A method for simulating the growth of cells on a general surface using the finite element method

Area of Science:

• Biomedical Engineering
• Computational Biology
• Mathematical Modeling

Background:

• Cell growth on nutrient-coated surfaces is crucial for tissue regeneration.
• Reaction-diffusion equations model the complex interplay between cell and nutrient densities.
• Accurate computational methods are needed to simulate these processes on intricate surfaces.

Purpose of the Study:

• To develop and present a finite element method (FEM) for solving reaction-diffusion equations that model cell and nutrient growth on general surfaces.
• To adapt diffusion equations from local element coordinates to global coordinates for comprehensive surface simulation.
• To demonstrate the applicability of the proposed FEM approach through illustrative examples.

Main Methods:

• A finite element method is employed to discretize a general surface into flat triangular elements.
• A coordinate transformation is utilized to convert diffusion equations from local element coordinates to global coordinates.
• The system of reaction-diffusion equations is solved numerically using the developed FEM framework.

Main Results:

• The finite element method effectively solves reaction-diffusion equations governing cell and nutrient dynamics on approximated general surfaces.
• The coordinate transformation successfully reconciles local and global frame diffusion equations.
• Simulations with typical examples validate the accuracy and utility of the proposed method.

Conclusions:

• The presented finite element method provides a robust computational tool for simulating cell and nutrient growth on surfaces relevant to tissue regeneration.
• This approach facilitates the understanding and optimization of regenerative medicine strategies.
• The method's adaptability to general surfaces enhances its applicability in complex biological scenarios.