A continuum mechanics-based model for cortical growth

Abstract

One method for the synthesis of object shapes is by using physical laws. A continuum mechanics-based model of growth is proposed here. An energy functional, a function of the shape of an elastic object, is defined. At every instant of the growth process, the shape of the object corresponds to a minimum of this energy functional; growth is taken to be a quasistatic process. The model is used to simulate the growth of a one-dimensional 'brain cortex'. Starting from almost smooth initial configurations, growth leads to the formation of complex folds or convolutions. It is demonstrated that apart from the constraint of fitting in the skull, two other constraints are both necessary and sufficient to robustly generate patterns actually seen in cortical contours. These are: a minimum thickness for cortical folds due to white matter, and a shear constraint on the white matter tracts. Finally, an interesting difference between periodic and non-periodic initial conditions is pointed out.