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Tutorial 22: Source estimation
Authors: Francois Tadel, Elizabeth Bock, Rey R Ramirez, John C Mosher, Richard M Leahy, Sylvain Baillet
You have in your database a forward model that explains how the cortical sources determine the values on the sensors. This is useful for simulations, but what we need next is to solve the inverse problem: how to estimate the sources when we have the recordings. This tutorial introduces the tools available in Brainstorm for solving this inverse problem.
WARNING: The new interface presented here does not include all the options yet. The mixed head models are not supported: to use them, use the old interface (menu "Compute sources" instead of "Compute sources 2016", described in the ?old tutorials).
WARNING: The documentation presented here is incomplete. Waiting for actions from John Mosher, please contact him directly for questions regarding this new implementation.
- Ill-posed problem
- Source estimation options
- Computing sources for an average
- Display: Cortex surface
- Why does it look so noisy?
- Display: MRI Viewer
- Display: MRI 3D
- Sign of constrained maps
- Unconstrained orientations
- Source map normalization
- Delete your experiments
- Computing sources for single trials
- Averaging in source space
- Note for beginners
- Averaging normalized values
- Display: Contact sheets and movies
- Model evaluation
- Advanced options: Minimum norm [TODO]
- Advanced options: LCMV beamformer
- Advanced options: Dipole modeling
- On the hard drive
- Additional documentation
Our goal is to estimate the activity of the thousands of dipoles described by our forward model. However we only have a few hundred spatial measurements as input (the number of sensors). This inverse problem is ill-posed, meaning there are an infinite number of source activity patterns that could generate exactly the same sensor topography. Inverting the forward model directly is impossible, unless we add some strong priors to our model.
Many solutions to the inverse problem have been proposed in the literature, based on different assumptions on the way the brain works and depending on the amount of information we already have on the effects we are studying. Among the many methods available, in Brainstorm, we present three general approaches to the inverse problem that represent the most widely used methods in MEG/EEG source imaging: minimum-norm solutions, beamformers, and dipole modeling.
These approaches have the advantage of being implemented in an efficient linear form: the activity of the sources is a linear recombination of the MEG/EEG recordings, such that it is possible to solve the inverse problem by applying a linear kernel (in the form of a matrix that multiples the spatial data at each point in time) which is easily stored. Subsequent data manipulation and source visualization is then much simpler, as are comparisons among these techniques.
Below we first describe the minimum norm imaging approach and its options, followed by the beamformer and dipole modeling, both of which are actually quite similar and only use a subset of the options available in the minimum norm approach.
Source estimation options
Before we start estimating the sources for the recordings available in our database, let's start with an overview of the options available. This section focuses on the options for the minimum norm estimates. The other methods are described in advanced sections at the end of this page.
Minimum norm imaging
Estimates the sources as the solution to a linear imaging problem, than can be interpreted in various ways (Tikhonov regularization, MAP estimation). The method finds a cortical current source density image that approximately fits the data when mapped through the forward model. The "illposedness" is dealt with by introducing a regularizer or prior in the form of a source covariance that favors solutions that are of minimum energy (or L2 norm).
Min norm requires specification of a noise and a source covariance matrix. Users can estimate a noise covariance matrix directly from recordings (for example, using pre-stim recordings in event related studies) or simply assume a white-noise identify matrix covariance as described below.The source covariance prior is generated from the options discussed in detail below.
- In contrast to the LCMV beamformer, in which the data covariance is estimated directly from the data, for minimum norm the data covariance is determine by the choice of source and data covariances and the forward model.
- Linearly constrained minimum variance (LCMV) beamformers compute an estimate of source activity at each location through spatial filtering. The spatial data are linearly combined with weights (the spatial filter) chosen separately for each location to ensure that the strength of a dipolar source at that location is correctly estimated (assuming a perfect head model).
- The remaining degrees of freedom in selecting the weights are used to minimize the total output power. This has the effect of suppressing contributions of sources from other locations to the estimated signal at the location of interest.
It should be noted however, that correlation between sources can at times lead to partial or full signal cancellation and the method can be sensitive to accuracy of the head model as described in (LINK: rl4).
LCMV beamformers require specification of the data covariance matrix, which is assumed to include contributions from background noise and the brain signals of interest. In practice, the data covariance is estimated directly from the recordings. A linear kernel (matrix) is formed from this data covariance matrix and the forward model. This kernel defines the spatial filters applied at each location. Multiplying by the data produces an output beamformer scanning image. These images can either be used directly, as is common practice with LCMV methods, or the largest peak(s) can be fit with a dipolar model at every time instance, as (LINK: rl5). More details.
