The role of mechanics during brain development

Silvia Budday,Paul Steinmann,Ellen Kuhl

doi:10.1016/j.jmps.2014.07.010

Abstract

Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated with neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl–von Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

Highlights

For more than a century, the unique surface morphology of the mammalian brain has fascinated scientists across all disciplines [39]: Why does the brain have this complex convoluted structure, and, more importantly, to which extent is brain structure correlated to brain function [66]? From a mechanics point of view, these questions naturally translate into the quest for a basic understanding of brain morphology [7]: What are the underlying mechanisms of brain folding?
We explore the effect of three key players in cortical folding: cortical thickness, stiffness, and growth
The remainder of this manuscript is organized as follows: In Section 2, we present our analytical model for cortical folding to establish analytical estimates for the critical time, the critical pressure, and the critical wavelength at the onset of folding

Summary

Introduction

The mammalian brain is composed of an outer cortical layer of gray matter, consisting primarily of cell bodies, and an inner subcortical core of white matter, consisting primarily of axons. Within the limited space inside the skull, gyrification, the folding of the cortical layer, is viewed as a process to maximize the number of cell bodies and minimize the distance between them [70]. The total number of neurons, the number of connections, and the signaling speed are directly correlated with the capacity of information processing. It is not surprising that the total brain volume, and the brain surface area, are viewed as strong indicators of intelligence [56]. The ratio between brain surface area and brain volume, and with it the degree of gyrification, can vary significantly between species [32]. With 86 billion neurons, 0.15 quadrillion connections, and a mass of 1,500 g, the human brain is often considered the most developed mammalian brain [30]

Results

Discussion

Conclusion