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Mathematical Model of Blood Flow in an Anatomically DetailedArterial Network of the Arm

Published online by Cambridge University Press:  13 June 2013

Sansuke M. Watanabe ,
Pablo J. Blanco  and
Raúl A. Feijóo
Sansuke M. Watanabe
Affiliation:
Universidade Federal Rural de Pernambuco, Unidade Acadêmica de Garanhuns, Garanhuns, Brazil.. [email protected] Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.; [email protected]; [email protected]; [email protected] Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
Pablo J. Blanco
Affiliation:
Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.; [email protected]; [email protected]; [email protected] Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
Raúl A. Feijóo
Affiliation:
Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.; [email protected]; [email protected]; [email protected] Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
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Abstract

A distributed-parameter (one-dimensional) anatomically detailed model for the arterialnetwork of the arm is developed in order to carry out hemodynamics simulations. This workfocuses on the specific aspects related to the model set-up. In this regard, stringentanatomical and physiological considerations have been pursued in order to construct thearterial topology and to provide a systematic estimation of the involved parameters. Themodel comprises 108 arterial segments, with 64 main arteries and 44 perforator arteries,with lumen radii ranging from 0.24 cm – axillary artery- to 0.018 cm – perforatorarteries. The modeling of blood flow in deformable vessels is governed by a well-known setof hyperbolic partial differential equations that accounts for mass and momentumconservation and a constitutive equation for the arterial wall. The variationalformulation used to solve the problem and the related numerical approach are described.The model rendered consistent pressure and flow rate outputs when compared with patientrecords already published in the literature. In addition, an application todimensionally-heterogeneous modeling is presented in which the developed arterial networkis employed as an underlying model for a three-dimensional geometry of a branching pointto be embedded in order to perform local analyses.

Keywords

Hemodynamicsanatomical modelvascular territoriesnumerical simulation
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 4: Direct and inverse modeling of the cardiovascular and respiratory systems , July 2013 , pp. 961 - 985
Copyright
© EDP Sciences, SMAI, 2013

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