Epilepsy consists of more than 40 clinical syndromes affecting 50 million people worldwide. Approximately 25 to 30% of the patients receiving medication have inadequate seizure control. Progressive changes are suggested by the existence of a so-called silent interval, often years in duration, between CNS infection, head trauma, or prolonged seizure (status epilepticus) and the later appearance of epilepsy. This process is known as epileptogenesis and is thought of as a cascade of dynamic biological events altering the balance between excitation and inhibition in neural networks. Understanding these changes is key to preventing the onset of epilepsy. To this end, high angular resolution diffusion weighted MR-imaging (HARDI) offers the possibility to non-invasively track structural changes in limbic structures (dentate gyrus etc.). Our goal is to develop mathematical models and efficient algorithms to process HARDI data acquired from rat brains that have been imaged during the epileptogenetic period and derive structural signatures that can be used to predict the onset of epilepsy. Note that there is no precedence to this work on structural signatures for use in prediction of the onset of epilepsy. ? ? Our mathematical model characterizes multiple fiber tracts at a voxel by a continuous probability density over 2-tensors instead of the now popular multi-tensor model. In the absence of multiple fibers at a voxel, the proposed density model defaults to a Gaussian which characterizes the presence of a single fiber. The novelty of this formulation lies in relating the signal and the probability density of the 2-tensors via the well known Laplace transform and for the Wishart densities, leads to a closed form solution. Additionally we propose to segment the 3D lattice of probability densities to extract the ROI and map out the fibers which will be validated using histology data. Several novel properties (Renyi entropy etc.) constituting the structural signature characterizing the epileptogenetic period will then be computed from the segmented ROI. These features will then be used in a Kernel-based clustering to label clusters over the epileptogenetic period. Prediction will then be achieved for a novel data set via a Bayesian optimization scheme. Validation of the prediction results will be done on data for which onset times of epilepsy are already known. The proposed research will significantly advance our understanding of limbic system reorganization caused not only by prolonged seizures, but also the effects of recurrent seizures and further hippocampus damage. ? ? ?
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