Vessel Wall Models for Simulation of Atherosclerotic Vascular Networks

Abstract

Abstract. There are two mathematical models of elastic walls of healthy and atherosclerotic blood vessels developed and studied. The models are included in a numerical model of global blood circulation via recovery of the vessel wall state equation. The joint model allows us to study the impact of arteries atherosclerotic disease of a set of arteries on regional haemodynamics.

Methods of Blood Flow Modelling

“…The coefficients of the elastic fiber-spring plaque model are taken from [143]. The velocity profiles in the external carotid continuation (No.94) and the arteries of the Willis circle (No.104,102) are shown in Fig.8.…”

“…To demonstrate the applicability of global blood circulation models, we present the study of atherosclerotic plaque impact on hemodynamics by means of our numerical model [141][142][143].…”

Mathematical modelling of atherosclerosis

“…However, such scaling does not modify function f . Recovery of function f in healthy and atheroclerotic vessel is considered in [166,167].…”

“…Therefore the strain in the axial direction is negligible [41]. The equilibrium state for the healthy thin vessel wall (with middle radius R and thickness H) composed of the Neo-Hookean material and inflated by internal pressure p 0 gives the nonlinear equation on the principal radial stretch λ r [166]:…”

Personalized Anatomical Meshing of the Human Body with Applications

“…The relationship was verified by fiber-spring model of vessel wall elasticity [32,33]. Equations (9.9)-(9.10) are discretized by a hybrid explicit scheme corresponding to the most accurate first order monotone scheme and the less oscillating second order scheme [15,17].…”