DEVELOPMENT OF A PREDICTIVE FRAMEWORK

DEVELOPMENT OF A PREDICTIVE FRAMEWORK TO FORECAST VENOUS STENOSIS

BY S. M. JAVID MAHMOUDZADEH AKHERAT

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mechanical and Aerospace Engineering in the Graduate College of the Illinois Institute of Technology

Approved Advisor

Chicago, Illinois December 2016

© Copyright by S. M. JAVID MAHMOUDZADEH AKHERAT December 2016

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ACKNOWLEDGMENT To my mother and sister, the angels in my life. The author would like to thank the adviser of this research, Dr. Kevin W. Cassel, from the Mechanical, Materials, and Aerospace Engineering Department of the Illinois Institute of Technology. I would also like to express my sincerest appreciations to Dr. Mohammad Dadkhah Tehrani from Illinois Institute of Technology and Dr. Xiaoping Qian from University of Wisconsin Madison, who provided significant insight on the shape optimization and hypothesis verification. I also thank Dr. Alan Dardik from Yale School of Medicine for the scientific knowledge he provided. Research reported in this publication is supported by the National Institute Of Diabetes And Digestive And Kidney Diseases of the National Institutes of Health under Award Number R01DK090769. The content is solely the responsibility of the author and does not necessarily represent the official views of the National Institutes of Health. The trial was conducted with good clinical practice and the Declaration of Helsinki and was registered at ClinicalTrials.gov (NCT 01693263) August 8, 2012. The study protocol was approved by the Institutional Review Board from the University of Chicago (Protocol number: 11- 0269) on August 10, 2011.

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TABLE OF CONTENTS Page ACKNOWLEDGEMENT . . . . . . . . . . . . . . . . . . . . . . . . .

iii

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . .

v

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

LIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . .

xi

ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

xii

CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . .

1

1.1. Background & Significance . . . . . . . . . . . . . . . . 1.2. Neointimal Hyperplasia . . . . . . . . . . . . . . . . . .

1 3

2. THE PROPOSED METHOD . . . . . . . . . . . . . . . . .

15

2.1. Three Dimensionality, Pulsatility, & Non-Newtonian Effects 2.2. The Proposed CFD & Shape Optimization Model . . . . . 2.3. CFD & Shape Optimization in the Literature . . . . . . .

16 33 45

3. RESULTS . . . . . . . . . . . . . . . . . . . . . . . . . . .

50

3.1. 3.2. 3.3. 3.4. 3.5. 3.6. 3.7.

. . . . . . .

50 52 61 72 75 80 84

4. DISCUSSIONS AND CONCLUSIONS . . . . . . . . . . . . .

88

4.1. Important Remarks . . . . . . . . . . . . . . . . . . . . 4.2. Future Work & Recommendations . . . . . . . . . . . . .

88 91

APPENDIX

Shape Parametrization Validation . . . . . . . . . . . Hypothesis Verification . . . . . . . . . . . . . . . . Discussions on Objective Functional . . . . . . . . . . Patient-Specific Bifurcated Venous Branches . . . . . . Patient-Specific Three-Dimensional Shape Optimization Prediction of the Time of Failure . . . . . . . . . . . Successful Dialysis Accesses . . . . . . . . . . . . . .

. . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

96

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LIST OF TABLES Table

Page

2.1

Patient-specific Quemada HRP for subject 27 at TM. . . . . . . .

24

2.2

Patient-specific Quemada HRP for subject 12 at TM. . . . . . . .

25

2.3

Physiological ranges of WSS in the literature [82, 12]. . . . . . . .

34

2.4

Parametrization schemes for shape optimization. . . . . . . . . . .

41

3.1

Shape parametrization schemes and the decrease in objective functional they provided in our patient-specific test case. . . . . . . . .

55

Patient-specific inlet Velocity read from Doppler measurements, blood viscosity from viscometry tests of blood samples drawn, and inlet venous diameters read from venogram for subjects 12, 32, 4, 128, and 44 at TM. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

69

Demographic information of eight patients who completed the study. The first four patients successfully maintained dialysis access, while the last four developed evident CAS and failed the treatment. Demographic information are inconclusive as to why the first 4 patient did not develop CAS. F: Female, M: Male, AA: African American, C: Caucasian . . . . . . . . . . . . . . . . . . . . . . . . . . . .

87

3.2

3.3

v

LIST OF FIGURES Figure 1.1

1.2

1.3

1.4

2.1 2.2 2.3 2.4 2.5 2.6 2.7

Page An example of protocol venogram showing the cephalic vein for subject 128 at time of maturation post surgical (a). An evident stenosis and excessive NH developed at the time of failure in the cephalic arch of subject 128, 24 months later (b). The blood flow is from right to left. . . . . . . . . . . . . . . . . . . . . . . . . . . .

4

Diagram of vessel wall with neointimal hyperplasia. The vessel wall is composed of three main layers, two elastic lamina, and the endothelium. Courtesy of Dr. Alan Dardik and Lynn Model, Yale School of Medicine [34]. . . . . . . . . . . . . . . . . . . . . .

6

Vessel wall constituents. A mixture of amorphous elastin, collagen fibers, and smooth muscle cells. Taken from the work of Figueroa et. al. with permission [25]. . . . . . . . . . . . . . . . . . . .

6

Cross section of vein with excessive NH, left group: healthy, right group: NH triggered by vein-graft implantation. L: Lumen A: Adventitia M: Media H: Hyplerplasia. Notice the narrowed lumen and the evolved hyperplastic red-tissue that has formed. Courtesy of Dr. Davies and Dr. Hagen of Duke University Medical Center [20]. Venograms are from a human subject from this study. Patient number 12 at time of maturation (upper left) and at failure (upper right), correlated to elucidate venous wall thickening. . . . . . . . . . .

9

Reconstructed cephalic vein geometry for subject 27 at TM. Venogram (top), 2D (middle), and the 3D geometry (bottom). . . . . . . .

17

Reconstructed cephalic vein geometry for subject 12 at TM. Venogram (top) and the 3D geometry (bottom). . . . . . . . . . . . . . .

