The physical origins of cortical morphology: a multi-scale surface-preserving analysis of cerebral cortices

There are many ways of comparing the morphological features of cerebral cortices: volumes and areas for grey and white matter, grey matter thickness, gyrification index, etc. Although tabulation of these is very informative in a comparative neuroanatomy context, it provides no a priori expectation of how these quantities should scale with respect to each other. However, by using simple, physics-inspired models and assumptions about cortical development we have been able to show that cortical folding in mammals follows a universal scaling law. The same law also applies across healthy humans, irrespective of sex, and across different regions of the same cortex.

This universality strongly implies that, on one hand, cortical morphology is self-similar with features of all sizes, down to a fundamental length, proportional to cortical thickness. On the other hand, it shows that descriptions based on a small set of numbers will fail to fully capture the regularities underlying the huge diversity of shapes in cortices within and across species. What is needed is a method that quantifies how much gyrification occurs at each length scales, from tenths of millimetres to tens of centimetres; from the smallest and more individualized folds to the largest and more stereotypical cortical structures.

We describe such a method, in which the grey and white matter surfaces in cortical images are coarse-grained over a number of iterative steps, in a way that preserves the surfaces' topological integrity and non-self-intersecting nature. In effect, this procedure progressively erases larger and larger morphological details while concomitantly increasing cortical thickness, until one obtains a fully smooth cortex. The cortices generated by this procedure are quantifiably similar to the actual cortices of less-gyrified mammalian species. The devil is indeed in the detail!

We believe this new method of coarse graining analysis, besides revealing a hitherto hidden regularity of nature, can become a powerful tool to characterize and compare cortices of different species and individuals, across development and ageing, and across health and disease. In particular, it seems that Alzheimer's disease affects more intensely morphology at a specific range of length scales, and perhaps we will able to characterize this condition more precisely by purely morphological methods.