An Extended Generalized Hill Model for Cardiac Tissue: Comparison with Different Approaches Based on Experimental Data

In this work we discuss advantages and drawbacks of active mechanics frameworks often used to represent the material response of cardiac tissue. A formal analysis of the models is followed by the application of these frameworks to represent the experimentally measured active and passive response of cardiac tissue. The active strain model is analyzed first and we show that, for commonly used material energies, this framework is not adequate to represent both active and passive tissue responses simultaneously. The active stress model and the generalized Hill model are discussed next. We incorporate the basic idea from Stålhand et al. (2008) to improve the generalized Hill model. Namely we propose to scale the active energy by a function of cross-bridge formation making the model physiologically more accurate. This modification also allows to relate the new Hill type model to the active stress framework. Finally, we show that this extended Hill model best represents the stress-strain response measured in equibiaxial stretch experiments.