18

Generated cephalic vein finite element mesh grid for subject 27 at TM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

19

Doppler-measured inlet cardiac pulse waveform for subject 12 at TM, measured by the interventional radiologist at the OR. . . . .

22

Quemada model fitted to viscometry data of subject 27 at TM. R2 = 0.999929. . . . . . . . . . . . . . . . . . . . . . . . . .

23

Quemada model fitted to viscometry data of subject 12 at TM. R2 = 0.999964. . . . . . . . . . . . . . . . . . . . . . . . . .

24

Streamlines at the last cardiac cycle of the simulation, t/tp = 1 for subject 27. The colors represent velocity magnitude. . . . . . . .

26

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2.8

Cross-sectional velocity contours superimposed on velocity magnitude pseudo-color plots at three different locations for three simulations. See figure 2.7 for axial locations. . . . . . . . . . . . . . .

27

Streamlines at the 6th half cycle time t/tp = 0.5 for subject 12. A recirculation zone close to the inlet in the Newtonian flow is absent in the two non-Newtonian counterparts. . . . . . . . . . . . . .

28

2.10 Critical TAWSS for subject 27 at t/tp = 1 of the 6th cycle. Red zones mark the locations where TWASS has dropped below 0.076 [Pa]. Newtonian flow exhibits a slightly larger red zone. . . . . .

29

2.11 Instantaneous WSS for subject 12 at t/tp = 0.5. Newtonian flow shows a slightly higher instantaneous WSS at the locations indicated with arrows. . . . . . . . . . . . . . . . . . . . . . . . . . .

30

2.12 Strong correlation between percent low WSS and percent low TAWSS for 22 patient-specific numerical domains (p < 0.001), taken from [33].

32

2.13 Data from 12 random patients’ cephalic vein physiological WSS distribution before the manipulative surgical creation of AVF [33]. . .

35

2.14 Streamfunction plots superimposed on WSS distribution at TM for subject number 12. Thick red lines in (a) illustrate the locations where the WSS drops below the lower threshold value (0.076 [Pa]), while thick green lines in (b) show the locations where the WSS is higher than the upper threshold value of 0.76 [Pa]. Both of these regions are outside of the physiologic WSS distribution range and hence, will trigger adaptive responses. . . . . . . . . . . . . . .

38

2.15 Shape optimization coupled with CFD flow chart.

. . . . . . . .

44

2.16 Two-dimensional numerical grid used for CFD-shape optimization simulations of subject 12 with 18800 domain elements and 866 boundary elements. . . . . . . . . . . . . . . . . . . . . . . . . . .

46

2.9

3.1

3.2

Shape parametrization strategy for the optimization module. Zero nodal displacement is enforced at the upper and lower walls end points by setting the corresponding qi to zero, while zero displacement is defined at the inlet and outlet edges. . . . . . . . . . .

53

Shape optimization performed for subject number 12 using: (a) Truncated Fourier Sines parametrization, (b) Modified Fourier Sines, (c) Hicks-Henns Bump Functions, and (d) Bernstein Basis Functions. The black frame illustrates the initial shape where the optimization started from and the pseudo-color velocity magnitude contours (m/s) show the evolved shape. . . . . . . . . . . . . .

54

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3.3

3.4

3.5

3.6

3.7

3.8

Initial patient-specific shape at TM superimposed on the predicted optimal shape. The red-zone depicts the excessive NH growth for subject 12 which results in a new luminal shape that better regulates the WSS distribution. This red-zone represents the newly generated SMC-tissue depicted in Figure 1.4 that has reduced the luminal diameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

56

WSS [Pa] versus X location [m] of the blood vessel on the upper and lower walls of patient-specific geometries for subject 12 at TM, at actual failure, and at predicted failure. Notice the regulated WSS [Pa] distribution upstream of the arch (−0.07[m] 6 x 6 0) and within the arch (−0.12[m] 6 x 6 −0.07[m]) at predicted failure compared to the WSS distribution at TM. Dashed-black line: upper wall at TM, dashed-red line: lower wall at TM, black-dotted with plus sign: upper wall at actual failure, red-dotted with plus sign: lower wall at actual failure, solid-blue line: upper wall at predicted failure, and solid-green line: lower wall at predicted failure. The blood flow is from right to left. . . . . . . . . . . . . . . . . .

58

The distribution of in-range WSS [Pa] for subject 12 at (a) TM, at (b) failure predicted by CFD coupled shape optimization, and (c) at actual patient-specific time of failure. The physiologic distribution range of WSS in the cephalic vein is 0.076 Pa 6 τw 6 0.76 Pa shown here by thick-blue lines. Optimal shape has a better in-range distribution compared to TM, and so does the actual patient-specific shape at the time of failure. Blue: 0.076 Pa 6 τw 6 0.76 Pa, Red: τw 6 0.076 Pa, Green: 0.76 Pa 6 τw . . . . . . . . . . . . . . . .

59

Transmural pressure [Pa] at (a) TM, (b) predicted failure, and (c) actual patient-specific failure mode. A pressure buildup causes hypertension within the venous system used for dialysis access, evident at both predicted failure and actual patient-specific hemodynamics.

60

Diameter [m] changes versus x location [m] of the blood vessel for subject 12. The dashed line shows diameter changes from TM to predicted failure and the solid line shows actual diameter changes in time until failure. The flow is from right to left. Notice the agreement between the actual and computational data when ∆D becomes negative i.e. the diameter has reduced locally. . . . . . .

62

Diameter [m] changes versus x location [m] of the blood vessel for subject 32. The dashed line shows diameter changes from TM to predicted failure and the solid line shows actual diameter changes in time until failure. The flow is from right to left. Notice the agreement between the actual and computational data when ∆D becomes negative i.e. the diameter has reduced locally. . . . . . .

63

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3.9

Evolution of the shape and the resultant restoration of WSS [Pa] at the time of failure for subject 12. . . . . . . . . . . . . . . . .

64

3.10 Evolution of the shape and the resultant restoration of WSS [Pa] at the time of failure for subject 4. . . . . . . . . . . . . . . . . .

