# [FieldTrip] units

Robert Oostenveld r.oostenveld at donders.ru.nl
Sun Mar 3 11:35:37 CET 2013

```On 1 Mar 2013, at 11:02, Nuria DoĆ±amayor Alonso wrote:

> Hey guys,
> just two very simple questions regarding units. I am calculating dipoles using planar gradiometer data from a 306 Neuromag system (input units T/cm), what are the units of the dipole moment? Also, what are the units of the LCMV beamformer?

The beamformer spatial filter boils down to this equation

w = inv(h' * inv(c) * h) * h' * inv(c)

where the data covariance c

c = d*d'/(n-1)

and d is the data expressed in units of signal strength.

Furthermore, h is the lead field expressed in "fieldstrength / dipole strength".

If you combine all, you see that w is expressed in dipole strength / signal strength. So multiplying w with d you get dipole strength. Or with (w' * c * w) you get squared dipole strength (i.e. dipole power).

Sofar the theory, Regretfully the practice aint so nice. Have a look at
http://bugzilla.fcdonders.nl/show_bug.cgi?id=963
or more in general
http://bugzilla.fcdonders.nl/buglist.cgi?quicksearch=units

There are a number of issues due to inconsistent dealing with units, which is largely due to the code not knowing about the units. One is that the neuromag data is in fieldstrentgh/distance for the planar channels, but fieldstrength for the magnetometers. The leadfield has always been computed as fieldstrength (i.e. the difference between the two coils, not divided by the distance). So the leadfield (which is in "fieldstrength" for all 306 channels) is inconsistent with the data (which is in "fieldstrength" for 102 and "fieldstrength/distance" for 204 channels). This results (as others have reported in the past) in the situation that magnetometers and planar gradiometers don't combine well in a single source reconstruction.

If you consider converting units from m to cm or mm, i.e. expressing data in different geometrical units, you have to consider that not onlt the coil poisitions change, but also the signal strength (1 T/mm = 10 T/cm). That has never been considered in the code, so there are also bugs related to this. Finally, the units of conductivity in the volume conduction model is not properly scaled with units (although I think that that does not affect MEG, but it does EEG).

So there are issues due to inconsistencies in units of signal strength, units of distance and units of conductivity. There are a number of action points defined in our bugzilla and I am working on getting them resolved together with Vladimir (also for SPM). At the moment I suggest you just to be careful with interpreting absolute units. Relative units (changes between conditions) and statistics are not affected.

best
Robert

> Thanks!
> Nuria
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