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NUMERICAL INVESTIGATIONS of UNOBSTRUCTED and OBSTRUCTED HUMAN URETER PERISTALSIS a Thesis Presented to the Graduate Faculty of T

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NUMERICAL INVESTIGATIONS of UNOBSTRUCTED and OBSTRUCTED HUMAN URETER PERISTALSIS a Thesis Presented to the Graduate Faculty of T NUMERICAL INVESTIGATIONS OF UNOBSTRUCTED AND OBSTRUCTED HUMAN URETER PERISTALSIS A Thesis Presented to The Graduate Faculty of The University of Akron In Partial Fulfillment of the Requirements for the Degree Master of Science Ahmed Tasnub Takaddus April, 2017 NUMERICAL INVESTIGATIONS OF UNOBSTRUCTED AND OBSTRUCTED HUMAN URETER PERISTALSIS Ahmed Tasnub Takaddus Thesis Approved: Accepted: Advisor Interim Dean of the College Dr. Abhilash J. Chandy Dr. Donald P. Visco Jr. Faculty Reader Executive Dean of the Graduate School Dr. Ajay Mahajan Dr. Chand K. Midha Faculty Reader Date Dr. Xiaosheng Gao Department Chair Dr. Sergio D. Felicelli ii ABSTRACT Urine transported through the ureter from the kidney to the urinary bladder by peristaltic mechanism. Some of the problems related to urine transportation in ureter is back-flow, severe pain or in some rare cases, rupture of the ureter wall in an obstructed ureter. Ureter flow can get obstructed due to mineral deposits, from highly concentrated urine in the kidney and these deposits also known as kidney stones can then travel through the urinary tract. A number of numerical analyses have been conducted on the ureter to understand the flow mechanics as well as to understand the wall properties. But very few studies exist focusing on an obstructed ureter. To fully understand the effect of obstruction in a ureter, a comparative study of obstructed and unobstructed human ureter is required. So in this paper, the first 2D axisymmetric study has been carried out on a human ureter, where the ureteral wall has been modelled as an isotropic hyper-elastic material, based on curve fit-data from previous literature. The peristalsis waves are created using contractile forces on the ureter wall. In addition, 2D axisymmetric studies have been con- ducted on both obstructed and unobstructed ureters, where the constitutive material for the ureter is assumed to be anisotropic hyperelastic based on a previous experiments on real human ureters. Here, urine is transported by the isolated bolus created by the expansive force acting on the outer surface of the ureter wall. Finally, a 3D comparative study has iii been done on ureter with 50%, 70% obstruction and no obstruction. The material prop- erties and wall mechanics for peristalsis are consistent with the previous cases. In all of these studies, both the fluid and structural domains are solved using a finite-element based fluid-structure interaction (FSI) approach between ureter wall and urine. The coupling be- tween the domains is two-way, so both fluid and structure influence each other. While all the 2D simulations are solved in fully coupled monolithic way, for the 3D cases, a segre- gated approach is used with different nonlinear solvers for fluid and structure. For all the simulations, the fluid domain is considered to be incompressible laminar flow. From the analysis of the results, it is observed that peristalsis flow has a slight ten- dency of generating backflow from the bladder to the outlet even without any obstruction. So failure of the one-way valve like junctions, for instance the junction between bladder and ureter, can cause urine reflux. As the size of the obstruction increases, amount of urine backflow also increases. Also, high peaks are observed in pressure gradient and wall shear stress values near the location of the obstruction, which may lead to severe pain and even in some rare cases rupture of the ureter wall. The main objective of this study is to quantify the effect of ureteral obstruction, which will help physicians to understand and assist in the treatment procedure of an obstructed ureter. iv ACKNOWLEDGEMENTS At first, I would like to thank my advisor Dr. Abhilash J. Chandy. This work is able to see the daylight because of his vision and guidance. It happened countless times, that I ran into a problem, and asked him what to do. His door was always open, and his advices always showed me a way. I would like to thank Dr. Ajay Mahajan and Dr. Xiaosheng Gao for their time to be in the committee, and truly grateful for their valuable and insightful comments. At last, I would like to thank my parents, as because of heir continuous support, I am where I am today. v TABLE OF CONTENTS Page LIST OF TABLES . viii LIST OF FIGURES . ix CHAPTER I. INTRODUCTION . 1 II. PROBLEM DESCRIPTION . 11 2.1 Geometry of the model . 11 2.2 Material Properties . 12 III. MATHEMATICAL FORMULATION . 16 3.1 Fluid . 16 3.2 Solid . 16 3.3 Fluid-Structure Interaction. 17 IV. METHODOLOGY . 19 4.1 Numerical Details . 19 4.2 Computational Mesh . 21 V. RESULTS . 30 5.1 2D axisymmetric unobstructed ureter with isotropic wall properties . 