kPa, respectively. The mean±SD of the shear coefficients, C44, C55, and C66 at

BxHTN were 5.27±1.7 kPa, 3.05±0.7 kPa, and 4.90±1.2 kPa, respectively, and at W8HTN were 8.55±2.6 kPa, 12.3±7.0 kPa, and 9.68±1.6 kPa, respectively. As before, C22 and C33 did not demonstrate any significant trend with disease progression and, C11 (p=0.05), C44

(p=0.02), C55 (p=0.03), and C66 (p=0.01) demonstrated a significant (p-values improved)

217

increase in stiffness from BxHTN to W8HTN in all the animals, even after excluding the outlier.

8.4 Discussion

This study investigates anisotropic MS in hypertensive animals using non-invasive waveguide cMRE. To the best of our knowledge, this study is the first of its kind and although the sample set is small (n=6) the results obtained show a promise for further investigation. MS did not increase significantly along all the elastic coefficients.

Significant increase in MS from BxHTN to W8HTN was observed in one of the compressional components (C11), in all the shear components (C44, C55, and C66), and an increasing trend was observed in the C22 direction.

Image Registration: In-vitro DTI was registered to in-vivo cMRE using a 2D non-rigid

Demon registration algorithm. It was observed that in all the animals post-sacrifice the size of the right ventricular blood pool increased and the septal wall collapsed which introduced structural changes between the in-vivo and in-vitro images. This contributed to skewed registration when the in-vitro b0 images from entire heart (with the right ventricle left intact) were registered to the in-vivo cMRE images. To account for this in the basal and mid-ventricular slices the pre-registration mask included only a portion of the right ventricle (insertion points) for anatomical markings, while in the apical slices the right ventricle was completely masked out. However, in some cases, mostly towards the apex the registration algorithm could not restore the septal wall and hence the septal wall was completely excluded from the post-registration masks in these slices. 218

Anisotropic Stiffness Measurements: In the HTN (prone to develop diastolic dysfunction) animals our findings indicate that the compressional stiffness coefficient along the fiber direction (C33) did not demonstrate any trend while on the other hand the compressional stiffness coefficient along the transverse directions increased at W8HTN. While C11 demonstrated a significant increase C22 demonstrated an increasing trend indicating that stiffness increased in directions orthogonal to the fibers. This trend is consistent with previous studies performed in aging hearts that demonstrated that reduction in conduction velocity which is associated with increase in fibrosis (eventually increases stiffness) is more pronounced in transverse directions [381, 382]. Aging is known to increase arterial stiffness that induces hypertension and is a major contributing factor in causing HFpEF

[188]. Additionally, in Chapter 3 it was demonstrated that the isotropic shear stiffness increased post renal wrapping surgery. Similar results were observed in the anisotropic shear stiffness measurements.

One animal was an outlier as it demonstrated a reverse trend at week 8 compared to all the other 5 animals. On further investigating this time-point, it was observed (qualitative) that the k-space (after the threshold was applied) power spectrum, post spatial-spectral filtering (broadband) for this particular animal was very broad (not restricted to a region) and not as clean as the other animals. Additionally, when we quantitatively analyzed the maximum intensity of the power spectrum it was observed that in general the values from the outlier were lower in all propagation directions when compared to the values obtained from all the other animals. A possible explanation to this anomaly could be that the windowing effect from the spatial-spectral filter could cause overlapping of peaks. This 219

interference in the spatial spectral peaks could in turn cause broadening, flattening and cancellation of the actual spectral peak. However, with or without the outlier our final conclusions remained the same.

Limitations: There are some limitations in our study. First, because of the absence of an in-vivo DTI sequence the fiber information was acquired in-vitro only after sacrificing the animal. However, differences can occur between the in-vivo cMRE images and post sacrifice DTI images due to: i) cardiac phase mismatch, and ii) alterations in position and orientation of the heart. Mismatch in cardiac phase can be incurred because although the cardiac phase of the in-vitro DTI is constant (arrested somewhere in diastole), the temporal resolution of the cMRE acquisition is not high enough to exactly match that phase. Additionally, position of the heart may change during in-vitro DTI (depends on the amount of air left in the lungs post sacrifice) and euthanizing the animal may contribute to structural changes causing misalignment between the two acquisitions. This was addressed by registering the in-vivo cMRE and in-vitro DTI images using a well- established non-rigid registration algorithm. Next, since the HTN animals demonstrated significant hypertrophy at W8HTN registration between the DTI at W8HTN and BxHTN had marginal mismatch. However, as mentioned earlier, any mismatch between cMRE and

DTI acquisitions post registration was excluded from the final mask used for the inversion. Despite, these limitations the initial feasibility study shows potential promise by demonstrating that certain anisotropic directions are affected more during HTN.

220

8.5 Conclusion

The results from this study demonstrate the feasibility of determining anisotropic MS in a

HTN animal model with stiffness increasing orthogonal to the fibers. This study has warranted further investigation, which in future can be used as a potential tool to develop novel drug therapies for HF.

The next chapter is the last chapter of this dissertation and it provides concluding remarks and a direction for future work.

221

Chapter 9: Summary and Future Work

Myocardial stiffness (MS) is the central determinant of cardiac function and has the potential to be used as a metric in the diagnosis of heart failure (HF) either with reduced ejection fraction (HFrEF) or with preserved ejection fraction (HFpEF). However, current clinical techniques used to measure MS are invasive in nature, provide a global stiffness estimate and do not measure the true intrinsic properties of the myocardium. This problem was addressed in this dissertation by implementing a novel non-invasive technique called cardiac magnetic resonance elastography (cMRE) that was used to measure spatiotemporal MS in HF animal models.

The first part of this dissertation implemented cMRE in HF animal models under the assumptions that the myocardium is a uniform, infinite, isotropic medium. Results obtained correlated well with currently used invasive diagnostic tools. Since the myocardium is known to exhibit structural anisotropy and HF has been shown to cause anisotropic alteration in mechanical properties of the myocardium, the next part of this dissertation investigated anisotropic properties of the myocardium. To this effect another novel technique called waveguide elastography that combines cMRE with diffusion tensor imaging ((DTI) provides fiber anisotropy information) was used to estimate anisotropic elastic properties. Prior to implementing waveguide elastography ex-vivo DTI was performed to evaluate structural changes in myocardial fiber architecture due to 222

HFrEF in ex-vivo specimens. Furthermore, a novel filtering technique was developed to reduce DTI acquisition time. Finally, waveguide cMRE was validated using finite element simulation and then implemented in-vivo in a hypertensive model to demonstrate the feasibility of estimating anisotropic mechanical properties of the myocardium in a disease condition prone to HF.

To the best of our knowledge, this is a ﬁrst attempt to extensively investigate the potential of cMRE as a diagnostic tool in different HF models and has demonstrated a promising future. However, there are several challenges that need to be addressed. Therefore, future work includes:

 Finite element simulation models with multiple actuations (to mimic the complex

wave propagation generated within the heart due to reverberation from all directions)

in structures that represent the geometry and anisotropy of the heart needs to be

developed to assess the performance of the waveguide inversion in more realistic

situations.

 The in-vivo cMRE image resolution was limited by the acquisition time in this

dissertation. Therefore, faster acquisition techniques need to be developed using

parallel acquisition and echo planar imaging. Reducing the acquisition time will also

assist in imaging patients whose capacity for breathhold scans is very limited.

 Implementing waveguide cMRE in other diseases that have the potential to trigger HF

and investigate if there is a difference in the way the anisotropic elastic coefficients

are being affected in the different disease models.

223

 To perform waveguide cMRE in patients it is important to implement in-vivo DTI

along with cMRE so that all acquisitions can be acquired in-vivo. The foundation to

perform in-vivo cardiac DTI has been established as shown in the in-vivo helical

angle map (Figure 59) obtained in a volunteer.

Figure 59: Helical Angle Map. Map showing feasibility of in-vivo cardiac DTI in a volunteer.

224

Appendix A: Waveguide Inversion Equation Derivation

Helmholtz decomposition implemented within the spatial spectral filter in the waveguide inversion algorithm is performed in k-space. As mentioned earlier, Helmholtz decomposition allows to separate a complicated wavefield into its longitudinal and transverse components. The decomposition states that the divergence of the wavefield nulls the transverse/shear components and preserves the longitudinal/compressional components, whereas the curl of the wavefield nulls the longitudinal/compressional components and preserves the transverse/shear components [259].

Mathematically, a vector function 푼 defined over 푅3 can be decomposed as:

푼 = 푼푳 + 푼푻 (73)

such that,

∇ ⋅ 푼푻 = 0, ∇ × 푼푳 = 0 (74)

It can be assumed that [392],

푼푳 = −∇휙, 푼푻 = ∇ × 흍 (75)

where 휙 is a smooth continuous scalar function and 휓 is a smooth vector function.

From Equation (73), Equations (74), and Equations (75) we obtain

∇ ⋅ 푼 = ∇ ⋅ 푼푳 = −Δ휙 (76) 225

and

∇ × 푼 = ∇ × 푼푻 = ∇ × ∇ × 흍 (77)

As demonstrated in [392] solutions for 휙(푟1) and 휓(푟1) gives:

1 ( ) ( ) 휙 풓ퟏ = ∫ (∇풓ퟐ ⋅ 푈 풓ퟐ ) 푑풓ퟐ 푅3 4휋 | 풓ퟏ − 풓ퟐ| (78)

1 ( ) ( ) 휓 풓ퟏ = ∫ (∇풓ퟐ × 푈 풓ퟐ ) 푑풓ퟐ 푅3 4휋 | 풓ퟏ − 풓ퟐ| (79)

Using 휙(푟1) obtained in Equation (78) in the expression for 푈퐿 in Equation (75) we get

1 ( ) ( ) 푼푳 풓ퟏ = ∇ ∫ (∇풓ퟐ ⋅ 푈 풓ퟐ ) 푑풓ퟐ 푅3 4휋 | 풓ퟏ − 풓ퟐ| 1 (80) ( ) = ∫ ∇풓ퟏ ( ) (∇풓ퟐ ⋅ 푈 풓ퟐ ) 푑풓ퟐ 푅3 4휋 | 풓ퟏ − 풓ퟐ|

Similarly, using 휓(풓ퟏ) obtained in Equation (79) in the expression for 푼푻 in Equation

(75) we get

1 ( ) ( ) 푈푇 풓ퟏ = ∇ × ∫ (∇풓ퟐ × 푼 풓ퟐ ) 푑풓ퟐ 푅3 4휋 | 풓ퟏ − 풓ퟐ| 1 (81) ( ) = ∫ ∇풓ퟏ ( ) × (∇풓ퟐ × 푈 풓ퟐ ) 푑풓ퟐ 푅3 4휋 | 풓ퟏ − 풓ퟐ|

Taking the Fourier transform of the Equations (80) and (81) defined for 푼푳(풓ퟏ) and

푼푻(풓ퟏ), respectively we obtain

226

1 푼 (풓 ) = ℑ {푼 } = ∫ ℑ풓 {∇풓 ( )} (∇풓 ⋅ 푈(풓ퟐ)) 푑풓ퟐ 푳 ퟏ 푟1 푳 ퟏ ퟏ 4휋|풓 − 풓 | ퟐ 푅3 ퟏ ퟐ

풌 −푖푘⋅푟2 ( ) = ∫ 푖 2 푒 (∇풓ퟐ ⋅ 푈 풓ퟐ ) 푑풓ퟐ 푅3 푘

풌 ( ) −푖푘⋅푟2 = 푖 2 ∫ (∇풓ퟐ ⋅ 푈 풓ퟐ ) 푒 푑풓ퟐ 푘 푅3

풌 = 푖 ℑ {∇ ⋅ 푼(풓 )} 푘2 풓ퟐ 풓ퟐ ퟐ (82)

where the following relationships were used

1 1 −푖푘⋅푟2 ℑ풓ퟏ { } = 2 푒 4휋|풓ퟏ − 풓ퟐ| 푘 (83)

1 풌 −푖푘⋅푟2 ℑ풓ퟏ {∇풓ퟏ ( )} = 푖 2 푒 4휋|풓ퟏ − 풓ퟐ| 푘 (84)

and similarly 푼푻(풌) yields,

푘 푼 (풌) = ℑ {푈 } = 푖 × ℑ {∇ × 푈(푟 )} 푻 푟1 푇 푘2 푟2 푟2 2 (85)

Equations (82) and (85), with the derivative property of the Fourier transform yields

풌 푼 (풌) = − (풌 ⋅ 푈(풌)) 푳 푘2 (86)

풌 푈 (풌) = − × (풌 × 푈(풌)) 푻 푘2 (87)

227

Equations (86) and (87) provide the k-space Helmholtz decomposition. The inverse

Fourier transform of these k-space representations gives the longitudinal and transverse displacement components in real space which are then used by the waveguide inversion algorithm to obtain the anisotropic elastic coefficients.

228

References

1. Luscher, T.F., Heart failure: the cardiovascular epidemic of the 21st century. Eur Heart J, 2015. 36(7): p. 395-7.

2. Mozaffarian, D., E.J. Benjamin, A.S. Go, D.K. Arnett, M.J. Blaha, M. Cushman, et al.;, Heart disease and stroke statistics--2015 update: a report from the American Heart Association. Circulation, 2015. 131(4): p. e29-322.

3. Heidenreich, P.A., N.M. Albert, L.A. Allen, D.A. Bluemke, J. Butler, G.C. Fonarow, et al.;, Forecasting the Impact of Heart Failure in the United States A Policy Statement From the American Heart Association. Circ-Heart Fail, 2013. 6(3): p. 606-619.

