Role of mechanical factors in cortical folding development

Deciphering mysteries of the structure-function relationship in cortical folding has emerged as the cynosure of recent research on brain. Understanding the mechanism of convolution patterns can provide useful insight into the normal and pathological brain function. However, despite decades of speculation and endeavors the underlying mechanism of the brain folding process remains poorly understood. This paper focuses on the three-dimensional morphological patterns of a developing brain under different tissue specification assumptions via theoretical analyses, computational modeling, and experiment verifications. The living human brain is modeled with a soft structure having outer cortex and inner core to investigate the brain development. Analytical interpretations of differential growth of the brain model provide preliminary insight into the critical growth ratio for instability and crease formation of the developing brain followed by computational modeling as a way to offer clues for brain's postbuckling morphology. Especially, tissue geometry, growth ratio, and material properties of the cortex are explored as the most determinant parameters to control the morphogenesis of a growing brain model. As indicated in results, compressive residual stresses caused by the sufficient growth trigger instability and the brain forms highly convoluted patterns wherein its gyrification degree is specified with the cortex thickness. Morphological patterns of the developing brain predicted from the computational modeling are consistent with our neuroimaging observations, thereby clarifying, in part, the reason of some classical malformation in a developing brain.

Figure 1

(a) Idealized spherical bilayer brain model; (b) and (c) biological foundation of neurogenesis we are interested in; (d) flow chart of how Trnp1 regulates the cortical folding pattern. The dashed line arrows suggest macroscale features of the cortex. Abbreviations: aRGC, apical RGC; bRGC, basal RGC; BP, basal progenitor; CP, cortical plate; VZ, ventricular zone; SVZ, subventricular zone; SP, subplate; IZ, intermediate zone.

Figure 2

Growth of a spherical bilayer brain model from the initial configuration to current configuration.

Figure 3

(a) Normalized deformation for the outer radius of cortex according to the isotropic growth ratios of cortex. Initial thickness of cortex is 2 and initial outer radius of cortex is 50 units. Cortex and core have the same material property. (b) Normalized tangential stress ($\sigma /{\mu }_s$) distribution in the cortex with different thicknesses. Isotropic growth ratio for cortex of all models is $g_s=2$.

Figure 4

Critical growth ratio for starting instability for isotropic and tangential growth of cortex. $\overline{C}$ is the normalized value as defined $\overline{C}=C/B$, where $C$ and $B$ are the initial unreformed inner and outer radius of cortex.

Figure 5

Morphological evolution steps for a growing bilayer spherical brain model; (a)–(f) initial thickness of cortex is 2 and initial outer layer of cortex (C) is 50 units. Contour shows displacement (figures are not in same scale).

Figure 6

Morphological evolution of the growing model with different thickness of cortex, ${\mu }_{\mathrm{cortex}}/{\mu }_{\mathrm{core}}=2$. Time steps from 1 to 3 show gyrification of models step by step (figures are not in same scale).

Figure 7

Morphological evolution of the growing model with different shear modulus ratio of cortex to core $\left(T/C=2/50\right)$. Time steps from 1 to 3 show gyrification of models step by step (figures are not in the same scale).

Figure 8

(a) Gyri annotation on adult brain gray matter surfaces, PreCG: precentral gyrus; PostCG: post-central gyrus. (b) Dependency of gyri thickness to the thickness of cortex. Gyral thickness is measured on gray matter (cortex) surfaces.

Figure 9

First row: three examples of three hinges on convoluted models; second row: similar gyral folding patterns on white matter surface in real brains. Red color regions highlight the crests of gyral regions which are based on T1-weighted MRI segmentation (figures are not in the same scale).