Dear Colleagues,
This is a very interesting discussion. I hope I can clarify some of the
questions in the previous emails.
First of all, I would like to briefly describe the way how SSS affects
the data in general. Apparently, the number of degrees of freedom of an
MEG signal is very high, in the case of Elekta Neuromag Oy the rank of
the data is 306 to begin with. However, due to the sampling theory of
neuromagnetic fields and the relatively low signal to noise ratio, most
of the dimensions in the signal space belong to random sensor noise
while the dimensionality of the brain and external interference signals
is much smaller. This means that only around 100 field components are
needed to practically represent the signals of interest and
interference. The SSS method has been designed in such a way that it
models those basic components with vector spherical harmonic expansions
that are truncated at the limit above which the components fall under
the sensor noise level. In accordance with the sampling theory, these
components correspond to very high spatial frequencies of the magnetic
field. The internal (brain) and external (interference) signals are both
included in the SSS matrix, and generally the angle between an
arbitrarily chosen pair of internal and external basis vectors is less
than 90 degrees, i.e., there is overlapping between them. The SSS basis,
however, is linearly independent and the decomposition into those basis
components is unique. Assuming that the sampling theory and quasistatic
Maxwell's equations hold, the brain signal estimate does not leak into
the external part and thus the spatial overlapping of the internal and
external signals does not cause a need for leadfield corrections, unlike
in the case of SSP where the orthogonal spatial projection slightly
modifies the brain signals. The effect of SSP is compensated for in the
Xfit software, for example.
The potential distortion to brain signals caused by SSS would happen due
to the truncation of the vector spherical harmonic expansion. We have
examined the effect of the truncation by simulations in Figs. 1-4 of our
paper (Taulu S, Simola J, Kajola M, IEEE Trans. Sign. Proc., vol. 53,
pp. 3359-3372 (2005)) and found out that the effect is practically
insignificant. In other words, manipulation of the leadfields should not
be necessary after SSS. If you like, you can create the transformation
matrix like Olaf suggested - MaxFilter does not return such a
transformation.
If you would like to experiment the effect of SSS on the leadfields, you
could try the following simple experiment:
1. Simulate the signal of any reasonable current dipole in Xfit. This
step utilizes full-rank leadfields with no linear transformation
performed on the data.
2. Run MaxFilter on the simulated file
3. Load the output file of MaxFilter into Xfit and perform source analysis
In step 3, Xfit assumes original leadfields without any matrix
manipulation and therefore the possible discrepancy is directly assessed
by comparing the results obtained with the original and SSS-processed
data because Xfit treats both of them in the same way: Without leadfield
correction. Based on our theory and experiments, there should be no
significant distortion in the field pattern or source localization even
without any leadfield manipulations.
I hope this clarifies the issue, and sorry for the length of this email.
Best regards,
Samu
Olaf Hauk wrote:
> If there is no "built in" way: One could create an artifical data set that
> contains only the identity matrix (n*n, n: number of sensors), and apply
> SSS to that in order to get the transformation matrix.
>
> Olaf
>
>
>
>
>> I think this is the key, Olaf.
>>
>> I apologise that my original email caused some confusion, because I was
>> not asking specifically about the temporal extension of SSS, but rather
>> the use of SSS generally.
>>
>> I would also hope that the SSS components reflecting environmental noise
>> sources in the outer sphere are only a small part of the sensor space
>> spanned by the leadfield matrix, so their removal would have little
>> affect on that matrix.
>>
>> However, my question remains: in order to compare "with and without"
>> leadfield correction (as Olaf suggests), how do I extract the necessary
>> correction (projection) from MaxFilter?
>>
>> Advice from MaxFilter experts (ie Neuromag?) much appreciated....
>>
>> Rik
>>
>>
>>
>>> Hi again, and sorry: I was a bit too quick, there is of course no "null
>>> space" in sensor space of the leadfield. But the question how much the
>>> SSS
>>> components have in common with the leadfield still remains, and if the
>>> overlap is small, how big the effect of such a leadfield correction on
>>> source estimates really is. Has anyone tried with and without?
