In vivo characterization of epileptic tissue with optical spectroscopy

For children with intractable seizures, surgical removal of epileptic foci, if identifiable and feasible, can be an effective way to reduce or eliminate seizures. The success of this type of surgery strongly hinges upon the ability to identify and demarcate those epileptic foci. The ultimate goal of this research project is to develop an effective technology for detection of unique in vivo pathophysiological characteristics of epileptic cortex and, subsequently, to use this technology to guide epilepsy surgery intraoperatively. In this PhD dissertation the feasibility of using optical spectroscopy to identify uniquein vivo pathophysiological characteristics of epileptic cortex was evaluated and proven using the data collected from children undergoing epilepsy surgery. ^ In this first in vivo human study, static diffuse reflectance and fluorescence spectra were measured from the epileptic cortex, defined by intraoperative ECoG, and its surrounding tissue from pediatric patients undergoing epilepsy surgery. When feasible, biopsy samples were taken from the investigated sites for the subsequent histological analysis. Using the histological data as the gold standard, spectral data was analyzed with statistical tools. The results of the analysis show that static diffuse reflectance spectroscopy and its combination with static fluorescence spectroscopy can be used to effectively differentiate between epileptic cortex with histopathological abnormalities and normal cortex in vivo with a high degree of accuracy. ^ To maximize the efficiency of optical spectroscopy in detecting and localizing epileptic cortex intraoperatively, the static system was upgraded to investigate histopathological abnormalities deep within the epileptic cortex, as well as to detect unique temporal pathophysiological characteristics of epileptic cortex. Detection of deep abnormalities within the epileptic cortex prompted a redesign of the fiberoptic probe. A mechanical probe holder was also designed and constructed to maintain the probe contact pressure and contact point during the time dependent measurements. The dynamic diffuse reflectance spectroscopy system was used to characterize in vivo pediatric epileptic cortex. The results of the study show that some unique wavelength dependent temporal characteristics (e.g., multiple horizontal bands in the correlation coefficient map γ(λref = 800 nm, λcomp ,t)) can be found in the time dependent recordings of diffuse reflectance spectra from epileptic cortex defined by ECoG.^

Rank and k-nullity of contact manifolds

We prove that the dimension of the 1-nullity distribution N(1) on a closed Sasakian manifold M of rankl is at least equal to 2l−1 provided that M has an isolated closed characteristic. The result is then used to provide some examples of k-contact manifolds which are not Sasakian. On a closed, 2n+1-dimensional Sasakian manifold of positive bisectional curvature, we show that either the dimension of N(1) is less than or equal to n+1 or N(1) is the entire tangent bundle TM. In the latter case, the Sasakian manifold Mis isometric to a quotient of the Euclidean sphere under a finite group of isometries. We also point out some interactions between k-nullity, Weinstein conjecture, and minimal unit vector fields.