Discrete and continuous models for tissue growth and shrinkage

Area of Science:

• Mathematical Biology
• Computational Biology
• Developmental Biology

Background:

• Domain growth significantly impacts particle redistribution in biological systems.
• Individual-based stochastic models offer detailed insights into biological movement and inherent stochasticity.
• Existing models often rely on deterministic, continuum approaches.

Purpose of the Study:

• To extend stochastic models of biological domain growth to incorporate diverse growth and shrinkage mechanisms.
• To validate the derived Fokker-Plank equation (FPE) against individual-level simulations.
• To develop a numerical approach for estimating drift and diffusion coefficients when analytical solutions are unavailable.

Main Methods:

• Development of a simple stochastic model for domain growth and shrinkage.
• Derivation of a Fokker-Plank equation (FPE) describing tracer particle evolution on a growing domain.
• Numerical estimation of drift and diffusion coefficients for FPE derivation.

Main Results:

• Demonstrated good agreement between mean tracer density from simulations and FPE solutions for various growth mechanisms.
• Successfully derived FPE coefficients for models incorporating domain shrinkage (element death).
• Validated the numerical coefficient estimation approach against analytical solutions.

Conclusions:

• The extended stochastic model accurately captures particle dynamics in growing and shrinking biological domains.
• The derived FPE provides a valuable tool for understanding particle evolution in these systems.
• The numerical coefficient estimation method enhances the applicability of FPEs in complex biological scenarios.