A FINITE ELEMENT FRAMEWORK FOR BULK-SURFACE COUPLED PDES TO SOLVE MOVING BOUNDARY PROBLEMS IN BIOPHYSICS

Area of Science:

• Biophysics
• Computational Science
• Applied Mathematics

Background:

• Moving boundary problems are crucial in biophysics, often involving complex bulk-surface partial differential equations (PDEs).
• Existing computational frameworks may struggle with interpretability, accuracy, and mesh distortion in these simulations.

Purpose of the Study:

• To develop and validate a new computational framework for simulating moving boundary problems in biophysics.
• To enhance interpretability, accuracy, and mesh distortion control in bulk-surface PDE solvers.

Main Methods:

• Adaptation of a structure preservation scheme for interpretability.
• Integration of an Arbitrary Lagrangian Eulerian (ALE) framework to mitigate mesh distortion.
• Application of a staggered approach for coupling different equation types.

Main Results:

• Demonstrated accuracy of the framework on advection-diffusion-reaction equations, Cahn-Hilliard type phase-field models, and Helfrich energy gradient flows.
• Verified convergence through numerical experiments and convergence studies.
• Successfully simulated biophysical models involving membrane deformation, showcasing broad applicability.

Conclusions:

• The developed computational framework offers an accurate and robust solution for moving boundary problems in biophysics.
• The framework successfully balances interpretability, accuracy, and mesh distortion management.
• This work has broad applicability in simulating complex biophysical phenomena, particularly those involving membrane dynamics.