Basic Research on Technical Methods of Risk Analysis for Developing Dementia with the use of Brain Waves

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The aim of this study is to find technical foundation of the risk analysis for developing dementia with the use of brain waves. Various statistical methods are examined for extracting available information for the diagnosis of developing dementia from fluctuations of brain waves. The results are summarized as shown below. (1) The method of extracting risk factors from spontaneous EEG based on the stochastic complex Ginzburg-Landau equation is established. The obtained facts by the method are listed as: (a) it is found that the frequency modulation of brain waves is subjected to a generalized Cauchy process; (b) the intermittency of frequency modulation can be ascribed to amplitude modulation via the effect of nonlinear pulling; c spatial homogenization of frequency modulation due to aging; (d) qualitative estimation of intermittency and its physical/physiological interpretation; (e) suggestion of " multiple-scattering scenario-due to brain-medium-change in developing dementia (2) Found … More ation of multiple risk factors associated with the developing dementia, and their dependencies: (a) dependency between mean frequency and its variance; (b) dependency between mean fractal dimension and its variance; c dependency between entropy and gradient of entropy as a function of scale; (d) examination of feasibility for Logistic regression method based on the examined risk factors. (3) Construction of Generalized Kubo oscillator for photo-stimulated EEG to examine brain functions: (a) proof of non-existence of entrainment for a modified Kubo oscillator, (b) examination of the existence of threshold of entrainment under photo stimulation, c examination of frequency modulation, (d) examination of higher order nonlinear responses; (e) implication of mechanism of parametric excitation in brain. (4) Results on statistical mathematical analysis on generalized Cauchy process: (a) foundation of non divergent statistical quantities in the parameter region wherein the ordinary variance diverges; (b) method of transformation from non canonical model into the canonical one; c proof far the equivalence of maximum likelihood estimator (MLE) estimator to the fluctuation-dissipation theorem; (d) explanation of profile change in the probability density (pdf) of frequency fluctuation for some demented persons; (e) exact analytic expression of the pdf and related WE with 3rd order nonlinear term in the white noise limit. Less