A model of uniform cortical composition predicts the scaling laws of the mammalian cerebrum

The size of the mammalian cerebrum spans more than 5 orders of magnitude. The smallest cerebrums have a smooth (lissencephalic) cortical surface, which gets increasingly folded (gyrencephalic) with cerebral size. Further, the proportion of white-to-gray matter volume increases with the total volume. These scaling relations have unusually little variation. Even though a number of theories and models have been proposed, it remains an open question, why this is so. Here, we show that almost all variance is explained by assuming a homogeneous composition of the cortex across mammals. On the basis of this assumption we derive quantitative analytical computational models. The first model predicts the cortical surface area from the gray and white matter volume. A single free parameter, for the height of cortical columns is estimated as{lambda} = 2.9 mm (r2 = 0.996). The second model predicts the white matter volume as a function of the gray volume and the cerebral size (with parameters for intra- and extra-gyral connections lint, lext; [Formula]). The models are validated by predicting the effective cortical thickness and the folding parameter{kappa} . The results accurately predict the human intraspecific variation of the surface relations. As expected, we find a reduced{lambda} for cetaceans, and that preterm human infants do not follow the model. We also find deviations of gray and white matter volume for large cerebrums. Overall, the models thus show how the regular architecture of the cortex shapes the cerebrum. We conclude that the mammalian cerebrum scales in an isomorphic, rather than isometric, manner.