Regularization of a Mathematical Model of the Wheatley Heart Valve

R J Rebolledo; S McKee; J A Cuminato; I W Stewart; D J Wheatley

doi:10.1115/1.4055034

Regularization of a Mathematical Model of the Wheatley Heart Valve

J Biomech Eng. 2023 Jan 1;145(1):014501. doi: 10.1115/1.4055034.

Authors

R J Rebolledo¹, S McKee², J A Cuminato³, I W Stewart⁴, D J Wheatley⁵

Affiliations

¹ ICMC, University of São Paulo at São Carlos, São Carlos-SP, Brazil; Faculty of Agricultural Engineering, University of Concepción, Chillán, Chile.
² Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK.
³ ICMC, University of São Paulo at São Carlos, São Carlos-SP, Brazil.
⁴ Faculty of Science, University of Strathclyde, Glasgow G1 1XH, UK.
⁵ School of Science and Engineering, University of Dundee, Dundee DD1 4HN, UK.

PMID: 35864783
DOI: 10.1115/1.4055034

Abstract

This note considers the mathematical model published in the Journal of Biomechanical Engineering by McKee et al. [McKee, S., Cuminato, J. A., Stewart, I. W., and Wheatley, D. J., 2021, "A Mathematical Representation of the Wheatley Heart Valve," ASME J. Biomech. Eng., 143(8), p. 081006]. The model presented there suffers from the fact that there is a line discontinuity in the first derivative producing what appears to be a kink in each of the leaflets. This note is concerned with regularizing the shape of the valve while holding to Wheatley's essential idea [Wheatley, D. J., 2016, "Heart Valve," U.S. Patent No. 9,259,313, UK Patent No. 2,982,340 (2017), European Patent No. 2,979,666 (2017)].

MeSH terms

Biomedical Engineering
Heart Valves*
Models, Biological*