4. CDC. Division for Heart Disease and Stroke Prevention - Heart Failure Fact Sheet. 2013.

5. Ludwig, C., Lehrbuch der Physiologie des Menschen. 1. neu bearb. Aufl. ed1858, Leipzig,: C.F. Winter. v. <1- >.

6. Mirsky, I. and J.S. Rankin, The effects of geometry, elasticity, and external pressures on the diastolic pressure-volume and stiffness-stress relations. How important is the pericardium? Circ Res, 1979. 44(5): p. 601-11.

7. Watanabe, S., J. Shite, H. Takaoka, T. Shinke, Y. Imuro, T. Ozawa, et al.;, Myocardial stiffness is an important determinant of the plasma brain natriuretic peptide concentration in patients with both diastolic and systolic heart failure. Eur Heart J, 2006. 27(7): p. 832-8.

229

8. Pislaru, C., C.J. Bruce, P.C. Anagnostopoulos, J.L. Allen, J.B. Seward, P.A. Pellikka, et al.;, Ultrasound strain imaging of altered myocardial stiffness: stunned versus infarcted reperfused myocardium. Circulation, 2004. 109(23): p. 2905-10.

9. Zile, M.R., C.F. Baicu, and W.H. Gaasch, Diastolic heart failure--abnormalities in active relaxation and passive stiffness of the left ventricle. N Engl J Med, 2004. 350(19): p. 1953-9.

10. Holmes, J.W., T.K. Borg, and J.W. Covell, Structure and mechanics of healing myocardial infarcts. Annu Rev Biomed Eng, 2005. 7: p. 223-53.

11. Ibrahim el, S.H., Myocardial tagging by cardiovascular magnetic resonance: evolution of techniques--pulse sequences, analysis algorithms, and applications. J Cardiovasc Magn Reson, 2011. 13: p. 36.

12. Osman, N.F., Detecting stiff masses using strain-encoded (SENC) imaging. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2003. 49(3): p. 605-8.

13. Osman, N.F., S. Sampath, E. Atalar, and J.L. Prince, Imaging longitudinal cardiac strain on short-axis images using strain-encoded MRI. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2001. 46(2): p. 324-34.

14. Gilliam, A.D. and F.H. Epstein, Automated motion estimation for 2-D cine DENSE MRI. IEEE Trans Med Imaging, 2012. 31(9): p. 1669-81.

15. Muthupillai, R. and R.L. Ehman, Magnetic resonance elastography. Nat Med, 1996. 2(5): p. 601-3.

230

16. Muthupillai, R., D.J. Lomas, P.J. Rossman, J.F. Greenleaf, A. Manduca, and R.L. Ehman, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science, 1995. 269(5232): p. 1854-7.

17. Muthupillai, R., P.J. Rossman, D.J. Lomas, J.F. Greenleaf, S.J. Riederer, and R.L. Ehman, Magnetic resonance imaging of transverse acoustic strain waves. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 1996. 36(2): p. 266-74.

18. Manduca, A., D.S. Lake, S.A. Kruse, and R.L. Ehman, Spatio-temporal directional filtering for improved inversion of MR elastography images. Med Image Anal, 2003. 7(4): p. 465-73.

19. Manduca, A., T.E. Oliphant, M.A. Dresner, J.L. Mahowald, S.A. Kruse, E. Amromin, et al.;, Magnetic resonance elastography: non-invasive mapping of tissue elasticity. Med Image Anal, 2001. 5(4): p. 237-54.

20. Muftuler, L.T., Quantifying morphology and physiology of the human body using MRI2013, Boca Raton, FL: CRC Press/Taylor & Francis Group.

21. Sinkus, R., Magnetic Resonance Elastography. Molecular Imaging Techniques: New Frontiers, 2013: p. 82-97.

22. Chan, Q.C.C., G. Li, R.L. Ehman, R.C. Grimm, R. Li, and E.S. Yang, Needle shear wave driver for magnetic resonance elastography. Magnet Reson Med, 2006. 55(5): p. 1175-1179.

23. Chen, Q.S., S.I. Ringleb, A. Manduca, R.L. Ehman, and K.N. An, A finite element model for analyzing shear wave propagation observed in magnetic resonance elastography. J Biomech, 2005. 38(11): p. 2198-2203.

231

24. Chen, Q.S., S.I. Ringleb, A. Manduca, R.L. Ehman, and K.N. An, Differential effects of pre-tension on shear wave propagation in elastic media with different boundary conditions as measured by magnetic resonance elastography and finite element modeling. J Biomech, 2006. 39(8): p. 1428- 1434.

25. Dutt, V., R.R. Kinnick, R. Muthupillai, T.E. Oliphant, R.L. Ehman, and J.F. Greenleaf, Acoustic shear-wave imaging using echo ultrasound compared to magnetic resonance elastography. Ultrasound Med Biol, 2000. 26(3): p. 397- 403.

26. Ehman, R.L. and J.F. Greenleaf, Magnetic-Resonance Elastography by Direct Visualization of Propagating Acoustic Strain Waves (Vol 269, Pg 1854, 1995). Science, 1995. 270(5236): p. 565-565.

27. Glaser, K.J., J.P. Felmlee, A. Manduca, and R.L. Ehman, Shear stiffness estimation using intravoxel phase dispersion in magnetic resonance elastography. Magnet Reson Med, 2003. 50(6): p. 1256-1265.

28. Glaser, K.J., J.P. Felmlee, T.E. Oliphant, A. Manduca, and R.L. Ehman, Young's modulus estimation from intravoxel phase dispersion in magnetic resonance elastography. Radiology, 2001. 221: p. 330-330.

29. Greenleaf, J.F., R. Muthupillai, P.J. Rossman, D.J. Lomas, S.J. Riederer, and R.L. Ehman, Measurement of tissue elasticity using magnetic resonance elastography. Rev Prog Q, 1997. 16: p. 19-26.

30. Greenleaf, J.F., R. Muthupillai, P.J. Rossman, J. Smith, A. Manduca, and R.L. Ehman, Direct visualization of strain waves by Magnetic Resonance Elastography (MRE). 1996 Ieee Ultrasonics Symposium, Proceedings, Vols 1 and 2, 1996: p. 467-472.

232

31. Kruse, S.A., J.A. Smith, A.J. Lawrence, M.A. Dresner, A. Manduca, J.F. Greenleaf, et al.;, Tissue characterization using magnetic resonance elastography: preliminary results. Phys Med Biol, 2000. 45(6): p. 1579-1590.

32. Manduca, A., V. Dutt, D.T. Borup, R. Muthupillai, J.F. Greenleaf, and R.L. Ehman, An inverse approach to the calculation of elasticity maps for magnetic resonance elastography. P Soc Photo-Opt Ins, 1998. 3338: p. 426- 436.

33. Manduca, A., R. Muthupillai, P.J. Rossman, J.F. Greenleaf, and R.L. Ehman, Image processing for magnetic resonance elastography. P Soc Photo-Opt Ins, 1996. 2710: p. 616-623.

34. Manduca, A., R. Muthupillai, P.J. Rossman, J.F. Greenleaf, and R.L. Ehman, Visualization of tissue elasticity by magnetic resonance elastography. Visualization in Biomedical Computing, 1996. 1131: p. 63-68.

35. Manduca, A., R. Muthupillai, P.J. Rossman, J.F. Greenleaf, and R.L. Ehman, Local wavelength estimation for magnetic resonance elastography. International Conference on Image Processing, Proceedings - Vol Iii, 1996: p. 527-530.

36. Manduca, A., R. Muthupillai, P.J. Rossman, J.F. Greenleaf, and R.L. Ehman, Image analysis for magnetic resonance elastography. P Ieee Embs, 1997. 18: p. 756-757.

37. Manduca, A., T.E. Oliphant, M.A. Dresner, D.S. Lake, J.F. Greenleaf, and R.L. Ehman, Comparative evaluation of inversion algorithms for magnetic resonance elastography. 2002 Ieee International Symposium on Biomedical Imaging, Proceedings, 2002: p. 997-1000.

233

38. Manduca, A., T.E. Oliphant, M.A. Dresner, J.L. Mahowald, S.A. Kruse, E. Amromin, et al.;, Magnetic resonance elastography: Non-invasive mapping of tissue elasticity. Med Image Anal, 2001. 5(4): p. 237-254.

39. McCracken, P.J., A. Manduca, J. Felmlee, and R.L. Ehman, Mechanical transient-based magnetic resonance elastography. Magnet Reson Med, 2005. 53(3): p. 628-639.

40. Oliphant, T.E., A. Manduca, R.L. Ehman, and J.F. Greenleaf, Complex-valued stiffness reconstruction for magnetic resonance elastography by algebraic inversion of the differential equation. Magnet Reson Med, 2001. 45(2): p. 299- 310.

41. Ringleb, S.I., Q.S. Chen, D.S. Lake, A. Manduca, R.L. Ehman, and K.N. An, Quantitative shear wave magnetic resonance elastography: Comparison to a dynamic shear material test. Magnet Reson Med, 2005. 53(5): p. 1197-1201.

42. Romano, A.J., P.B. Abraham, P.J. Rossman, J.A. Bucaro, and R.L. Ehman, Determination and analysis of guided wave propagation using magnetic resonance elastography. Magnet Reson Med, 2005. 54(4): p. 893-900.

43. Romano, A.J., J.A. Bucaro, and R.L. Ehman, An inversion method for the determination of elastic moduli in tissue using magnetic resonance elastography. 2002 Ieee International Symposium on Biomedical Imaging, Proceedings, 2002: p. 1009-1010.

44. Rydberg, J.N., R.C. Grimm, and R.L. Ehman, Rapid magnetic resonance elastography (MRE) using fast spin-echo (FSE). Radiology, 2001. 221: p. 329- 330.

234

45. Smith, J.A. and R.L. Ehman, Extraction of propagating waves in cine images from magnetic resonance elastography. Mater Eval, 2000. 58(12): p. 1395- 1401.

46. Smith, J.A., R. Muthupillai, P.J. Rossman, T.C. Hulshizer, J.F. Greenleaf, and R.L. Ehman, Characterization of biomaterials using magnetic resonance elastography. Rev Prog Q, 1997. 16: p. 1323-1330.

47. Bensamoun, S.F., K.J. Glaser, S.I. Ringleb, Q. Chen, R.L. Ehman, and K.N. An, Rapid magnetic resonance elastography of muscle using one-dimensional projection. Journal of Magnetic Resonance Imaging, 2008. 27(5): p. 1083-1088.

48. Dyvorne, H., G.H. Jajamovich, M.I. Fiel, S.L. Friedman, D.T. Dieterich, C. Donnerhack, et al.;, Noninvasive Detection of liver fibrosis with multiparametric Magnetic Resonance Imaging compared to Transient Elastography. Hepatology, 2013. 58: p. 962a-963a.

49. Ehman, R.L., Quantitative assessment of the mechanical properties of tissues with magnetic resonance elastography. Comput Method Biomec, 2008. 11: p. 11-12.

50. Kolipaka, A., K.P. Mcgee, A. Manduca, A.J. Romano, K.J. Glaser, P.A. Araoz, et al.;, Magnetic Resonance Elastography: Inversions in Bounded Media. Magnet Reson Med, 2009. 62(6): p. 1533-1542.

51. Kwon, O.I., C. Park, H.S. Nam, E.J. Woo, J.K. Seo, K.J. Glaser, et al.;, Shear Modulus Decomposition Algorithm in Magnetic Resonance Elastography. IEEE Trans Med Imaging, 2009. 28(10): p. 1526-1533.

52. Litwiller, D.V., Y.K. Mariappan, and R.L. Ehman, Magnetic Resonance Elastography. Curr Med Imaging Rev, 2012. 8(1): p. 46-55.

235

53. Mariappan, Y.K., K.J. Glaser, and R.L. Ehman, Magnetic Resonance Elastography: A Review. Clin Anat, 2010. 23(5): p. 497-511.

54. Mariappan, Y.K., P.J. Rossman, K.J. Glaser, A. Manduca, and R.L. Ehman, Magnetic Resonance Elastography with a Phased-array Acoustic Driver System. Magnet Reson Med, 2009. 61(3): p. 678-685.

55. McGee, K.P., D. Lake, Y. Mariappan, R.D. Hubmayr, A. Manduca, K. Ansell, et al.;, Calculation of shear stiffness in noise dominated magnetic resonance elastography data based on principal frequency estimation. Phys Med Biol, 2011. 56(14): p. 4291-309.

56. Oudry, J., J. Chen, K.J. Glaser, V. Miette, L. Sandrin, and R.L. Ehman, Cross- Validation of Magnetic Resonance Elastography and Ultrasound-Based Transient Elastography: A Preliminary Phantom Study. Journal of Magnetic Resonance Imaging, 2009. 30(5): p. 1145-1150.

57. Silva, A.M., R.C. Grimm, K.J. Glaser, Y.L. Fu, T. Wu, R.L. Ehman, et al.;, Magnetic resonance elastography: evaluation of new inversion algorithm and quantitative analysis method. Abdom Imaging, 2015. 40(4): p. 810-817.

58. Yin, M., O. Rouviere, K.J. Glaser, and R.L. Ehman, Diffraction-biased shear wave fields generated with longitudinal magnetic resonance elastography drivers. Magn Reson Imaging, 2008. 26(6): p. 770-780.

