Influence of cross-sectional velocity profile on flow characteristics of arterial wall modeled as elastic and viscoelastic material.

Abstract

In the present work, blood flow behavior in a single artery and in arterial network is studied using time domain based one-dimensional wave propagation model retaining the nonlinear convective force. 1-D Navier-Stokes equation is used to model the flow behavior of the blood, using three unknown parameters: flow rate (q), cross-sectional area of artery (A) and pressure (p) based formulation. Three different approximate velocity profile functions across the cross-section namely modified flat, parabolic and the one proposed by Bessems are used to calculate the nonlinear convective force and the frictional force. Two different constitutive models, linear elastic model and standard linear solid model (Zener model) are used to model the arterial wall mechanical behavior. The system of partial differential equations is discretized using finite element and Crank Nicolson methods in space and time domains, respectively. Based on the formulation, an in house finite element code is developed to simulate flow behavior in both a single artery as well as in arterial network consisting of 20 small and large size arteries. Simulations are performed by enforcing a flow rate at the inlet and Windkessel model at the outlet. The results for elastic arterial wall model are found to be in good agreement with the results available in the literature. The flow rate/pressure predictions using different velocity profile functions are found to be nearly the same, however the Bessems velocity profile predicts more closer to 3D results compared to modified flat and parabolic profiles. Whereas, significant difference is found in the results predicted using elastic and viscoelastic artery wall models.