Incorporating domain growth into hybrid methods for reaction-diffusion systems

Area of Science:

• Computational Biology
• Mathematical Modeling
• Physical Chemistry

Background:

• Reaction-diffusion mechanisms model diverse phenomena across spatial scales, from intracellular dynamics to vegetation patterns.
• Domain growth is vital for biological processes such as embryonic development and wound healing.
• Existing numerical models for growing domains have limitations regarding spatial scales and particle numbers.

Purpose of the Study:

• To develop novel hybrid methods for simulating reaction-diffusion systems on growing domains.
• To extend prominent static-domain hybrid methods to accommodate domain growth.
• To provide detailed algorithms for practical implementation of these new methods.

Main Methods:

• Development of three new hybrid methods tailored for growing domains.
• Extension of existing spatially extended hybrid methods originally designed for static domains.
• Validation against three representative reaction-diffusion systems.

Main Results:

• The developed hybrid methods accurately simulate reaction-diffusion systems on growing domains.
• The methods demonstrate unbiased modeling capabilities across different spatial scales.
• Successful extension of static-domain hybrid approaches to dynamic, growing domains.

Conclusions:

• The new hybrid methods offer a robust and accurate approach for simulating multi-scale phenomena on growing domains.
• These methods bridge a gap in computational modeling for biological and physical systems involving domain growth.
• The provided algorithms facilitate the application of these advanced modeling techniques.