sLORETA

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1

Dear Matti,

I would like to compare amplitudes of activation in response to auditory stimuli in the right and left temporal labels. I used sLORETA and noticed significant differences in the timecourses during pre-stimulus baseline. As the sLORETA uses noise normalization, I guess that this effect is due to different level of noise in the two labels. Would it be correct to scale the sLORETA timecourses by e.g. dividing them by the mean pre-stimulus value before statistical comparison of the left and right labels?

I have also a related question. The MNE software uses the same inverse operator for MNE and sLORETA. Is it at all identical to the sLORETA by Pascual-Marqui (Standardized low-resolution brain electromagnetic tomography (sLORETA): Technical details. METHODS AND FINDINGS IN EXPERIMENTAL AND CLINICAL PHARMACOLOGY, 2002, 24: 5-12) ?

With regards,
Elena

2

Hi Elena,
   Just my 2 cents (below) before Matti gives his expert opinion..

Dear Matti,

I would like to compare amplitudes of activation in response to auditory
stimuli in the right and left temporal labels. I used sLORETA and noticed
significant differences in the timecourses during pre-stimulus baseline.
As the sLORETA uses noise normalization, I guess that this effect is due
to different level of noise in the two labels. Would it be correct to
scale the sLORETA timecourses by e.g. dividing them by the mean
pre-stimulus value before statistical comparison of the left and right
labels?

Dividing by the mean is slightly less principled since mean is not a
'scale' parameter but rather a 'location' parameter. The scaling used in
EEGLAB (especially for time-frequency maps) in this situation is a z-score
derived as follows:

If x(t) is the original timecourse in a label:

z(t) = (x(t) - mean(x(baseline)))/std(x(baseline)) ;

This would give use the same time series whether you use MNE or dSPM or
sLORETA since they are just scaled versions of each other with the scale
factor being constant in time.

I have also a related question. The MNE software uses the same inverse
operator for MNE and sLORETA. Is it at all identical to the sLORETA by
Pascual-Marqui (Standardized low-resolution brain electromagnetic
tomography (sLORETA): Technical details. METHODS AND FINDINGS IN
EXPERIMENTAL AND CLINICAL PHARMACOLOGY, 2002, 24: 5-12) ?

It is identical to Pascual-Marqui's solution. 'sLORETA' is a misnomer in
the sense that it is not a noise-normalized version of LORETA but rather a
normalization of MNE using a slightly different denominator (related to
the resolution matrix).

Rey Ramirez's article on scholarpedia is a nice condensation of many of
the source localization methods in use:
http://www.scholarpedia.org/article/Source_localization

Regards,
Hari

3

Dear Hari,

The scaling you suggest will make the data look ?nice?, with the same mean and SD in the baseline. However, if will not resolve the problem.

According to MNE manual sLORETA scales signal to noise in some way. It seems that it proportionally decreases amplitude of the signall-of-interest if it contains more noise. Is there a way to correct for this down-scaling of the signal-of-interest by the sLORETA or would it be more correct to use MNE?

Thanks,
Elena

4

Dear Elena,

The scaling you suggest will make the data look ?nice?, with the same mean and SD in the baseline. However, if will not resolve the problem.

using a z-score makes the data 'nice' but also the estimates comparable.

It's not clear, at least to me, what the problem is when you do this
on your data.

Alex

5

Hi Elena,

Dear Hari,

The scaling you suggest will make the data look ?nice?, with the same mean
and SD in the baseline. However, if will not resolve the problem.

If the baseline has enough (handwaving) time points, then the scaling
would produce timecourses where each point is distributed as N(0,1) (in
the null) for both left and right labels and hence OK for statistical
comparison purposes. Also since you are dividing out the sLORETA scaling
(which is the same for all time points), it is identical to the z-scores
you get from MNE.

According to MNE manual sLORETA scales signal to noise in some way. It
seems that it proportionally decreases amplitude of the
signall-of-interest if it contains more noise. Is there a way to correct
for this down-scaling of the signal-of-interest by the sLORETA or would it
be more correct to use MNE?

