Kin Foon Kevin Wong’s research while affiliated with The Institute of Statistical Mathematics and other places

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.

Mirror-symmetrical bimanual movement is more stable than parallel bimanual movement. This is well established at the kinematic level. We used functional MRI (fMRI) to evaluate the neural substrates of the stability of mirror-symmetrical bimanual movement. Right-handed participants (n=17) rotated disks with their index fingers bimanually, both in mirror-symmetrical and asymmetrical parallel modes. We applied the Akaike causality model to both kinematic and fMRI time-series data. We hypothesized that kinematic stability is represented by the extent of neural "cross-talk": as the fraction of signals that are common to controlling both hands increases, the stability also increases. The standard deviation of the phase difference for the mirror mode was significantly smaller than that for the parallel mode, confirming that the former was more stable. We used the noise-contribution ratio (NCR), which was computed using a multivariate autoregressive model with latent variables, as a direct measure of the cross-talk between both the two hands and the bilateral primary motor cortices (M1s). The mode-by-direction interaction of the NCR was significant in both the kinematic and fMRI data. Furthermore, in both sets of data, the NCR from the right hand (left M1) to the left (right M1) was more prominent than vice versa during the mirror-symmetrical mode, whereas no difference was observed during parallel movement or rest. The asymmetric interhemispheric interaction from the left M1 to the right M1 during symmetric bimanual movement might represent cortical-level cross-talk, which contributes to the stability of symmetric bimanual movements.

We present a new approach of explaining instantaneous causality in multivariate fMRI time series by a state space model. A given single time series can be divided into two noise-driven processes, a common process shared among multivariate time series and a specific process refining the common process. By assuming that noises are independent, a causality map is drawn using Akaike noise contribution ratio theory. The method is illustrated by an application to fMRI data recorded under visual stimulation.

We present a new approach to modelling non-stationarity in EEG time series by a generalized state space approach. A given time series can be decomposed into a set of noise-driven processes, each corresponding to a different frequency band. Non-stationarity is modelled by allowing the variances of the driving noises to change with time, depending on the state prediction error within the state space model. The method is illustrated by an application to EEG data recorded during the onset of anaesthesia.