Spatio-Temporal Data Analysis using Weak Linear Models

J Porrill, J V Stone, J E W Mayhew, J Berwick and P Coffey

(1) Psychology Department, Sheffield University, Sheffield, S10 2UR, England.

We wish to recover information about underlying biological signal sources from optical imaging (OI) and functional magnetic resonance imaging (fMRI) data. Techniques for the analysis of spatio-temporal data-sets into component spatial and temporal modes can be divided, roughly speaking, into those which are are purely descriptive, such as principal component analysis, and those which require that temporal behaviour be specified in advance, such as General Linear Model analysis. We define here an intermediate class of weak temporal models which can utilise incomplete prior information about temporal responses suggested by experimental protocols (for example causality or periodicity). These weak models leave associated spatial modes under-constrained. We propose that this ill-posed problem be regularised using the entropy measure underlying spatial independent component analysis. The performance of the regularised weak linear model algorithm will be illustrated by application to OI and fMRI data sets.

Results

We have applied the weak causal model to the analysis of multi-spectral optical imaging data taken from rat barrel cortex during whisker stimulation (3).

The algorithm recovers highly causal, biologically plausible, estimates of the response of oxygenated and de-oxygenated hamemoglobin concentrations to stimulation. These are shown in Figure (1) together with the corresponding spatial activity maps which clearly identify a whisker barrel as the main area responding to whisker stimulation (this has been verified histologically). Our analysis supplies independent evidence for the important de-oxy dip response to stimulation which has been reported elsewhere (3, 4).

We have applied a weak periodic analysis to a human fMRI data set obtained during exposure to a box-car auditory stimulus. The preliminary results shown in Figure (2) confirm those obtained by conventional analysis techniques and the recovered activity maps and time series seem on visual inspection to be cleaner than those obtained by other methods.

References

[1] McKeown MJ, (1998). Proceedings of the National Academy of Sciences, 95, 803-801.

[2] Bell, AJ Sejnowski, TJ, (1995). Neural Computation, 7, 1129-1159.

[3] Mayhew J, Hou Y, Zheng B, Vuksanovic B, Askew S, Berwick J Coffey P (1998). Neuroimage, in Press.

[4] Malonek, Grinvald, Science, (1996). Science, 7.