Constitutive and Computational Modelling with Fluid-Structure Interactions of Venous Tissues

Minisymposium: Direct and Inverse Methods for Cardiovascular and Pulmonary Mechanics
Presenting Author: Nayyan Kaul*
Other Author(s): Hsiao Ying Shadow Huang
Time/Location: July 20, 2017 @ 10:55 a.m.-11:15 a.m. in 514C
Text: Venous valve tissues, while used in vein reconstruction surgeries and bio prosthetic valves with moderate success, does not have extensive studies on their structure and modelling. Their inherent anisotropic, non-linear behavior combined with severe diseases inflicting the veins like chronic venous insufficiency warrants understanding the structure and material behavior of venous valve tissues. With the scant information on uniaxial and biaxial mechanical properties of jugular venous valve and wall tissue from any previous studies, the current focus of our study was to understand the material behavior by determining an established phenomenological strain energy based constitutive relation for the tissues. First, we used bovine veins to experimentally study the behavior of valve leaflet tissue and adjoining wall tissue (from proximal and distal end of the vein) under different biaxial testing protocols. Second, we looked at the behavior of numerical partial derivatives of strain energy to select a suitable functional form of strain energy for wall and valve tissue from the literature [1-3]. Using this strain energy descriptor, we determined Cauchy stress and compared it with experimental results under displacement controlled biaxial testing protocols to find material specific model parameters by Powell's method algorithm. We then implemented our selected constitutive models along with material specific model parameters using user defined material subroutines (UMAT) in a commercial FEM package ABAQUS with fluid-solid interactions (FSI) functionality. We observe the blood flow behavior differences around a bileaflet versus a trileaflet valve during opening/closing in the vein. Isolated and coupled effects from hemodynamic, hydrostatic, and hydrodynamic variations are studied based on the FSI simulations. Results indicated that whereas wall tissue strain energy can be explained using a polynomial nonlinear function, the valve tissue, due to higher nonlinearities, requires an exponential function. This study can prove helpful in primary stages of bio-prosthetic designs; replacement surgeries; can be of support to any future studies investigating structural models and to study valvular diseases by giving a way to understand material properties, and to form a continuum model required for numerical analyses and simulations. References: [1] Humphrey JD, Strumpf RK, Yin FCP. Journal of Biomechanical Engineering. 1990; 112(3):333-339. doi: 10.1115/1.2891193. [2] Humphrey JD, Strumpf RK, Yin FCP. Journal of Biomechanical Engineering. 1990; 112(3):340-346. doi: 10.1115/1.2891194. [3] May-Newman K, Yin FCP. Journal of Biomechanical Engineering. 1998; 120(1):38-47. doi: 10.1115/1.2834305.