- In some sense the simplest model: we fit a single current dipole at each point in time to the data. We do this by computing a linear kernel (similar to the min norm and LCMV methods) which when multiplied by the data produces a dipole scanning image whose strongest peak represents the most likely location of a dipolar source.
As with LMCV, the dipole scanning images can be viewed directly, or the single best dipole fit (location and orientation) computed, as described in (LINK: rl6). More details.
- Still under much debate, even among our Brainstorm team. In cases where sources are expected to be focal (e.g. interictal spikes in epileptic patients, or early components of sensory evoked responses) the single dipole can be precise in terms of localization. For cases where sources are expected to be distributed, the min norm method makes the least restrictive source assumptions. LCMV beamformers fall somewhere between these two cases.
- One advantage of Brainstorm is that all three approaches can be easily run and compared. If the results are concordant among all three techniques, then our underlying assumptions of source modeling, head modeling, and data statistics are confirmed. If the results are disparate, then a more in depth study is needed to understand the consequences of our assumptions and therefore which technique may be preferred. The next several sections discuss in detail the options associated with the "mininum norm imaging" method.
The minimum norm estimate computed by Brainstorm represents a measure of the current found in each point of the source grid (either volume or surface). As discussed on the user forum, the units are strictly kept in A-m, i.e. we do not normalize by area (yielding A/m, i.e. a surface density) or volume (yielding A/m^2, i.e. a volume density). Nonetheless, it is common to refer these units as a "source density" or "current density" maps when displayed directly.
More commonly, however, current density maps are normalized. The value of the estimated current density is normalized at each source location by a function of either the noise or data covariance. Practically, this normalization has the effect of compensating for the effect of depth dependent sensitivity and resolution of both EEG and MEG. Current density maps tend to preferentially place source activity in superficial regions of cortex, and resolution drops markedly with sources in deeper sulci. Normalization tends to reduce these effects as nicely shown by (LINK ?). We have implemented the two most common normalization methods: dSPM and sLORETA.
Current density map: Produces a "depth-weighted" linear L2-minimum norm estimate current density using the method also implemented in Matti Hamalainen's MNE software. For a full description of this method, please refer to the MNE manual, section 6, "The current estimates". Units: picoamper-meter (pA-m).
dSPM: Implements dynamical Statistical Parametric Mapping (Dale, 2000). The MNE is computed as above. The noise covariance and linear inverse kernel are then used to also compute estimates of noise variance at each location in the current density map. The MNE current density map is normalized by the square root (standard deviation) of these variance estimates. As a result dSPM gives a z-score statistical map. Units: unitless "z".
sLORETA: Standardized LOw Resolution brain Electromagnetic TomogrAphy (Pasqual-Marqui, 2002). As with dSPM, the MNE current density map is normalized at each point. While dSPM computes the normalization based on the noise covariance, sLORETA replaces the noise covariance with the data covariance. (LINK ?) show an alternative form using a "resolution" kernel that may be calculated instead. We use the "resolution" form here. Units: unitless.
Recommended option: Discussed in the section Source map normalization below.
Source model: Dipole orientations
At each point in the source grid, the current dipole may point arbitrarily in three directions. In this section of the options, we describe alternatives for constraining orientation:
Constrained: Normal to cortex: Only for "surface" grids. At each grid point, we model only one dipole, oriented normally to the cortical surface. This is based on the anatomical observation that in the cortex, the pyramidal neurons are mainly organized in macro-columns that are perpendicular to the cortex surface.
Size of the inverse operator: [Nvertices x Nchannels].
Loose: Only for "surface" grids. As introduced by (LINK ?), at each point in the surface grid the dipole direction is constrained to be normal to the local cortical surface. Two additional elemental dipoles are also allowed, in the two directions tangential to the cortical surface. As contrasted with "unconstrained," these two tangential elemental dipoles are constrained to have an amplitude that is a fraction of the normal dipole, recommended to be between 0.1 and 0.6. Thus the dipole is only "loosely" constrained to be normal to the local cortical surface.
Size of the inverse operator: [3*Nvertices x Nchannel].
Unconstrained: Either "surface" or "volume" grids. At each grid point, we leave undefined the assumed orientation of the source, such that three "elemental" dipoles are needed to model the source. In Brainstorm, our elemental dipoles are in the x, y, and z ("Cartesian") directions, as compared to other software that may employ polar coordinates. Thus for "N" vertices, we are calculating the estimate for "3*N" elemental dipoles.
