Abstracts

Rationale: Computational modeling has suggested that brain function is optimized when overall connectivity is at a special level called critical connectivity. Prolonged deviations away from critical connectivity leads to degraded function and may manifest as neurological disease. We have proposed in particular that prolonged periods of connectivity above critical connectivity (or supercritical connectivity) can lead to epileptogenesis. However, testing this idea with in vivo models is difficult because, with current electrode monitoring systems, one can monitor only a tiny part of the intact brain. In this case, it is possible to over- or underestimate total connectivity. Subsampling error of this kind can be severe. We are developing a new measure of connectivity that is meant to be insensitive to subsampling errors. Methods: A single shank with 16 electrode contacts is inserted in rat hippocampus. Electrophysiological data are acquired at 12 KHz for 2 minute intervals at baseline, during kainate injection and at weekly intervals up to 6 weeks post-injection. The raw voltage measurements are then high-pass filtered at 200 Hz to remove synaptic potentials. The amplitudes are squared and normalized by subtracting out the means and dividing by the standard deviations. The normalized square amplitudes are referred to as Z-values. The distribution functions for the Z-values (i.e., D(Z,n) for electrode n) are constructed, one for each electrode, and plotted on a log-log scale. If the neural system is critical, then the resulting log[D(Z,n)] vs log[Z] curve should be a straight line. If the neural system is subcritical, then the curve should curve downwards. If the neural system is supercritical, there should be a region where log[D(Z,n)] curves upward before turning down again. The curvature of this curve is referred to as the curvature measure. Results: Preliminary results from two rats show that the curvature measure is slightly negative in the normal rat prior to kainate injection. It increases steadily after kainate injection and becomes positive by six weeks after injection. Conclusions: The curvature measure may prove to be a useful marker of supercritical connectivity and epileptogenesis.