Improving the stability of cardiac mechanical simulations

Area of Science:

• Computational mechanics
• Biomedical engineering
• Cardiac modeling

Background:

• Finite element methods (FEM) are crucial for simulating cardiac mechanics.
• Patient-specific cardiac models face challenges with large deformations and tension gradients, often causing numerical solver failures.
• Robust and stable simulations are essential for clinical applications and parameter investigations.

Purpose of the Study:

• To present a novel numerical method to enhance the stability and robustness of large deformation mechanics simulations in cardiac modeling.
• To improve the convergence of nonlinear solvers in complex cardiac simulations.
• To enable reliable simulations of cardiac function on personalized patient geometries.

Main Methods:

• Introduced a compressibility penalty to the standard incompressible formulation of large deformation mechanics.
• Compared the method's performance with direct discretization and isochoric/deviatoric split formulations.
• Evaluated the impact of the penalty on incompressibility constraints and solver convergence using Newton's method.

Main Results:

• The compressibility penalty significantly improved solver stability and reduced deviations from the incompressibility constraint.
• The method maintained the expected order of convergence under mesh refinement.
• Simulations showed nearly identical pressure-volume relations compared to standard methods.
• Enabled stable simulations of diastolic and systolic function on personalized patient geometries.

Conclusions:

• The proposed compressibility penalty method offers a straightforward and effective way to enhance the stability of cardiac mechanical simulations.
• This approach overcomes common numerical challenges, facilitating more reliable patient-specific cardiac modeling.
• The method supports robust simulations essential for clinical translation and advanced research in cardiac mechanics.