The brain undergoes a wide variety of morphological changes over time. These may occur during typical development or injury recovery, but might also be induced by disease or as effects of prescribed treatments. In order to track these changes, we are developing tensor-based methods which characterize volumetric differences between brain structures with dense (pointwise) correspondences. This work makes use of mathematics developed for continuum mechanics, e.g. elastic and fluid deformations. We are also developing non-linear image registration methods in the same vein.
The statistical analysis of the resulting deformation fields is conducted using Lie group methods and log-Euclidean metrics, which operate on the space of symmetric matrices. We are currently investigating similar methods for the deformation of tensor fields (e.g. those recovered via Diffusion Weighted MRI), as well as genetic influence over variations in the deformation maps.
We are analyzing growth patterns during normal and abnormal brain development. There are some exciting findings, which we reported recently in the journal Nature, exploring the extremely complex dynamics of brain growth in children ranging from 6 to 15 years of age. Some very nice articles were written about these findings in the news media. Detailed maps of growth patterns in young children, who were scanned repeatedly with MRI, can be found here. Current work is creating time-lapse movies of brain development based on repeated MRI scans of children as they grow up. We are studying how these brain changes are accelerated or derailed in children and teenagers who develop schizophrenia, or bipolar disorder. We are also developing new brain mapping techniques to help study brain changes in developmental disorders. We are mapping cortical and subcortical structural differences in autistic children and Fragile X syndrome. Another project maps subtle cortical abnormalities in a genetic disorder of brain development: Williams syndrome, where we recently mapped the profile of cortical abnormalities.