Regularization of a mathematical model of the Wheatley heart valve

Rebolledo, Ramiro J and McKee, Sean and Cuminato, José Alberto and Stewart, Iain W and Wheatley, David (2022) Regularization of a mathematical model of the Wheatley heart valve. Journal of Biomechanical Engineering, 145 (1). BIO-21-1427. ISSN 0148-0731 (https://doi.org/10.1115/1.4055034)

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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)].

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