A Mathematical Model Of Solute Dynamics In
A Curved Artery
Author(s)
G. Pontrelli & A. Tatone
Abstract
A mathematical model for the mass transport and diffusion process in arteries is
presented. Blood flow is described by the unsteady Navier-Stokes equation, and
solute dynamics by an advection-diffusion equation. A linearization procedure
over the steady state solution is carried out and an asymptotic analysis is used
to study the influence of a small curvature with respect to the straight tube. Some
numerical experiments in cases of physiological interest are presented: the results
show the characteristics of the long wave propagation and the role played by the
geometry on the solute distribution.
Keywords: solute dynamics, arterial transport, curved tubes, advection-diffusion
equation, numerical methods.
1 Introduction
Mass transport and diffusion phenomena inside the arterial lumen and through the
vascular wall are of great importance for physiological functions, such as oxygenation,
nourishment of tissues and metabolic processes. Some mathematical models
coupling 3D flow and solute dynamics have been developed in recent years [1–4].
They are defined in a finite arterial segment of arbitrary shape, where an inflow
solute distribution is provided [1, 2]. Some of them consider also absorption and
exchange through the vascular tissues [3]. All these models provide the local concentration
pattern and are useful to understand the relationship between the local
flow pattern, the nourishment of arterial tissues and possible pathologies derived
when such a process is altered [4].
On the other hand, fluid dynamical factors such as flow separation, recirculation
and wall shear stress are correlated to the atherosclerotic lesions. It is known
Keywords
solute dynamics, arterial transport, curved tubes, advection-diffusion
equation, numerical methods.
Related Book
Other papers in this volume
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