A generalized mathematical representation of the shape of the Wheatley heart valve and the associated static stress fields upon opening and closing

Oliveira, H L and McKee, S and Buscaglia, G C and Cuminato, J A and Stewart, I W and Wheatley, D J (2022) A generalized mathematical representation of the shape of the Wheatley heart valve and the associated static stress fields upon opening and closing. IMA Journal of Applied Mathematics. hxac016. ISSN 1464-3634 (https://doi.org/10.1093/imamat/hxac016)

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Abstract

This note extends previous work of the authors modelling the Wheatley valve by using six intersecting and contiguous ellipses to obtain a generalized mathematical representation of the Wheatley valve: this provides a number of free parameters that could be employed to obtain an optimal design. Since optimality is multi-objective with many of the objectives conflicting we focus on the stresses imposed on the valve by a constant force field. Three distinctly different designs are chosen and an analysis of the stresses is undertaken, conclusions are drawn and results are discussed.

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