
内容記述 
Human being has long been challenging to understand functions and organizations of the brain. With striking developments of various measurement apparatus and methodology after twentieth century, we have accumulated not only the knowledge about the mechanism of our brain but also measurements of brain activities from various aspects. In order to make the best use of these data combined with a priori knowledge, the development of statistical methods is indispensable. <br /> Nowadays the functional Magnetic Resonance Imaging (fMRI)technique and the electroencephalography (EEG) are two common tools for the understanding of human cognition as well as for the clinical diagnosis. By the fMRI technique, the change of regional cerebral blood flow, which is supposed to result from electrical neuronal activities on the corresponding local region, is measured as temporally successive images covering the whole brain volume with high spatial resolution but low temporal resolution. By the EEG, evoke potentials can be measured in several tens positions on the scalp surface with high temporal resolution as a consequence of the transmission of electric currents (a collection of electrical neuronal activities) inside the brain.<br /> In this thesis, for the purpose of analyzing these two kind of the data sets, the methodology in the field of time series analysis will be applied and developed. Since these two data sets have distinct properties, the purpose and the tool for analysis are also distinct. Therefore this thesis consists of two parts, the inverse problem of the EEG and the causal analysis for the fMRI data.<br /> In the first part of this thesis, the dynamical inverse problem of the EEG generation will be discussed. Since the EEG recording is an indirect observation of electrical sources inside the brain, the inference to localize the sources, called the 'inverse problem' are necessary. In general, in order to solve the inverse problem we have to combine additional information to the observation because it is impossible to uniquely determine the solution from the observation itself. In this thesis, we will consider the dynamical inverse problem so that general spatiotemporal constraints can be incorporated. This aspect has been neglected in many previous studies of the inverse problem of the EEG generation in spite of its importance. <br /> Mathematically the dynamical inverse problem will be formulated as the state estimation problem. The system equation in the state space representation describes general spatiotemporal constraints. By assuming a parametric model for the dynamics, we can choose in a sense the 'best fitting' constraints onto the solution. In principle both the parameter estimation and the state estimation (the solution) can be done by means of the celebrated Kalman filtering algorithm. <br /> However due to high dimensionality of the state in the EEG application, the difficulty occurs in the computational aspect. As alternatives of ordinary Kalman filtering, the author will propose three approximate filtering algorithms; the recursive penalized least squares (RPLS) method, observable projection Kalman filtering and partitioned (spatiotemporal) Kalman filtering. The different ways of approximation of covariance matrices of the filtered and predicion states are employed in these algorithms. The simulation study will demonstrate similarity of the solutions via three methods in the case of simple dynamics. However the difference of three solutions could become larger when the dynamics becomes complex. It would be necessary to examine the situation of problems and validity of the assumption. <br /> The data analysis of real α wave will show two sources located in the occipital region of both the left and right hemisphere, which has been reported in the previous studies. In addition, the estimated dynamics inside and outside the occipital region is observed to differ in periodicity using a regional AR model as the dynamics. <br /> In the latter part of this thesis, the methodology to evaluate the effective connectivity of the fMRI data will be investigated. In the fMRl studies, recently, more attention has been paid to the analysis of the effective connectivity defined as "the influence that one neural system exerts over another" (Friston 1995). In order to accomplish this purpose, the method developed in the multivariate time series analysis will be applied. It is a crucial advantage of this approach that no assumption about the direction of connectivity is required, whereas the structural equation model, the most common approach to evaluate the effective connectivity so far, requires to determine and to restrict the direction of connectivity apriori. <br /> For this purpose, the author proposes to apply the Akaike's noise contribution ratio (ANCR), which quantifies the influence on one time series from another time series. Using the data from the random dot experiment, the change of the connectivity between two conditions will be evaluated by the ANCR as a measure. As a result, the increase of the connectivity on the task condition is observed compared with the connectivity on the control condition. 