59. Zheng, Y., G. Li, M. Chen, Q.C.C. Chan, S.G. Hu, X.N. Zhao, et al.;, Magnetic Resonance Elastography with twin pneumatic drivers for wave compensation. 2007 Annual International Conference of the Ieee Engineering in Medicine and Biology Society, Vols 1-16, 2007: p. 2611-2613.

60. Garteiser, P., R.S. Sahebjavaher, L.C. Ter Beek, S. Salcudean, V. Vilgrain, B.E. Van Beers, et al.;, Rapid acquisition of multifrequency, multislice and

236

multidirectional MR elastography data with a fractionally encoded gradient echo sequence. NMR Biomed, 2013. 26(10): p. 1326-35.

61. Doyley, M.M., Q. Feng, J.B. Weaver, and K.D. Paulsen, Performance analysis of steady-state harmonic elastography. Phys Med Biol, 2007. 52(10): p. 2657- 74.

62. Doyley, M.M., I. Perreard, A.J. Patterson, J.B. Weaver, and K.M. Paulsen, The performance of steady-state harmonic magnetic resonance elastography when applied to viscoelastic materials. Med Phys, 2010. 37(8): p. 3970-9.

63. McGarry, M., C.L. Johnson, B.P. Sutton, E.E. Van Houten, J.G. Georgiadis, J.B. Weaver, et al.;, Including spatial information in nonlinear inversion MR elastography using soft prior regularization. IEEE Trans Med Imaging, 2013. 32(10): p. 1901-9.

64. McGarry, M.D., C.L. Johnson, B.P. Sutton, J.G. Georgiadis, E.E. Van Houten, A.J. Pattison, et al.;, Suitability of poroelastic and viscoelastic mechanical models for high and low frequency MR elastography. Med Phys, 2015. 42(2): p. 947-57.

65. McGarry, M.D., E.E. Van Houten, C.L. Johnson, J.G. Georgiadis, B.P. Sutton, J.B. Weaver, et al.;, Multiresolution MR elastography using nonlinear inversion. Med Phys, 2012. 39(10): p. 6388-96.

66. McGarry, M.D., E.E. Van Houten, P.R. Perrinez, A.J. Pattison, J.B. Weaver, and K.D. Paulsen, An octahedral shear strain-based measure of SNR for 3D MR elastography. Phys Med Biol, 2011. 56(13): p. N153-64.

67. Pattison, A.J., M. McGarry, J.B. Weaver, and K.D. Paulsen, Spatially-resolved hydraulic conductivity estimation via poroelastic magnetic resonance elastography. IEEE Trans Med Imaging, 2014. 33(6): p. 1373-80.

237

68. Perrinez, P.R., F.E. Kennedy, E.E. Van Houten, J.B. Weaver, and K.D. Paulsen, Modeling of soft poroelastic tissue in time-harmonic MR elastography. IEEE Trans Biomed Eng, 2009. 56(3): p. 598-608.

69. Van Houten, E.E., M.I. Miga, J.B. Weaver, F.E. Kennedy, and K.D. Paulsen, Three-dimensional subzone-based reconstruction algorithm for MR elastography. Magnet Reson Med, 2001. 45(5): p. 827-37.

70. Van Houten, E.E., D. Viviers, M.D. McGarry, P.R. Perrinez, Perreard, II, J.B. Weaver, et al.;, Subzone based magnetic resonance elastography using a Rayleigh damped material model. Med Phys, 2011. 38(4): p. 1993-2004.

71. Wang, H., J.B. Weaver, Perreard, II, M.M. Doyley, and K.D. Paulsen, A three- dimensional quality-guided phase unwrapping method for MR elastography. Phys Med Biol, 2011. 56(13): p. 3935-52.

72. Weaver, J.B., E.E. Van Houten, M.I. Miga, F.E. Kennedy, and K.D. Paulsen, Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion. Med Phys, 2001. 28(8): p. 1620-8.

73. Klatt, D., U. Hamhaber, P. Asbach, J. Braun, and I. Sack, Noninvasive assessment of the rheological behavior of human organs using multifrequency MR elastography: a study of brain and liver viscoelasticity. Phys Med Biol, 2007. 52(24): p. 7281-7294.

74. Klatt, D., T.K. Yasar, T.J. Royston, and R.L. Magin, Sample interval modulation for the simultaneous acquisition of displacement vector data in magnetic resonance elastography: theory and application. Phys Med Biol, 2013. 58(24): p. 8663-8675.

238

75. Kotecha, M., D. Klatt, and R.L. Magin, Monitoring Cartilage Tissue Engineering Using Magnetic Resonance Spectroscopy, Imaging, and Elastography. Tissue Eng Part B-Re, 2013. 19(6): p. 470-484.

76. Riek, K., D. Klatt, H. Nuzha, S. Mueller, U. Neumann, I. Sack, et al.;, Wide- range dynamic magnetic resonance elastography. J Biomech, 2011. 44(7): p. 1380-1386.

77. Rump, J., D. Klatt, J. Braun, C. Warmuth, and I. Sack, Fractional encoding of harmonic motions in MR elastography. Magnet Reson Med, 2007. 57(2): p. 388-395.

78. Yin, Z.Y., R.L. Magin, and D. Klatt, Simultaneous MR Elastography and Diffusion Acquisitions: Diffusion-MRE (dMRE). Magnet Reson Med, 2014. 71(5): p. 1682-1688.

79. Braun, J., K. Braun, and I. Sack, Electromagnetic actuator for generating variably oriented shear waves in MR elastography. Magnet Reson Med, 2003. 50(1): p. 220-222.

80. Braun, J., G. Buntkowsky, J. Bernarding, T. Tolxdorff, and I. Sack, Simulation and analysis of magnetic resonance elastography wave images using coupled harmonic oscillators and Gaussian local frequency estimation. Magn Reson Imaging, 2001. 19(5): p. 703-713.

81. Hirsch, S., F. Beyer, J. Guo, S. Papazoglou, H. Tzschaetzsch, J. Braun, et al.;, Compression-sensitive magnetic resonance elastography. Phys Med Biol, 2013. 58(15).

82. Papazoglou, S., U. Hamhaber, J. Braun, and I. Sack, Algebraic Helmholtz inversion in planar magnetic resonance elastography. Phys Med Biol, 2008. 53(12): p. 3147-3158.

239

83. Papazoglou, S., S. Hirsch, J. Braun, and I. Sack, Multifrequency inversion in magnetic resonance elastography. Phys Med Biol, 2012. 57(8): p. 2329-2346.

84. Papazoglou, S., C. Xu, U. Hamhaber, E. Siebert, G. Bohner, R. Klingebiel, et al.;, Scatter-based magnetic resonance elastography. Phys Med Biol, 2009. 54(7): p. 2229-2241.

85. Plewes, D.B., C. Luginbuhl, C. Macgowan, and I. Sack, An inductive method to measure mechanical excitation spectra for MRI elastography. Concept Magn Reson B, 2004. 21B(1): p. 32-39.

86. Rump, J., C. Warmuth, J. Braun, and I. Sack, Phase preparation in steady-state free precession MR elastography. Magn Reson Imaging, 2008. 26(2): p. 228- 235.

87. Sack, I., Magnetic resonance elastography. Deut Med Wochenschr, 2008. 133(6): p. 247-251.

88. Sack, I., Magnetic resonance elastography 2.0: High resolution imaging of soft tissue elasticity, viscosity and pressure. Deut Med Wochenschr, 2013. 138(47): p. 2426-2430.

89. Sack, I., G. Buntkowsky, J. Bernarding, and J. Braun, Magnetic resonance elastography: A method for the noninvasive and spatially resolved observation of phase transitions in gels. J Am Chem Soc, 2001. 123(44): p. 11087-11088.

90. Sack, I., G. Buntkowsky, J. Bernarding, T. Tolxdorff, and J. Braun, New approach for analyzing magnetic resonance elastography images. Medical Imaging 2001: Physics of Medical Imaging, 2001. 2(25): p. 868-874.

240

91. Sack, I., E. Gedat, J. Bernarding, G. Buntkowsky, and J. Braun, Magnetic resonance elastography and diffusion-weighted imaging of the sol/gel phase transition in agarose. J Magn Reson, 2004. 166(2): p. 252-261.

92. Sack, I., C.K. Mcgowan, A. Samani, C. Luginbuhl, W. Oakden, and D.B. Plewes, Observation of nonlinear shear wave propagation using magnetic resonance elastography. Magnet Reson Med, 2004. 52(4): p. 842-850.

93. Van Houten, E.E.W., M.M. Doyley, F.E. Kennedy, K.D. Paulsen, and J.B. Weaver, A three-parameter mechanical property reconstruction method for MR-based elastic property imaging. IEEE Trans Med Imaging, 2005. 24(3): p. 311-324.

94. Kolipaka, A., S.R. Aggarwal, K.P. McGee, N. Anavekar, A. Manduca, R.L. Ehman, et al.;, Magnetic Resonance Elastography Derived Stiffness as a Method to Estimate Myocardial Contractility. Proceedings of the 20th Annual Meeting of ISMRM, Melbourne, Australia, 2012.

95. Kolipaka, A., S.R. Aggarwal, K.P. McGee, N. Anavekar, A. Manduca, R.L. Ehman, et al.;, Magnetic resonance elastography as a method to estimate myocardial contractility. J Magn Reson Imaging, 2012. 36(1): p. 120-7.

96. Kolipaka, A., P. Araoz, K.P. McGee, A. Manduca, and R.L. Ehman, In Vivo Cardiac MR Elastography in a Single Breath Hold. Proceedings of the 18th Annual Meeting of ISMRM, Stockholm, Sweden, 2010: p. 519.

97. Kolipaka, A., P.A. Araoz, K.P. McGee, A. Manduca, and R.L. Ehman, Magnetic resonance elastography as a method for the assessment of effective myocardial stiffness throughout the cardiac cycle. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2010. 64(3): p. 862-70.

241

98. Kolipaka, A., G.P. Chatzimavroudis, R.D. White, M.L. Lieber, and R.M. Setser, Relationship between the extent of non-viable myocardium and regional left ventricular function in chronic ischemic heart disease. J Cardiovasc Magn Reson, 2005. 7(3): p. 573-9.

99. Kolipaka, A., K.P. McGee, S.R. Aggarwal, Q. Chen, N. Anavekar, A. Manduca, et al.;, A Feasibility Study: MR Elastography as a Method to Compare Stiffness Estimates in Hypertrophic Obstructive Cardiomyopathy and in Normal Volunteers. Proceedings of the 19th Annual Meeting of ISMRM, Montreal, Canada, 2011.

100. Kolipaka, A., K.P. McGee, S.R. Aggarwal, Q. Chen, N. Anavekar, A. Manduca, et al.;, Regional quantification of Myocardial Stiffness using MR Elastography. Proceedings of the 19th Annual Meeting of ISMRM, Montreal, Canada, 2011: p. 15.

101. Kolipaka, A., K.P. McGee, P. Araoz, A. Manduca, and R.L. Ehman, MR Elastography as a method for the assessment of myocardial stiffness throughout the cardiac cycle. Proceedings of the 17th Annual Meeting of ISMRM, Hawaii, USA, 2009: p. 1790.

102. Kolipaka, A., K.P. McGee, P.A. Araoz, K.J. Glaser, A. Manduca, and R.L. Ehman, Evaluation of a rapid, multiphase MRE sequence in a heart- simulating phantom. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2009. 62(3): p. 691-8.

103. Kolipaka, A., K.P. McGee, P.A. Araoz, K.J. Glaser, A. Manduca, A.J. Romano, et al.;, MR elastography as a method for the assessment of myocardial stiffness: comparison with an established pressure-volume model in a left ventricular model of the heart. Magnetic resonance in medicine : official journal of the

242

Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2009. 62(1): p. 135-40.

104. Kolipaka, A., K.P. McGee, A. Manduca, N. Anavekar, R.L. Ehman, and P.A. Araoz, In vivo assessment of MR elastography-derived effective end-diastolic myocardial stiffness under different loading conditions. J Magn Reson Imaging, 2011. 33(5): p. 1224-8.

105. Kolipaka, A., K.P. McGee, A. Manduca, A.J. Romano, K.J. Glaser, P.A. Araoz, et al.;, Magnetic resonance elastography: Inversions in bounded media. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2009. 62(6): p. 1533-42.

106. Kolipaka, A., D. Woodrum, P.A. Araoz, and R.L. Ehman, MR elastography of the in vivo abdominal aorta: a feasibility study for comparing aortic stiffness between hypertensives and normotensives. J Magn Reson Imaging, 2012. 35(3): p. 582-6.

107. Wassenaar, P.A., C.N. Eleswarpu, S.A. Schroeder, X. Mo, B.D. Raterman, R.D. White, et al.;, Measuring age-dependent myocardial stiffness across the cardiac cycle using MR elastography: A reproducibility study. Magnet Reson Med, 2015.

108. Elgeti, T., M. Beling, B. Hamm, J. Braun, and I. Sack, Elasticity-based determination of isovolumetric phases in the human heart. J Cardiovasc Magn Reson, 2010. 12: p. 60.

109. Elgeti, T., M. Beling, B. Hamm, J. Braun, and I. Sack, Cardiac magnetic resonance elastography: toward the diagnosis of abnormal myocardial relaxation. Invest Radiol, 2010. 45(12): p. 782-7.

243

110. Elgeti, T., F. Knebel, R. Hattasch, B. Hamm, J. Braun, and I. Sack, Shear-wave amplitudes measured with cardiac MR elastography for diagnosis of diastolic dysfunction. Radiology, 2014. 271(3): p. 681-7.

