Shock wave formation in compliant arteries

Cristóbal Rodero; J. Alberto Conejero; Ignacio García-Fernández

doi:10.3934/eect.2019012

Article Contents

2019, Volume 8, Issue 1: 221-230. Doi: 10.3934/eect.2019012

This issue Previous Article Optimal scalar products in the Moore-Gibson-Thompson equation Next Article Anti-plane shear Lamb's problem on random mass density fields with fractal and Hurst effects

Shock wave formation in compliant arteries

1.
Division of Imaging Sciences and Biomedical Engineering, King's College London, St. Thomas' Hospital, SE1 7EH London, United Kingdom
2.
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, E-46022 València, Spain
3.
CoMMLab, Departament d'Informàtica, Universitat de València, E-46100 Burjassot, València, Spain

* Corresponding author: J. Alberto Conejero
* Corresponding author: J. Alberto Conejero

Received: February 28, 2018

Revised: June 30, 2018

Early access: December 2018

Published: January 2019

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Abstract

We focus on the problem of shock wave formation in a model of blood flow along an elastic artery. We analyze the conditions under which this phenomenon can appear and we provide an estimation of the instant of shock formation. Numerical simulations of the model have been conducted using the Discontinuous Galerkin Finite Element Method. The results are consistent with certain phenomena observed by practitioners in patients with arteriopathies, and they could predict the possible formation of a shock wave in the aorta.

Keywords:

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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Figure 1. An artery as a compliant tube, where variable x denotes the spatial coordinate and t the temporal one.

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Figure 2. Decomposition of the domain $ D $.

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Figure 3. Several beat like boundary conditions (23) for $u(0, 0) = 0$.

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Figure 4. Formation of a shock wave with a beat-like boundary condition. The discontinuity at $x = 20$ is due to the nature of the DG method, which provides two values in the frontier between elements.

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