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Peristaltic pumping of fluid is a fundamental method of transport in many biological
processes. In some instances, particles of appreciable size are transported along with the
fluid, such as ovum transport in the oviduct or kidney stones in the ureter. In some of
these biological settings, the fluid may be viscoelastic. In such a case, a nonlinear
constitutive equation to describe the evolution of the viscoelastic contribution to the
stress tensor...
The fully coupled description of blood flow and mass transport in
blood vessels requires extremely robust numerical methods. In order
to handle the heterogeneous coupling between blood flow and plasma filtration,
addressed by means of Navier-Stokes and Darcy's equations,
we need to develop a numerical scheme capable to deal with
extremely variable parameters, such as the blood viscosity and
Darcy's permeability of the arterial walls. In this paper, we describe a finite element method for...
The fully coupled description of blood flow and mass transport in
blood vessels requires extremely robust numerical methods. In order
to handle the heterogeneous coupling between blood flow and plasma filtration,
addressed by means of Navier-Stokes and Darcy's equations,
we need to develop a numerical scheme capable to deal with
extremely variable parameters, such as the blood viscosity and
Darcy's permeability of the arterial walls. In this paper, we describe a finite element method for...
Blood rheology is completely determined by its major corpuscles which are erythrocytes,
or red blood cells (RBCs). That is why understanding and correct mathematical description
of RBCs behavior in blood is a critical step in modelling the blood dynamics. Various
phenomena provided by RBCs such as aggregation, deformation, shear-induced diffusion and
non-uniform radial distribution affect the passage of blood through the vessels. Hence,
they have...
This paper is concerned with the numerical simulation of a thermodynamically compatible
viscoelastic shear-thinning fluid model, particularly well suited to describe the
rheological response of blood, under physiological conditions. Numerical simulations are
performed in two idealized three-dimensional geometries, a stenosis and a curved vessel,
to investigate the combined effects of flow inertia, viscosity and viscoelasticity in
these geometries....
In this paper we outline the hyperbolic system of governing equations describing one-dimensional blood flow in arterial networks. This system is numerically discretised using a discontinuous Galerkin formulation with a spectral/ element spatial approximation. We apply the numerical model to arterial networks in the placenta. Starting with a single placenta we investigate the velocity waveform in the umbilical artery and its relationship with the distal bifurcation geometry and the terminal resistance....
In this paper we outline the hyperbolic system of governing equations
describing one-dimensional blood flow in arterial networks. This
system is numerically discretised using a discontinuous Galerkin
formulation with a spectral/hp element spatial approximation. We
apply the numerical model to arterial networks in the
placenta. Starting with a single placenta we investigate the velocity waveform
in the umbilical artery and its relationship with the distal
bifurcation geometry and the terminal resistance....
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.
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