30 5.2 2D axisymmetric unobstructed ureter with anisotropic wall properties . 38 vi 5.3 2D axisymmetric obstructed ureter with anisotropic wall properties . 50 5.4 3D axisymmetric obstructed and unobstructed ureter with anisotropic wall properties . 63 5.5 Conclusions . 73 VI. SUMMARY . 75 BIBLIOGRAPHY . 78 vii LIST OF TABLES Table Page 4.1 Number of mesh elements for the different cases presented in this study. 25 viii LIST OF FIGURES Figure Page 1.1 A cross-sectional picture of ureter showing it’s three layers [1]. 8 1.2 Urine reflux due to ureterovesical junction valves failure [2]. 9 1.3 Luminar change of ureter during peristalsis [3]. 10 2.1 Stress-strain curve fitting using five parameter money-rivlin model in circumferential direction. 14 4.1 Geometry and mesh of the fluid and structural domain. (a) mesh be- fore deformation and (b) mesh after deformation for 2D axisymmetric unobstructed ureter with isotropic wall properties. 22 4.2 Computational mesh of the fluid and structural domains for 2D axisym- metric unobstructed ureter with anisotropic wall properties. 23 4.3 von Mises stress at a point 15 cm away from the ureter vs. time for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 26 4.4 Geometry and mesh of the fluid and structural domain for 2D axisym- metric obstructed ureter with anisotropic wall properties. 27 4.5 Mesh convergence study for three different element number for 2D ax- isymmetric obstructed ureter with anisotropic wall properties. 28 4.6 Geometry and mesh of the fluid and structural domain for 3D axisym- metric obstructed and unobstructed ureter with anisotropic wall properties. 29 5.1 Urine flow rate at ureter inlet for 2D axisymmetric unobstructed ureter with isotropic wall properties. 31 ix 5.2 Contour of von-misses stress for structure and streamline of velocity vector overlapped with velocity vector arrows for flow field at time, t=4 = 25:5s for 2D axisymmetric unobstructed ureter with isotropic wall properties. 32 5.3 Velocity profile at ureter inlet for 2D axisymmetric unobstructed ureter with isotropic wall properties. 35 5.4 Pressure gradient along the ureter wall for 2D axisymmetric unob- structed ureter with isotropic wall properties. 36 5.5 Wall shear stress along the ureter wall for 2D axisymmetric unobstructed ureter with isotropic wall properties. 37 5.6 Pressure contours of the flow filed for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 39 5.7 Streamlines colored by velocity magnitude superimposed with velocity vectors of the flow filed for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 40 5.8 Urine flow rate at various cross-sections along the length of the ureter for four different times for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 42 5.9 Velocity profile at inlet or four different times for 2D axisymmetric un- obstructed ureter with anisotropic wall properties. 43 5.10 Pressure gradient along the ureter wall for four different times for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 44 5.11 Wall shear stress along the ureter wall or four different times for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 45 5.12 von Mises Stress plot in the ureter wall both for linear and hyperelastic material. 48 5.13 von Mises stress (top) and displacement (bottom) along the ureter wall at time, t = 6:5 s for 2D axisymmetric unobstructed ureter with anisotropic wall properties. 49 5.14 Volume flow rate along the ureter length at 6 different time instants for 2D axisymmetric obstructed ureter with anisotropic wall properties. 51 5.15 Velocity profile at ureter inlet for 2D axisymmetric obstructed ureter with anisotropic wall properties. 52 x 5.16 Percentage of cross-sectional area blockage with time at the the stone center for 2D axisymmetric obstructed ureter with anisotropic wall properties. 53 5.17 Pressure gradient along ureter wall for 2D axisymmetric obstructed ureter with anisotropic wall properties. 55 5.18 Wall shear stress along ureter wall for 2D axisymmetric obstructed ureter with anisotropic wall properties. 56 5.19 Contour of von mises stress for the structure, along with streamlines overlapped with velocity vectors for the fluid flow for 2D axisymmetric obstructed ureter with anisotropic wall properties. 62 5.20 Inlet mass flow rate at four different time instances, t = 2:25 s, t = 2:75 s, t = 3:25 s, and t = 3:4 s, for the Unobstructed and 50% and 70% obstructions. 64 5.21 Pressure gradient along the length of the ureter at four different time instances, t = 2:25 s, t = 2:75 s, t = 3:25 s, and t = 3:4 s, for the Unob- structed and 50% and 70% obstructions.. 65 5.22 Wall shear stress along the length of ureter at four different time in- stances, t = 2:25 s, t = 2:75 s, t = 3:25 s, and t = 3:4 s, for the Unob- structed and 50% and 70% obstructions.. 66 5.23 Velocity vector of urine coloured with velocity magnitude and ureter wall deformation for 70% blockage .
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