Computational modeling of chemo-electro-mechanical coupling: a novel implicit monolithic finite element approach

Area of Science:

• Computational biology
• Biophysics
• Cardiovascular research

Background:

• Current pharmacological treatments for cardiac disease lack understanding of local cell biochemistry's impact on global function.
• Bridging the gap between cellular-level biochemical processes and whole-heart mechanical behavior is crucial for advancing cardiac medicine.

Purpose of the Study:

• To develop a novel, unified computational strategy for simulating excitable biological systems across multiple scales.
• To integrate chemical, electrical, and mechanical fields within a single cardiac model.
• To enable patient-specific simulations of cardiac function.

Main Methods:

• A monolithic finite element scheme was employed for spatial discretization of governing equations.
• A global-local split was utilized, introducing deformation and transmembrane potential globally, and chemical variables locally.
• Implicit backward Euler and incremental iterative Newton-Raphson schemes ensured algorithmic stability and convergence.

Main Results:

• The proposed algorithm successfully simulates the integrated chemical, electrical, and mechanical fields during a cardiac cycle.
• Simulations were performed on patient-specific geometry, demonstrating robustness and stability.
• Achieved calculation times of approximately 4 days on a standard desktop computer.

Conclusions:

• The developed unified strategy provides a robust and stable method for simulating complex cardiac dynamics.
• This computational approach offers a powerful tool for understanding how cellular biochemistry influences overall cardiac function.
• Enables patient-specific modeling for potential advancements in cardiac disease treatment and drug development.