Quantifying tissue growth, shape and collision via continuum models and Bayesian inference

TL;DR

This study combines experimental data, mathematical models, and Bayesian inference to quantify tissue growth, shape, and collision, highlighting the importance of pressure-driven models over random motion assumptions in multi-tissue interactions.

Contribution

It introduces a Bayesian framework to calibrate continuum models of tissue interaction, demonstrating the superiority of pressure-based models in predicting tissue collision outcomes.

Findings

Pressure-based models outperform random motion models in tissue collision simulations.

Both models are identifiable and can replicate single tissue expansion features.

Pressure influences tissue shape and collision dynamics significantly.

Abstract

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach combining data from recent experiments, mathematical modelling, and Bayesian parameter inference, to describe the self-assembly of multiple epithelial sheets by growth and collision. We use two simple and well-studied continuum models, where cells move either randomly or following population pressure gradients. After suitable calibration, both models prove to be practically identifiable, and can reproduce the main features of single tissue expansions. However, our findings reveal that whenever tissue-tissue interactions become relevant, the random motion assumption can lead to unrealistic behaviour. Under this setting, a model accounting for population pressure from different cell populations is more appropriate and shows a better agreement with experimental measurements. Finally, we discuss how tissue shape and pressure affect multi-tissue collisions. Our work thus provides a systematic approach to quantify and predict complex tissue configurations with applications in the design of tissue composites and more generally in tissue engineering.