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

本研究的目的是为利用脑电波进行痴呆的风险分析寻找技术基础。为了从脑电波的波动中提取可用于诊断发展中的痴呆症的有用信息，研究了各种统计方法。研究结果总结如下。(1)建立了基于随机复数Ginzburg-Landau方程的自发性脑电危险因素提取方法。通过该方法得到的事实如下：(A)发现脑电波的频率调制服从广义柯西过程；(B)频率调制的间歇性可归因于非线性拉动效应的幅度调制；(C)衰老导致的频率调制的空间均质化；(D)对间歇性的定性估计及其物理/生理解释；(E)在痴呆的发生中，提出了“由于脑介质的改变而导致的多重散射情景”的建议(2)发现…与进展性痴呆相关的多个危险因素及其相关性：(A)平均频率及其方差之间的相关性；(B)平均分维及其方差之间的相关性；(C)作为尺度函数的熵和熵梯度之间的相关性；(D)基于所检查的危险因素的Logistic回归方法的可行性。(3)光刺激脑电信号的广义Kubo振荡器的构建：(A)证明了改进的Kubo振荡器不存在夹带现象；(B)考察了光刺激下夹带阈值的存在；(C)考察了频率调制；(D)考察了高阶非线性反应；(E)脑内参数兴奋机制的含义。(4)广义柯西过程的统计数学分析结果：(A)在常方差发散的参数区域建立非发散统计量；(B)从非正则模型到正则模型的转换方法；c证明极大似然估计(MLE)估计量与波动耗散定理的等价性；(D)解释某些痴呆者频率波动的概率密度(Pdf)的轮廓变化；(E)pdf的精确解析表达式以及与白噪声极限中的三阶非线性项相关的We。较少

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