65

3.11 Evolution of the shape and the resultant restoration of WSS [Pa] at the time of failure for subject 32. . . . . . . . . . . . . . . . .

66

3.12 Evolution of the shape and the resultant restoration of WSS [Pa] at the time of failure for subject 128. . . . . . . . . . . . . . . . .

67

3.13 Evolution of the shape and the resultant restoration of WSS [Pa] at the time of failure for subject 44. . . . . . . . . . . . . . . . .

68

3.14 Comparison between, (a) Marsden’s cost functional, (b), the proposed cost functional, and (c) patient-specific geometry at failure. .

71

3.15 Comparison between, (a) WSSG minimization, (b) the proposed objective functional, and (c) patient-specific geometry at failure. .

73

3.16 Maximum ∆D obtained using various different target values of WSS in the shape optimization study. The same occluded shape and max ∆D resulted from using multiple different target values from the cephalic vein’s physiologic WSS range of 0.076 to 0.76 [Pa]. . . . .

74

3.17 Venous bifurcation venogram at (a) TM and (b) at the time of failure. Subject number 119. . . . . . . . . . . . . . . . . . . . .

76

3.18 Flow field [m/s] of the bifurcated case under investigation (a) at the time of failure and (b) predicted by shape optimization and CFD.

77

3.19 WSS [Pa] distribution (a) at TM (b) at predicted failure. Blue: 0.076 Pa 6 τw 6 0.76 Pa, Red: τw 6 0.076 Pa, Green: 0.76 Pa 6 τw .

78

3.20 Three-dimensional CFD coupled with shape optimization.

. . . .

81

3.21 The three-dimensional WSS distribution at (a) TM, at (b) failure predicted by CFD coupled shape optimization, and (c) at actual patient-specific time of failure. Blue: 0.076 Pa 6 τw 6 0.76 Pa, Red: τw 6 0.076 Pa, Green: 0.76 Pa 6 τw . . . . . . . . . . . . .

82

3.22 Gaussian normal distribution of four time-of-failure patient packets from our 37 ESRD patient cohort. . . . . . . . . . . . . . . . .

83

3.23 Subject 57 at (a) TM, (b) 12 months, and (c) 24 months post dialysis access creation. A constant inlet velocity of 30 cm s was recored for this patient throughout the treatment. . . . . . . . . . . . . . .

85

ix

4.1

4.2

Flowchart of the proposed framework. This workflow enables prediction of AVF failure and patient-specific treatment planning and interventional decision making. . . . . . . . . . . . . . . . . .

92

Time of failure plotted versus average inlet blood flow velocity prior to failure for patients who developed NH and failed the dialysis treatment by 36, 24, and 12 months post access surgery. Notice the adverse strong correlation of increased inlet flow and the quicker time of failure. . . . . . . . . . . . . . . . . . . . . . . . . .

94

x

LIST OF SYMBOLS Symbol

Definition

µ

Blood Viscosity

µF

Plasma Viscosity

γ˙

Shear Rate

Hct, φ

Hematocrit

τ

Shear Stress

DII ρ

Second Invariant of Strain Rate Tensor Blood Density

WSS, τw

Wall Shear Stress

TAWSS

Time-Averaged Wall Shear Stress

s

Geometrical Edge Parameter

qi

Optimization Parameters

di

Scale Factors

τy

Yield Stress

tp

Cardiac Cycle Period

J

Optimization Objective Functional

Bn (s)

Bernstein Basis Function

k0

Lower Limit Viscosity

k∞

Higher Limit Viscosity

∆D

Venous Diameter Changes

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ABSTRACT The end stage renal disease (ESRD) patient population is growing at a troubling rate, calling for a focused attention to investigate the chronic kidney diseases, their characteristics and our lines of defense against them. One major medical treatment for ESRD patients is hemodialysis which is facilitated through vascular access (VA). The vascular access of particular interest in this investigation as well as the medical community is the brachiocephalic fistula (BCF), which is a form of arteriovenous fistula (AVF), created surgically by connecting the brachial artery and the cephalic vein. It is commonly used for elderly patients and for those with poor circulation systems, e.g. diabetics. The extreme hemodynamic environment that BCF creates triggers the onset of neointimal hyperplasia (NH) in most of these patients which leads to access failure and a high morbidity and mortality rate. This process happens in a matter of months, providing an excellent translational medicine experimental stage to observe as the vessel walls react and adapt to the new hemodynamically violent conditions. Through extensive analysis of the venous deformation and subsequent hemodynamics of a patient cohort of 160, a prognosticative framework to predict the vein deformation in these patients prior to the occurrence of the failure has been developed. The obtained results are the consequence of the integration of clinical practice and computational science. The proposed method was first based on our hypothesis which roots the NH in non-physiological wall shear stresses (WSS), and was then improved and modified using rigorous optimization and numerical approaches. This finding is essential to the modification of the current VA techniques to increase the patency of the AVFs, to prevent the diminishing functionality of the access, and to increase the life expectancy of ESRD patients. Moreover, this finding will further assist us in comprehension of the human vasculature growth and remodeling (G&R) through bypassing the analysis of unknown biological phenomena, as it is achieved purely by juxtaposing well-defined mathematical, physical, and medical concepts. xii

1

CHAPTER 1 INTRODUCTION 1.1 Background & Significance “So should we venture on the study of every kind of creature without horror, for each and all will reveal something that is natural, and therefore beautiful.” – Charles Singer [75]

Chronic kidney failure is a rapidly growing physiological condition in the western countries, which in most cases develops to result in total kidney failure. At failure stage, the patients are called end stage renal disease patients. As off 2011, the number of patients being treated for ESRD globally was estimated to be 2,786,000 with an annual global growth rate of 6% to 7% [28]. Of these 2,786,000 ESRD patients, approximately 2,164,000 were undergoing hemodialysis treatment. From a global view, most dialysis patients can be allocated to three major geographical regions: the USA, the European Union and Japan. Around 48% of all dialysis patients are treated in these 29 countries. Other studies put the toll in United States around 700,000 as of 2015, with a 3.5 factor among the African American community [81]. About 73.6 million Americans, or one in every three people, have high blood pressure, which is the second leading cause of chronic kidney disease, painting a not very bright future for the country’s health and medical care system if the current growth trend continues. A lack of in-depth knowledge on this progressive disease as well as the art of clinical intervention and treatment management is vivid. The current method for curing ESRD is kidney transplantation. The method requires a donor and usually a very long wait time to acquire a donor with matching hematological characteristics. Consequently, patients are kept on hemodialysis while

