Movement Compensation in Magnetoencephalography Analysis
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EVOKED response data in magneto-encephalography (MEG) typically has a very low signal-to-noise ratio(SNR). To address this problem, in the course of an experiment stimuli are periodically applied to a subject dozens of times and averaging is typically used to improve the SNR. While the temporal response of interest to the stimulus will not be affected by subject movement with respect to the sensor array, the spatial signature of the signal of interest across the sensor array will. As a consequence of this, in the absence of any means of incorporating head movement information into MEG signal processing algorithms, in order to stimulate the subject enough times to increase SNR to necessary levels we must require the subject to remain perfectly still throughout the experiment. This requirement is not practical in conscious subjects, necessary to undergo stimulation, of age 1 to 6 years, a critical period of cognitive development. This motivates our work of incorporating subject head movement information into MEG signal processing algorithms. de Munck, et al.  employ Legendre polynomials to correct MEG data for movement by the minimum norm interpolation method of H�am�al�ainen and Ilmoniemi  and extrapolation of the data to a reference MEG grid. This method requires attaching magnetic coils to the subject head which is not agreeable with the subject age group we are interested in working with. Uutela, Taulu, et al.  suggest using the minimum norm estimate of the cortical current in each position to recalculate the magnetic field at a standardized sensor location. Taula, et al.  propose a method of standardizing multiple head positions called Signal Space Separation (SSS). SSS is based on expanding the magnetic field in terms of spherical harmonics. SSS has been applied to movement compensation in localization studies. Imada, et al.  employ SSS to correct for movements less than 7 millimeters in an infant speech perception localization study. Medvedovsky, et al  compare localization performance of two variants of SSS head movement compensation with median nerve stimulation and suggest limiting movement to less than 3 centimeters yields good results. Wehner, et al.  evaluated SSS when performing source localization of auditory evoked responses in 8-12 year old children and found that SSS can compensate for the spatial smoothing caused by head movements. The SSS approach does not appear to have been studied in the context of recovering evoked response morphology. A second approach to dealing with head movement is to incorporate the head movement into the forward models used in the signal processing algorithms for performing source localization or estimation. In principle, directly incorporating movement into the signal processing alhorithms offers potential improvement over two-step approaches that first rely on interpolation. Uutela et al.  propose averaging the minimum norm estimate of cortical currents computed using each epoch. However, this approach does not exploit the full extent of available information, i.e., find the one minimum norm solution simultaneously satisfying the sets of linear equations associated with each head postion. Consequently, as discussed above, the low SNR associated with each individual epoch limits the quality of the individual solutions. We present two approaches for estimating the repeated component of the evoked response while relaxing the requirement that the subject remain perfectly still. One approach uses Signal Space Separation to ?transform? the data from multiple distinct head positions to a reference position. At this point we apply the work of Dogand?zi�c and Nehorai . The second approach extends the same work of Dogand?zi�c and A. Nehorai by incorporating head movement information into the source models. Section II of this paper develops the theory of the two approaches of this work. The efficacy of each approach is demonstrated in Section III using simulated and phantom MEG data. Section IV presents a discussion of the proposed methods. Our notation uses bold lower and uppercase symbols to denote vectors and matrices, respectively.