111. Elgeti, T., J. Rump, U. Hamhaber, S. Papazoglou, B. Hamm, J. Braun, et al.;, Cardiac magnetic resonance elastography. Initial results. Invest Radiol, 2008. 43(11): p. 762-72.

112. Elgeti, T., H. Tzschatzsch, S. Hirsch, D. Krefting, D. Klatt, T. Niendorf, et al.;, Vibration-synchronized magnetic resonance imaging for the detection of myocardial elasticity changes. Magnet Reson Med, 2012. 67(4): p. 919-24.

113. Romano, A., R. Mazumder, S. Choi, B.D. Clymer, R.D. White, and A. Kolipaka, Waveguide Magnetic Resonance Elastography of the Heart. Proceedings of the 21st Annual Meeting of ISMRM, Utah, USA, 2013: p. 2431.

114. Sack, I., J. Rump, T. Elgeti, A. Samani, and J. Braun, MR elastography of the human heart: noninvasive assessment of myocardial elasticity changes by shear wave amplitude variations. Magnet Reson Med, 2009. 61(3): p. 668-77.

115. Robert, B., R. Sinkus, J.L. Gennisson, and M. Fink, Application of DENSE-MR- elastography to the human heart. Magnet Reson Med, 2009. 62(5): p. 1155-63.

116. Elgeti, T., M. Laule, N. Kaufels, J. Schnorr, B. Hamm, A. Samani, et al.;, Cardiac MR Elastography: Comparison with left ventricular pressure measurement. Journal of Cardiovascular Magnetic Resonance, 2009. 11.

117. Haettatsch, R., H. Tzschaetzsch, F. Knebel, T. Elgeti, M. Schultz, R. Klaua, et al.;, Palpating the heart: in vivo cardiac time harmonic elastography under guidance of b-mode ultrasound with real time elastographic feedback. Eur Heart J, 2014. 35: p. 1135-1136.

244

118. Pappano, A.J., W.G. Wier, and M.N. Levy, Cardiovascular physiology. 10th ed. Mosby physiology monograph series2013, Philadelphia, PA: Elsevier/Mosby. xii, 292 p.

119. Roberts, D.E., L.T. Hersh, and A.M. Scher, Influence of Cardiac Fiber Orientation on Wavefront Voltage, Conduction-Velocity and Tissue Resistivity in the Dog. Circ Res, 1979. 44(5): p. 701-712.

120. Streeter, D.D., Jr., H.M. Spotnitz, D.P. Patel, J. Ross, Jr., and E.H. Sonnenblick, Fiber orientation in the canine left ventricle during diastole and systole. Circ Res, 1969. 24(3): p. 339-47.

121. LeGrice, I.J., Y. Takayama, and J.W. Covell, Transverse shear along myocardial cleavage planes provides a mechanism for normal systolic wall thickening. Circ Res, 1995. 77(1): p. 182-93.

122. Rohmer, D., A. Sitek, and G.T. Gullberg, Reconstruction and visualization of fiber and Laminar structure in the normal human heart from ex vivo diffusion tensor magnetic resonance Imaging (DTMRI) data. Invest Radiol, 2007. 42(11): p. 777-789.

123. Nielsen, P.M., I.J. Le Grice, B.H. Smaill, and P.J. Hunter, Mathematical model of geometry and fibrous structure of the heart. Am J Physiol, 1991. 260(4 Pt 2): p. H1365-78.

124. LeGrice, I.J., B.H. Smaill, L.Z. Chai, S.G. Edgar, J.B. Gavin, and P.J. Hunter, Laminar structure of the heart: ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol, 1995. 269(2 Pt 2): p. H571-82.

125. Legrice, I.J., P.J. Hunter, and B.H. Smaill, Laminar structure of the heart: a mathematical model. Am J Physiol, 1997. 272(5 Pt 2): p. H2466-76.

245

126. Hunter, P.J., Myocardial constitutive laws for continuum mechanics models of the heart. Adv Exp Med Biol, 1995. 382: p. 303-18.

127. Costa, K.D., Y. Takayama, A.D. McCulloch, and J.W. Covell, Laminar fiber architecture and three-dimensional systolic mechanics in canine ventricular myocardium. Am J Physiol, 1999. 276(2 Pt 2): p. H595-607.

128. Cowin, S.C. and J.D. Humphrey, Cardiovascular soft tissue mechanics2001, Dordrecht ; Boston: Kluwer Academic Publishers. xii, 246 p.

129. Remme, E.W., P.J. Hunter, O. Smiseth, C. Stevens, S.I. Rabben, H. Skulstad, et al.;, Development of an in vivo method for determining material properties of passive myocardium. J Biomech, 2004. 37(5): p. 669-78.

130. Arts, T., K.D. Costa, J.W. Covell, and A.D. McCulloch, Relating myocardial laminar architecture to shear strain and muscle fiber orientation. Am J Physiol Heart Circ Physiol, 2001. 280(5): p. H2222-9.

131. Harrington, K.B., F. Rodriguez, A. Cheng, F. Langer, H. Ashikaga, G.T. Daughters, et al.;, Direct measurement of transmural laminar architecture in the anterolateral wall of the ovine left ventricle: new implications for wall thickening mechanics. Am J Physiol Heart Circ Physiol, 2005. 288(3): p. H1324-30.

132. Takayama, Y., K.D. Costa, and J.W. Covell, Contribution of laminar myofiber architecture to load-dependent changes in mechanics of LV myocardium. Am J Physiol Heart Circ Physiol, 2002. 282(4): p. H1510-20.

133. Helm, P.A., L. Younes, M.F. Beg, D.B. Ennis, C. Leclercq, O.P. Faris, et al.;, Evidence of structural remodeling in the dyssynchronous failing heart. Circ Res, 2006. 98(1): p. 125-32.

246

134. Walker, J.C., J.M. Guccione, Y. Jiang, P. Zhang, A.W. Wallace, E.W. Hsu, et al.;, Helical myofiber orientation after myocardial infarction and left ventricular surgical restoration in sheep. J Thorac Cardiovasc Surg, 2005. 129(2): p. 382- 90.

135. Zimmerman, S.D., J. Criscione, and J.W. Covell, Remodeling in myocardium adjacent to an infarction in the pig left ventricle. Am J Physiol Heart Circ Physiol, 2004. 287(6): p. H2697-704.

136. Scollan, D.F., A. Holmes, R. Winslow, and J. Forder, Histological validation of myocardial microstructure obtained from diffusion tensor magnetic resonance imaging. Am J Physiol, 1998. 275(6 Pt 2): p. H2308-18.

137. Levy, M.N., A.J. Pappano, and R.M.C.p. Berne, Cardiovascular physiology. 9th ed. ed2007, Edinburgh: Elsevier Mosby.

138. Braunwald, E., Heart disease : a textbook of cardiovascular medicine. 1st ed1980, Philadelphia: Saunders.

139. Borlaug, B.A. and M.M. Redfield, Diastolic and Systolic Heart Failure Are Distinct Phenotypes Within the Heart Failure Spectrum. Circulation, 2011. 123(18): p. 2006-2013.

140. Najjar, S.S., Heart failure with preserved ejection fraction failure to preserve, failure of reserve, and failure on the compliance curve. J Am Coll Cardiol, 2009. 54(5): p. 419-21.

141. Owan, T.E. and M.M. Redfield, Epidemiology of diastolic heart failure. Prog Cardiovasc Dis, 2005. 47(5): p. 320-32.

142. Fonarow, G.C., W.G. Stough, W.T. Abraham, N.M. Albert, M. Gheorghiade, B.H. Greenberg, et al.;, Characteristics, treatments, and outcomes of patients

247

with preserved systolic function hospitalized for heart failure - A report from the OPTIMIZE-HF registry. J Am Coll Cardiol, 2007. 50(8): p. 768-777.

143. Go, A.S., D. Mozaffarian, V.L. Roger, E.J. Benjamin, J.D. Berry, M.J. Blaha, et al.;, Heart Disease and Stroke Statistics--2014 Update: A Report From the American Heart Association. Circulation, 2013.

144. Owan, T.E., D.O. Hodge, R.M. Herges, S.J. Jacobsen, V.L. Roger, and M.M. Redfield, Trends in prevalence and outcome of heart failure with preserved ejection fraction. N Engl J Med, 2006. 355(3): p. 251-9.

145. Lam, C.S., E. Donal, E. Kraigher-Krainer, and R.S. Vasan, Epidemiology and clinical course of heart failure with preserved ejection fraction. Eur J Heart Fail, 2011. 13(1): p. 18-28.

146. Bhatia, R.S., J.V. Tu, D.S. Lee, P.C. Austin, J. Fang, A. Haouzi, et al.;, Outcome of heart failure with preserved ejection fraction in a population-based study. N Engl J Med, 2006. 355(3): p. 260-9.

147. Chen, M.A., Heart Failure with Preserved Ejection Fraction in Older Adults. American Journal of Medicine, 2009. 122(8): p. 713-723.

148. Bhuiyan, T. and M.S. Maurer, Heart Failure with Preserved Ejection Fraction: Persistent Diagnosis, Therapeutic Enigma. Curr Cardiovasc Risk Rep, 2011. 5(5): p. 440-449.

149. Yancy, C.W., M. Lopatin, L.W. Stevenson, T. De Marco, and G.C. Fonarow, Clinical presentation, management, and in-hospital outcomes of patients admitted with acute decompensated heart failure with preserved systolic function: a report from the Acute Decompensated Heart Failure National Registry (ADHERE) Database. J Am Coll Cardiol, 2006. 47(1): p. 76-84.

248

150. Zile, M.R., B. Kjellstrom, T. Bennett, Y. Cho, C.F. Baicu, M.F. Aaron, et al.;, Effects of Exercise on Left Ventricular Systolic and Diastolic Properties in Patients With Heart Failure and a Preserved Ejection Fraction Versus Heart Failure and a Reduced Ejection Fraction. Circ-Heart Fail, 2013. 6(3): p. 508- +.

151. Little, W.C., Heart failure with a normal left ventricular ejection fraction: diastolic heart failure. Trans Am Clin Climatol Assoc, 2008. 119: p. 93-99; discussion 99-102.

152. Cleland, J.G.F. and J. McGowan, Heart failure due to ischaemic heart disease: Epidemiology, pathophysiology and progression. J Cardiovasc Pharmacol, 1999. 33: p. S17-S29.

153. Libby, P. and P. Theroux, Pathophysiology of coronary artery disease. Circulation, 2005. 111(25): p. 3481-8.

154. Gheorghiade, M. and R.O. Bonow, Chronic heart failure in the United States: a manifestation of coronary artery disease. Circulation, 1998. 97(3): p. 282-9.

155. Zeymer, U. and K.L. Neuhaus, [Acute coronary thrombosis and myocardial ischemia following chemotherapy of Hodgkin's disease]. Onkologie, 1990. 13(3): p. 221-4.

156. Zhou, J., M. Chew, H.B. Ravn, and E. Falk, Plaque pathology and coronary thrombosis in the pathogenesis of acute coronary syndromes. Scand J Clin Lab Invest Suppl, 1999. 230: p. 3-11.

157. Conti, C.R., Role of coronary artery spasm in ischemic heart disease. Therapeutic implications. G Ital Cardiol, 1984. 14(11): p. 901-10.

158. Lanza, G.A., G. Careri, and F. Crea, Mechanisms of coronary artery spasm. Circulation, 2011. 124(16): p. 1774-82. 249

159. Maseri, A., R. Mimmo, S. Chierchia, C. Marchesi, A. Pesola, and A. Labbate, Coronary-Artery Spasm as a Cause of Acute Myocardial Ischemia in Man. Chest, 1975. 68(5): p. 625-633.

160. Visner, M.S., C.E. Arentzen, D.G. Parrish, E.V. Larson, M.J. O'Connor, A.J. Crumbley, 3rd, et al.;, Effects of global ischemia on the diastolic properties of the left ventricle in the conscious dog. Circulation, 1985. 71(3): p. 610-9.

161. Krayenbuehl, H.P., O.M. Hess, and H. Nonogi, On Whether There Is a True Increase in Myocardial Stiffness during Myocardial Ischemia. American Journal of Cardiology, 1989. 63(10): p. E78-E82.

162. Reiber, J.H.C., P.W. Serreys, and C.J. Slager, Quantitative coronary and left ventricular cineangiography : methodology and clinical applications1986, Boston [Mass.] ; Lancaster: Nijhoff.

163. Cohn, P.F.e., Diagnosis and therapy of coronary artery disease1979, Boston: Little,Brown.

164. McCans, J.L. and J.O. Parker, Left ventricular pressure-volume relationships during myocardial ischemia in man. Circulation, 1973. 48(4): p. 775-85.

165. Miyaji, K., S. Sugiura, S. Omata, Y. Kaneko, T. Ohtsuka, and S. Takamoto, Myocardial tactile stiffness: a variable of regional myocardial function. J Am Coll Cardiol, 1998. 31(5): p. 1165-73.

166. Marsch, S.C.U., V.A. Wanigasekera, W.A. Ryder, S.S. Wong, and P. Foex, Graded Myocardial-Ischemia Is Associated with a Decrease in Diastolic Distensibility of the Remote Nonischemic Myocardium in the Anesthetized Dog. J Am Coll Cardiol, 1993. 22(3): p. 899-906.