2 on a wait list to receive the kidney transplant. Most patients experience multiple months up to a couple of years on hemodialysis. It has been estimated that 13 patients die daily waiting to receive a kidney transplant in the US alone. The hemodialysis treatment is facilitated with various forms of Vascular Access (VA). VAs are surgical connections between arteries and veins that are created by a vascular surgeon in the operation room. The unfortunate fact is that there is a high failure rate associated with VA and a resultant high mortality rate. The VA preferred for hemodialysis is arteriovenous fistula (AVF) due to its relatively low infection and thrombosis reports1 . There are two type of AVF available, brachiocephalic fistula (BCF) and radiocephalic fistula (RCF). The type of AVF with the most favorable outcomes is the RCF. However, in elderly patients with underlying vascular disease, particularly diabetics, this access often fails to mature [61, 69]. If the RCF is not viable, BCF is the next recommended option. The BCF is a high flow conduit in which the cephalic vein is joined to the brachial artery, typically in an end-to-side or side-to-side arrangement. The resulting hemodynamics in the vein are extreme. In part due to the hight flows, the BCF has an average functional duration of only 3.6 years. This is in contrast to RCF, which often exceed 5 years [69]. Two leading causes of BCF dysfunction and failure are stenosis in the curved arch segment of the cephalic vein near its junction with the axillary vein, cf. figure 1.1 and secondly, failure to mature altogether or primary nonfunction 2 . Stenosis in the mentioned location is termed cephalic arch stenosis (CAS). In fact, it is well known 1

Other types of hemodialysis access, such as PTFE, have a surprising failure rate of 50% to 77%. Catheters are an immediate dialysis access that should be avoided at all costs due to an extremely high thrombotic incidence rate [70]. PTFE failure is also due to intimal thickening. 2

Maturation failure is observed to reach 50% of the population in some studies according to [70]. In this study’s cohort, however, this number is significantly lower at 26%.

3 that the universal response of a vein when introduced to (in the case of VAs) or inserted into (in the case of vein-grafts) the arterial circulation is the development of neointimal hyperplasia [20, 21, 17] which then develops to become a stenotic lesion. CAS is difficult to treat, often requiring repeated costly interventional procedures or surgical revision to maintain access patency. Other failure locations observed in fistulae include the anastomosis (artery-vein connection) region and in the outflow vein (immediately proximal to anastomosis). Due to its critical importance in vascular access, researchers are working to improve our understanding of the causes of fistula failure, see [68, 42, 43, 31, 32, 74, 11]. These studies find that both low and high WSS play a critical role in failure of arteriovenous fistulae. According to Hammes et. al. [31] CAS can lead to high venous pressure and fatal thrombotic incidents. Low WSS, which can arise from very high flow rates in curved vessels, is thought to be a major cause of NH. Existence of regions with NH point to the body’s effort to increase the WSS back to a physiologically acceptable range [45, 77]. Early detection of potential CAS sites can vastly increase the treatment and intervention options to mitigate the further development and consequences of CAS. In this study, the response of the cephalic vein’s geometry to the extreme hemodynamic environment established by the creation of a fistula is characterized with the aim to elucidate the mechanism of VA failure. Thereafter, based on these results, a novel framework is proposed that can predict the onset and development of NH prior to its occurrence. For the sake of clarity, a cellular level discussion of NH and its features and effects is presented in the following section. 1.2 Neointimal Hyperplasia 1.2.1 Histology.

Blood vessel walls consist of three layers: intima, media, and

adventitia (see figures 1.2 and 1.3). The innermost layer, intimal layer (tunica intima/interna), is the one that is lined with endothelial cells in direct contact with the

4

(a)

(b)

Figure 1.1. An example of protocol venogram showing the cephalic vein for subject 128 at time of maturation post surgical (a). An evident stenosis and excessive NH developed at the time of failure in the cephalic arch of subject 128, 24 months later (b). The blood flow is from right to left.

5 flow of blood. Endothelial cells are covered by a layer called Internal Elastic Lamina (IEL) which consists of mesh-like type IV collagen fibers and adhesion molecules, rich in elastin and collagen. Endothelial cells have a strategic position and are a biologically sensitive entity, i.e. they react to chemical, mechanical, and humoral stimuli. In response to environmental factors, they produce vasoactive substances that dilates or constricts the passageway of blood. In parallel, they can produce growth-inhibiting factors as well. The middle layer, tunica media, mainly consists of abundant circular Smooth Muscle Cells (SMC) or Myocytes which are embedded in another elastic layer called External Elastic Lamina (EEL). According to the authors of [77, 34], the content of SMC in tunica media varies depending on the location of the vessel, the closer vasculature is to the pulsating heart the more is the content of elastin and the farther away the more is the one of SMC. The outer most layer of the vessel, tunica adventitia/exterana, is mostly comprised of fibroblasts and type I collagen, loose connective tissue and irregularly arranged elastin. The vein wall mimics the same architecture as in arteries with the difference that the media and adventitia are markedly larger in arteries to support higher flow rate-induced waves and fluid pressure. NH is a term referring to the formation of a thickened arterial/venous intimal layer which is followed by occlusion of the vessel (figures 1.1 and 1.4). It is a condition which follows post-surgery trauma, stenting, angioplasty, changes of WSS or any similar insult to the vessel walls, as a result of which, the thickening of the vessel wall and continuous (sometimes ever-changing) wall deformation and hemodynamicdriven adaptation occurs. According to the medical community, the term neointimal hyperplasia is used to differentiate from the uninjured arterial or venous endothelium [34]. Lynn and Dardik (ibid.) believe that the study of IH stems back to 1850s independent investigations by Rokitansky and Virchow on atherosclerosis (Davies claims the first study of intimal hyperplasia dates back to 1906). In 1970s, however, the SMC origin of NH was elucidated from animal experimentations which distinguished

6

Figure 1.2. Diagram of vessel wall with neointimal hyperplasia. The vessel wall is composed of three main layers, two elastic lamina, and the endothelium. Courtesy of Dr. Alan Dardik and Lynn Model, Yale School of Medicine [34].

