An active strain electromechanical model for cardiac tissue

Area of Science:

• Computational mechanics
• Biomedical engineering
• Applied mathematics

Background:

• Cardiac tissue exhibits complex electromechanical coupling, essential for heart function.
• Existing models often simplify the interplay between electrical propagation and mechanical deformation.
• Understanding this coupling is crucial for diagnosing and treating cardiac conditions.

Purpose of the Study:

• To develop and validate a novel finite element approximation for the electromechanical coupling in cardiac tissue.
• To incorporate the active strain assumption and nonlinear elasticity into a unified mathematical framework.
• To accurately model the influence of electrical activity on tissue mechanics.

Main Methods:

• A finite element approximation was developed for a system of partial differential equations.
• The model utilizes an active strain assumption with multiplicative decomposition of the deformation tensor.
• Piecewise quadratic and linear finite elements were employed for different physical variables (displacement, pressure, electrical potentials).

Main Results:

• The proposed model successfully captures key features of cardiac electromechanical coupling.
• Numerical tests demonstrate the efficiency and accuracy of the developed finite element scheme.
• The model integrates electrical propagation (bidomain/monodomain equations) with nonlinear elasticity.

Conclusions:

• The developed finite element method provides an accurate and efficient tool for simulating cardiac electromechanics.
• This model enhances our understanding of the interplay between electrical and mechanical processes in the heart.
• The approach offers a robust framework for future investigations into cardiac electrophysiology and mechanics.