On the myocardium modeling under multimodal deformations: a comparison between costa’s, Holzapfel and Ogden’s formulations

In this study we evaluate the performance of different constitutive biomechanical models, focusing on their ability to reproduce the mechanical behavior of myocardial tissue under various deformation modes. Three constitutive models were analyzed assuming incompressible formulations: the invariant-based formulation of the Costa model, the Holzapfel–Ogden (HO) model, and its extended version (HOE). The study aimed to identify which model provides the best fit for different experimental data, including equibiaxial (EBx), true biaxial (TBx), simple triaxial shear (STS), and combined data sets (Equibiaxial + Shear, True biaxial + Shear). The results showed that the Costa model generally performed better when considering combined datasets, providing a good balance between fitting accuracy and parameter stability, while using the least number of parameters among the contrasted models. The HO model demonstrated reasonable fitting abilities but struggled with non-equibiaxial conditions and clearly orthotropic simple shear datasets. The extended HOE model improved the fitting performance of the standard HO formulation for more complex data, particularly in shear tests, but introduced additional complexity and a higher number of parameters. Therefore, our study highlights the importance of analyzing which validated constitutive formulation is able to adapt to the available experimental data, especially when mixed deformation modes are involved. While all the three models tested performed adequately, the Costa model proved to be the most versatile, especially when dealing with various experimental conditions, providing insights for future research on biomechanical modeling of cardiac tissue.