Onedimensional models for blood flow in arteries
 Luca Formaggia,
 Daniele Lamponi,
 Alfio Quarteroni
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In this paper a family of onedimensional nonlinear systems which model the blood pulse propagation in compliant arteries is presented and investigated. They are obtained by averaging the NavierStokes equation on each section of an arterial vessel and using simplified models for the vessel compliance. Different differential operators arise depending on the simplifications made on the structural model. Starting from the most basic assumption of pure elastic instantaneous equilibrium, which provides a wellknown algebraic relation between intramural pressure and vessel section area, we analyse in turn the effects of terms accounting for inertia, longitudinal prestress and viscoelasticity. The problem of how to account for branching and possible discontinuous wall properties is addressed, the latter aspect being relevant in the presence of prosthesis and stents. To this purpose a domain decomposition approach is adopted and the conditions which ensure the stability of the coupling are provided. The numerical method here used in order to carry out several test cases for the assessment of the proposed models is based on a finite element TaylorGalerkin scheme combined with operator splitting techniques.
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 Title
 Onedimensional models for blood flow in arteries
 Journal

Journal of Engineering Mathematics
Volume 47, Issue 34 , pp 251276
 Cover Date
 20031201
 DOI
 10.1023/B:ENGI.0000007980.01347.29
 Print ISSN
 00220833
 Online ISSN
 15732703
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 bloodflow models
 cardiovascular system
 finite elements
 simulation
 Industry Sectors
 Authors

 Luca Formaggia ^{(1)}
 Daniele Lamponi ^{(2)}
 Alfio Quarteroni ^{(1)} ^{(2)}
 Author Affiliations

 1. MOX, Dipartimento di Matematica, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy
 2. Institut de Mathématiques (FSB/IMA), Ecole Polytecnique Fédérale de Lausanne, CH1015, Lausanne, Switzerland