A Mathematical Representation of the Wheatley Heart Valve

McKee, Sean; Cuminato, José Alberto; Stewart, Iain W.; Wheatley, David J.

doi:10.1115/1.4050753

Cited by 2 publications

(7 citation statements)

References 9 publications

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“…The first is to present a new analytical expression describing the geometry of leaflets for WHVs. This new expression employs contiguous and intersecting ellipses, which in turn encompasses and expands upon the equations presented by the authors previously (McKee et al (2021)). The second consists in proposing a mechanical model capable of simulating the opening and closing movements of the WHV.…”

Section: Introductionmentioning

confidence: 81%

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

Oliveira

McKee

Buscaglia

et al. 2022

IMA Journal of Applied Mathematics

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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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Section: Introductionmentioning

confidence: 81%

“…Both ν and n contribute to the degree of ellipticity, or, equivalently, the degree to which the valve deviates from the previous circular design (e.g. McKee et al (2021) ). The parameter m is a measure of the deviation from linearity when constructing the side walls.…”

Section: Possible Generalised Designs Of the Wheatley Valvementioning

confidence: 99%

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

Oliveira

McKee

Buscaglia

et al. 2022

IMA Journal of Applied Mathematics

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“…The attachment angle, on the other hand, is unconstrained. The unstressed configuration was specified using the mathematical representation proposed by McKee et al 22 …”

Section: Models and Methodsmentioning

confidence: 99%

“…The attachment angle, on the other hand, is unconstrained. The unstressed configuration was specified using the mathematical representation proposed by McKee et al 22 A single-mode isotropic Ogden hyperelastic solid is adopted as the constitutive model. Its energy density function is defined by:…”

Section: Wav Finite Element Modelmentioning

confidence: 99%

“…[19][20][21] This shape can be obtained from the union of parameterized elliptical (or circular as special case) contour lines, which is convenient for optimization and manufacturing processes. 22,23 These parametric geometries can also be used to construct computational models to better understand the mechanical behavior of the tri-leaflet assembly. 24 This approach is being increasingly explored in the design of state-of-the-art valves.…”

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confidence: 99%

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Three‐dimensional fluid–structure interaction simulation of the Wheatley aortic valve

Oliveira,

Buscaglia,

Paz

et al. 2023

Numer Methods Biomed Eng

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Valvular heart diseases (such as stenosis and regurgitation) are recognized as a rapidly growing cause of global deaths and major contributors to disability. The most effective treatment for these pathologies is the replacement of the natural valve with a prosthetic one. Our work considers an innovative design for prosthetic aortic valves that combines the reliability and durability of artificial valves with the flexibility of tissue valves. It consists of a rigid support and three polymer leaflets which can be cut from an extruded flat sheet, and is referred to hereafter as the Wheatley aortic valve (WAV). As a first step towards the understanding of the mechanical behavior of the WAV, we report here on the implementation of a numerical model built with the ICFD multi‐physics solver of the LS‐DYNA software. The model is calibrated and validated using data from a basic pulsatile‐flow experiment in a water‐filled straight tube. Sensitivity to model parameters (contact parameters, mesh size, etc.) and to design parameters (height, material constants) is studied. The numerical data allow us to describe the leaflet motion and the liquid flow in great detail, and to investigate the possible failure modes in cases of unfavorable operational conditions (in particular, if the leaflet height is inadequate). In future work the numerical model developed here will be used to assess the thrombogenic properties of the valve under physiological conditions.

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A Mathematical Representation of the Wheatley Heart Valve

Abstract: Starting from a hand-drawn contour plot, this note develops a set of intersecting and contiguous circles whose perimeter, upon extending appropriately to three dimensions, can be seen to be a natural mathematical representation of the Wheatley heart valve.

Cited by 2 publications

References 9 publications

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

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

Three‐dimensional fluid–structure interaction simulation of the Wheatley aortic valve

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