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Journal of Engineering Mathematics

, Volume 77, Issue 1, pp 19–37 | Cite as

Physical determining factors of the arterial pulse waveform: theoretical analysis and calculation using the 1-D formulation

  • Jordi Alastruey
  • Tiziano Passerini
  • Luca Formaggia
  • Joaquim Peiró
Open Access
Article

Abstract

The shape of the arterial pulse waveform is intimately related to the physical properties of the cardiovascular system. It is clinically relevant to measure those properties that are related to cardiovascular function, such as the local elasticity and viscosity of the arterial wall, total compliance and net peripheral resistance of the systemic arterial tree. Most of these properties cannot be directly measured in vivo, but they can be calculated from pressure, flow and wall displacement measurements that can be obtained in vivo. We carry out a linear analysis of the one-dimensional (1-D) equations of blood flow in Voigt-type visco-elastic vessels to study the effects on pulse wave propagation of blood viscosity, flow inertia, wall visco-elasticity, total arterial compliance, net resistance, peripheral outflow pressure, and flow rate at the aortic root. Based on our analysis, we derive methods to calculate the local elastic and viscous moduli of the arterial wall, and the total arterial compliance, net resistance, time constant and peripheral outflow pressure of the systemic arterial tree from pressure, flow and wall displacement data that can be measured in vivo. Analysis of in vivo data is beyond the scope of this study, and therefore, we verify the results of our linear analysis and assess the accuracy of our estimation methods using pulse waveforms simulated in a nonlinear visco-elastic 1-D model of the larger conduit arteries of the upper body, which includes the circle of Willis in the cerebral circulation.

Keywords

Circle of Willis Flow inertia Nonlinear one-dimensional modelling Peripheral outflow pressure Pulse wave propagation Systemic arteries Voigt-type visco-elasticity Wall compliance Windkessel pressure 

Notes

Acknowledgments

This work was supported by a British–Italian partnership programme for young researchers (British Council/MIUR). Jordi Alastruey was also funded by a British Heart Foundation Intermediate Basic Science Research Fellowship (FS/09/030/27812) and the Centre of Excellence in Medical Engineering funded by the Wellcome Trust and EPSRC under grant number WT 088641/Z/09/Z. Luca Formaggia gratefully acknowledges the support of MIUR through a PRIN07 grant.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

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Copyright information

© The Author(s) 2012

Authors and Affiliations

  • Jordi Alastruey
    • 1
  • Tiziano Passerini
    • 2
    • 3
  • Luca Formaggia
    • 2
  • Joaquim Peiró
    • 4
  1. 1.Department of Biomedical Engineering, Division of Imaging Sciences and Biomedical EngineeringKing’s College London, King’s Health Partners, St. Thomas’ HospitalLondonUK
  2. 2.Dipartimento di Matematica F. BrioschiPolitecnico di MilanoMilanItaly
  3. 3.Department of Mathematics and Computer ScienceEmory UniversityAtlantaUSA
  4. 4.Department of AeronauticsImperial CollegeLondonUK

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