Physical models for brain cortical growth and folding
Applied Mathematics & Statistics, and Scientific Computation, University of Maryland
(February 7, 2003 1:30 PM - 2:30 PM)
The computation of shape change from physical principles, or morphodynamics, is an interesting problem in developmental biology. After a brief introduction, the talk will consist of three parts. In the first, a continuum model for the folding of brain cortical contours, in which growth is induced by a change in reference metric will be presented; with suitable constraints, this model gives rise to a variety of shapes akin to those actually seen. In the second part, the inverse (control) problem of estimating a time-dependent reference metric from initial and final data is used to match cortical contours, and is compared with an active contour method. Finally, the "symmetry" aspect of the growth will be discussed, and it is proposed that: a symmetry analysis of an equivalence class of models in the spirit of Sophus Lie may provide a useful taxonomy of such patterns, and that the domains of pseudogroups as the objects of symmetry breaking will be of interest in future mathematical developments. An integration of physics with biology in such fields will provide for a new discipline which we may call bioformatics.