Les magnétomètres, les gradiomètres ? quel moyennage utiliser

Download pdf file: :gradiomagnetofren_v2.pdf|

The Elekta Triux system has 102 measurement points over the head, arranged on a (more or less) spherical surface. At each measurement point, there are a magnetometer and two planar gradiometers.
Each magnetometer is made of a single coil loop. It measures the radial component (aligned with the radius of the sensors sphere) of the magnetic field flowing in or out the head.
Each planar gradiometer is made of two identical coils A and B connected in series but wound in opposition. It measures the difference between the magnetic field radial component in A and the magnetic field radial component in B. Thus, it gives the spatial derivative (or gradient) of the radial component of the magnetic field between A and B.
Neuronal sources generates magnetic fields that ‘turns’ around the source main axis (or dipolar moment); magnetic fields can therefore be seen as flowing circularly in a plan orthogonal to current sources. For a neuronal source parallel to the scalp (generally called a tangential source), the resulting magnetic field is thus perpendicular to the scalp. The strength of the field decreases as the square of the distance to the source. You can see it as follows: magnetic fields flow in circles orthogonal to the current source, and the bigger the diameter of the circles, the smaller the magnetic field strength.

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For a deep source, only the widest circles will reach out of the head, and the signal seen by a magnetometer will depend on the extent to which the circles are locally orthogonal to the coil (departing from orthogonality results in signal decrease) and on the strength of the current source.
As seen by magnetometers, the cartography of magnetic fields take the form of bipolar pattern with one positive maximum and one negative maximum symmetrically arranged perpendicularly to the source axis (these maxima are the exit and entry points of the magnetic field circles, in and out the head). Moreover, the deeper the source, the further away of each other will be these maxima, because the diameter of the magnetic field circles seen by the magnetometers increases.
In contrast, gradiometers tend to see only close-by sources, that is sources for which the circles formed by the magnetic fields lead to one coil of the gradiometer seeing the outgoing field while the other one sees the flowing-in field; this gives opposite values on each coil of the gradiometer, which are summed by the reverse wounding. Geometrically one can see that the optimal source depth is of the order of the distance between the two gradiometer coils, viz. 2.5 cm in our Elekta Triux 306-sensor system.

As seen by planar gradiometers, the cartography of the magnetic field gradients take the form of monopolar patterns with maxima just over the sources.
In the Elekta system the two planar gradiometers at a given measurement point are arranged orthogonally. Combining the two measures from the two gradiometers gives a vector from which one can derive two values:
A scalar value that is the norm of the vector; this value is always positive. You can perform usual measures of latency, amplitude, and associated statistics on this value but no computation involving frequency decomposition or source localization. The computation of the norm is not linear with respect to the magnetic field value (and thus with respect to the neuronal activity). The main advantage of the gradiometer norm is the location of the maximum just above the corresponding source.
A direction that is orthogonal to the direction of the source in the plan tangential to the scalp (thus the direction should be parallel to the sulcus wall). You can potentially study the stability of this direction at one given time trial by trial as it is done with phase synchrony computation.

Visualization of Elekta data

Muse can display cartography from the magnetometers data and gradiometers data (norm and direction).

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Handling gradiometer data for evoked potential computation

As stated above, the computation of the norm is not linear. Thus, computing the norm of the average and computing the average of the norm are not equivalent.
Within-subject averaging of evoked responses
Computing the norm of the gradiometer then averaging it is equivalent to average the intensity of the sources without taking into account their orientation. On a raw signal where both random sources and sources linked to the task are activated, it leads to an increase of the background noise (activities not linked to the task), because the repeatability of the orientation of the sources related to the task across trials contributes to the evoked response. In a given subject, with a stable head position in the helmet, the sources linked to the task should have the same orientation at one given time trial after trial. Thus computing first the average and then the norm should be preferred. You will obtain the intensity of the sources that are the most stable in direction.
Within subject difference
It is possible to compute difference between conditions A and B. Results will show positive (or negative values if activities was higher during A (respectively lower during A). Computing first the difference and then the norm will results in an always positive results which may prove difficult to interpret.

The norm and associated vector direction can be visualized in Muse.

