Pressure boundary conditions for blood flows

Abstract

Simulations of blood flows in arteries require numerical solutions of fluidstructure interactions involving Navier-Stokes equations coupled with large displacement visco-elasticity for the vessels.Among the various simplifications which have been proposed, the surface pressure model leads to a hierarchy of simpler models including one that involves only the pressure. The model exhibits fundamental frequencies which can be computed and compared with the pulse. Yet unconditionally stable time discretizations can be constructed by combining implicit time schemes with Galerkin-characteristic discretization of the convection terms in the Navier-Stokes equations. Such problems with prescribed pressure on the walls will be shown to be efficient and accurate as an approximation of the full fluid structure interaction problem.

Boundary conditions involving pressure for the Stokes problem and applications in computational hemodynamics

“…Numerical experiments in the nite element framework enforce this type of boundary conditions through a penalty method, for Newtonian [12,5] and generalized Newtonian uids [5]. Recent developments concern the Navier-Stokes problem in the context of a simpli ed uid-structure model for blood ows [21]. This so-called Surface Pressure Model is analyzed in [10].…”

Numerical simulation of the fractional flow reserve (FFR)

“…As for the boundary conditions, even if their choice is crucial for this kind of studies, we decided to make few simplifications in order to be able to address the problem. At the inlet, we impose a sinusol wave function to illustrate the pulsatile property of the flow, as in many works [8], [7] and [9]. At the outlet, we assume that the vessel following the portion of interest is long enough before getting to the small tissues, or having a change in the vessel caliber, so there is no resistance effect.…”

“…of the arterial portion is able to move. In a first place, a generalized linear Koiter model is adopted for the structure, as in [8]. In this case, the arterial wall is a 1D layer with a thickness .…”

A simplified fluid–structure model for arterial flow. Application to retinal hemodynamics

“…In order to render the motion of the wall, a transpiration approach is adopted. A zero-th order transpiration was investigated in [14,19,15], and proves to be satisfactory to study the propagation of pressure waves. However, in view of the application that motivated this work [17] (hemodynamic autoregulation), it is important to compute the flow variation induced by the wall dynamics.…”