A model for hierarchical patterns under mechanical stresses

TL;DR

This paper introduces a phase field model for understanding how mechanical stresses during growth lead to hierarchical pattern formation in biological tissues, specifically explaining leaf venation network development.

Contribution

It presents a novel phase field approach to model mechanically-induced pattern formation, linking growth, stress, and hierarchical structure in tissues.

Findings

Hierarchical patterns emerge from growth and irreversibility in 1D models.

Simulations suggest a mechanism for leaf venation hierarchy.

Further work needed for detailed growth-stress coupling.

Abstract

We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.