# Surface tension controls the onset of gyrification in brain organoids

## TL;DR

This study models brain organoids as elastic bodies influenced by surface tension, revealing how cortex growth and cell stiffness affect gyrification and the development of brain folds, with implications for understanding lissencephaly.

## Contribution

It introduces a morpho-elasticity-based mathematical model incorporating surface tension to explain gyrification mechanics in brain organoids, highlighting the role of cell stiffness in lissencephaly.

## Key findings

- Surface tension significantly influences organoid mechanics.
- Gyrification is triggered by cortex growth and surface tension.
- Reduced cell stiffness delays or inhibits folding onset.

## Abstract

Understanding the mechanics of brain embryogenesis can provide insights on pathologies related to brain development, such as lissencephaly, a genetic disease which cause a reduction of the number of cerebral sulci. Recent experiments on brain organoids have confirmed that gyrification, i.e. the formation of the folded structures of the brain, is triggered by the inhomo-geneous growth of the peripheral region. However, the rheology of these cellular aggregates and the mechanics of lissencephaly are still matter of debate. In this work, we develop a mathematical model of brain organoids based on the theory of morpho-elasticity. We describe them as non-linear elastic bodies, composed of a disk surrounded by a growing layer called cortex. The external boundary is subjected to a tissue surface tension due the intercellular adhesion forces. We show that the resulting surface energy is relevant at the small length scales of brain organoids and significantly affects the mechanics of cellular aggregates. We perform a linear stability analysis of the radially symmetric configuration and we study the post-buckling behaviour through finite element simulations. We find that the process of gyrification is triggered by the cortex growth and modulated by the competition between two length scales: the radius of the organoid and the capillary length due to surface tension. We show that a solid model can reproduce the results of the in-vitro experiments. Furthermore, we prove that the lack of brain sulci in lissencephaly is caused by a reduction of the cell stiffness: the softening of the organoid strengthens the role of surface tension, delaying or even inhibiting the onset of a mechanical instability at the free boundary.