Figure 1.3. Vessel wall constituents. A mixture of amorphous elastin, collagen fibers, and smooth muscle cells. Taken from the work of Figueroa et. al. with permission [25].

7 NH from atherosclerosis thereafter (cf. [10]). In later studies, scientists like Imperato [40] postulated that the process of “fibrous proliferation” occurs at areas of “very high or very low flow ”, while there were others with parallel investigations, calling the phenomenon arterialization of the vein grafts or fibro-cellular thickening. Either way, NH exhibits fibroblast and SMC agglomeration in the intimal layer of both arterial and venous systems. Fibroblasts synthesize ECM and collagen, delineating the collagen abundance in NH regions. Understanding mechanism behind NH is imperative as it has been reported that 30% to 50% of vein grafts, vascular accesses, and angioplasty procedures have been eventually complicated by NH [34]. In the current clinical-computational investigation, almost 90% of the human subjects who received BCF for dialysis experienced CAS and access failure due to the excessive NH (33 subjects out of 37). Angioplasty, endarterectomy, and other endovascular surgeries performed to resurrect the access have been reported to have an immediate success rate of 95%. However, even with most experienced hands, according to Davies [20], restenosis occurs in 30 to 50 percent in angioplasty operations only within the first year post surgery. There are a lot of other studies which put all patients in the process of developing NH and restenosis incidence post surgery, but with different progression rates. On an important note, we feel the necessity to clarify that there are marked similarities in pathophysiology of venous and arterial NH. The merit in the study of venous NH comes when the similarity between the etiology of venous NH and arterial atherosclerosis is deemed, particularly in renal failure patients 3 . Supporting the 3

According to Fung ([86] p.264 and p.295), veins contain a lower amount of elastin, exhibiting a lower elastic modulus having abundance of collagen. This might explain the predisposition of venous systems to IH/NH development and not other form of vascular incidents. These constituents are each observed separately with a continuum mechanics modus operandi. Thereafter, the forces and stresses that flow of blood exerts on the vessel wall, and hence on each constituent, is quantified.

8 claims of Dardik [34] and Wali et. al. [83], histology analysis of our colleagues in University of Chicago Medical School Nephrology Section have revealed accumulation of SMC and inflammatory cell infiltration, accumulation of collagen, and loss of IEL and endothelium. Their results authenticate the statements of Chaudhury et. al. in [70] that stenosed native AVF (whether wrist or elbow) exhibit venous neointimal hyperplasia composed of smooth muscle cells with expression of cytokines and endothelin etc. Also, uremia which is seen in many kidney failure patients has been shown to exacerbate endothelial dysfunction, predisposing the patient to venous hyperplastic intimal deformation [34, 70]. Additionally, another foray of the investigators of the current study to elucidate the veins’ topographical changes also confirmed that veins adhere to the same WSS and pathophysiological postulations suggested for arteries, as far as adaptation, dilation, and remodeling is concerned [12]. Therefore, the study of NH in the ESRD cohort under observation here will benefit the medical and biomedical community with stenosis/re-stenosis forecasting knowledge in both venous and arterial systems. It is also worth the readers attention to appreciate the pressing need for prognosticative approaches towards NH post AVF, as the stenting, angioplasty, and other invasive interventional treatments will injure endothelia and might expose SMC to the blood stream which would, again, circle back to NH response and restenosis.

9

Figure 1.4. Cross section of vein with excessive NH, left group: healthy, right group: NH triggered by vein-graft implantation. L: Lumen A: Adventitia M: Media H: Hyplerplasia. Notice the narrowed lumen and the evolved hyperplastic red-tissue that has formed. Courtesy of Dr. Davies and Dr. Hagen of Duke University Medical Center [20]. Venograms are from a human subject from this study. Patient number 12 at time of maturation (upper left) and at failure (upper right), correlated to elucidate venous wall thickening.

10 1.2.2

Pathobiology and Pathophysiology.

It is hypothesized that NH is

a response to abnormal or injurious conditions in the venous or arterial systems. However, it is unclear if this adaptive response is a normal physiological response or whether it is an abnormal pathophysiological response [34]. Davies and Hagen in [20] categorized the NH into Hyperacute, Acute, and Chronic, which happen on a time scale of multiple hours, weeks, or months, respectively. The type of NH lesion detected in ESRD patients is mostly chronic. Also, the distribution pattern of neointimal hyperplastic lesions might diffuse throughout the whole vessel, or can be focal to the anastomosis or specific regions in the vein. Again, both distributed and focal patterns are observed in the ESRD patients. Figure 1.1 depicts a distributedtype NH in one of our patients. During the process of harvesting the vein for re-implantation in the arterial system in the vein-graft operation, when the surgeon performs the dilation to check for leaks and side branches, and also the disruption of the adventitia blood supply during harvest from its bed, all cause injury to the vein which later on will potentially result in NH. Additionally, after vein-graft implantation and the creation of anastomosis, the newly created anastomotic site inherently generates turbulent-like varying flows, similar to the native branch, predisposing the new anastomosis to NH. “Distal bypass to crural vessels often have extremely poor runoff with high resistance, leading to turbulence, low shear stress, and increased propensity to NIH [neointimal hyperplasia]. Conversely, very high flow, such as that found in AVF or graft, is not laminar but turbulent, also creating areas of varying shear and propensity to NIH. In grafts used for hemodialysis access, there are also repeated injuries from the needle-sticks to access the graft three times a week.” – [34]

The author agrees with the statements of Lynn and Dardik, but also would add that low flow rates and laminar flow characteristics would as well create the so called “low shear ” susceptible regions, given our experience with a large patient

