Orthotropic active strain models for the numerical simulation of cardiac biomechanics

• Published in: International journal for numerical methods in biomedical engineering Vol. 28; no. 6-7; pp. 761 - 788
• Main Authors: Rossi, Simone, Ruiz-Baier, Ricardo, Pavarino, Luca F., Quarteroni, Alfio
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.06.2012
• Subjects: active strain formulation; cardiac mechanics; Computer Simulation; Finite Element Analysis; finite element discretization; Humans; Models, Cardiovascular; Myocytes, Cardiac - physiology; nonlinear incompressible elasticity; nonlinear incompressible elasticity; cardiac mechanics; finite element discretization; active strain formulation
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.2473

SUMMARY A model for the active deformation of cardiac tissue considering orthotropic constitutive laws is introduced and studied. In particular, the passive mechanical properties of the myocardium are described by the Holzapfel‐Ogden relation, whereas the activation model is based on the concept of active strain. There, an incompatible intermediate configuration is considered, which entails a multiplicative decomposition between active and passive deformation gradients. The underlying Euler–Lagrange equations for minimizing the total energy are written in terms of these deformation factors, where the active part is assumed to depend, at the cell level, on the electrodynamics and on the specific orientation of the cardiomyocytes. The active strain formulation is compared with the classical active stress model from both numerical and modeling perspectives. The well‐posedness of the linear system derived from a generic Newton iteration of the original problem is analyzed, and different mechanical activation functions are considered. Taylor–Hood and MINI finite elements are used in the discretization of the overall mechanical problem. The results of several numerical experiments show that the proposed formulation is mathematically consistent and is able to represent the main features of the phenomenon, while allowing savings in computational costs. Copyright © 2012 John Wiley & Sons, Ltd. We propose a particular model to describe the active deformation of the myocardial tissue employing an active strain formulation (top left figure). We provide a thorough comparison with respect to active stress models from the mathematical and computational viewpoints (displacements and two pressure profiles, right panel). Furthermore, our numerical results agree with experimental observations in terms of torsion of the left ventricle (basal and apical) and in terms of end‐systolic principal and shear strains (bottom left panel).