Modeling the Deformation of the Elastin Network in the Aortic Valve

This paper is concerned with proposing a suitable structurally motivated strain energy function, denoted by W-e(elastin network), for modeling the deformation of the elastin network within the aortic valve (AV) tissue. The AV elastin network is the main noncollagenous load-bearing component of the valve matrix, and therefore, in the context of continuum-based modeling of the AV, the W-e(elastin network) strain energy function would essentially serve to model the contribution of the isotropic matrix. To date, such a 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 to customize a structurally motivated W-e(elastin network) 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, The Role of Elastin in Aortic Valve Mechanics, J. Biomech., 31, pp. 115-123) 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 the frequently used models in the literature, as well as the Arruda-Boyce model as the gold standard of the network chain models. It is shown that our proposed W-e(elastin network) function, together with the general exponential and the Arruda-Boyce models provide excellent fits to the data, with R-2 values in excess of 0.98, while the neo-Hookean function is entirely inadequate for modeling the AV elastin network. However, the general exponential function may not be amenable to rigorous interpretation, as there is no structural meaning attached to the model. It is also shown that the parameters estimated by the Arruda-Boyce model are not mathematically and structurally valid, despite providing very good fits. We thus conclude that our proposed strain energy function W-e(elastin network) is the preferred choice for modeling the behavior of the AV elastin network and thereby the isotropic matrix. This function may therefore be superimposed onto that of the anisotropic collagen fibers family in order to develop a structurally motivated continuum-based model for the AV.