Divergence of detachment forces in the finite Voronoi model

TL;DR

This paper investigates the divergence of detachment forces in the finite Voronoi model, revealing how force divergence affects tissue fracture simulations and proposing regularization and calibration methods for accurate modeling.

Contribution

It introduces a regularization for the finite Voronoi model to address force divergence issues and calibrates the model against a deformable polygon model for better fracture analysis.

Findings

Force divergence causes unphysical dependence of fracture times on time step size.

Regularization mitigates the divergence and stabilizes fracture simulations.

Calibration against a polygon model links tissue mechanics to fracture behavior.

Abstract

Detachment and fracture are central to many tissue-level processes, but they are challenging to simulate with Voronoi-type models that typically assume a confluent tissue. Here we analyze the finite Voronoi model, a nonconfluent extension of conventional Voronoi models, in which cell boundaries are composed of straight Voronoi edges and circular arcs of fixed radius $\ell$. When the line tension on cell-medium interfaces exceeds the tension on cell-cell contacts, we find that the model exhibits a strong time-step dependence in the fracture timescale of initially intact active clusters: decreasing $\Delta t$ can unphysically suppress cluster rupture events. We trace this behavior to a divergence of detachment forces in the finite Voronoi model and introduce a simple regularization. Finally, we calibrate the near-detachment mechanics against a deformable polygon model and examine how key physical parameters control the tissue fracture timescale under two different calibration strategies. Our results show that, for studies focused on fracture or intercellular adhesion in nonconfluent monolayers, a physically motivated calibration of near-detachment mechanics in the finite Voronoi model is essential.