11 cohort with a surprising variety in flow characteristics. Nevertheless, the triggering pathophysiological factors of NH can be categorized as [11, 12, 36, 77, 37, 34, 62, 70, 51, 35, 46]:

• Injury – Due to mechanical trauma at the time of surgery4 or dialysis needle – Denudation of endothelium (τw ≥ 30 Pa) • Inflammation • Hemodynamically exerted low wall shear stresses

While the processes that regulate the NH development are under investigation on a molecular level, it is known that NH is a summation of complex cell proliferation, migration, and ECM deposition, in general. The proliferation/migration of SMC is thought to require a phenotypic modulation [62, 34]. Post injury WSS changes endows the SMC in the media to gain the mobility to migrate from the media into the intima, where they proliferate and synthesize contractile proteins (synthetic phenotype). These are, in fact, the active type of smooth muscle that are seen in the histology observation of progressed NH lesions [34, 62, 83, 70, 71, 20, 52, 26, 84]. Approximately 30 percent of the medial SMCs become “activated” or “proliferative” in this scenario, in the sense that they start DNA synthesis and begin to replicate. In addition, Platelett-Derived Growth Factors (PDGF), Epidermal Growth Factor (EGF), and Fibroblast Growth Factor (FGF) are found in SMC and endothelia which are implicated by SMC phenotype switch. The point is, the origin of the synthetic SMC 4

VA creation surgery for stenosis and angioplasty/stenting surgery for restenosis, all can causes damage to endothelia. The damaged to the tissue can go as deep as SMC at which point the media gets exposed to blood stream.

12 in NH sites is debated and unknown, that is excluding the cellular signaling pathways (signal transduction) such as RAS-MAPK and PI3K-AKTt which are naturally very intricate phenomena. It is known, however, that once the SMCs switch phenotype from contractile to synthetic, they become migrative and proliferative, and hence, large number of SMC in the cell culture has become a universal indicative factor of NH regardless of the origin. There are also numerous other factors acting in concert modulating the migration of cells as well as production and deposition of ECM which are, if known, far outside of the scope of this endeavour, for which the reader is recommended to consult the aforementioned medical literature. There is a pressing need for quantification of these information. Humphrey in [39], section 9.5.3, also states the lack of rigorous mathematical modeling of wall adaptations post injury which correlates kinetics and mechanics. To sum up, all that is known to us about NH is merely:

1. Agglomeration of SMC via migration and proliferation (increase in intimal cell population) 2. Accumulation of ECM and collagen fibers 3. Loss of elastin in IEL and possibly EEL

However, we are yet to quantify and determine the constitutive relations of production and removal of the constituents which would capture exact functional behavior of collagen turnover etc. as well as the comprehension of etiology of NH and the intercellular/intracellular cycle of events that lead to its progression. Human histological data, specifically, for renal failure patients venous NH is drastically rare and unreliable5 . This lack of information makes it difficult to produce first-principle 5

Dr. Alan Dardik, Yale University School of Medicine, personal communication, October 6th, 2015.

13 constitutive equations that capture the stress-mediated behavior of constituents in time in terms of production, removal, and turnover. Taylor and Humphrey [77] and many others ([38], [72], etc.) mentioned that mechanical loading on the blood vessel’s wall can induce changes in gene expression. This change in gene expression is associated with cellular and sub-cellular activity. They trigger signals in cells that initiate proliferation, migration, differentiation, synthesis, apoptosis/cell suicide, etc. that sum up to carry the tasks of adaptation and development during maturity and maladaptive consequences during vascular disease onset and progression. Multiple theories have been developed to describe these subcellular biochemical activities, none of which is widely accepted and agreed upon. What is clearly known and accepted is best articulated by the scientist in [77]. We quote: “Overall wall thickness tends to be regulated so as to maintain the circumferential wall stress near a target value, hence motivating the study of wall mechanics whereas smooth muscle is primarily responsible for synthesizing matrix proteins during development, it endows the mature vessel with its ability to constrict or dilate and thereby regulate blood flow locally. Smooth muscle hyperthrophy (increase in size), hyperplasia (increase in number), apoptpsis (cell suicide), and migration each play essential roles in diseases such as aneurysm, atherosclerosis, and hypertension.” – C. A. Taylor and J. D. Humphrey

Hypertension or high blood pressure is also another well-known disease. As of 2013, 70 million Americans are estimated to have the condition (29% or every one in three) [87]. It will worsen the vulnerability to heart disease, stroke, and renal disease. During the progression of the disease, thickening of the wall due to an increase in the SMCs and Extra Cellular Matrix (ECM), specially collagen, is detected which is a manifestation of NH. This change in wall properties and geometry will instigate an intricate feedback loop, according to our hypothesis, to modify WSS, creating a more complex hemodynamically evolving system which seeks to reach a homeostatic state

14 and hence, creating more problems in the vasculature. In particular, high venous and arterial pressure is know to reduce mean WSS, which initiates the system’s response by a down-regulation of endothelia-derived vasodilators like potent nitric-oxide (NO) parallel to an up-regulation of potent vasoconstrictors like endothelin-1 (ET-1 is promoter of SMCs proliferation and synthesis of collagen fibers), adhesion molecules like ICAM-1 and VCAM-1 [77, 25, 34]. These substances and biochemical reaction not only change the current mechanical state of the system, they also influence the rate of turnover of individual constituents which is an unknown realm of cellular biology. In the following dissertation, the biological knowledge and the medical definitions of the problem stated is translated into the language of engineering and prescribed thoroughly using first principle mathematics and physics. In Chapter two, the development phase of a novel computational approach to predict the dialysis mode of failure on a patient-specific basis which is based on a physiology-rooted hypothesis is presented in fine details. Thereafter, in Chapter three, the discussion is further extended to verification of the numerical method developed as well as the validity of the obtained results compared to available real life patient-specific clinical data. Lastly in Chapter four, the application suggested for this newly developed technology and the realms for further improvements in the future are brought to readers attention.

