Small brain, large brain -- a quest for nature's scale-up rules

A scaling model of the gyrencephalic mammalian brain, invoking identical repeating cortical units, whose number and size both increase with increasing brain size, was described previously (Prothero, 1997a,b). Each repeating unit, of microscopic dimensions, is viewed as extending from the pial membrane to the underlying white matter. The model predicts discrete scaling exponents, all integral multiples of 1/9, as a function of brain size, as follows: cortical thickness (1/9), outer cortical surface area (6/9), total (folded) cortical surface area (8/9), cortical volume (9/9), white matter volume (9/9), neuron line-count (0/9) and neuron volume density (-3/9). In the present paper extensions to the model give discrete exponents for the scaling of the cross-sectional area of the corpus callosum (6/9), for mean foliar and gyral width (each 1/9), for foliar number (2/9), for mean foliar length (3/9), for mean foliar and gyral perimeter (each 3/9) and for total foliar and total gyral length (each 5/9). The predicted scaling exponent for cross-sectional area of the corpus callosum is in reasonable agreement with the empirical observations. Needed are more precise and more extensive data on cortical folding to stringently test the model predictions relating to cortical folding. On the whole, the model is in good agreement with a diverse body of empirical data bearing on the scaling of the gyrencephalic mammalian brain.