A viscoactive constitutive modeling framework with variational updates for the myocardium.

Area of Science:

• Biomedical Engineering
• Computational Biology
• Mechanics of Materials

Background:

• Cardiac mechanics involves complex active and passive material behaviors.
• Existing models often treat active tension and deformation separately.
• A unified framework is needed to accurately capture cardiac tissue dynamics.

Purpose of the Study:

• To develop a constitutive modeling framework for contractile cardiac mechanics using a single variational principle.
• To integrate hyperelasticity, rate-dependent force generation, and dissipation within a unified model.
• To provide a robust computational tool for simulating cardiac tissue deformation and function.

Main Methods:

• Formulation of a variational principle for cardiac mechanics.
• Development of a three-element, Hill-type model with multiplicative decomposition of deformation gradient.
• Incorporation of internal variables (stretch ratios) and kinetic potential functions.
• Coupling of kinetic equations with calcium transients and finite element method (FEM).

Main Results:

• Derivation of incremental stress-strain relations and kinetic rate equations from the variational principle.
• Successful analysis at the material point level and simulation of 3D tissue slab deformation.
• Accurate simulation of left ventricular contraction and relaxation, yielding key kinematic measures like ejection fraction.

Conclusions:

• The proposed variational framework provides a unified approach to cardiac mechanics.
• The model effectively captures active contraction, relaxation, and passive hyperelasticity.
• This framework offers a powerful tool for computational modeling and simulation of cardiac function.