View source for MEG

===About MEG===
'''Magnetoencephalography''' ('''MEG''') is a [[wikipedia:functional neuroimaging|functional neuroimaging]] technique for mapping brain activity by recording [[wikipedia:magnetic field|magnetic field]]s produced by electrical currents occurring naturally in the [[wikipedia:human brain|brain]], using very sensitive [[wikipedia:magnetometer|magnetometer]]s. Arrays of [[wikipedia:SQUID|SQUID]]s (superconducting quantum interference devices) are currently the most common magnetometer.
===Motion Correction===
This is less of an issue with MEG than it is with fMRI because head motion is explicitly recorded with HPI coils. Motion correction is part of the initial [http://imaging.mrc-cbu.cam.ac.uk/meg/Maxfilter Maxfilter] processing which also removes noise from external magnetic fields.
===Dealing with Volume Conduction===
Spurious zero-lag correlations stemming from volume conduction are the main obstacle when using MEG data for connectivity analysis. Different solutions have been proposed, for instance the [http://dx.doi.org/10.1002/hbm.20346 Phase Lag Index]. The signal-envelope based approach by [http://dx.doi.org/10.1038/nn.3101 Hipp et al. 2012] seems to work well for some.
===Wavelet Decomposition and Hilbert transform===
If using R, the ''waveslim'' package provides all the necessary functions. However, if the Hipp method is used, it is more straightforward to simply bandpass the data and apply a [[wikipedia:Hilbert transform|Hilbert transform]] to get the complex valued [[wikipedia:analytic signal|analytic signal]] <math>\hat X(t)</math> with respect to the original signal <math>x(t)</math> by calculating:

<blockquote>
<math>
\hat S(f) = 2 \operatorname{u}(f) S(f) = \left [ 1 + \sgn(f) \right ] S(f)
</math>
</blockquote>

where:
*<math>S(f)</math> is the [[wikipedia:Fourier transform|Fourier transform]] of <math>x(t)</math>,
*<math>\operatorname{u}(f)</math> is the [[wikipedia:Heaviside step function|Heaviside step function]],
*<math>\sgn(f)</math> is the [[wikipedia:sign function|sign function]],

Then the '''analytic signal''' of <math>x(t)</math> is the inverse Fourier transform of <math>\hat S(f)</math>:

<blockquote>
<math>
\hat X(t) = \mathcal{F}^{-1}[\hat S(f)]
</math>
</blockquote>

===Orthogonalized envelope correlation===
Signal envelope and phase obtained in this way can subsequently be used to calculate the ''orthogonalized envelope correlation'' <math>{\rm C}_\perp (\hat X,\hat Y)</math> proposed by Hipp et al. as a connectivity metric for MEG.
First all signals are pairwise orthogonalized:

<blockquote>
<math>
\hat Y_{\perp^X}(t) = \Im \left ( \hat Y(t)\frac{\hat X^\dagger(t)}{|\hat X(t)|} \right)\hat e_{\perp^X}(t)
</math>
</blockquote>
Then the envelope correlations are calculated in both directions and averaged to give the final result:
<blockquote>
<math>
{\rm C}_\perp (\hat X,\hat Y) = \frac{{\rm Corr}(|\hat X|,|\hat Y_{\perp^X}|)+{\rm Corr}(|\hat Y|,|\hat X_{\perp^Y}|)}{2}
</math>
</blockquote>
In practice this will be a (symmetric) correlation matrix of dimensions <math>N \times N</math> where <math>N</math> is the number of original timeseries (e.g. cortical ROIs defined by the [https://surfer.nmr.mgh.harvard.edu/fswiki/CorticalParcellation Desikan Freesurfer template]).

==See also==
The [http://imaging.mrc-cbu.cam.ac.uk/meg/CbuMeg CBU Wiki] is the best resource for everything MEG.