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Advanced Numerical Methods in the Mathematical Sciences

Rana Zakerzadeh, University of Pittsburgh
Effect of Poroelasticity and Viscoelasticity on the Fluid-Structure Interaction in Arteries

Abstract

We discuss a computational framework to investigate the effect of using a poroelastic and viscoelastic material models in the interaction between the blood flow and the arterial wall for large arteries. The present study attempts to analyze the distribution and dissipation of the energy delivered to arteries in order to identify the most appropriate model for studying FSI problems in soft tissue.

In order to approximate this problem, we develop a partitioned, loosely coupled finite element solver based on weak enforcement of interface conditions using Nitsche's method. Blood is modeled as an incompressible, viscous, Newtonian fluid using the Navier-Stokes equations and the arterial wall consists of a thick material which is modeled as a Biot system in poroelastic case that describes the mechanical behavior of a homogeneous and isotropic elastic skeleton, and connecting pores filled with fluid. Moreover, viscoelastic mechanical properties of vessel walls were modeled by utilizing a simple linearly viscoelastic model which is based on Kelvin-Voigt viscoelasticity.

The conservation of the energy principle has been applied systematically to the arteries to assess energy exchange between different compartments of the model. Energy estimation for each constitutive model of the arterial wall is derived from weak formulation for the coupled problem, and numerical tests are performed using physiological parameters to support its accuracy.