Abstract :
We study a coupled system of ordinary differential equations and quasilinear hyperbolic partial differential equations that models
a blood circulatory system in the human body. The mathematical system is a multiscale model in which a part of the system, where
the flow can be regarded as Newtonian and homogeneous, and the vessels are long and large, is modeled by a set of hyperbolic PDEs
in a one-spatial-dimensional network, and in the other part, where either vessels are too thin or the flow pattern is too complicated
(such as in the heart), the flow is modeled as a lumped element by a set of ordinary differential equations as an analog of an electric
circuit. The mathematical system consists of pairs of PDEs, one pair for each vessel, coupled at each junction through a system
of ODEs. This model is a generalization of the widely studied models of arterial networks. We give a proof of the well-posedness
of the initial-boundary value problem by showing that the classical solution exists, is unique, and depends continuously on initial,
boundary and forcing functions and their derivatives.
© 2008 Elsevier Inc. All rights reserved.