250

167. Edwards, C.H., 2nd, J.S. Rankin, P.A. McHale, D. Ling, and R.W. Anderson, Effects of ischemia on left ventricular regional function in the conscious dog. Am J Physiol, 1981. 240(3): p. H413-20.

168. Downing, S.E., Wall tension and myocardial dysfunction after ischemia and reperfusion. Am J Physiol, 1993. 264(2 Pt 2): p. H386-93.

169. Bourdillon, P.D., B.H. Lorell, I. Mirsky, W.J. Paulus, J. Wynne, and W. Grossman, Increased regional myocardial stiffness of the left ventricle during pacing-induced angina in man. Circulation, 1983. 67(2): p. 316-23.

170. Honda, H., J. Tani, T. Miyazaki, Y. Koiwa, T. Takishima, and K. Shirato, Increased regional systolic myocardial stiffness of the left ventricle during coronary artery occlusion in a dog: analysis of the finite element model. The Tohoku journal of experimental medicine, 1995. 177(2): p. 125-37.

171. Bristow, J.D., B.E. Van Zee, and M.P. Judkins, Systolic and diastolic abnormalities of the left ventricle in coronary artery disease. Studies in patients with little or no enlargement of ventricular volume. Circulation, 1970. 42(2): p. 219-28.

172. Henderson, A.H., W.W. Parmley, and E.H. Sonnenblick, The series elasticity of heart muscle during hypoxia. Cardiovasc Res, 1971. 5(1): p. 10-4.

173. Ko, S.M., Y.W. Kim, S.W. Han, and J.B. Seo, Early and delayed myocardial enhancement in myocardial infarction using two-phase contrast-enhanced multidetector-row CT. Korean J Radiol, 2007. 8(2): p. 94-102.

174. Pasotti, M., F. Prati, and E. Arbustini, The pathology of myocardial infarction in the pre- and post-interventional era. Heart, 2006. 92(11): p. 1552-6.

175. Fishbein, M.C., D. Maclean, and P.R. Maroko, The histopathologic evolution of myocardial infarction. Chest, 1978. 73(6): p. 843-9. 251

176. Gupta, K.B., M.B. Ratcliffe, M.A. Fallert, L.H. Edmunds, Jr., and D.K. Bogen, Changes in passive mechanical stiffness of myocardial tissue with aneurysm formation. Circulation, 1994. 89(5): p. 2315-26.

177. Laird, J.D. and H.P. Vellekoop, Time Course of Passive Elasticity of Myocardial Tissue Following Experimental Infarction in Rabbits and Its Relation to Mechanical Dysfunction. Circ Res, 1977. 41(5): p. 715-721.

178. Przyklenk, K., C.M. Connelly, R.J. Mclaughlin, R.A. Kloner, and C.S. Apstein, Effect of Myocyte Necrosis on Strength, Strain, and Stiffness of Isolated Myocardial Strips. Am Heart J, 1987. 114(6): p. 1349-1359.

179. Whittaker, P., D.R. Boughner, and R.A. Kloner, Analysis of healing after myocardial infarction using polarized light microscopy. Am J Pathol, 1989. 134(4): p. 879-93.

180. Holmes, J.W., J.A. Nunez, and J.W. Covell, Functional implications of myocardial scar structure. Am J Physiol, 1997. 272(5 Pt 2): p. H2123-30.

181. Rigolli, M. and G.A. Whalley, Heart failure with preserved ejection fraction. J Geriatr Cardiol, 2013. 10(4): p. 369-76.

182. Farhangkhoee, H., Z.A. Khan, H. Kaur, X. Xin, S. Chen, and S. Chakrabarti, Vascular endothelial dysfunction in diabetic cardiomyopathy: pathogenesis and potential treatment targets. Pharmacol Ther, 2006. 111(2): p. 384-99.

183. Conrad, C.H., W.W. Brooks, J.A. Hayes, S. Sen, K.G. Robinson, and O.H. Bing, Myocardial fibrosis and stiffness with hypertrophy and heart failure in the spontaneously hypertensive rat. Circulation, 1995. 91(1): p. 161-70.

184. Hamdani, N. and W.J. Paulus, Myocardial titin and collagen in cardiac diastolic dysfunction: partners in crime. Circulation, 2013. 128(1): p. 5-8.

252

185. Mohammed, S.F., S.A. Mirzoyev, W.D. Edwards, A. Dogan, D.R. Grogan, S.M. Dunlay, et al.;, Left ventricular amyloid deposition in patients with heart failure and preserved ejection fraction. JACC Heart Fail, 2014. 2(2): p. 113- 22.

186. Loffredo, F.S., A.P. Nikolova, J.R. Pancoast, and R.T. Lee, Heart failure with preserved ejection fraction: molecular pathways of the aging myocardium. Circ Res, 2014. 115(1): p. 97-107.

187. Borlaug, B.A., M.M. Redfield, V. Melenovsky, G.C. Kane, B.L. Karon, S.J. Jacobsen, et al.;, Longitudinal changes in left ventricular stiffness: a community-based study. Circ Heart Fail, 2013. 6(5): p. 944-52.

188. Lee, H.Y. and B.H. Oh, Aging and arterial stiffness. Circ J, 2010. 74(11): p. 2257-62.

189. Frohlich, E.D., C. Apstein, A.V. Chobanian, R.B. Devereux, H.P. Dustan, V. Dzau, et al.;, Medical Progress - the Heart in Hypertension. New Engl J Med, 1992. 327(14): p. 998-1008.

190. Cuspidi, C., M. Ciulla, and A. Zanchetti, Hypertensive myocardial fibrosis. Nephrol Dial Transplant, 2006. 21(1): p. 20-3.

191. Koren, M.J., R.B. Devereux, P.N. Casale, D.D. Savage, and J.H. Laragh, Relation of left ventricular mass and geometry to morbidity and mortality in uncomplicated essential hypertension. Ann Intern Med, 1991. 114(5): p. 345- 52.

192. Rossi, M.A., Connective tissue skeleton in the normal left ventricle and in hypertensive left ventricular hypertrophy and chronic chagasic myocarditis. Med Sci Monit, 2001. 7(4): p. 820-32.

253

193. Diez, J., B. Lopez, A. Gonzalez, and R. Querejeta, Clinical aspects of hypertensive myocardial fibrosis. Curr Opin Cardiol, 2001. 16(6): p. 328-35.

194. Klotz, S., I. Hay, G. Zhang, M. Maurer, J. Wang, and D. Burkhoff, Development of heart failure in chronic hypertensive Dahl rats: focus on heart failure with preserved ejection fraction. Hypertension, 2006. 47(5): p. 901-11.

195. Gomez, A., H. Unruh, and S.N. Mink, Altered left ventricular chamber stiffness and isovolumic relaxation in dogs with chronic pulmonary hypertension caused by emphysema. Circulation, 1993. 87(1): p. 247-60.

196. Borlaug, B.A., C.S.P. Lam, V.L. Roger, R.J. Rodeheffer, and M.M. Redfield, Contractility and Ventricular Systolic Stiffening in Hypertensive Heart Disease Insights Into the Pathogenesis of Heart Failure With Preserved Ejection Fraction. J Am Coll Cardiol, 2009. 54(5): p. 410-418.

197. Nikolic, S., E.L. Yellin, K. Tamura, H. Vetter, T. Tamura, J.S. Meisner, et al.;, Passive properties of canine left ventricle: diastolic stiffness and restoring forces. Circ Res, 1988. 62(6): p. 1210-22.

198. Zile, M.R. and D.L. Brutsaert, New concepts in diastolic dysfunction and diastolic heart failure: Part I: diagnosis, prognosis, and measurements of diastolic function. Circulation, 2002. 105(11): p. 1387-93.

199. Vasan, R.S. and D. Levy, Defining diastolic heart failure: a call for standardized diagnostic criteria. Circulation, 2000. 101(17): p. 2118-21.

200. Kass, D.A., J.G.F. Bronzwaer, and W.J. Paulus, What mechanisms underlie diastolic dysfunction in heart failure? Circ Res, 2004. 94(12): p. 1533-1542.

201. Borbely, A., J. van der Velden, Z. Papp, J.G. Bronzwaer, I. Edes, G.J. Stienen, et al.;, Cardiomyocyte stiffness in diastolic heart failure. Circulation, 2005. 111(6): p. 774-81. 254

202. Quarta, C.C., J.L. Kruger, and R.H. Falk, Cardiac Amyloidosis. Circulation, 2012. 126(12): p. E178-E182.

203. Chew, C., G.M. Ziady, M.J. Raphael, and C.M. Oakley, The functional defect in amyloid heart disease. The "stiff heart" syndrome. Am J Cardiol, 1975. 36(4): p. 438-44.

204. Mirzoyev, S.A., W.D. Edwards, S.F. Mohammed, J.L. Donovan, V.L. Roger, D.R. Grogan, et al.;, Cardiac Amyloid Deposition is Common in Elderly Patients with Heart Failure and Preserved Ejection Fraction. Circulation, 2010. 122(21).

205. Ton, V.K., M. Mukherjee, and D.P. Judge, Transthyretin cardiac amyloidosis: pathogenesis, treatments, and emerging role in heart failure with preserved ejection fraction. Clin Med Insights Cardiol, 2014. 8(Suppl 1): p. 39-44.

206. Aguilar, D., A. Deswal, K. Ramasubbu, D.L. Mann, and B. Bozkurt, Comparison of Patients With Heart Failure and Preserved Left Ventricular Ejection Fraction Among Those With Versus Without Diabetes Mellitus. American Journal of Cardiology, 2010. 105(3): p. 373-377.

207. Willemsen, S., J.W. Hartog, Y.M. Hummel, M.H. van Ruijven, I.C. van der Horst, D.J. van Veldhuisen, et al.;, Tissue advanced glycation end products are associated with diastolic function and aerobic exercise capacity in diabetic heart failure patients. Eur J Heart Fail, 2011. 13(1): p. 76-82.

208. van Heerebeek, L., N. Hamdani, M.L. Handoko, I. Falcao-Pires, R.J. Musters, K. Kupreishvili, et al.;, Diastolic stiffness of the failing diabetic heart - Importance of fibrosis, advanced glycation end products, and myocyte resting tension. Circulation, 2008. 117(1): p. 43-51.

255

209. Katz, A.M., Ernest Henry Starling, his predecessors, and the "Law of the Heart". Circulation, 2002. 106(23): p. 2986-92.

210. Frank, O., Zur Dynamik des Herzmuskels. Z Biol, 1895. 32: p. 370-437.

211. Patterson, S.W., H. Piper, and E.H. Starling, The regulation of the heart beat. J Physiol, 1914. 48(6): p. 465-513.

212. Patterson, S.W. and E.H. Starling, On the mechanical factors which determine the output of the ventricles. J Physiol, 1914. 48(5): p. 357-79.

213. Knowlton, F.P. and E.H. Starling, The influence of variations in temperature and blood-pressure on the performance of the isolated mammalian heart. J Physiol, 1912. 44(3): p. 206-19.

214. Markwalder, J. and E.H. Starling, On the constancy of the systolic output under varying conditions. J Physiol, 1914. 48(4): p. 348-56.

215. Hoffman, B.F., A.L. Bassett, and Bartelst.Hj, Some Mechanical Properties of Isolated Mammalian Cardiac Muscle. Circ Res, 1968. 23(2): p. 291-&.

216. Pinto, J.G. and Y.C. Fung, Mechanical properties of the heart muscle in the passive state. J Biomech, 1973. 6(6): p. 597-616.

217. Abbott, B.C. and J. Lowy, Stress relaxation in muscle. Proc R Soc Lond B Biol Sci, 1956. 146(923): p. 281-8.

218. Abbott, B.C. and W.F. Mommaerts, A study of inotropic mechanisms in the papillary muscle preparation. J Gen Physiol, 1959. 42(3): p. 533-51.

219. Kass, D.A. and W.L. Maughan, From 'Emax' to pressure-volume relations: a broader view. Circulation, 1988. 77(6): p. 1203-12.

256

220. Little, W.C., The left ventricular dP/dtmax-end-diastolic volume relation in closed-chest dogs. Circ Res, 1985. 56(6): p. 808-15.

221. McKay, R.G., J.M. Aroesty, G.V. Heller, H. Royal, J.A. Parker, K.J. Silverman, et al.;, Left ventricular pressure-volume diagrams and end-systolic pressure- volume relations in human beings. J Am Coll Cardiol, 1984. 3(2 Pt 1): p. 301- 12.

222. Campbell, K.B., R.D. Kirkpatrick, G.G. Knowlen, and J.A. Ringo, Late-Systolic Pumping Properties of the Left-Ventricle - Deviation from Elastance- Resistance Behavior. Circ Res, 1990. 66(1): p. 218-233.

223. Mirsky, I. and A. Pasipoularides, Clinical assessment of diastolic function. Prog Cardiovasc Dis, 1990. 32(4): p. 291-318.

224. Mirsky, I., T. Tajimi, and K.L. Peterson, The development of the entire end- systolic pressure-volume and ejection fraction-afterload relations: a new concept of systolic myocardial stiffness. Circulation, 1987. 76(2): p. 343-56.

225. Chowdhury, S.M., R.J. Butts, J. Buckley, A.M. Hlavacek, T.Y. Hsia, S. Khambadkone, et al.;, Comparison of Pressure-Volume Loop and Echocardiographic Measures of Diastolic Function in Patients With a Single- Ventricle Physiology. Pediatr Cardiol, 2014. 35(6): p. 998-1006.

