A Mathematical Framework for Predicting the Location and Extent of Complex Cardiac Ruptures
Autores: Francisco Javier Roldan Gomez
Tipo: Short Note
Número: Volume 1, Issue 1
Fecha de publicación: 2026-11-04
Recibido: 2026-10-15
Aceptado: 2026-11-02
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Resumen
Cardiac rupture after myocardial infarction is a high-mortality complication whose spatial pattern remains poorly predicted. This note argues that the appropriate mathematical framework is anisotropic computational fracture mechanics, specifically the coupling of finite element analysis with a crack phase-field model that incorporates myocardial fiber orientation. The clinical observation that dissection paths originate where the components of the helical ventricular myocardial band converge suggests a geometric and material discontinuity, which we formalize as a weak interface in a fibrous continuum. We identify the mathematical objects involved: an anisotropic hyperelastic constitutive law, a phase-field variable governed by an energy-based anisotropic criterion, and a finite element discretization that resolves the fiber field from diffusion tensor imaging. The result is a field theory of material failure that predicts a rupture surface rather than a probability, and it constitutes the natural mathematical extension of the author's clinical research line.