Two Circle Construction of the Reinforced Wheatley Valve

Abstract In earlier papers (McKee et al. in J Biomech Eng 143(8):081006, 2021; Rebolledo et al. in J Biomech Eng 145(1):014501, 2023), a mathematical representation of the Wheatley heart valve was developed dependent on two related parameters. In this article, we introduce a mathematical representation based on two related, but arguably more natural parameters, namely, the radius of a large circle and the radius of a smaller circle lying within the larger circle. In the previous design it was found (Oliveira et al. in Int J Numer Meth Biomed Eng 40(2):e3792, 2024) that under severe back pressure central bending of the leaflets was observed. In order to counter this, the idea of a structural support in the form of stays embedded within the leaflets is introduced. Each leaflet consists of two concatenated surfaces. In this paper, all the stays associated with the “first” surface will be shown to lie on that surface, i.e., can be embedded within the surface. Furthermore, they can be shown to meet at a common point when they are extended. This is also true of all stays for the “second” surface, although the common point will be different in this case. The proposed analytical expressions are used to perform computational simulations of reinforced Wheatley valves. The results show that both the number and position of the stays contribute to reducing local buckling, but may decrease the geometric orifice area. This observation shows that the proposed geometric parametrisation is appropriate for correctly designing of S-shaped leaflet reinforcements.