Journal
SIAM JOURNAL ON APPLIED MATHEMATICS
Volume 82, Issue 4, Pages 1167-1193Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M1424482
Keywords
cardiac perfusion; nonlinear poromechanics; constitutive modeling
Categories
Funding
- ERC [740132]
- project Modeling the heart across the 562 scales: From cardiac cells to the whole organ [PRIN 2017AXL54F 003]
- European Research Council (ERC) [740132] Funding Source: European Research Council (ERC)
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The importance of myocardial perfusion in the early stage of cardiac disease is not well researched. This study proposes a mathematical model that considers the interactions among the systemic circulation, coronary vessels, and myocardium. By decoupling the computational cost, the model accurately simulates a heartbeat under healthy conditions and effectively captures phenomena arising from the interaction of multiple components.
The importance of myocardial perfusion at the outset of cardiac disease remains largely understudied. To address this topic we present a mathematical model that considers the systemic circulation, the coronary vessels, the myocardium, and the interactions among these com-ponents. The core of the whole model is the description of the myocardium as a multicompartment poromechanics system. A novel decomposition of the poroelastic Helmholtz potential involved in the poromechanics model allows for a quasi-incompressible model that adequately describes the physical interaction among all components in the porous medium. We further provide a rigorous mathematical analysis that gives guidelines for the choice of the Helmholtz potential. To reduce the computational cost of our integrated model we propose decoupling the deformation of the tissue and systemic cir-culation from the porous flow in the myocardium and coronary vessels, which allows us to apply the model also in combination with precomputed cardiac displacements, obtained form other models or medical imaging data. We test the methodology through the simulation of a heartbeat in healthy conditions that replicates the systolic impediment phenomenon, which is particularly challenging to capture as it arises from the interaction of several parts of the model.
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