A two-field computational model couples cellular brain development with cortical folding

Abstract

The convoluted macroscopic shape of the mammalian brain plays an important role for brain function. To date, the link between the cellular processes during brain development and normal or abnormal cortical folding on the macroscopic scale remains insufficiently understood. Disruption of cellular division, migration, or connectivity may lead to malformations of cortical development associated with neurological disorders like schizophrenia, autism, or epilepsy. Here, we use a computational model, which couples an advection-diffusion model with finite growth, to assess the link between cellular division and migration on the cell scale and growth and cortical folding on the tissue or organ scale. It introduces the cell density as independent field controlling volumetric growth. This allows us to numerically study the influence of cell migration velocity, cell diffusivity, and the temporally changing local stiffness of brain tissue on the cortical folding process during normal brain development. We show that the model is capable of capturing the local distribution of cells through the comparison with histologically stained sections of the developing human brain. Our results further demonstrate that it is important to take temporal changes in tissue stiffness into account, which naturally occur during brain development. The present study constitutes an important step towards a computational model that could help to better understand, diagnose, and, eventually, treat neurological disorders arising from abnormal cellular development and cortical malformations.

Statement of Significance

While it is now well established that mechanical instabilities play an important role for cortical folding in the developing human brain, the mechanisms on the cellular scale leading to those macroscopic structural changes remain insufficiently understood. Here, we demonstrate that a two-field mechanical model coupling cell division and migration with volume growth is capable of capturing the spatial and temporal distribution of the cell density and the corresponding cortical folding pattern observed in the human fetal brain. The presented model provides a platform to obtain important insights into the cellular mechanisms underlying normal cortical folding and, even more importantly, malformations of cortical development.