Yes.. the sLORETA solution scales the MNE by a factor that depends on SNR
at each vertex. Thus it supresses noisy vertices a little. The MNE is the
unscaled version which is in current units (say nano Amps) and hence you
can compare the left and right directly in a physiological sense. However
the localization will be biased towards superficial sources and noisy
sources. So one other thing you could do is use dSPM or sLORETA to do the
localization/selecting labels etc.. and then use the MNE time series from
those vertices for comparison.

Regards,
Hari

6

Yes.. the sLORETA solution scales the MNE by a factor that depends on SNR
at each vertex. Thus it supresses noisy vertices a little. The MNE is the
unscaled version which is in current units (say nano Amps) and hence you
can compare the left and right directly in a physiological sense.

that can be problematic as MNE amplitudes are biased by the number of
dipoles with the same forward field. Comparing MNE in one location between
conditions is ok but comparing raw MNE between 2 brain regions is a problem.

I would really do a z-score if it's any better than raw dSPM or sLORETA.

Alex

7

Dear all,

As has been pointed out, both the Pascual-Marqui estimate (sLORETA) and
Dale's estimate (dSPM) normalize the MNE source estimate by the noise
estimate at each source point.

Slightly related issue. I have recently been trying to implement the
sLORETA noisenorm in Matlab. Sharing some lines of code to illustrate the
difference between dSPM and sLORETA estimates (I may be wrong):

%----------------------------------
%The common steps work as follows:
%----------------------------------
inv_op = mne_prepare_inverse_operator(inv_op, 1, 1/snr, 1);
inv_op.operator =
diag(sparse(sqrt(inv_op.source_cov.data)))*inv_op.eigen_leads.data*diag(sparse(inv_op.reginv))*inv_op.eigen_fields.data*inv_op.whitener*inv_op.proj;

% Extract the source covariance
R = diag(sparse(inv_op.source_cov.data));
% Whiten the forward solution
G = inv_op.whitener*fwd_op.sol.data;
% Whiten the noise covariance
% C is not necessarily an identity because of the projections and SSS
% (some entries are zero)
C = inv_op.whitener*inv_op.noise_cov.data*inv_op.whitener';

% Compute the inverse operator
inv_op.operator = R*G'*pinv(G*R*G' + 1/snr*C)*inv_op.whitener;
% Apply the inverse retaining only surface normal components
source = inv_op.operator(:,3:3:end)' * signal;

%---------------------
%dSPM works as follows:
%---------------------
% Apply the Dale noisenorm which has been precomputed in your inverse
operator structure inv_op
dSPMsource = inv_op.noisenorm * source;

%------------------------
%sLORETA works as follows:
%------------------------
% Compute the sloreta operator
for k=1:2*Ng
  inv_op.sloretanoisenorm{k}.data =
pinv(inv_op.operator2(3*k-2:3*k,:)*G(:,3*k-2:3*k));
end

% Apply the sLORETA noisenorm
for k=1:2*Ng
  sLORETAsource(k,:slight_smile: =
source(3*k-2:3*k,:)'*inv_op.sloretanoisenorm{k}.data*source(3*k-2:3*k,:);

Kind regards,
Pavan

Yes.. the sLORETA solution scales the MNE by a factor that depends on
SNR
at each vertex. Thus it supresses noisy vertices a little. The MNE is
the
unscaled version which is in current units (say nano Amps) and hence you
can compare the left and right directly in a physiological sense.

that can be problematic as MNE amplitudes are biased by the number of
dipoles with the same forward field. Comparing MNE in one location between
conditions is ok but comparing raw MNE between 2 brain regions is a
problem.

I would really do a z-score if it's any better than raw dSPM or sLORETA.

Alex
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Pavan Ramkumar
Brain Research Unit
MEG Core
Low Temperature Laboratory
Aalto University School of Science
Espoo, Finland

8

FYI we did the sLORETA matlab code with Matti last week.

it's there

https://github.com/mne-tools/mne-matlab

and the related commit:

https://github.com/mne-tools/mne-matlab/commit/a7328324e5f56bbf4caa7582db4aa2fe4c5697e9

Alex