Unbiased on-lattice domain growth

Area of Science:

• Computational biology
• Mathematical modeling of biological processes

Background:

• Domain growth is crucial for embryonic development, tissue growth, and limb regeneration.
• Existing on-lattice reaction-diffusion models face challenges incorporating domain growth accurately.
• A common method leads to unphysical particle accumulation at domain boundaries, particularly with low diffusion rates.

Purpose of the Study:

• To present an alternative method for incorporating domain growth into reaction-diffusion models.
• To address the issue of particle buildup at domain boundaries.
• To demonstrate the accuracy of the new method in scenarios where the previous method fails.

Main Methods:

• Development of a novel computational method for simulating domain growth.
• Comparison of the new method against a previously established technique.
• Analysis of model performance across different parameter regimes, focusing on diffusion and growth rates.

Main Results:

• The proposed method effectively prevents unphysical particle buildup at domain boundaries.
• The new method demonstrates superior accuracy in scenarios with low diffusion relative to domain growth.
• The study identifies parameter ranges where the original method remains computationally feasible.

Conclusions:

• The developed method offers a more robust approach for modeling domain growth in biological systems.
• This advancement is critical for accurate simulations of processes like embryonic development and tissue regeneration.
• Understanding parameter limitations is key for selecting appropriate modeling techniques.