Self-Similarity and Spatial Periodicity in Cerebral Cortical Patterning: Structural Design Notes for Neural Tissue Architects

Abstract

Tissue engineering is a powerful tool with which to systematically identify the determinants of biological functions. Applied to the design and fabrication of biomimetic brains, tissue engineering serves to disentangle the complex anatomy of neural circuits and pathways by recapitulating structure-function relationships in simplified model systems. The complex neuroanatomy of the cerebral cortex, with its enigmatic columnar and stratified cytoarchitectonic organization, represents a major challenge toward isolating the minimal set of elements that are required to assemble neural tissues with cognitive functions. Whereas considerable efforts have highlighted important genetic and physical correlates of early cortical tissue patterning, no substantive attempt to identify the determinants of how the cortices acquire their relatively conserved, narrow range of numbered layers is evident in the literature. Similarly, it is not yet clear whether cortical columns and laminae are functionally relevant or epiphenomena of embryonic neurodevelopment. Here, we demonstrate that spatial frequencies (m−1) derived from the width-to-height ratios of cerebral cortical columns predict sinusoids with a narrow range of spatial cycles over the average cortical thickness. The resulting periodicities, denoted by theoretical wavenumbers, reflect the number of observed cortical layers among humans and across several other species as revealed by a comparative anatomy approach. We present a hypothesis that cortical columns and their periodic layers are emergent of the intrinsic spatial dimensions of neurons and their nested, self-similar aggregate structures including minicolumns. Finally, we discuss the implications of periodic tissue patterns in the context of neural tissue engineering.