A mathematical model for irreversible damage of the collagen scaffold in the myocardium
Abstract
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.
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BibTeX
@misc{radisic2026mathematical,
title = {{A mathematical model for irreversible damage of the collagen scaffold in the myocardium}},
author = {Irena Radišić and Francesco Regazzoni and Luca Dede' and Alfio Quarteroni},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15243},
eprint = {2609.15243},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15243},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A mathematical model for irreversible damage of the collagen scaffold in the myocardium
AU - Irena Radišić
AU - Francesco Regazzoni
AU - Luca Dede'
AU - Alfio Quarteroni
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.15243
UR - https://arxiv.org/abs/2609.15243
AB - 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.
ER -