Tohru Ozaki

Model driven EEG/fMRI fusion of brain oscillations

This article reviews progress and challenges in model driven EEG/fMRI fusion with a focus on brain oscillations. Fusion is the combination of both imaging modalities based on a cascade of forward models from ensemble of post‐synaptic potentials (ePSP) to net primary current densities (nPCD) to EEG; and from ePSP to vasomotor feed forward signal (VFFSS) to BOLD. In absence of a model, data driven fusion creates maps of correlations between EEG and BOLD or between estimates of nPCD and VFFS. A consistent finding has been that of positive correlations between EEG alpha power and BOLD in both frontal cortices and thalamus and of negative ones for the occipital region. For model driven fusion we formulate a neural mass EEG/fMRI model coupled to a metabolic hemodynamic model. For exploratory simulations we show that the Local Linearization (LL) method for integrating stochastic differential equations is appropriate for highly nonlinear dynamics. It has been successfully applied to small and medium sized networks, reproducing the described EEG/BOLD correlations. A new LL‐algebraic method allows simulations with hundreds of thousands of neural populations, with connectivities and conduction delays estimated from diffusion weighted MRI. For parameter and state estimation, Kalman filtering combined with the LL method estimates the innovations or prediction errors. From these the likelihood of models given data are obtained. The LL‐innovation estimation method has been already applied to small and medium scale models. With improved Bayesian computations the practical estimation of very large scale EEG/fMRI models shall soon be possible. Hum Brain Mapp, 2009.

Decomposition of neurological multivariate time series by state space modelling.

Decomposition of multivariate time series data into independent source components forms an important part of preprocessing and analysis of time-resolved data in neuroscience. We briefly review the available tools for this purpose, such as Factor Analysis (FA) and Independent Component Analysis (ICA), then we show how linear state space modelling, a methodology from statistical time series analysis, can be employed for the same purpose. State space modelling, a generalization of classical ARMA modelling, is well suited for exploiting the dynamical information encoded in the temporal ordering of time series data, while this information remains inaccessible to FA and most ICA algorithms. As a result, much more detailed decompositions become possible, and both components with sharp power spectrum, such as alpha components, sinusoidal artifacts, or sleep spindles, and with broad power spectrum, such as FMRI scanner artifacts or epileptic spiking components, can be separated, even in the absence of prior information. In addition, three generalizations are discussed, the first relaxing the independence assumption, the second introducing non-stationarity of the covariance of the noise driving the dynamics, and the third allowing for non-Gaussianity of the data through a non-linear observation function. Three application examples are presented, one electrocardigram time series and two electroencephalogram (EEG) time series. The two EEG examples, both from epilepsy patients, demonstrate the separation and removal of various artifacts, including hum noise and FMRI scanner artifacts, and the identification of sleep spindles, epileptic foci, and spiking components. Decompositions obtained by two ICA algorithms are shown for comparison.

An Akaike State-Space Controller for RBF-ARX Models

Radial basis function autoregressive with exogenous inputs (RBF-ARX) models have been shown to be useful in modeling the nonlinear behavior of a variety of complex systems. In particular, Peng have shown how the RBF-ARX model may be used to model the selective catalytic reduction (SCR) process for real data from a thermal power plant, and have simulated control of the plant using the generalized predictive control (GPC) method of Clarke very effectively. However, the GPC approach requires constrained nonlinear optimization at each control step, which is time-consuming and computationally very expensive. Here, in place of the GPC approach, the authors use a variation of the Kalman state-space approach to control, which involves only the solution of a set of Riccati equations at each step. As is well known, the usual Kalman state-space representation breaks down when we need to control a system depending on inputs extending several lags into the past, but to avoid this problem, we have used the state-space approach of Akaike and Nakagawa. Although this was originally developed for the linear case, here we show how the representation may be extended for use with the nonlinear RBF-ARX model. The straightforward tuning procedure is illustrated by several examples. Comparisons with the GPC method also show the effectiveness and computational efficiency of the Akaike state-space controller method. The robustness of the method is demonstrated by showing how the RBF-ARX model fitted to one data sequence from the SCR process may be used to construct a high performance controller for other sequences taken from the same process. Akaike state-space control may also be easily extended to the multi-input-multi-output case, making it widely applicable in practice.

Generalized state-space models for modeling nonstationary EEG time-series

In this chapter we discuss a comprehensive framework for decomposing nonstationary time-series into a set of constituent processes. Our methodology is based on autoregressive moving-average (ARMA) modeling and on state-space modeling. For the purpose of modeling nonstationary phenomena, such as sudden phase transitions in dynamical behavior, we employ “generalized autoregressive conditional heteroscedastic modeling” (GARCH modeling), a technique originally introduced in the field of financial data analysis; however, this technique first needs to be generalized to the case of state-space modeling. Models are obtained through maximum-likelihood estimation; the innovation approach to time-series prediction helps us to derive an approximative expression for the likelihood of given data. We present three application examples relevant to the analysis of nonstationary phenomena in EEG time-series; the first case is the transition from the conscious state into anesthesia in a human patient, the second is the transition into epileptic seizure in a human patient, and the third is the transition between two sleep stages in a sheep fetus. The modeling algorithm does not require any prior information on the timing of such nonstationary phenomena.

Spatial Time Series Modeling for fMRI Data Analysis in Neurosciences

Abstract The statistical analysis of spatial and temporal data is discussed from the viewpoint of an fMRI connectivity study. The limitations of the well-known SPM method for the characterization of fMRI connectivity study are pointed out. The use of an innovation approach with NN-ARX is suggested to overcome the limitations of the SPM modeling. The maximum likelihood method is presented for the NN-ARX model estimation. The exploratory use of innovations for the identification of brain connectivity between remote voxels is discussed.