How the cortex gets its folds: an inside-out, connectivity-driven model for the scaling of Mammalian cortical folding

Larger mammalian cerebral cortices tend to have increasingly folded surfaces, often considered to result from the lateral expansion of the gray matter (GM), which, in a volume constrained by the cranium, causes mechanical compression that is relieved by inward folding of the white matter (WM), or to result from differential expansion of cortical layers. Across species, thinner cortices, presumably more pliable, would offer less resistance and hence become more folded than thicker cortices of a same size. However, such models do not acknowledge evidence in favor of a tension-based pull onto the GM from the inside, holding it in place even when the constraint imposed by the cranium is removed. Here we propose a testable, quantitative model of cortical folding driven by tension along the length of axons in the WM that assumes that connections through the WM are formed early in development, at the same time as the GM becomes folded, and considers that axonal connections through the WM generate tension that leads to inward folding of the WM surface, which pulls the GM surface inward. As an important necessary simplifying hypothesis, we assume that axons leaving or entering the WM do so approximately perpendicularly to the WM-GM interface. Cortical folding is thus driven by WM connectivity, and is a function of the fraction of cortical neurons connected through the WM, the average length, and the average cross-sectional area of the axons in the WM. Our model predicts that the different scaling of cortical folding across mammalian orders corresponds to different combinations of scaling of connectivity, axonal cross-sectional area, and tension along WM axons, instead of being a simple function of the number of GM neurons. Our model also explains variations in average cortical thickness as a result of the factors that lead to cortical folding, rather than as a determinant of folding; predicts that for a same tension, folding increases with connectivity through the WM and increased axonal cross-section; and that, for a same number of neurons, higher connectivity through the WM leads to a higher degree of folding as well as an on average thinner GM across species.