Comparison and critical analysis of invariant-based models with respect to their ability in fitting human aortic valve data

With the increase of life expectancy and population average age, heart valve diseases have become more frequent, representing an always increasing percentage among cardiovascular diseases, which are the predominant cause of death in the western country. For this reason, research activities within such a context and, in particular, computer-based predictions of valve behavior are strongly motivated. Consequently, the study of the tissue mechanical response and the constitutive relationships for modeling material behavior represent crucial a aspect to be investigated in order to perform realistic simulations. The mechanical response of the aortic valve tissue depends on the contribution, composition, and interaction of different constituents, such as collagen fibers and elastin network. Accordingly, constitutive laws including non-linearity and anisotropy are necessary. Clearly, the complexity of a constitutive model increases more as it takes into account the histological structure of the tissue. Numerous constitutive models have been developed to describe arterial tissue, but relatively few models have been calibrated specifically for the aortic valve. This study focuses on the investigation of constitutive models so far proposed in the literature which could be suitable to capture the mechanical behavior of the aortic valvular tissue. To make the right choice, the comparison between these constitutive models is done in terms of the fitting quality achieved with respect to human aortic valve data proposed in the literature. For this purpose, an optimization technique based on the nonlinear least square method is used. The obtained material parameters could be later used in finite element analysis adopted, in this last decade, as an innovative approach to support the operation planning procedure and the design of artificial grafts.