Human cortical folding across regions within individual brains follows universal scaling law

Abstract

Different cortical regions vary systematically in their morphology. Here we investigate if the scaling law of cortical morphology, which was previously demonstrated across both human subjects and mammalian species, still holds within a single cortex across different brain regions. By topologically correcting for regional curvature, we could analyse how different morphological parameters co-vary within single cortices. We show in over 1500 healthy individuals that, despite their morphological diversity, regions of the same cortex obey the same universal scaling law, and age morphologically at similar rates. In Alzheimer’s disease, we observe a premature ageing in the morphological parameters that was nevertheless consistent with the scaling law. The premature ageing effect was most dramatic in the temporal lobe. Thus, while morphology can vary substantially across cortical regions, subjects, and species, it always does so in accordance with a common scaling law, suggesting that the underlying processes driving cortical gyrification are universal.

Independent morphological variables correlate with Aging, Mild Cognitive Impairment, and Alzheimer’s Disease

“…α was defined as 1.25 to calculate K, S, and I to study how cortical gyrification changes within the selected diagnostics, allowing comparisons with previous investigations. The presented data fit the model and has a slope comparable to previous findings (20,21). However, there are limitations in comparing our results to prior publications due to the differences in acquisition parameters, acquisition equipment, and FreeSurfer versions that could imply confounding components (26,27).…”

“…The significant difference between discriminating power of K's values with and without the age effect suggests that the parietal lobe is more affected by disease than aging. It is not possible to confirm the results from (21), which K is better discriminating Alzheimer's Disease from healthy aging in younger individuals (Supplementary Note, Fig. 5).…”

“…Further, we have shown that structural damages described by K correlate with cognitive decline and biochemical CSF changes related to AD. From the chosen independent parameters, K is a natural descriptor of cortical folding and global brain morphology as it is: i) a universal law for mammals, including lissencephalic and cetaceans; ii) based on physical properties, iii) aggregate structural information from Areas and Cortical Thickness, iv) is based on empirical evidence (19) and, v) it is proven to have a robust behavior when applied to smaller regions of interest in the human cortex (21). In addition, brain gyrification variables S and I are mathematically derived from K, but they are independent.…”

“…We defined as ROI the whole hemisphere, frontal, temporal, occipital, and lateral lobes (based on FreeSurfer definition of lobes). The lobes' area measurements were corrected by their integrated Gaussian Curvature, removing the partition size effect and enabling a direct comparison between lobes and hemisphere cortical folding (21). Due to processing errors, eleven subjects were excluded during the FreeSurfer processing or data extraction steps.…”

“…A follow-up study by Wang et al, 2016 (20) described the universal law of gyrification for the human brain across gender, age, and pathology, with further confirmation that the universal law is also respected in smaller fractions of the cortex by applying the at four lobes (Frontal, Occipital, Parietal, and Temporal Lobes)(21). In Wang et al 2021 (22), by taking the logarithmic variables log 10 A T , log 10 A E and log 10 T 2 as the base space, it was proposed a new set of independent variables to described brain morphology derived from perpendicular planes of log 10 k: K (Equation 1), representing the axonal tension, S (Equation 2), that encapsulates brain shape, and I (Equation 3), representing brain volume.…”