An efficient Cellular Potts Model algorithm that forbids cell fragmentation

TL;DR

This paper introduces a new Cellular Potts Model algorithm that prevents cell fragmentation at all temperatures, improving realism, computational efficiency, and restoring detailed balance for more accurate long-term simulations.

Contribution

The authors develop a novel CPM algorithm that forbids cell fragmentation across all temperatures, enhancing realism and computational efficiency while maintaining detailed balance.

Findings

Prevents cell fragmentation at all temperatures.

Increases computational efficiency over standard CPM.

Restores detailed balance for consistent long-term results.

Abstract

The Cellular Potts Model (CPM) is a lattice based modeling technique which is widely used for simulating cellular patterns such as foams or biological tissues. Despite its realism and generality, the standard Monte Carlo algorithm used in the scientific literature to evolve this model preserves connectivity of cells on a limited range of simulation temperature only. We present a new algorithm in which cell fragmentation is forbidden for all simulation temperatures. This allows to significantly enhance realism of the simulated patterns. It also increases the computational efficiency compared with the standard CPM algorithm even at same simulation temperature, thanks to the time spared in not doing unrealistic moves. Moreover, our algorithm restores the detailed balance equation, ensuring that the long-term stage is independent of the chosen acceptance rate and chosen path in the temperature space.