The use of nonlinear mathematical dynamics is claimed to be revolutioning some sciences, because deterministic models can be made of unresolved physical and chemical phenomena (e.g., Brownian motion, turbulent flow, etc.). Several laboratories have attempted to apply nonlinear dynamics, th t is, the correlation dimension (D2) to the electroencephalogram of humans. Our laboratory, being skeptical, tested some of their claims on surface potentials in a simple model system, the olfactory bulb). The bulb has the same cell types and intrinsic neurochemistry as neocortex, but has a much simpler and better understood neurophysiology. Algorithms were developed t estimate D2, which led to the conviction that low-dimentional chaos DOES EXIST in the bulb. Using brief epochs and behavioral control, stationarity was observed; by eliminating spurious autocorrelations, linear correlation- integrals were achieved to calculate D2; by studying known chaotic attractors, rules were developed for sampling the attractor. Following thi experience, we now propose to determine whether or not the nonlinear dynamical analyses can be applied to real neocortex. Our first Specific Ai is to evalute D2 during various normal cortical conditions: quiet wakefulness, sleep and event-related reactions. Because of the sensitivity of the D2-meausre and its potential clinical application, Specific Aim 2 is to evalute D2 during known pathological conditions in the cortex: hypernoradrenergic reactivity (hypertension in SHR and renovascular rat models) and hypernoradrenergic innervation (epilepsy in the tottering-mouse model).
Specific Aim 3 is to determine whether or not D2-values are sensitive to therapeutic interventions. If D2 is found to be sensitive to normal and abnormal cortical functioning, then its use can be developed for the diagnosis of cerebral (and perhaps preclinical) pathology and the evaluation of therapies. Because of its process-specific signature, D2 can be used to map anatomical loci which contribute to the singular dynamical system. Furthermore, the integer and fractional portions of D2 have theoretical implications regarding the number of independent variables in t e stationary process and whether or not it may factal. (key words: nonlinea dynamics, chaos, fractals, cerebral cortex, event-related potentials, sleep epilepsy, hypertension, noradrenergic response).
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