15

CHAPTER 2 THE PROPOSED METHOD The ultimate goal in this endeavor was to develop a computational, noninvasive technology that can predict the onset of neointimal hyperplastic deformations in the ESRD dialysis patient population to further assist the clinical development of its treatment. The flow of blood is simulated using CFD, which calls for a thorough comprehension of the underlying physics of the problem that will be translated as boundary conditions, material definitions, solver configurations, etc. into the CFD module. In this chapter, an in depth discussion of the CFD module’s assumptions and definitions is presented. Thereafter, the implementation of the defined CFD module and its coupling with a shape optimization module that will shape the basis of the presented framework is explored. Over the course of five years, we have built a large database of hemodynamic, demographic, and statistical information for nearly 160 ESRD patients (37 completed the study by the end of the fifth year, consult [33]). Our patients developed maturity of vascular access 8 – 32 weeks post surgery. Maturity is reached when the vessel has dilated sufficiently and has adapted itself to the arterial blood flow that it has been newly exposed to. Thereafter, the superficial vein can be accessed with the dialysis needle to facilitate the high blood flow rate needed for hemodialysis. Time of maturation (TM) is thus the starting point of the chronic dialysis treatment. Patient-specific geometry and hemodynamic information (protocol venograms, Doppler velocity measurement, Whole Blood Viscosity (WBV), hematocrit, etc.) are our modeling inputs, which are available from our database. The implementation of the CFD module in our framework and considerations regarding boundary condition assumptions and the constitutive relations are discussed in the ensuing chapter.

16 Previously the non-Newtonian effects and the patient-specific cardiac waveforms (i.e. pulsatile or Womersley flow) were visited and the effects of the mentioned assumptions on the CFD simulations were quantified and reported [33, 6, 55, 5, 3, 53, 16, 54, 4]. Since the CFD simulation of patient-specific hemodynamics is an integral constituent of the proposed framework, the author feels the necessity to reiterate the non-Newtonian and pulsatility effects, particularly when applied to the three-dimensional patient-specific simulations as that would ultimately set the proof-of-concept basis for the proposed method. In the following, we will revisit our CFD protocol and the application of constitutive relations in pulsatile hemodynamics within the three-dimensional patient-specific domains. 2.1 Three Dimensionality, Pulsatility, & Non-Newtonian Effects Patient-specific venograms and flow rates obtained clinically are used to reconstruct the geometries and inlet velocity profiles, respectively. In addition, rheological parameters are incorporated in this investigation. In Figures 2.1 and 2.2, sample venograms are shown for subjects 27 and 12, both at TM and the generated geometries are illustrated, respectively. Intravascular Ultrasound (IVUS) or Magnetic Resonance Angiography (MRA) imaging can be used as the basis for three-dimensional geometry reconstruction, but are not widely clinically available and are not feasible for large patient cohorts like the one we studied in the last five years. Consequently, to be able to regenerate the three-dimensional CAD models, two-dimensional geometries (extracted via image processing as described in [6]) were rotated 360 degrees along their respective centerline to produce the three-dimensional geometries shown in figures 2.1 and 2.2 (see also figure 2.3 for a detailed view). The resulting three-dimensional geometries seem to represent the actual patient-specific veins with relatively fine anatomical-luminal details. COMSOL Multiphysics CFD solver and post-processor were utilized in this

17

Figure 2.1. Reconstructed cephalic vein geometry for subject 27 at TM. Venogram (top), 2D (middle), and the 3D geometry (bottom).

18

Figure 2.2. Reconstructed cephalic vein geometry for subject 12 at TM. Venogram (top) and the 3D geometry (bottom).

19

Figure 2.3. Generated cephalic vein finite element mesh grid for subject 27 at TM.

20 study. Using a Galerkin-Petrov unsteady solver, conservation of momentum and mass are solved.    T ρ (∂t u + u · ∇u) = −∇p + ∇ · µ ∇u + (∇u) + ρf,

(2.1)

∇ · u = 0,

(2.2)

in which, ρ is density, u is the fluid velocity vector, p is the pressure, µ is the apparent viscosity, which is the focus of this sub-study, and f is the summation of body forces acting on the fluid. The third term on the right-hand side is the contribution to viscous effects that arises from non-Newtonian effects. For Newtonian cases, this term is set to zero in the non-stress formulation Walls are taken to be impermeable and rigid with no-slip boundary conditions applied throughout the domain. A zero pressure Dirichlet boundary condition along with a zero traction are applied at the outlet and the unsteady simulations start from rest. Blood flow in the cephalic vein is laminar and can be taken to be almost steady under physiological condition. Post VA surgery and introduction of the arterial flow into the venous system, however, leads to pulsation becoming appreciable in the vein. Therefore, the inlet cardiac pulse waveform is taken from the patient-specific Doppler measurement. The vessel’s diameter is obtained from the venograms, which are done simultaneously with the Doppler ultrasound by an Interventional Radiologist. The Doppler-measured inlet pulse wave functions for subject 12 is depicted in figure 2.4, for example. The period of pulsation in the cephalic vein as read and interpreted by the interventional radiologist for subjects 12 and 27 are tp = 0.7s and tp = 0.91s, respectively. Computations for three-dimensional smulations are performed using a numerical grid consisting of 10 layers of boundary-layer elements, 1.2M free tetrahedral domain elements, and 216K boundary elements (figure 2.3), obtained from a mesh independence study. The unsteady solver was run for 6 complete cardiac cycles

21 for each patient-specific case considered here. The time step size of 10−4 s was found to be accurate and computationally efficient. The same patient-specific inlet cardiac waveform profile was considered for the companion non-Newtonian simulations. Newtonian viscosity is constant and is taken to be equal to the asymptotic viscosity for high shear rates. For subject 27 at TM and subject 12 at TM, this value is equal to µ = 0.00269 and µ = 0.00287 Pa.s, respectively. 2.1.1 CFD Procedure. In order to quantify the differences between CFD results based on the Newtonian assumption and implementation of non-Newtonian models, various simulations were performed according to the data of subjects 27 and 12 at TM with the Quemada and Casson models using the following approaches for viscosity implementation in CFD:

