Annals of Biomedical Engineering

, Volume 44, Issue 10, pp 3047–3068 | Cite as

A Novel Analytical Approach to Pulsatile Blood Flow in the Arterial Network

  • Joaquín Flores
  • Jordi Alastruey
  • Eugenia Corvera Poiré
Article
  • 643 Downloads

Abstract

Haemodynamic simulations using one-dimensional (1-D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. We propose a novel linear 1-D dynamical theory of blood flow in networks of flexible vessels that is based on a generalized Darcy’s model and for which a full analytical solution exists in frequency domain. We assess the accuracy of this formulation in a series of benchmark test cases for which computational 1-D and 3-D solutions are available. Accordingly, we calculate blood flow and pressure waves, and velocity profiles in the human common carotid artery, upper thoracic aorta, aortic bifurcation, and a 20-artery model of the aorta and its larger branches. Our analytical solution is in good agreement with the available solutions and reproduces the main features of pulse waveforms in networks of large arteries under normal physiological conditions. Our model reduces computational time and provides a new approach for studying arterial pulse wave mechanics; e.g.,  the analyticity of our model allows for a direct identification of the role played by physical properties of the cardiovascular system on the pressure waves.

Keywords

1-D arterial haemodynamics Pulse wave propagation 1-D blood flow modelling Generalized Darcy’s model Benchmark test cases 

Notes

Acknowledgments

The authors would like to thank Drs Nan Xiao and Alberto Figueroa for providing all 3-D data used in this study. JFG acknowledges financial support from CONACYT (Mexico) through fellowship 240094. JA gratefully acknowledges the support of an EPSRC Project Grant (EP/K031546/1), the Centre of Excellence in Medical Engineering (funded by the Wellcome Trust and EPSRC under Grant Number WT 088641/Z/09/Z), and the National Institute for Health Research (NIHR) Biomedical Research Centre at Guys and St Thomas’ NHS Foundation Trust in partnership with King’s College London. ECP declares that the research leading to these results has received funding from the European Union Seventh Framework Programme (FP7-PEOPLE-2011-IIF) under Grant Agreement N0 301214, as well as financial support from CONACYT (Mexico) through Projects 83149 and 219584.

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Copyright information

© Biomedical Engineering Society 2016

Authors and Affiliations

  1. 1.Departamento de Física y Química Teórica, Facultad de QuímicaUniversidad Nacional Autónoma de México, Ciudad UniversitariaMexicoMexico
  2. 2.Division of Imaging Sciences and Biomedical EngineeringSt. Thomas’ Hospital, King’s College LondonLondonUK
  3. 3.Departament de Física FonamentalUniversitat de BarcelonaBarcelonaSpain

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