Secondary instabilities modulate cortical complexity in the mammalian brain

Abstract

Disclosing the origin of convolutions in the mammalian brain remains a scientific challenge. Primary folds form before we are born: they are static, well defined and highly preserved across individuals. Secondary folds occur and disappear throughout our entire lifetime: they are dynamic, irregular and highly variable among individuals. While extensive research has improved our understanding of primary folding in the mammalian brain, secondary folding remains understudied and poorly understood. Here, we show that secondary instabilities can explain the increasing complexity of our brain surface as we age. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we explore the critical conditions for secondary instabilities. We show that with continuing growth, our brain surface continues to bifurcate into increasingly complex morphologies. Our results suggest that even small geometric variations can have a significant impact on surface morphogenesis. Secondary bifurcations, and with them morphological changes during childhood and adolescence, are closely associated with the formation and loss of neuronal connections. Understanding the correlation between neuronal connectivity, cortical thickness, surface morphology and ultimately behaviour, could have important implications on the diagnostics, classification and treatment of neurological disorders.

Keywords:

• brain
• morphogenesis
• cortical folding
• instability
• bifurcation
• period-doubling

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was supported by the German National Science Foundation grant STE 544/50-1 to Silvia Budday and Paul Steinmann, by the Stanford Bio-X Interdisciplinary Initiatives Program, by the National Science Foundation CAREER award CMMI 0952021, and by the National Institutes of Health grant U01 HL119578 to Ellen Kuhl.