226. Penicka, M., J. Bartunek, H. Trakalova, H. Hrabakova, M. Maruskova, J. Karasek, et al.;, Heart failure with preserved ejection fraction in outpatients with unexplained dyspnea: a pressure-volume loop analysis. J Am Coll Cardiol, 2010. 55(16): p. 1701-10.

227. Burkhoff, D., Pressure-volume loops in clinical research: a contemporary view. J Am Coll Cardiol, 2013. 62(13): p. 1173-6.

257

228. Burkhoff, D., I. Mirsky, and H. Suga, Assessment of systolic and diastolic ventricular properties via pressure-volume analysis: a guide for clinical, translational, and basic researchers. Am J Physiol Heart Circ Physiol, 2005. 289(2): p. H501-12.

229. Angeli, F.S., M. Shapiro, N. Amabile, G. Orcino, C.S. Smith, T. Tacy, et al.;, Left Ventricular Remodeling after Myocardial Infarction: Characterization of a Swine Model on beta-Blocker Therapy. Comp Med, 2009. 59(3): p. 272-279.

230. Sagawa, K., The end-systolic pressure-volume relation of the ventricle: definition, modifications and clinical use. Circulation, 1981. 63(6): p. 1223-7.

231. Fung, Y.C., Mathematical Representation of Mechanical Properties of Heart Muscle. J Biomech, 1970. 3(4): p. 381-&.

232. Demer, L.L. and F.C. Yin, Passive biaxial mechanical properties of isolated canine myocardium. J Physiol, 1983. 339: p. 615-30.

233. Sacks, M.S. and C.J. Chuong, Biaxial mechanical properties of passive right ventricular free wall myocardium. J Biomech Eng, 1993. 115(2): p. 202-5.

234. Gennisson, J.L., T. Deffieux, M. Fink, and M. Tanter, Ultrasound elastography: principles and techniques. Diagn Interv Imaging, 2013. 94(5): p. 487-95.

235. Varghese, T., Quasi-Static Ultrasound Elastography. Ultrasound Clin, 2009. 4(3): p. 323-338.

236. Bouchard, R.R., S.J. Hsu, P.D. Wolf, and G.E. Trahey, In vivo cardiac, acoustic- radiation-force-driven, shear wave velocimetry. Ultrason Imaging, 2009. 31(3): p. 201-13.

258

237. Hsu, S.J., R.R. Bouchard, D.M. Dumont, P.D. Wolf, and G.E. Trahey, In vivo assessment of myocardial stiffness with acoustic radiation force impulse imaging. Ultrasound in medicine & biology, 2007. 33(11): p. 1706-19.

238. Pislaru, C., M.W. Urban, I. Nenadic, and J.F. Greenleaf, Shearwave Dispersion Ultrasound Vibrometry Applied to In Vivo Myocardium. Ieee Eng Med Bio, 2009: p. 2891-2894.

239. Nenadic, I.Z., M.W. Urban, C. Pislaru, M. Bernal, and J.F. Greenleaf, Fourier Space Analysis of Mechanical Wave Dispersion for Transthoracic in vivo Measurements of Left-Ventricular Viscoelasticity. Ifmbe Proc, 2012. 37: p. 520-523.

240. Urban, M.W., C. Pislaru, I.Z. Nenadic, R.R. Kinnick, and J.F. Greenleaf, Measurement of Viscoelastic Properties of In Vivo Swine Myocardium Using Lamb Wave Dispersion Ultrasound Vibrometry (LDUV). IEEE Trans Med Imaging, 2013. 32(2): p. 247-261.

241. Zerhouni, E.A., D.M. Parish, W.J. Rogers, A. Yang, and E.P. Shapiro, Human heart: tagging with MR imaging--a method for noninvasive assessment of myocardial motion. Radiology, 1988. 169(1): p. 59-63.

242. Ambale-Venkatesh, B., A.C. Armstrong, C.Y. Liu, S. Donekal, K. Yoneyama, C.O. Wu, et al.;, Diastolic function assessed from tagged MRI predicts heart failure and atrial fibrillation over an 8-year follow-up period: the multi- ethnic study of atherosclerosis. Eur Heart J Cardiovasc Imaging, 2014. 15(4): p. 442-9.

243. Rogers, W.J., Jr., C.M. Kramer, G. Geskin, Y.L. Hu, T.M. Theobald, D.A. Vido, et al.;, Early contrast-enhanced MRI predicts late functional recovery after reperfused myocardial infarction. Circulation, 1999. 99(6): p. 744-50.

259

244. Gerber, B.L., J. Garot, D.A. Bluemke, K.C. Wu, and J.A. Lima, Accuracy of contrast-enhanced magnetic resonance imaging in predicting improvement of regional myocardial function in patients after acute myocardial infarction. Circulation, 2002. 106(9): p. 1083-9.

245. Elgeti, T., M. Beling, B. Hamm, J. Braun, and I. Sack, Cardiac Magnetic Resonance Elastography Toward the Diagnosis of Abnormal Myocardial Relaxation. Invest Radiol, 2010. 45(12): p. 782-787.

246. Elgeti, T., J. Rump, U. Hamhaber, S. Papazoglou, B. Hamm, J. Braun, et al.;, Cardiac Magnetic Resonance Elastography Initial Results. Invest Radiol, 2008. 43(11): p. 762-772.

247. Glaser, K.J., A. Manduca, and R.L. Ehman, Review of MR elastography applications and recent developments. J Magn Reson Imaging, 2012. 36(4): p. 757-74.

248. Chen, J., C. Ni, and T. Zhuang, Imaging mechanical shear waves induced by piezoelectric ceramics in magnetic resonance elastography. Chinese Sci Bull, 2006. 51(6): p. 755-760.

249. Uffmann, K., C. Abicht, W. Grote, H.H. Quick, and M.E. Ladd, Design of an MR-Compatible piezoelectric actuator for MR elastography. Concept Magnetic Res, 2002. 15(4): p. 239-254.

250. Moran, P.R., A flow velocity zeugmatographic interlace for NMR imaging in humans. Magn Reson Imaging, 1982. 1(4): p. 197-203.

251. Bernstein, M.A. and K.F. King, Handbook of MRI pulse sequences2004, Amsterdam ; Oxford: Academic Press.

252. Venkatesh, S.K. and R. Ehman, Magnetic Resonance Elastography, 2014, Springer. 260

253. Auld, B.A., Acoustic fields and waves in solids. 2nd ed1990, Malabar, Fla.: R.E. Krieger.

254. Hwu, C., Anisotropic elastic plates2010, New York: Springer. xvi, 673 p.

255. Knutsson, H., C.F. Westin, and G. Granlund, Local Multiscale Frequency and Bandwidth Estimation. Ieee Image Proc, 1994: p. 36-40.

256. Baldwin, S.L., M. Yang, K.R. Marutyan, K.D. Wallace, M.R. Holland, and J.G. Miller, Ultrasonic detection of the anisotropy of protein cross linking in myocardium at diagnostic frequencies. IEEE Trans Ultrason Ferroelectr Freq Control, 2007. 54(7): p. 1360-9.

257. Romano, A., P.B. Abraham, S.I. Ringleb, P.J. Rossman, J.A. Bucaro, and R.L. Ehman, Determination of Anisotropic Velocity Profiles in Muscle Using Wave-Guide Constrained Magnetic Resonance Elastography. Proceedings of the 14th Annual Meeting of ISMRM, Seattle, Washington, USA, 2006: p. 1725.

258. Romano, A., J. Guo, T. Prokscha, T. Meyer, S. Hirsch, J. Braun, et al.;, In vivo waveguide elastography: Effects of neurodegeneration in patients with amyotrophic lateral sclerosis. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2013.

259. Romano, A., M. Scheel, S. Hirsch, J. Braun, and I. Sack, In vivo waveguide elastography of white matter tracts in the human brain. Magn Reson Med, 2012. 68(5): p. 1410-22.

260. Romano, A.J., P.B. Abraham, P.J. Rossman, J.A. Bucaro, and R.L. Ehman, Determination and analysis of guided wave propagation using magnetic resonance elastography. Magn Reson Med, 2005. 54(4): p. 893-900.

261

261. Romano, A.J., J.A. Bucaro, R.L. Ehman, and J.J. Shirron, Evaluation of a material parameter extraction algorithm using MRI-based displacement measurement. Ieee T Ultrason Ferr, 2000. 47(6): p. 1575-1581.

262. Basser, P.J. and D.K. Jones, Diffusion-tensor MRI: theory, experimental design and data analysis - a technical review. NMR Biomed, 2002. 15(7-8): p. 456-67.

263. Basser, P.J., S. Pajevic, C. Pierpaoli, J. Duda, and A. Aldroubi, In vivo fiber tractography using DT-MRI data. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2000. 44(4): p. 625-32.

264. Basser, P.J. and C. Pierpaoli, Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B, 1996. 111(3): p. 209-19.

265. Le Bihan, D., J.F. Mangin, C. Poupon, C.A. Clark, S. Pappata, N. Molko, et al.;, Diffusion tensor imaging: concepts and applications. J Magn Reson Imaging, 2001. 13(4): p. 534-46.

266. Mekkaoui, C., S. Huang, H.H. Chen, G. Dai, T.G. Reese, W.J. Kostis, et al.;, Fiber architecture in remodeled myocardium revealed with a quantitative diffusion CMR tractography framework and histological validation. J Cardiovasc Magn Reson, 2012. 14: p. 70.

267. Strijkers, G.J., A. Bouts, W.M. Blankesteijn, T.H. Peeters, A. Vilanova, M.C. van Prooijen, et al.;, Diffusion tensor imaging of left ventricular remodeling in response to myocardial infarction in the mouse. NMR Biomed, 2009. 22(2): p. 182-90.

262

268. Wu, E.X., Y. Wu, J.M. Nicholls, J. Wang, S. Liao, S. Zhu, et al.;, MR diffusion tensor imaging study of postinfarct myocardium structural remodeling in a porcine model. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2007. 58(4): p. 687-95.

269. Wu, E.X., Y. Wu, H. Tang, J. Wang, J. Yang, M.C. Ng, et al.;, Study of myocardial fiber pathway using magnetic resonance diffusion tensor imaging. Magn Reson Imaging, 2007. 25(7): p. 1048-57.

270. Wu, Y., C.W. Chan, J.M. Nicholls, S. Liao, H.F. Tse, and E.X. Wu, MR study of the effect of infarct size and location on left ventricular functional and microstructural alterations in porcine models. J Magn Reson Imaging, 2009. 29(2): p. 305-12.

271. Wu, Y., H.F. Tse, and E.X. Wu, Diffusion tensor MRI study of myocardium structural remodeling after infarction in porcine model. 2006 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Vols 1-15, 2006: p. 3166-3169.

272. Wu, Y., L.J. Zhang, C. Zou, H.F. Tse, and E.X. Wu, Transmural heterogeneity of left ventricular myocardium remodeling in postinfarct porcine model revealed by MR diffusion tensor imaging. J Magn Reson Imaging, 2011. 34(1): p. 43-9.

273. Nielles-Vallespin, S., C. Mekkaoui, P. Gatehouse, T.G. Reese, J. Keegan, P.F. Ferreira, et al.;, In vivo diffusion tensor MRI of the human heart: Reproducibility of breath-hold and navigator-based approaches. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2012.

263

274. Reese, T.G., R.M. Weisskoff, R.N. Smith, B.R. Rosen, R.E. Dinsmore, and V.J. Wedeen, Imaging myocardial fiber architecture in vivo with magnetic resonance. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 1995. 34(6): p. 786-91.

275. Tseng, W.Y., T.G. Reese, R.M. Weisskoff, T.J. Brady, and V.J. Wedeen, Myocardial fiber shortening in humans: initial results of MR imaging. Radiology, 2000. 216(1): p. 128-39.

276. Dou, J., T.G. Reese, W.Y. Tseng, and V.J. Wedeen, Cardiac diffusion MRI without motion effects. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2002. 48(1): p. 105-14.

277. Gamper, U., P. Boesiger, and S. Kozerke, Diffusion imaging of the in vivo heart using spin echoes--considerations on bulk motion sensitivity. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2007. 57(2): p. 331-7.

278. Toussaint, N., M. Sermesant, C.T. Stoeck, S. Kozerke, and P.G. Batchelor, In vivo human 3D cardiac fibre architecture: reconstruction using curvilinear interpolation of diffusion tensor images. Med Image Comput Comput Assist Interv, 2010. 13(Pt 1): p. 418-25.

279. Wu, M.T., M.Y. Su, Y.L. Huang, K.R. Chiou, P. Yang, H.B. Pan, et al.;, Sequential changes of myocardial microstructure in patients postmyocardial infarction by diffusion-tensor cardiac MR: correlation with left ventricular structure and function. Circ Cardiovasc Imaging, 2009. 2(1): p. 32-40, 6 p following 40.

264

280. Wu, M.T., W.Y. Tseng, M.Y. Su, C.P. Liu, K.R. Chiou, V.J. Wedeen, et al.;, Diffusion tensor magnetic resonance imaging mapping the fiber architecture remodeling in human myocardium after infarction: correlation with viability and wall motion. Circulation, 2006. 114(10): p. 1036-45.

281. Kitzman, D.W. and B. Upadhya, Heart failure with preserved ejection fraction: a heterogenous disorder with multifactorial pathophysiology. J Am Coll Cardiol, 2014. 63(5): p. 457-9.

282. Upadhya, B., G.E. Taffet, C.P. Cheng, and D.W. Kitzman, Heart failure with preserved ejection fraction in the elderly: scope of the problem. J Mol Cell Cardiol, 2015. 83: p. 73-87.

