Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations

Abstract

The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to the development of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model—the transversely isotropic version of the Mooney–Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and the polynomial forms (R2=0.92–0.99 versus 0.91–0.97) compared to the combined polynomial-exponential SEDF (R2=0.65–0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 versus 0.30), indicating a more well-defined search space. Finally, the exponential and the combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential form leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets owing to its superb fitting capabilities and smaller parameter's confidence regions.