A CONTINUUM MECHANICS-BASED MODEL FOR CORTICAL GROWTH

One method for the synthesis of object shapes is by using physical law s. A continuum mechanics-based model of growth is proposed here. An en ergy functional, a function of the shape of an elastic object, is defi ned. At every instant of the growth process, the shape of the object c orresponds 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 initia l configurations, growth leads to the formation of complex folds or co nvolutions. It is demonstrated that apart from the constraint of fitti ng in the skull, two other constraints are both necessary and sufficie nt to robustly generate patterns actually seen in cortical contours. T hese are: a minimum thickness for cortical folds due to white matter, and a shear constraint on the white matter tracts. Finally, an interes ting difference between periodic and non-periodic initial conditions i s pointed out. (C) 1997 Academic Press Limited.