Universality in human cortical folding in health and disease

Abstract

The folding of the cortex in mammalian brains across species has recently been shown to follow a universal scaling law that can be derived from a simple physics model. However, it was yet to be determined whether this law also applies to the morphological diversity of different individuals in a single species, in particular with respect to factors, such as age, sex, and disease. To this end, we derived and investigated the cortical morphology from magnetic resonance images (MRIs) of over 1,000 healthy human subjects from three independent public databases. Our results show that all three MRI datasets follow the scaling law obtained from the comparative neuroanatomical data, which strengthens the case for the existence of a common mechanism for cortical folding. Additionally, for comparable age groups, both male and female brains scale in exactly the same way, despite systematic differences in size and folding. Furthermore, age introduces a systematic shift in the offset of the scaling law. In the model, this shift can be interpreted as changes in the mechanical forces acting on the cortex. We also applied this analysis to a dataset derived from comparable cohorts of Alzheimer's disease patients and healthy subjects of similar age. We show a systematically lower offset and a possible change in the exponent for Alzheimer's disease subjects compared with the control cohort. Finally, we discuss implications of the changes in offset and exponent in the data and relate it to existing literature. We, thus, provide a possible mechanistic link between previously independent observations. brain morphogenesis | cortical gyrification | folding | aging | Alzheimer's disease T he expansion of the cerebral cortex is the most obvious feature of mammalian brain evolution and generally accompanied by increasing degrees of folding of the cortical surface. The mechanisms that drive gyrification have been a matter of intense research interest lately (1-4), with a number of proposals being put forward to explain it. Most such studies have focused on human cortices, using detailed MRI data to postulate folding as driven by the [possibly differential (5) or multilayered (6)] expansion of the cortical surface. In contrast, we have recently proposed a model (7), in which folding is a consequence of the dynamics of surface expansion and self-avoidance coupled with a negative tension term. This model was partly inspired by the axonal tension hypothesis by Van Essen (8) and the statistical physics of membranes (9). By assuming that healthy adult mammalian cortices have a shape that minimizes an effective free energy term that takes into account these effects, this model predicts a power law relation between cortical average thickness T, exposed area A e , and total area A t , namely[1]The only free parameter is k, or offset, a dimensionless coefficient that is presumed to be related to both the axonal tension and the pressure of cerebral spinal fluid (CSF) (supplemental text in ref. 7). In geometric terms, the variables T, A t , and A e ass...

White matter volume and white/gray matter ratio in mammalian species as a consequence of the universal scaling of cortical folding

“…individuals for healthy human cortices is statistically indistinguishable from 1.25 once subjects are separated by age (17); across different age groups, there is a small but systematic decrease in the value of k with aging, possibly due to age-related changes in axonal mechanical plasticity. This suggests that the discrepancy between theoretical and empirical exponents in our comparative neuroanatomy data may be due to a "smearing" of the data along the direction of age-related changes in the morphological variables, as our dataset is not controlled by (species-equivalent) age.…”

Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci

“…In the particular case of brain morphogenesis, it was proposed by the Swiss anatomist Wilhelm His in his 1874 essay "Unsere Körperform" that Entwicklungsmechanik, developmental mechanics, is the key driver for the characteristic folding pattern of our brain [9]. Motivated by this idea [10], there is now a common understanding [11][12][13][14][15] that the folding pattern of our brain is the result of differential growth and morphoelastic instabilities [16][17][18].…”

Creative destruction: a basic computational model of cortical layer formation

“…First steps have been taken in this direction, leading to neuronal self-organization of biologically plausible axonal arborizations (Bauer et al 2012), complex network properties of synaptic connectivity and computationally powerful circuit function (Bauer et al 2014). We also aim at extending our simulations using modern software tools (Gonzalez de Aledo et al 2018;), which will enable simulations that give rise to a detailed model of neural tissue dynamics including folding patterns (Wang et al 2016). Given that our model can account for a wide range of layered neocortical cytoarchitecture, only small amendments are likely to be necessary to explain also other layered structures in the central nervous system, such as the retina or hippocampus.…”