Hello,
May I ask a very basic question: for the dSPM calculation, what does it mean when I get a negative dSPM value diaplyed on the cortical mantle (i.e. without choosing the default “Absolute values” in the image display)? I heard it should all be positive for the dSPM values due to the F-distribution, is that true?
Thanks.
Helen
Hi Helen:
A negative value means that the magnitude of the activity is less than during the baseline period you have selected as reference for dSPM.
If still unclear, we would need more details regarding your data and the design of the epoch time windows you would be considering as ‘noise’ or ‘baseline’ vs ‘response’.
Cheers,
Thanks a lot, Sylvain.
I read the paper by Dale (“Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity”, Anders Dale et al, Neuron, 2000). I’m curious how to go from equations in that paper to the dSPM value calculated by Brainstorm.
Let’s say I’m calculating dSPM with the “Source orientations” being selected as “Constrained (Normal/Cortex)” in brainstorm, then is it true that brainstorm uses the equation 6 in that paper to calculate the dSPM value?
Next, if I then calculate dSPM with the “Source orientations” being selected as “Unconstrained” in brainstorm, then is it true that brainstorm switches to the equation 7 in that paper to calculate the dSPM value?
This is a question for Rey Ramirez (UW), who wrote those functions for Brainstorm.
I’m forwarding him the question.
Yes, the way BST computes the dSPM for fixed orientations is equivalent to eq6.
Each row of the inverse imaging kernel will be equivalent to w_i ./ sqrt( w_i * C * w_i^T);
So all we do is multiply the data with that row vector to get z_i(t). The way I wrote it allows BST to compute the dSPM values as an inner product, which is the most concise way, computationally speaking.
The same is true about eq7, but the explanation is a little bit more involved.
In BST, I wrote the function so that when you multiply the data vector x(t) with the 3 by m matrix of the imaging kernel for the ith position you get a 3 element vector, where m is the number of channels. If you square the values of that 3 element vector and sum them, you will get the q_i(t) of eq 7, which is the noise-normalized estimate of the current dipole power.
So if anyone wants to get q_i(t), they should take the modulus of the 3-element vector (i.e., its norm) and square it.
I’ll be glad to answer any more detailed questions.
Cheers,
Rey
Thanks a lot, Rey and Francois.
So, when BST computes the dSPM for fixed orientations using equation 6, the dSPM value will have positive or negative sign depending on if the orientation of the cauculated source dipole is parallel or anti-parallel to the predetermined surface normal at that source location. Is this correct?
For the other situation (i.e. calculating dSPM with the “Source orientations” being selected as “Unconstrained” or “loose” in brainstorm), when I display dSPM value on the cortical mantle I always seem to get positive values regardless of whether I choose the default display option “Absolute values” or not. Does this imply that somehow brainstorm automatically displays q_i(t) as the dSPM value after taking the modulus of the 3-element vector (i.e., its norm) and squaring it?
Dear Helen,
Yes, with those inverse models, when the orientation of the dipoles is constrained, the sign changes depending on the orientation of the current.
When the orientation is not constrained (loose or free), we estimate the currents for three orthogonal dipoles at each vertex of the cortical surface. With three values at each point, it is not possible to represent a cortical map that represents the three orientations at once. If you display the source maps by double-clicking on them from the database explorer, what you observe is the norm of the three orientations at each vertex, for one given time instant (sqrt(x^2+y^2+z^2)). In this case, the sign is lost.
If you want to see the signed values for each orientation, you can create a scout and display its time series, with the option “Values: Relative” selected in the scouts tab.
Cheers,
Francois
Thanks a lot, Francois.
I’m a bit puzzled now. According to what you said, for the dSPM values calculated by assuming fixed orientations, a negative dSPM value only means the current orientation in that vertex is opposite to a predetermined surface normal orientation. If so, then the dSPM sign has nothing to do with whether the magnitude of activity is bigger or smaller than the baseline period selected as reference for dSPM. Is this correct?
You are right, Helen, this is a part that required clarification indeed.
When the sign of the current is preserved in dSPM, it’s quite equivalent to computing a z-score of the current amplitude. The sign indicates whether the current is flowing either inward or outward the cortical mantle, mean-centered about the baseline average. The magnitude is expressed in standard deviations from the baseline. Now another option is to discard the sign information and consider changes in magnitudes in absolute values only. This lets you appreciate whether the changes in current magnitude post-baseline is substantial, regardless of the orientation of the flow. One way to proceed is to compute a wMNE current estimate, and compute a z-score of the source map, while checking the ‘Use Absolute Values’ option. The sign of the resulting transformed current map now indicates whether the magnitude of the currents is greater or smaller than on the baseline or another condition, ruling out the confounding effect of the orientation of the current flow.
Hope this clarifies a bit.
A complement from Rey Ramirez:
With fixed orientations the sign of the dSPM value indeed reflects the direction of the current flow in the MNE solution. In fact, the dSPM values are just MNE values that have been noise normalized. If the noise covariance matrix was the identity matrix, this would be equivalent to setting all the rows of the MNE inverse operator to have an L2-norm of 1. The noise projects differently to different source points and hence the normalizing factor in the denominator will be different across space. In essence, the MNE current estimates are being noise normalized based on the noise covariance matrix (see the denominator in the equation), which can be estimated from all the pre-stimulus unaveraged periods taken from all conditions or from an empty room recording. This normalization is what makes the dSPM values be distributed as a t-statistic for fixed dipole orientations.
Thank you very much, Sylvain and Francois and Rey. I think I understand the dSPM situation much better now, 