A curvature flow approach to dorsal closure modelling

TL;DR

This paper introduces a curvature flow model for dorsal closure in embryonic drosophila, providing mathematical analysis, numerical methods, and simulations that align with observed biological data.

Contribution

It develops a novel curvature-based model, proves its mathematical properties, and offers a stable numerical scheme with biological data simulations.

Findings

Global existence and convergence of the model

Stable numerical approximation scheme

Simulations matching experimental data

Abstract

In this paper we propose and study a curvature-based mathematical model for dorsal closure in embryonic drosophila. Using an analysis that mixes maximum-principle and integral-estimates, we establish global existence and convergence for data that mimics the initial geometry of a dorsal closure event. Further, we present a numerical approximation scheme for the flow, establishing stability, consistence, and convergence. We also give sample simulations of the flow with initial configurations that include experimentally observed data.