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

Published online by Cambridge University Press:  15 August 2004

Vuk Milišić  and
Alfio Quarteroni
Vuk Milišić
Affiliation:
Chair of Modelling and Scientific Computing, IACS, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. [email protected].
Alfio Quarteroni
Affiliation:
Chair of Modelling and Scientific Computing, IACS, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland. [email protected]. MOX, Dipartimento di Matematica, Politecnico di Milano, 20133 Milano, Italy. [email protected].
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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.

Keywords

Multiscale modellingparabolic equationshyperbolic systemslumped parameters modelsblood flow modelling.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 38 , Issue 4 , July 2004 , pp. 613 - 632
Copyright
© EDP Sciences, SMAI, 2004

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