CORTICAL GROWTH : A CONTINUUM MODEL AND ITS CONTROL

Abstract

In this thesis, we present a comprehensive treatment on simulation of brain growth in one dimension. We carry it out in two steps. Our first step is the introduction of a continuum-mechanical model for cortical growth. Our point of view is that biological growth processes, like brain growth, are the result of a continuous change in elastic equilibrium configurations. This change is induced by a change in reference metric, which at a more microscopic level is the result of cellular reproduction. In the presence of constraints, growth can lead to folded or buckled configurations. This is demonstrated explicitly in a discrete mechanical model. It is worth emphasizing here that the picture we have of growth is that the process incorporates plasticity implicitly, i.e., there is no build-up of stress as a consequence of growth. This is a natural requirement and it is our view that any realistic growth model must take this into account. We also see how constraints such as the white matter constraint and shear constraint can be easily included in the model by the inclusion of corresponding terms in the energy functional. This method allowed us to stay within the class of realistic shapes as growth proceeds. Our second step in the realistic simulation of brain growth is the development of a control theoretic model in order to arrive at an observed morphology in a cortical contour through a growth process. We compare the control-theoretic model based solutions with an active contour based approach. The active contour approach uses the given folded configuration information for defining an image potential in a region which can pull a curve placed in the potential field towards the given folded configuration. We end the thesis with an overview on the work done, and suggest topics for future investigation.