Regularization of a mathematical model of the Wheatley heart valve

Ramiro J Rebolledo; Sean McKee; José Alberto Cuminato; Iain W Stewart; David Wheatley

doi:10.1115/1.4055034

Regularization of a mathematical model of the Wheatley heart valve

Ramiro J Rebolledo, Sean McKee, José Alberto Cuminato, Iain W Stewart, David Wheatley

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

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)].

Original language	English
Article number	BIO-21-1427
Number of pages	3
Journal	Journal of Biomechanical Engineering
Volume	145
Issue number	1
DOIs	https://doi.org/10.1115/1.4055034
Publication status	Published - 19 Jul 2022

Keywords

regularization
mathematical model
Wheatley heart valve
valve
biomechanical engineering
shapes

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10.1115/1.4055034

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title = "Regularization of a mathematical model of the Wheatley heart valve",

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)].",

keywords = "regularization, mathematical model, Wheatley heart valve, valve, biomechanical engineering, shapes",

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T1 - Regularization of a mathematical model of the Wheatley heart valve

AU - Rebolledo, Ramiro J

AU - McKee, Sean

AU - Cuminato, José Alberto

AU - Stewart, Iain W

AU - Wheatley, David

PY - 2022/7/19

Y1 - 2022/7/19

N2 - 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)].

AB - 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)].

KW - regularization

KW - mathematical model

KW - Wheatley heart valve

KW - valve

KW - biomechanical engineering

KW - shapes

UR - https://discovery.dundee.ac.uk/en/publications/regularization-of-a-mathematical-model-of-the-wheatley-heart-valv

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DO - 10.1115/1.4055034

M3 - Article

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JO - Journal of Biomechanical Engineering

JF - Journal of Biomechanical Engineering

SN - 0148-0731

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M1 - BIO-21-1427

ER -

Regularization of a mathematical model of the Wheatley heart valve

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