Hidden markov models and multimodal imaging of human sleep

Daniel Glaser, William Penny, Karl Friston, Sophie Schwartz, Pierre Maquet, Chris Frith, Karl Friston

Inst of Cognitive Neuroscience, UCL
Functional Imaging Lab, Institute of Neurology, UCL

Subject: Modeling & Analysis

Abstract
The cellular mechanisms which generate and maintain sleep are now known in great detail. These processes are reflected, although indirectly, in surface EEG recordings. The characterisation of sleep, in humans, could benefit from the simultaneous recording of EEG and fMRI data. Indeed, constraining the analysis of fMRI time series with parameters that reflect the underlying sleep stages would provide unprecedented information on the neurophysiology of sleep. However, considerable difficulties attend such recordings, namely scanner, pulse and movement artefacts. In this abstract we will describe the processing and analysis strategies we have adopted in treating some pilot data.
The subject was a male volunteer aged 29 who was not sleep deprived. The recording began shortly after midnight and six-channel EEG (Fz, Cz, Pz, O1, O2, T6; reference : left mastoid) and vertical EOG were acquired at 5 kHz. To maintain a constant acoustic environment, a fMRI acquisition sequence was continuously executed, but initially data were discarded. Data retention began automatically after 30 minutes to provide nearly an hour of continuous recording.
To extract sleep stages from the EEG we initially used adaptive noise cancellation as described by Allen et al. (2000) to remove the scanner and pulse artefacts. Inspection of the time-frequency plot confirmed the effectiveness of this procedure. The next step transformed the EEG time-series into a plausible predictor of the fMRI data. From pragmatic considerations, the features extracted should have significant power in the temporal frequency band of haemodynamic responses and subject to the noise properties of the scanner i.e. ranging from a couple of seconds to a minute or two. We chose initially to focus on alpha and sleep spindles in the 8-12 Hz and 12-15 Hz bands respectively.
First, a time frequency analysis, adapted from Tallon-Baudry et al. (1996) was used to estimate the power in the relevant band throughout the hour of data. This continuous regressor was then convolved with a canonical haemodynamic response function (HRF) to form a prediction of the BOLD signal. The ensuing design matrix for a SPM analysis included the movement parameters from the realignment of the image data.
Second, we applied a hidden Markov Model (HMM) to the EEG data to detect states corresponding to sleep spindles (Penny and Roberts, 1999). This model generated sleep stage-specific auto regressive (AR) coefficients for each hidden state. The transition matrix and the states were initialized using prior knowledge and canonical examples of spindles, artefacts and other features. The prediction of the model was then entered as a box-car regressor (also convolved with a HRF) into the SPM analysis.
Finally we applied a HMM to the imaging data and the EEG combined. This provides a true multimodal 'generative' integration employing a physiologically validated forward model. The results of this analysis will be contrasted with the 'correlative' integration (using EEG to predict fMRI).

Allen et al. NeuroImage, 2000, 12, 230
Tallon-Baudry et al. J. Neurosci., 1996, 16, 4240
Penny & Roberts, Comput Biomed Res. 1999 Dec;32(6):483-502.

Supported by Wellcome Trust and MRC