A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics.

Area of Science:

• Computational mechanics
• Biomedical engineering
• Cardiovascular modeling

Background:

• Accurate numerical simulations of cardiac mechanics require coupling the heart with circulatory system models.
• Lumped parameter networks (0D fluid models) are commonly used for blood flow, but coupling them with 3D cardiac models presents challenges.
• Developing efficient and accurate numerical coupling methods is crucial due to strong physical interactions.

Purpose of the Study:

• To present a modular framework for implicitly coupling 3D finite element cardiac mechanics simulations with 0D blood circulation models.
• To extend previous 3D fluid-0D fluid coupling to 3D structure-0D fluid coupling within a unified scheme.
• To assess the effectiveness, temporal convergence, and computational cost of the proposed numerical scheme.

Main Methods:

• Developed a modular framework for implicit coupling of 3D finite element cardiac mechanics and 0D lumped parameter circulation models.
• Extended a previously established 3D fluid-0D fluid coupling scheme to a 3D structure-0D fluid approach.
• Utilized a unified coupling scheme inspired by the Approximate Newton Method for stability and flexibility.

Main Results:

• The coupled 3D structure-0D fluid model successfully simulates physiological cardiac behavior.
• An idealized left ventricle example demonstrated accurate pressure-volume loops and natural recapitulation of cardiac cycle phases.
• The framework shows effectiveness, good temporal convergence, and reasonable computational cost.

Conclusions:

• The proposed modular framework enables accurate and efficient coupling of 3D cardiac mechanics and 0D circulation models.
• The unified numerical scheme combines the stability of monolithic methods with the flexibility of partitioned approaches.
• This work advances cardiovascular modeling by providing a robust tool for simulating heart-circulatory interactions.