283. Senni, M., W.J. Paulus, A. Gavazzi, A.G. Fraser, J. Diez, S.D. Solomon, et al.;, New strategies for heart failure with preserved ejection fraction: the importance of targeted therapies for heart failure phenotypes. Eur Heart J, 2014. 35(40): p. 2797-815.

284. Paulus, W.J. and C. Tschope, A novel paradigm for heart failure with preserved ejection fraction: comorbidities drive myocardial dysfunction and remodeling through coronary microvascular endothelial inflammation. J Am Coll Cardiol, 2013. 62(4): p. 263-71.

285. Penicka, M., M. Vanderheyden, and J. Bartunek, Diagnosis of heart failure with preserved ejection fraction: role of clinical Doppler echocardiography. Heart, 2014. 100(1): p. 68-76.

286. Kasner, M., D. Westermann, P. Steendijk, R. Gaub, U. Wilkenshoff, K. Weitmann, et al.;, Utility of Doppler echocardiography and tissue Doppler imaging in the estimation of diastolic function in heart failure with normal ejection fraction: a comparative Doppler-conductance catheterization study. Circulation, 2007. 116(6): p. 637-47. 265

287. Petrie, M.C., K. Hogg, L. Caruana, and J.J. McMurray, Poor concordance of commonly used echocardiographic measures of left ventricular diastolic function in patients with suspected heart failure but preserved systolic function: is there a reliable echocardiographic measure of diastolic dysfunction? Heart, 2004. 90(5): p. 511-7.

288. Grollman, A., A simplified procedure for inducing chronic renal hypertension in the mammal. P Soc Exp Biol Med, 1944. 57(1): p. 102-104.

289. Holzapfel, G.A.E. and R.W.E. Ogden, Biomechanics of soft tissue in cardiovascular systems2003: Springer.

290. Kahan, T. and L. Bergfeldt, Left ventricular hypertrophy in hypertension: its arrhythmogenic potential. Heart, 2005. 91(2): p. 250-6.

291. McVeigh, E.R. and E. Atalar, Cardiac tagging with breath-hold cine MRI. Magnet Reson Med, 1992. 28(2): p. 318-27.

292. Giri, S., Y.C. Chung, A. Merchant, G. Mihai, S. Rajagopalan, S.V. Raman, et al.;, T2 quantification for improved detection of myocardial edema. J Cardiovasc Magn Reson, 2009. 11: p. 56.

293. Messroghli, D.R., A. Greiser, M. Frohlich, R. Dietz, and J. Schulz-Menger, Optimization and validation of a fully-integrated pulse sequence for modified look-locker inversion-recovery (MOLLI) T1 mapping of the heart. J Magn Reson Imaging, 2007. 26(4): p. 1081-6.

294. Kellman, P., J.R. Wilson, H. Xue, M. Ugander, and A.E. Arai, Extracellular volume fraction mapping in the myocardium, part 1: evaluation of an automated method. J Cardiovasc Magn Reson, 2012. 14: p. 63.

295. Dunn, F.G., Hypertension and Myocardial-Infarction. J Am Coll Cardiol, 1983. 1(2): p. 528-532. 266

296. Kellman, P. and M.S. Hansen, T1-mapping in the heart: accuracy and precision. J Cardiovasc Magn Reson, 2014. 16: p. 2.

297. Verbeke, G. and G. Molenberghs, Linear mixed models for longitudinal data2000, New York ; London: Springer.

298. Mayet, J. and A. Hughes, Cardiac and vascular pathophysiology in hypertension. Heart, 2003. 89(9): p. 1104-9.

299. Zile, M.R., J.S. Gottdiener, S.J. Hetzel, J.J. McMurray, M. Komajda, R. McKelvie, et al.;, Prevalence and Significance of Alterations in Cardiac Structure and Function in Patients With Heart Failure and a Preserved Ejection Fraction. Circulation, 2011. 124(23): p. 2491-2501.

300. Kahan, T. and L. Bergfeldt, Left ventricular hypertrophy in hypertension: Its arrhythmogenic potential. Heart, 2005. 91(2): p. 250-256.

301. Mihl, C., W.R.M. Dassen, and H. Kuipers, Cardiac remodelling: concentric versus eccentric hypertrophy in strength and endurance athletes. Neth Heart J, 2008. 16(4): p. 129-+.

302. Ahmed, M.I., R.V. Desai, K.K. Gaddam, B.A. Venkatesh, S. Agarwal, S. Inusah, et al.;, Relation of torsion and myocardial strains to LV ejection fraction in hypertension. JACC Cardiovasc Imaging, 2012. 5(3): p. 273-81.

303. Hart, C.Y., D.M. Meyer, H.D. Tazelaar, J.P. Grande, J.C. Burnett, Jr., P.R. Housmans, et al.;, Load versus humoral activation in the genesis of early hypertensive heart disease. Circulation, 2001. 104(2): p. 215-20.

304. Munagala, V.K., C.Y. Hart, J.C. Burnett, Jr., D.M. Meyer, and M.M. Redfield, Ventricular structure and function in aged dogs with renal hypertension: a model of experimental diastolic heart failure. Circulation, 2005. 111(9): p. 1128-35. 267

305. Kumar, V., A.K. Abbas, and J.C. Aster, Robbins and Cotran pathologic basis of disease. Ninth edition. ed. xvi, 1391 pages.

306. Bogen, D.K., A. Needleman, and T.A. McMahon, An analysis of myocardial infarction. The effect of regional changes in contractility. Circ Res, 1984. 55(6): p. 805-15.

307. Wolk, M.J., S. Scheidt, and T. Killip, Heart failure complicating acute myocardial infarction. Circulation, 1972. 45(5): p. 1125-38.

308. Wenk, J.F., K. Sun, Z. Zhang, M. Soleimani, L. Ge, D. Saloner, et al.;, Regional left ventricular myocardial contractility and stress in a finite element model of posterobasal myocardial infarction. J Biomech Eng, 2011. 133(4): p. 044501.

309. Gotte, M.J., T. Germans, I.K. Russel, J.J. Zwanenburg, J.T. Marcus, A.C. van Rossum, et al.;, Myocardial strain and torsion quantified by cardiovascular magnetic resonance tissue tagging: studies in normal and impaired left ventricular function. J Am Coll Cardiol, 2006. 48(10): p. 2002-11.

310. McComb, C., D. Carrick, J.D. McClure, R. Woodward, A. Radjenovic, J.E. Foster, et al.;, Assessment of the relationships between myocardial contractility and infarct tissue revealed by serial magnetic resonance imaging in patients with acute myocardial infarction. The international journal of cardiovascular imaging, 2015. 31(6): p. 1201-9.

311. Neizel, M., D. Lossnitzer, G. Korosoglou, T. Schaufele, H. Peykarjou, H. Steen, et al.;, Strain-encoded MRI for evaluation of left ventricular function and transmurality in acute myocardial infarction. Circ Cardiovasc Imaging, 2009. 2(2): p. 116-22.

268

312. Kim, W., M.H. Jeong, D.S. Sim, Y.J. Hong, H.C. Song, J.T. Park, et al.;, A porcine model of ischemic heart failure produced by intracoronary injection of ethyl alcohol. Heart Vessels, 2011. 26(3): p. 342-8.

313. Galvez-Monton, C., C. Prat-Vidal, I. Diaz-Guemes, V. Crisostomo, C. Soler- Botija, S. Roura, et al.;, Comparison of two preclinical myocardial infarct models: coronary coil deployment versus surgical ligation. J Transl Med, 2014. 12: p. 137.

314. Crisostomo, V., J. Maestre, M. Maynar, F. Sun, C. Baez-Diaz, J. Uson, et al.;, Development of a closed chest model of chronic myocardial infarction in Swine: magnetic resonance imaging and pathological evaluation. ISRN Cardiol, 2013. 2013: p. 781762.

315. Carlsson, M., N.F. Osman, P.C. Ursell, A.J. Martin, and M. Saeed, Quantitative MR measurements of regional and global left ventricular function and strain after intramyocardial transfer of VM202 into infarcted swine myocardium. Am J Physiol-Heart C, 2008. 295(2): p. H522-H532.

316. Park, C.H., E.Y. Choi, H.M. Kwon, B.K. Hong, B.K. Lee, Y.W. Yoon, et al.;, Quantitative T2 mapping for detecting myocardial edema after reperfusion of myocardial infarction: validation and comparison with T2-weighted images. The international journal of cardiovascular imaging, 2013. 29 Suppl 1: p. 65-72.

317. Messroghli, D.R., T. Niendorf, J. Schulz-Menger, R. Dietz, and M.G. Friedrich, T1 mapping in patients with acute myocardial infarction. J Cardiovasc Magn Reson, 2003. 5(2): p. 353-9.

318. Messroghli, D.R., K. Walters, S. Plein, P. Sparrow, M.G. Friedrich, J.P. Ridgway, et al.;, Myocardial T1 mapping: application to patients with acute and chronic myocardial infarction. Magnet Reson Med, 2007. 58(1): p. 34-40. 269

319. Ugander, M., A.J. Oki, L.Y. Hsu, P. Kellman, A. Greiser, A.H. Aletras, et al.;, Extracellular volume imaging by magnetic resonance imaging provides insights into overt and sub-clinical myocardial pathology. Eur Heart J, 2012. 33(10): p. 1268-1278.

320. Kellman, P., J.R. Wilson, H. Xue, W.P. Bandettini, S.M. Shanbhag, K.M. Druey, et al.;, Extracellular volume fraction mapping in the myocardium, part 2: initial clinical experience. J Cardiovasc Magn Reson, 2012. 14: p. 64.

321. Sutton, M.G. and N. Sharpe, Left ventricular remodeling after myocardial infarction: pathophysiology and therapy. Circulation, 2000. 101(25): p. 2981- 8.

322. Pfeffer, M.A. and E. Braunwald, Ventricular remodeling after myocardial infarction. Experimental observations and clinical implications. Circulation, 1990. 81(4): p. 1161-72.

323. Buckberg, G.D., M.L. Weisfeldt, M. Ballester, R. Beyar, D. Burkhoff, H.C. Coghlan, et al.;, Left ventricular form and function: scientific priorities and strategic planning for development of new views of disease. Circulation, 2004. 110(14): p. e333-6.

324. Konstam, M.A., D.G. Kramer, A.R. Patel, M.S. Maron, and J.E. Udelson, Left ventricular remodeling in heart failure: current concepts in clinical significance and assessment. JACC Cardiovasc Imaging, 2011. 4(1): p. 98-108.

325. Tseng, W.Y., T.G. Reese, R.M. Weisskoff, and V.J. Wedeen, Cardiac diffusion tensor MRI in vivo without strain correction. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 1999. 42(2): p. 393-403.

270

326. Sosnovik, D.E., R. Wang, G. Dai, T.G. Reese, and V.J. Wedeen, Diffusion MR tractography of the heart. J Cardiovasc Magn Reson, 2009. 11: p. 47.

327. McGill, L.A., T.F. Ismail, S. Nielles-Vallespin, P. Ferreira, A.D. Scott, M. Roughton, et al.;, Reproducibility of in-vivo diffusion tensor cardiovascular magnetic resonance in hypertrophic cardiomyopathy. J Cardiovasc Magn Reson, 2012. 14: p. 86.

328. Garrido, L., V.J. Wedeen, K.K. Kwong, U.M. Spencer, and H.L. Kantor, Anisotropy of water diffusion in the myocardium of the rat. Circ Res, 1994. 74(5): p. 789-93.

329. Holmes, A.A., D.F. Scollan, and R.L. Winslow, Direct histological validation of diffusion tensor MRI in formaldehyde-fixed myocardium. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2000. 44(1): p. 157-61.

330. Chen, J., S.K. Song, W. Liu, M. McLean, J.S. Allen, J. Tan, et al.;, Remodeling of cardiac fiber structure after infarction in rats quantified with diffusion tensor MRI. Am J Physiol Heart Circ Physiol, 2003. 285(3): p. H946-54.

331. Sosnovik, D.E., R. Wang, G. Dai, T. Wang, E. Aikawa, M. Novikov, et al.;, Diffusion spectrum MRI tractography reveals the presence of a complex network of residual myofibers in infarcted myocardium. Circ Cardiovasc Imaging, 2009. 2(3): p. 206-12.

332. Leemans, A., B. Jeurissen, J. Sijbers, and D.K. Jones, ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data Proceedings of the 17th Annual Meeting of ISMRM, Hawaii, USA, 2009: p. 3537.

333. Shepherd, T.M., P.E. Thelwall, G.J. Stanisz, and S.J. Blackband, Aldehyde fixative solutions alter the water relaxation and diffusion properties of

271

nervous tissue. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2009. 62(1): p. 26-34.

334. Crawford, G.N. and R. Barer, The Action of Formaldehyde on Living Cells as Studied by Phase-contrast Microscopy. Journal of Microscopical Science, 1951. 92(4): p. 403-52.

335. D'Arceuil, H.E., S. Westmoreland, and A.J. de Crespigny, An approach to high resolution diffusion tensor imaging in fixed primate brain. Neuroimage, 2007. 35(2): p. 553-65.

336. Pattany, P.M., W.R. Puckett, K.J. Klose, R.M. Quencer, R.P. Bunge, L. Kasuboski, et al.;, High-resolution diffusion-weighted MR of fresh and fixed cat spinal cords: evaluation of diffusion coefficients and anisotropy. AJNR Am J Neuroradiol, 1997. 18(6): p. 1049-56.

