Mathematical modeling of biomechanical elastic and hyperelastic properties of the myocardium

Abstract

BACKGROUND: The study of mechanical properties of biological tissues is extremely informative and is one of the most important areas of biomechanics. Knowledge of these aspects of biological objects based on experimental data can become a source of new medical and technical solutions for the reconstruction of organs and the development of replacement materials. AIM: Passive mechanical properties of isolated myocardium are compared with linear, bilinear, exponential and the most common hyperelastic models (neohookean, Mooney–Rivlin, Ogden, Yeoh, polynomial and Veronda–Westmann). MATERIALS AND METHODS: Literature data on mechanical tests of autopsy material obtained from mongrel dogs were used as initial data. To search for the most advanced calculation algorithms the computer algebra system was used, the Mathcad 15.0 software package and the multifunctional finite element analysis application ANSYS 2022 R2 were used. Direct comparison of models was made based on mathematical statistics. RESULTS: Among the first group of models, the results closest to the experimental data were demonstrated by the exponential model R = 0.9958/0.9984 (in the longitudinal/transverse direction with respect to the myocardial fibers), the lowest accuracy was demonstrated by the linear model R = 0.9813/0.9803. Young’s moduli of linear, bilinear and exponential models and material constants of hyperelastic models are determined. The coefficient of elastic anisotropy of the myocardium, defined as the ratio of the elastic moduli of the linear model measured along and across the direction of the fibers, is equal to 2.18, which is very different from the literature data for the myocardium of the human heart. Deformation along the fibers of the heart muscle is more energy-consuming in the direction along the fibers than in the transverse direction (3.81 and 2.52 mJ/cm3). The most accurate hyperelastic models turned out to be the 2nd order polynomial model R = 0.9971 and the 3rd order Yeoh model R = 0.997. The largest deviations and the lowest correlation coefficient between the experimental and model data were demonstrated by the simple neohookean model R = 0.974 with a single parameter μ. The numerical values of the parameters of hyperelastic models obtained by calculation methods used practically did not differ from each other (≤2.16%). CONCLUSIONS: The study demonstrated the importance of selecting the correct mechanical model for isolated myocardium. The data obtained can be useful in virtual interventions (simulations) for predicting outcomes and supporting clinical decisions, developing replacement materials and structures made of them for reconstructive operations on heart structures.