Classification of fractional order biomarkers for anomalous diffusion using q-space entropy.

In this study, we applied continuous random walk theory (CTRW) to develop a new model that characterizes anomalous diffusion in magnetic resonance imaging experiments. Furthermore, we applied a classification scheme based on information theoretic a techniques to characterize the degree of heterogeneity and complexity in biological tissues. From a CTRW approach, the Fourier transform of the generalized solution to the diffusion equation comes in the form of the Mittag-Leffler function. In this solution form, the relative stochastic uncertainty in the diffusion process can be computed with spectral entropy. We interrogated both white and gray matter regions of a fixed rat brain with diffusion - weighted magnetic resonance imaging experiments up to 26,000 s/mm² by independently weighting q and Δ. to investigate the effects on the diffusion phenomena. Our model fractional order parameters, α and ß, and entropy measure, H(q, Δ), differentiated between tissue types and extracted differing information within a region of interest based on the type of diffusion experiment performed. By combining fractional order modeling and information theory, new and powerful biomarkers are available to characterize tissue microstructure and provide contextual information about the anatomical complexity.

Circadian control of neural excitability in an animal model of temporal lobe epilepsy.

We provide experimental evidence for the emerging imbalance in the firing activity of two distinct classes (type 1 and type 2) of population spikes recorded from the hippocampal area CA1 in an animal model of temporal lobe epilepsy. We show that during the latent period of epileptogenesis following status epilepticus inducing brain injury, there is a sustained increase in the firing rate of type 1 population spikes (PS1) with a concurrent decrease in the firing rate of type 2 population spikes (PS2). Both PS1 and PS2 firing rates are observed to follow a circadian rhythm and are in-phase in control rats. Following brain injury there is an abrupt phase shift in the circadian activity of the PS firing rates. We hypothesize that this abrupt phase shift is the underlying cause for the emergence of imbalance in the firing activity of the two PS. We test our hypothesis in the framework of a simple two-dimensional Wilson-Cowan model that describes the interaction between firing activities of populations of excitatory and inhibitory neurons.