337. Sun, S.W., J.J. Neil, and S.K. Song, Relative indices of water diffusion anisotropy are equivalent in live and formalin-fixed mouse brains. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2003. 50(4): p. 743-8.

338. Thavarajah, R., V.K. Mudimbaimannar, J. Elizabeth, U.K. Rao, and K. Ranganathan, Chemical and physical basics of routine formaldehyde fixation. J Oral Maxillofac Pathol, 2012. 16(3): p. 400-5.

339. Nguyen, C.T., Z. Fan, Y. Xie, B. Sharif, J. Dawkins, E. Tseliou, et al.;, Preliminary application of in vivo cardiac diffusion weighted MRI in chronic myocardial infarction porcine model. Journal of Cardiovascular Magnetic Resonance 2014. 16 (Suppl 1)(Suppl 1): p. 56.

272

340. D'Arceuil, H. and A. de Crespigny, The effects of brain tissue decomposition on diffusion tensor imaging and tractography. Neuroimage, 2007. 36(1): p. 64- 8.

341. Shepherd, T.M., J.J. Flint, P.E. Thelwall, G.J. Stanisz, T.H. Mareci, A.T. Yachnis, et al.;, Postmortem interval alters the water relaxation and diffusion properties of rat nervous tissue--implications for MRI studies of human autopsy samples. Neuroimage, 2009. 44(3): p. 820-6.

342. Mekkaoui, C., S. Huang, G. Dai, T.G. Reese, J.N. Ruskin, U. Hoffmann, et al.;, Myocardial infarct delineation in vivo using diffusion tensor MRI and the tractographic propagation angle. Journal of Cardiovascular Magnetic Resonance, 2013. 15(1).

343. Mekkaoui, C., S. Huang, G. Dai, T.G. Reese, U. Hoffmann, M.P. Jackowski, et al.;, The Tractographic Propagation Angle: A Novel Tool to Detect Infarction and Characterize Myocardial Microstructure. Proceedings of the 19th Annual Meeting of ISMRM, Montreal, Canada 2011: p. 3402.

344. Hunter, P.J., A.J. Pullan, and B.H. Smaill, Modeling total heart function. Annu Rev Biomed Eng, 2003. 5: p. 147-77.

345. Kanai, A. and G. Salama, Optical mapping reveals that repolarization spreads anisotropically and is guided by fiber orientation in guinea pig hearts. Circ Res, 1995. 77(4): p. 784-802.

346. Taccardi, B., R.L. Lux, P.R. Ershler, R. MacLeod, T.J. Dustman, and N. Ingebrigtsen, Anatomical architecture and electrical activity of the heart. Acta Cardiol, 1997. 52(2): p. 91-105.

273

347. Waldman, L.K., D. Nosan, F. Villarreal, and J.W. Covell, Relation between transmural deformation and local myofiber direction in canine left ventricle. Circ Res, 1988. 63(3): p. 550-62.

348. Cutler, M.J., D. Jeyaraj, and D.S. Rosenbaum, Cardiac electrical remodeling in health and disease. Trends Pharmacol Sci, 2011. 32(3): p. 174-80.

349. Weisman, H.F., D.E. Bush, J.A. Mannisi, and B.H. Bulkley, Global cardiac remodeling after acute myocardial infarction: a study in the rat model. J Am Coll Cardiol, 1985. 5(6): p. 1355-62.

350. Tezuka, F., Muscle-Fiber Orientation in Normal and Hypertrophied Hearts. Tohoku J Exp Med, 1975. 117(3): p. 289-297.

351. Tseng, W.Y., J. Dou, T.G. Reese, and V.J. Wedeen, Imaging myocardial fiber disarray and intramural strain hypokinesis in hypertrophic cardiomyopathy with MRI. J Magn Reson Imaging, 2006. 23(1): p. 1-8.

352. Martin-Fernandez, M., E. Munoz-Moreno, L. Cammoun, J.P. Thiran, C.F. Westin, and C. Alberola-Lopez, Sequential anisotropic multichannel Wiener filtering with Rician bias correction applied to 3D regularization of DWI data. Med Image Anal, 2009. 13(1): p. 19-35.

353. Hamarneh, G. and J. Hradsky, Bilateral filtering of diffusion tensor MR images. 2006 Ieee International Symposium on Signal Processing and Information Technology, Vols 1 and 2, 2006: p. 507-512.

354. Basu, S., T. Fletcher, and R. Whitaker, Rician noise removal in diffusion tensor MRI. Medical Image Computing and Computer-Assisted Intervention - Miccai 2006, Pt 1, 2006. 4190: p. 117-125.

274

355. Pizurica, A., W. Philips, I. Lemahieu, and M. Acheroy, A versatile wavelet domain noise filtration technique for medical imaging. IEEE Trans Med Imaging, 2003. 22(3): p. 323-31.

356. Parker, G.J., J.A. Schnabel, M.R. Symms, D.J. Werring, and G.J. Barker, Nonlinear smoothing for reduction of systematic and random errors in diffusion tensor imaging. J Magn Reson Imaging, 2000. 11(6): p. 702-10.

357. Chen, B. and E.W. Hsu, Noise removal in magnetic resonance diffusion tensor imaging. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2005. 54(2): p. 393-401.

358. Castano-Moraga, C.A., C. Lenglet, R. Deriche, and J. Ruiz-Alzola, A Riemannian approach to anisotropic filtering of tensor fields. Signal Process, 2007. 87(2): p. 263-276.

359. McGraw, T., B.C. Vemuri, Y. Chen, M. Rao, and T. Mareci, DT-MRI denoising and neuronal fiber tracking. Med Image Anal, 2004. 8(2): p. 95-111.

360. Bai, H., Y. Gao, S. Wang, and L. Luo, A robust diffusion tensor estimation method for DTI. Journal of Computer Research and Development, 2008. 45: p. 1232-1238.

361. Liu, M., B.C. Vemuri, and R. Deriche, A robust variational approach for simultaneous smoothing and estimation of DTI. Neuroimage, 2013. 67: p. 33- 41.

362. Pennec, X., P. Fillard, and N. Ayache, A Riemannian framework for tensor computing. Int J Comput Vision, 2006. 66(1): p. 41-66.

275

363. Fillard, P., X. Pennec, V. Arsigny, and N. Ayache, Clinical DT-MRI estimation, smoothing, and fiber tracking with log-Euclidean metrics. IEEE Trans Med Imaging, 2007. 26(11): p. 1472-82.

364. Lin, L.I., A Concordance Correlation-Coefficient to Evaluate Reproducibility. Biometrics, 1989. 45(1): p. 255-268.

365. Bland, J.M. and D.G. Altman, Statistical Methods for Assessing Agreement between Two Methods of Clinical Measurement. Lancet, 1986. 1(8476): p. 307-310.

366. Kocica, M.J., A.F. Corno, F. Carreras-Costa, M. Ballester-Rodes, M.C. Moghbel, C.N.C. Cueva, et al.;, The helical ventricular myocardial band: global, three- dimensional, functional architecture of the ventricular myocardium. Eur J Cardio-Thorac, 2006. 29: p. S21-S40.

367. Ross, D.N., Torrent-Guasp's anatomical legacy. Eur J Cardiothorac Surg, 2006. 29 Suppl 1: p. S18-20.

368. Jones, D.K., The effect of gradient sampling schemes on measures derived from diffusion tensor MRI: a Monte Carlo study. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2004. 51(4): p. 807-15.

369. Lau, A.Z., E.M. Tunnicliffe, R. Frost, P.J. Koopmans, D.J. Tyler, and M.D. Robson, Accelerated human cardiac diffusion tensor imaging using simultaneous multislice imaging. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2015. 73(3): p. 995-1004.

370. Nguyen, C., Z. Fan, B. Sharif, Y. He, R. Dharmakumar, D.S. Berman, et al.;, In vivo three-dimensional high resolution cardiac diffusion-weighted MRI: a

276

motion compensated diffusion-prepared balanced steady-state free precession approach. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2014. 72(5): p. 1257-67.

371. Nielles-Vallespin, S., C. Mekkaoui, P. Gatehouse, T.G. Reese, J. Keegan, P.F. Ferreira, et al.;, In vivo diffusion tensor MRI of the human heart: reproducibility of breath-hold and navigator-based approaches. Magnetic resonance in medicine : official journal of the Society of Magnetic Resonance in Medicine / Society of Magnetic Resonance in Medicine, 2013. 70(2): p. 454-65.

372. Smerup, M., P. Agger, E.A. Nielsen, S. Ringgaard, M. Pedersen, P. Niederer, et al.;, Regional and epi- to endocardial differences in transmural angles of left ventricular cardiomyocytes measured in ex vivo pig hearts: functional implications. Anat Rec (Hoboken), 2013. 296(11): p. 1724-34.

373. Costa, K.D., J.W. Holmes, and A.D. McCulloch, Modelling cardiac mechanical properties in three dimensions. Philos T Roy Soc A, 2001. 359(1783): p. 1233- 1250.

374. Roger, V.L., A.S. Go, D.M. Lloyd-Jones, E.J. Benjamin, J.D. Berry, W.B. Borden, et al.;, Heart disease and stroke statistics--2012 update: a report from the American Heart Association. Circulation, 2012. 125(1): p. e2-e220.

375. Rosano, G.M., M. Fini, G. Caminiti, and G. Barbaro, Cardiac metabolism in myocardial ischemia. Curr Pharm Des, 2008. 14(25): p. 2551-62.

376. Chang, S.A., S.C. Lee, Y.H. Choe, H.J. Hahn, S.Y. Jang, S.J. Park, et al.;, Effects of hypertrophy and fibrosis on regional and global functional heterogeneity in hypertrophic cardiomyopathy. Int J Cardiovasc Imaging, 2012.

277

377. Westermann, D., M. Kasner, P. Steendijk, F. Spillmann, A. Riad, K. Weitmann, et al.;, Role of left ventricular stiffness in heart failure with normal ejection fraction. Circulation, 2008. 117(16): p. 2051-60.

378. Paulus, W.J. and J.J.M. van Ballegoij, Treatment of Heart Failure With Normal Ejection Fraction An Inconvenient Truth! J Am Coll Cardiol, 2010. 55(6): p. 526-537.

379. Kitzman, D.W., Diastolic dysfunction: one piece of the heart failure with normal ejection fraction puzzle. Circulation, 2008. 117(16): p. 2044-6.

380. Kass, D.A., J.G. Bronzwaer, and W.J. Paulus, What mechanisms underlie diastolic dysfunction in heart failure? Circ Res, 2004. 94(12): p. 1533-42.

381. Koura, T., M. Hara, S. Takeuchi, K. Ota, Y. Okada, S. Miyoshi, et al.;, Anisotropic conduction properties in canine atria analyzed by high- resolution optical mapping: preferential direction of conduction block changes from longitudinal to transverse with increasing age. Circulation, 2002. 105(17): p. 2092-8.

382. Cooper, L.L., K.E. Odening, M.S. Hwang, L. Chaves, L. Schofield, C.A. Taylor, et al.;, Electromechanical and structural alterations in the aging rabbit heart and aorta. Am J Physiol Heart Circ Physiol, 2012. 302(8): p. H1625-35.

383. Aguado-Sierra, J., A. Krishnamurthy, C. Villongco, J. Chuang, E. Howard, M.J. Gonzales, et al.;, Patient-specific modeling of dyssynchronous heart failure: A case study. Prog Biophys Mol Bio, 2011. 107(1): p. 147-155.

384. Wang, V.Y., A.J. Wilson, G.P. Sands, A.A. Young, I.J. LeGrice, and M.P. Nash, Microstructural Remodelling and Mechanics of Hypertensive Heart Disease. 8th International Conference of the Functional Imaging and Modeling of the Heart, Maastricht, The Netherlands, 2015.

278

385. Thirion, J.P., Image matching as a diffusion process: an analogy with Maxwell's demons. Med Image Anal, 1998. 2(3): p. 243-60.

386. Pennec, X., P. Cachier, and N. Ayache, Understanding the "Demon's Algorithm": 3D non-rigid registration by gradient descent. Lect Notes Comput Sc, 1999. 1679: p. 597-605.

387. Wang, H., L. Dong, J. O'Daniel, R. Mohan, A.S. Garden, K.K. Ang, et al.;, Validation of an accelerated 'demons' algorithm for deformable image registration in radiation therapy. Phys Med Biol, 2005. 50(12): p. 2887-905.

388. Vercauteren, T., X. Pennec, A. Perchant, and N. Ayache, Non-parametric diffeomorphic image registration with the demons algorithm. Med Image Comput Comput Assist Interv, 2007. 10(Pt 2): p. 319-26.

389. Vercauteren, T., X. Pennec, A. Perchant, and N. Ayache, Diffeomorphic demons: efficient non-parametric image registration. Neuroimage, 2009. 45(1 Suppl): p. S61-72.

390. Lombaert, H., L. Grady, X. Pennec, N. Ayache, and F. Cheriet, Spectral Demons– Image Registration via Global Spectral Correspondence, in Computer Vision- ECCV 20122012, Springer Berlin Heidelberg.

391. Kroon, D.J. and C.H. Slump, Mri Modalitiy Transformation in Demon Registration. 2009 Ieee International Symposium on Biomedical Imaging: From Nano to Macro, Vols 1 and 2, 2009: p. 963-966.

392. Arfken, G.B., Mathematical methods for physicists. 2d ed1970, New York,: Academic Press. xx, 815 p.

279