• Newtonian Simulation: The asymptotic viscosity values at high shear rates obtained from viscometry data for subject 27 and 12 at TM are used. • Non-Newtonian Simulation: The hemorheological parameters (HRP) for Quemada’s viscoelastic model [67] generated using a least-squares regression technique to the empirical rheologic data of patient-specific viscometry tests. The model directly utilizes Hct as an independent parameter for both subjects under investigation (Figures 2.5-2.6 and tables 2.1-2.2). µ (γ, ˙ φ) = µF

!−2 1 1 k0 + k∞ γ˙ r2 φ . 1− 2 1 + γ˙ 12

(2.3)

r

where µF is the solvent medium (plasma) viscosity which is a patient specific quantity but ranges very little from one patient to another. Plasma viscosity equals to an invariant value of 0.00127 [Pa.s] throughout our ESRD patient cohort. γ˙ r is the reduced shear rate equal to

γ˙ , γ˙ c

in which γ˙ c is called the critical

shear rate defined by a phenomenological kinetic model [67, 50]. In the current

22

Figure 2.4. Doppler-measured inlet cardiac pulse waveform for subject 12 at TM, measured by the interventional radiologist at the OR.

23

Figure 2.5. Quemada model fitted to viscometry data of subject 27 at TM. R2 = 0.999929. disertation, γ˙ c is taken to be equal to

U , l

which is the ratio between the inlet

velocity and the characteristic length • Non-Newtonian Simulation: Casson’s viscoplastic model [15] incorporated to capture the non-Newtonian effects. The yield stress term in the model directly utilizes Hct as an independent parameter. #2 " r  2 1/4 2 τ (φ) γ ˙ y , + µ (γ, ˙ τy (φ)) = η2 4 2 |γ| ˙

(2.4)

where τy = 0.1 (0.625Hct)3 and η = µF (1 − Hct)−2.5 . The τy facilitates the yield stress dependence in the Casson model and Hct is the red blood cell content of the patient blood sample termed technically as hematocrit. Refer to [6, 55, 5] for details on the implementation of patient-specific HRP in the CFD application.

Previously, we reported the same approach to compare various constitutive relations in 2D patient-specific domains. More details can be found in [6]. 2.1.2 CFD Results. The differences between the aforementioned Newtonian and

24

Figure 2.6. Quemada model fitted to viscometry data of subject 12 at TM. R2 = 0.999964. Table 2.1. Patient-specific Quemada HRP for subject 27 at TM. Parameter

Value

k0

3.55129

k∞

1.00834

φ

0.322

γ˙ c (Sec−1 )

204.25

non-Newtonian assumptions can be perceived through analysis of the CFD results. Results of all three simulations (Newtonian, Quemada, Casson) seem to be comparable qualitatively and the visual differences are inconspicuous. In order to spot the most conspicuous discrepancies, streamfunction plots, WSS, and time averaged wall shear stress (TAWSS) are depicted in figures 2.7 through 2.11 for both patientspecific cases studied here. A closer observation of the results can highlight some detectable differences for comparison purposes, while we reiterate that the differences between patient-specific pulsatile Newtonian and non-Newtonian three-dimensional hemodynamic CFD simulations considered here are minimal.

25

Table 2.2. Patient-specific Quemada HRP for subject 12 at TM. Parameter

Value

k0

3.48006

k∞

1.20599

φ

0.281

γ˙ c (Sec−1 )

217.33

Because of the higher viscosity at low shear rates, non-Newtonian flow is less prone to form recirculation zones near walls and eddies in general. Following the same line of reasoning, one would expect that owing to the overall increase in viscosity, the reversed flow regions occurring in a non-Newtonian flow field would be smaller in size and slower in velocity than that of a Newtonian flow. Figure 2.7 illustrates the streamlines resulting from the three simulations for subject 27. Close to the inlet and adjacent to the upper wall, a recirculation zone forms in the Newtonian simulation, which is absent in the same location of the Quemada simulation and weaker in the Casson counterpart. This effect occurs in two more indicated recirculation zones within the downstream domain, pointing to the fact that non-Newtonian and viscous effects are slightly damping the violent flow behavior brought about by geometrical peculiarity, which agrees with the findings of [27]. Figure 2.8 is shown to clarify this statement. Multiple cut-planes are created to illustrate the velocity contours within the flow at the mentioned locations. At all three cross-sectional locations x1 , x2 , and x3 , the recirculation zone present behaves differently in non-Newtonian simulations, with the jet-like centerline flow pushed to the right. The same effect is observed in figure 2.9, where a small separation region is formed close to the inlet in the Newtonian flow simulation of subject 12, which is nonexistent in the nonNewtonian counterparts. Moreover, the Newtonian simulation of subject 12 has a slightly stronger swirling motion close to the outlet region.

26

Figure 2.7. Streamlines at the last cardiac cycle of the simulation, t/tp = 1 for subject 27. The colors represent velocity magnitude.

27

Figure 2.8. Cross-sectional velocity contours superimposed on velocity magnitude pseudo-color plots at three different locations for three simulations. See figure 2.7 for axial locations.

28

Figure 2.9. Streamlines at the 6th half cycle time t/tp = 0.5 for subject 12. A recirculation zone close to the inlet in the Newtonian flow is absent in the two non-Newtonian counterparts.

29

Figure 2.10. Critical TAWSS for subject 27 at t/tp = 1 of the 6th cycle. Red zones mark the locations where TWASS has dropped below 0.076 [Pa]. Newtonian flow exhibits a slightly larger red zone.

30

Figure 2.11. Instantaneous WSS for subject 12 at t/tp = 0.5. Newtonian flow shows a slightly higher instantaneous WSS at the locations indicated with arrows.

31 As mentioned before, particular attention in this investigation is placed on the WSS and TAWSS6 distributions on patient-specific geometries. From a clinical point of view, the WSS is the primary hemodynamic quantity of interest, because low WSS may lead to the development of NH that could potentially result in development of stenotic lesions. It is documented in the literature that the threshold value for WSS to initiate NH is 0.076 Pascal [82, 6, 55]. In a parallel study, we substantiated this value via an integrated clinical, computational, and statistical study in [33] for our ESRD population. In the same study, we found only a 3.2% difference in the length of the low-WSS (≤ 0.076 Pa) and low-TAWSS (