Active Flows and Deformable Surfaces in Development

TL;DR

This paper reviews advances in hydrodynamic models of active flows on curved, deformable surfaces, focusing on biological tissues during development and discussing theoretical, numerical, and future directions.

Contribution

It highlights the challenges in modeling active flows on deformable surfaces and discusses the integration of geometry, dynamics, and biological applications in developmental biology.

Findings

Identification of active kinetic coefficients dependence

Insights into curvature-active flow interactions

Discussion of numerical and analytical challenges

Abstract

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients -- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.