Modelling the deformation of the elastin network in the aortic valve

This paper is concerned with proposing a suitable structurally-motivated strain energy function for modelling the deformation of the elastin network within the aortic valve (AV) tissue. The AV elastin network is the main non-collagenous load-bearing component of the valve matrix and therefore, within the context of continuum-based modelling of the AV, it essentially serves as the contribution of the 'isotropic matrix'. To date, such function has mainly been considered as either a generic neo-Hookean term or a general exponential function. In this paper, we take advantage of the established structural analogy between the network of elastin chains and the freely jointed molecular chain networks, and customise a structurally-motivated function on this basis. The ensuing stress-strain (force-stretch) relationships are thus derived and fitted to the experimental data points reported by Vesely (1998) for intact AV elastin network specimens under uniaxial tension. The fitting results are then compared with those of the neo-Hookean and the general exponential models, as well as the Arruda-Boyce model as the gold standard of the network chain models. It is shown that the neo-Hookean function is entirely inadequate for modelling the AV elastin network, while the parameters estimated by the Arruda-Boyce model are not mathematically and structurally valid. Since the general exponential function is purely phenomenological, we conclude that our proposed strain energy function may be the preferred choice for modelling the behaviour of the AV elastin network, and thereby the 'isotropic matrix'.