Analysis of lumped parameter models for blood flow simulations and their relation with 1D models

¹ Chair of Modelling and Scientific Computing, IACS, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. vuk.milisic@epfl.ch.
² MOX, Dipartimento di Matematica, Politecnico di Milano, 20133 Milano, Italy. alfio.quarteroni@epfl.ch.

Received: 6 February 2004
Revised: 24 March 2004

Abstract

This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee the convergence, and the energy estimates of the limit 1D equations.