A mathematical model for irreversible damage of the collagen scaffold in the myocardium

RESUMO

We propose a dissipative, irreversible damage model for anisotropic media in large deformations to address the damage process of the myocardium following a cardiac infarction. We model damage to the collagen in the cleavage planes resulting from an increased load to the passive tissue. Starting from variational principles, we derive a quasi-static differential model governing the irreversible evolution of the damage. We apply our model to two test cases. First, a rectangular passive slab geometry to which an indenter-like load is applied. Then, we couple our model with a model for the numerical simulation of left ventricular electromechanics. Our results show that a redistribution of the load within a left ventricle occurring following a cardiac infarction can produce the damage to the collagen scaffold in the infarcted area consistent with experimental results. This is indicative of the fact that passive load-dependent dissipative phenomena are implicated in post-infarction remodelling.