Impact of Force Function Formulations on the Numerical Simulation of Centre-Based Models

Area of Science:

• Computational biology
• Biophysics
• Mathematical modeling

Background:

• Centre-based models are crucial for simulating multicellular systems in cancer and developmental biology.
• The choice of force functions significantly impacts model behavior, robustness, and efficiency.
• Different software implementations use varying default force functions, raising questions about interchangeability.

Purpose of the Study:

• To analyze the numerical properties and limitations of three common force functions in centre-based models.
• To provide guidance for modelers on selecting and parameterizing force functions.
• To understand the impact of force function choice on simulation outcomes.

Main Methods:

• Empirical comparison of three popular force functions.
• Parameter tuning to achieve consistent cell-division relaxation times.
• Simulation of a 2D monolayer undergoing proliferation and mechanical relaxation.

Main Results:

• Consistent relaxation times across different force functions lead to agreement in population radius.
• Numerical stability is insufficient to prevent unphysical cell trajectories post-division.
• Large time steps can introduce geometrical discrepancies at the population level.

Conclusions:

• Careful parameterization of force functions is essential for reliable centre-based modeling.
• Time step selection requires consideration beyond mere numerical stability to avoid artifacts.
• This study aids in understanding the implications of force function choice in computational biology.