Warning: Due to the non linear nature of norm computation, you cannot apply directly time-frequency analysis or source localization on the norm. However, when using the default averaging option, dataHandler averages the data arithmetically on each gradiometer at every measurement point (equivalent to vectorial sum); you then see the norm of these data under Muse because Muse computes the norm for the purpose of visualization, but the underlying data are unchanged. It means that you can still import your evoked potentials in BrainStorm and perform localization.

Take home message:
Within subject, compute the average (default mode in dataHandler) then compute the norm of the results (this will require a further command line, see below for example)

data averaging:

  dataHandler -r -avg run01_sss.fif -sync COND_A -time -0.1 0.4 -rbm COND_A -0.1 0.1 -lpf 30 AVG_COND_A.fif

norm computation:

  dataHandler -r -planar AVG_COND_A.fif -new PLANAR_

Between-subject averaging (grand mean):

To compute a grand average between subjects, we will follow an opposite way. Indeed, on each subject the above described averaging gives stable sources linked to the stimulation and task but the directions of these sources is likely to be variable from one subject to another due both to the variability in anatomy and to the variability in subject’s position in the MEG helmet at the time of recording. For this reason, it is advised to compute first the norm of evoked responses and then their grand average across subjects. This allows increasing the signal to noise ratio of the grand average, whereas taking into account the direction would decrease it (if the direction are completely random you may end up with a quasi null value).

Take home message:
For grand averaging, it is preferable to average the norm of the individual evoked data (use the –planar option together with –avg for dataHandler)

  dataHandler -r -planar -avg SUBJECT*/AVG_COND_A.fif  GRD_AVG_COND_A.fif

As a result one of the gradiometers will be set to zero while the other will contain the averaged norm data.

Between subject difference (grand average of differences)

It is recommended to first get the averaged data in each subject (in cond A and cond B). Then compute the scalar value of this (-planar option; needs to be done in a second step); Then compute the difference of norms for condA minus condB, in each subjects, then grand average without the –planar option this time because otherwise we set all values to positive values.

Time-frequency computation

For gradiometers, at this point, we propose to compute time-frequency transform on each gradiometer, at every measurement point. The frequency spectrum power obtained on each gradiometer can then be averaged for each trial and across trials to obtained induced oscillatory activity. The order of the averaging does matter here, all power values are positive and thus no cancellation can occur.

Comment visualiser magnétomètres et gradiomètres ?

CARTOFIFF necessite qu il y ait dans le fichier tous les magnetometres et tous les gradiometres.
Il ne faut surtout pas changer la selection de capteurs par defaut ( = tous les magnetometres )
La carto aura alors 3 layers: un pour les magnetometres, un pour la norme des gradiometres et un pour les vecteurs des gradiometres
Elle correspond aux fichiers classiques .fif, c'est a dire ceux qui stockent chacune des composantes des gradiometres separement (la norme n'est pas stockee dans le fichier, elle est calculee au vol au moment de la visu)
L "autre" carto est plus "tolerante" : elle autorise de regler la selection de capteurs, a condition que la selection contienne une seule categorie de capteurs (soit des magnetometres, soit des gradiometres, soit des EEG, ... et pas forcement tous, par exemple uniquement les gradiometres dont le nom se termine par 2). Par contre, elle ne prend absolument pas en compte l'information "vectorielle". Elle ignore qu un gradiometre 2 est associe a un gradiometre 3.
Pour des fichiers .fif classiques, elle permet par exemple de regarder uniquement les magnetometres ( <=> layer magnetometres de la CartoFIFF ), ou bien uniquement les gradiometres qui finissent par 2, ou bien uniquement les gradiometres qui finissent par 3 ou n importe quelle combinaison de gradiometres (ceux qui finissent par 2 et par 3 appartiennent a la meme categorie "gradiometre"). Dans ce cas, regarder uniquement les gradiometres 2 ou uniquement les gradiometres 3 a pas forcement beaucoup de sens (on regarde une seule composante d'un vecteur) et regarder tous les gradiometres simultanement non plus car on calcule une interpolation avec 2 valeurs differentes (celle du 2 et celle du 3) au meme point.
Par contre, si un fichier (calcule avec -planar) contient une norme dans les gradiometres 2 et une autre information dans les gradiometres 3, alors en selectionnant uniquement les gradiometres 2, on obtiendra une carto des normes (l information des gradiometres 3 sera ignoree).

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