Multiscale modelling and analysis of growth of plant tissues

TL;DR

This paper develops a multiscale framework linking microscopic cell structures to macroscopic tissue mechanics in growing plant tissues, enabling efficient predictions of tissue behavior based on cellular properties.

Contribution

It introduces a homogenization-based approach to derive tissue-scale models from microscopic structures, bridging cellular details with tissue-level mechanics.

Findings

Macroscopic models accurately predict tissue behavior in various configurations

Homogenization effectively links microscopic properties to macroscopic tissue mechanics

Finite element simulations validate the multiscale modeling approach

Abstract

How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links between microscopic and macroscopic tissue properties, we perform a multiscale analysis of a model of growing plant tissue with subcellular resolution. We use homogenization to rigorously derive the corresponding macroscopic tissue scale model. Tissue scale mechanical properties are computed from microscopic structural and material properties, taking into account deformation by the growth field. We then consider case studies and numerically compare the detailed microscopic model and the tissue-scale model, both implemented using finite element method. We find that the macroscopic model can be used to efficiently make predictions about several configurations of interest. Our work will help making links between microscopic measurements and macroscopic observations in growing tissues.