Tube law parametrization using in vitro data for one‐dimensional blood flow in arteries and veins

Author:

Colombo Chiara1ORCID,Siviglia Annunziato1ORCID,Toro Eleuterio F.2,Bia Daniel3ORCID,Zócalo Yanina3ORCID,Müller Lucas O.4ORCID

Affiliation:

1. Department of Civil, Environmental and Mechanical Engineering University of Trento Trento Italy

2. Laboratory of Applied Mathematics, DICAM University of Trento Trento Italy

3. Department of Physiology, Faculty of Medicine University of the Republic Montevideo Uruguay

4. Department of Mathematics University of Trento Trento Italy

Abstract

AbstractThe deformability of blood vessels in one‐dimensional blood flow models is typically described through a pressure‐area relation, known as the tube law. The most used tube laws take into account the elastic and viscous components of the tension of the vessel wall. Accurately parametrizing the tube laws is vital for replicating pressure and flow wave propagation phenomena. Here, we present a novel mathematical‐property‐preserving approach for the estimation of the parameters of the elastic and viscoelastic tube laws. Our goal was to estimate the parameters by using ovine and human in vitro data, while constraining them to meet prescribed mathematical properties. Results show that both elastic and viscoelastic tube laws accurately describe experimental pressure‐area data concerning both quantitative and qualitative aspects. Additionally, the viscoelastic tube law can provide a qualitative explanation for the observed hysteresis cycles. The two models were evaluated using two approaches: (i) allowing all parameters to freely vary within their respective ranges and (ii) fixing some of the parameters. The former approach was found to be the most suitable for reproducing pressure‐area curves.

Publisher

Wiley

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