Mathematical Model of Blood Flow in an Anatomically Detailed Arterial Network of the Arm
1 Universidade Federal Rural de
Pernambuco, Unidade Acadêmica de Garanhuns, Garanhuns, Brazil.
2 Laboratório Nacional de Computação Científica, LNCC, Petrópolis, Brazil.
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3 Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica, INCT-MACC, Petrópolis, Brazil.
A distributed-parameter (one-dimensional) anatomically detailed model for the arterial network of the arm is developed in order to carry out hemodynamics simulations. This work focuses on the specific aspects related to the model set-up. In this regard, stringent anatomical and physiological considerations have been pursued in order to construct the arterial topology and to provide a systematic estimation of the involved parameters. The model 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 – perforator arteries. The modeling of blood flow in deformable vessels is governed by a well-known set of hyperbolic partial differential equations that accounts for mass and momentum conservation and a constitutive equation for the arterial wall. The variational formulation used to solve the problem and the related numerical approach are described. The model rendered consistent pressure and flow rate outputs when compared with patient records already published in the literature. In addition, an application to dimensionally-heterogeneous modeling is presented in which the developed arterial network is employed as an underlying model for a three-dimensional geometry of a branching point to be embedded in order to perform local analyses.
Mathematics Subject Classification: 76Z05 / 92C10 / 92C30
Key words: Hemodynamics / anatomical model / vascular territories / numerical simulation
© EDP Sciences, SMAI, 2013