>>>
>>> Olaf
>>>
>>>
>>>
>>>
>>>> I would say one has to think about SSSt as a temporal filtering method
>>>> -
>>>> and you don't correct your leadfield after low-pass filtering either,
>>>> for
>>>> example. But this raises another interesting question: If SSS (with or
>>>> without ST) only removes activity from sources outside the sensor
>>>> array,
>>>> it should only remove patterns that are in the null space of the
>>>> leadfield
>>>> - i.e. no correction would be required. If it removes patterns that are
>>>> NOT in the null space of the leadfield, these sources could potentially
>>>> be
>>>> generated inside the head (where the brain is) - i.e. it might remove
>>>> signal! I would hope that it's the former.
>>>>
>>>> Olaf
>>>>
>>>>
>>>>
>>>>
>>>>> Burkhard -
>>>>>
>>>>> I thought so too, but another colleague thought this was not the case.
>>>>> So if the Neuromag experts don't give the definite answer, we could
>>>>> have
>>>>> a vote?
>>>>>
>>>>> ;-)
>>>>> Rik
>>>>>
>>>>> Burkhard Maess wrote:
>>>>>
>>>>>
>>>>>> Hi Rik,
>>>>>>
>>>>>> this is an interesting question - but I think the temporal projection
>>>>>> does not modify the spatially organized leadfield. SSSt takes out the
>>>>>> part of the data which correllates highly between both expansions,
>>>>>> but
>>>>>> you can not describe it by a certain spatial pattern as in the case
>>>>>> of
>>>>>> the SSP.
>>>>>>
>>>>>> Cheers,
>>>>>> Burkhard
>>>>>>
>>>>>>
>>>>>> Rik Henson wrote:
>>>>>>
>>>>>>
>>>>>>> Dear Neuromeg -
>>>>>>>
>>>>>>> Could you let me know how I can correct my leadfields for prior
>>>>>>> SSSt?
>>>>>>> In other words, I have a leadfield matrix, L, of n sensors x p
>>>>>>> sources, and would like to extract some form of projection matrix
>>>>>>> from Maxfilter that I can apply to L in order to remove those
>>>>>>> components of the sensor data that have been removed by SSSt.
>>>>>>>
>>>>>>> Many thanks
>>>>>>> Rik
>>>>>>>
>>>>>>>
>>>>>>>
>>>>> --
>>>>>
>>>>> -------------------------------------------------------
>>>>> Dr Richard Henson
>>>>> MRC Cognition & Brain Sciences Unit
>>>>> 15 Chaucer Road
>>>>> Cambridge
>>>>> CB2 7EF, UK
>>>>>
>>>>> Office: +44 (0)1223 355 294 x522
>>>>> Mob: +44 (0)794 1377 345
>>>>> Fax: +44 (0)1223 359 062
>>>>>
>>>>> http://www.mrc-cbu.cam.ac.uk/people/rik.henson/personal
>>>>> -------------------------------------------------------
>>>>>
>>>>>
>>>>>
>>>> --
>>>>
>>>>
>>>>
>>>
>>>
>> --
>>
>> -------------------------------------------------------
>>
>> DR RICHARD HENSON
>>
>> MRC Cognition & Brain Sciences Unit
>> 15 Chaucer Road
>> Cambridge, CB2 7EF
>> England
>>
>> EMAIL: [log in to unmask]
>> URL: http://www.mrc-cbu.cam.ac.uk/people/rik.henson/personal
>>
>> TEL +44 (0)1223 355 294 x522
>> FAX +44 (0)1223 359 062
>> MOB +44 (0)794 1377 345
>>
>> -------------------------------------------------------
>>
>>
>
>
>
--
Dr. Samu Taulu
Elekta Neuromag Oy
Street address: Siltasaarenkatu 18-20, Helsinki, Finland
Mailing address: P.O. Box 68, 00530 Helsinki, Finland
Tel: +358 9 756 240 83 (direct), +358 9 756 2400 (operator)
Fax: +358 9 756 240 11
E-mail: [log in to unmask]
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