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Peristaltic Pumping of Solid Particles Immersed in a Viscoelastic Fluid

J. Chrispell, L. Fauci (2011)

Mathematical Modelling of Natural Phenomena

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...

Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*

Carlo D'Angelo, Paolo Zunino (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Robust numerical approximation of coupled Stokes' and Darcy's flows applied to vascular hemodynamics and biochemical transport*

Carlo D'Angelo, Paolo Zunino (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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...

Segregation of Flowing Blood: Mathematical Description

A. Tokarev, G. Panasenko, F. Ataullakhanov (2011)

Mathematical Modelling of Natural Phenomena

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...

Simulation of the Three-Dimensional Flow of Blood Using a Shear-Thinning Viscoelastic Fluid Model

T. Bodnár, K.R. Rajagopal, A. Sequeira (2011)

Mathematical Modelling of Natural Phenomena

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....

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke, Kim H. Parker, Ling Y. Wee, Nicholas M. Fisk, Spencer J. Sherwin (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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/ h p 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....

Time domain computational modelling of 1D arterial networks in monochorionic placentas

Victoria E. Franke, Kim H. Parker, Ling Y. Wee, Nicholas M. Fisk, Spencer J. Sherwin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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....

Vessel Wall Models for Simulation of Atherosclerotic Vascular Networks

Yu. Vassilevski, S. Simakov, V. Salamatova, Yu. Ivanov, T. Dobroserdova (2011)

Mathematical Modelling of Natural Phenomena

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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