Numerical investigation of biomechanically coupled growth in cortical folding
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ORIGINAL PAPER
Numerical investigation of biomechanically coupled growth in cortical folding Shuolun Wang1 · Nagehan Demirci2 · Maria A. Holland1,2 Received: 29 April 2020 / Accepted: 17 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Cortical folding—the process of forming the characteristic gyri (hills) and sulci (valleys) of the cortex—is a highly dynamic process that results from the interaction between gene expression, cellular mechanisms, and mechanical forces. Like many other cells, neurons are sensitive to their mechanical environment. Because of this, cortical growth may not happen uniformly throughout gyri and sulci after the onset of cortical folding, which is accompanied by patterns of tension and compression in the surrounding tissue. Here, as an extension of our previous work, we introduce a biomechanically coupled growth model to investigate the importance of interaction between biological growth and mechanical cues during brain development. Our earlier simulations of cortical growth consisted of a homogeneous growing cortex attached to an elastic subcortex. Here, we let the evolution of cortical growth depend on a geometrical quantity—the mean curvature of the cortex—to achieve preferential growth in either gyri or sulci. As opposed to the popular pre-patterning hypothesis, our model treats inhomogeneous cortical growth as the result of folding rather than the cause. The model is implemented numerically in a commercial finite element software Abaqus/Explicit in Abaqus reference manuals, Dassault Systemes Simulia, Providence (2019) by writing user-defined material subroutine (VUMAT). Our simulations show that gyral–sulcal thickness variations are a phenomenon particular to low stiffness ratios. In comparison with cortical thickness measurements of N = 28 human brains via a consistent sampling scheme, our simulations with similar cortical and subcortical stiffnesses suggest that cortical growth is higher in gyri than in sulci. Keywords Biomechanics · Brain development · Curvature · Finite elements
1 Introduction Cortical folding has been long studied by joint efforts of researchers from different backgrounds of neuroscience, biology, medical imaging, mechanics, etc. (Sejnowski et al. 1988; Sun and Hevner 2014; Fischl and Dale 2000; Tallinen et al. 2014). This process is associated with a dramatic increase in brain size and complexity, giving the folded, or gyrencephalic, brains of humans and other mammals a superior information processing capability compared to other species with smooth, or lissencephalic, brains. Deviation from typical development is correlated with * Maria A. Holland maria‑[email protected] 1
Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA
Bioengineering Graduate Program, University of Notre Dame, Notre Dame, IN 46556, USA
2
many neurological disorders such as lissencephaly, polymicrogyria, and autism spectrum disorder (Walker 1942; Barkovich et al. 1999; Nordahl et al. 2007). Henc
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