Size of the inverse operator: [3*Nvertices x Nchannels].
Recommended option: The constrained options use one dipole per grid point instead of three, therefore the source files are smaller, faster to compute and display, and more intuitive to process because we don't have to think about recombining the three values into one. On the other hand, in the cases where its physiological assumptions are not verified, typically when using an MNI template instead of the anatomy of the subject, the normal orientation constraint may fail to represent certain activity patterns. Unconstrained models can help in those cases. See further discussion on constrained vs unconstrained solutions below in section Why does it looks so noisy.
We automatically detect and display the sensors found in your head model. In the example above, only one type of sensors is found ("MEG"). You can select one or all of the sensors found in your model, such as MEG and EEG.
However, cross-modality calculations are quite dependent on the accuracy by which you have provided adequate covariance calculations and consistency of the head models across sensor types. As of Fall of 2016, we have also elected to NOT account for cross-covariances between different sensor types, since regularization and stability of cross-modalities is quite involved. For multiple sensor types, the recommendation is that you try each individually and then combined, to test for discordance.
Computing sources for an average
Using the above selections, we now discuss explicit directions on how to compute and visualize.
Select the options: Minimum norm imaging, Current density map, Constrained: Normal to cortex.
- The other menu "Compute sources" launches the interface that was used previously in Brainstorm. We are going to keep maintaining the two implementations in parallel for a while for compatibility and cross-validation purposes.
Display: Cortex surface
Right-click on the sources for the deviant average > Cortical activations > Display on cortex.
In the filter tab, add a low-pass filter at 40Hz.
- You can edit the display properties in the Surface tab:
Transparency: Change the transparency of the source activity on the cortex surface.
Take a few minutes to understand what the amplitude threshold represents.
The threshold level is indicated in the colorbar with a horizontal white line.
Why does it look so noisy?
The source maps look very noisy and discontinuous, they show a lot of disconnected patches. This is due to the orientation constraint we imposed on the dipoles orientations. Each value on the cortex should be interpreted as a vector, oriented perpendicular to the surface. Because of the brain’s circumvolutions, neighboring sources can have significantly different orientations, which also causes the forward model response to change quickly with position. As a result, the orientation-constrained minimum norm solution can produce solutions that vary rapidly with position on the cortex resulting in the noisy and disjointed appearance.
It is therefore important not to always interpret disconnected colored patches as independent sources. You cannot expect high spatial resolution with this technique (~5-10mm at best). Most of the time, a cluster of disconnected source patches in the same neighborhood that show the same evolution in time can be interpreted as "there is some significant activity around here, but with some uncertainty as to its precise location".
For data exploration, orientation-constrained solutions may be a good enough representation of brain activity, mostly because it is fast and efficient. You can often get a better feeling of the underlying brain activity patterns by making short interactive movies: click on the figure, then hold the left or right arrows of your keyboard.
Activity patterns will also look sharper when we compute dSPM or sLORETA normalized measures (later in this tutorial). In most of the screen captures in the following sections, the contrast of the figures has been enhanced for illustration purposes. Don't worry if it looks a lot less colorful on your screen. Of course, ultimately statistical analysis of these maps is required to make scientific inferences from your data.
Display: MRI Viewer
Right-click on the sources for the deviant average > Cortical activations > Display on MRI (MRI Viewer).
- You can configure this figure with the following options:
MIP Functional: Same as for MIP Anatomy, but with the layer of functional values.
Amplitude threshold: In the Surface tab of the Brainstorm window.
Current time: At the top-right of the Brainstorm window (or use the time series figure).
Display: MRI 3D
Right-click on the source file > Cortical activations > Display on MRI (3D).
Right-click and move your mouse to move the slices (or use the Resect panel of the Surface tab).
Sign of constrained maps
You should pay attention to the sign of the current amplitudes that are given by the minimum norm method: they can be positive or negative and they oscillate around zero. Display the sources on the surface, set the amplitude threshold to 0%, then configure the colormap to show relative values (uncheck the "Absolute values" option), you will see those typical stripes of positive and negative values around the sulci. Double-click on the colorbar after testing this to reset the colormap.
This pattern is due to the orientation constraint imposed on the dipoles. On both sides of a sulcus, we have defined dipoles that are very close to each other, but with opposite orientations. If we have a pattern of activity on one side of a suclus that can be modeled as a current dipole (green arrow), the limited spatial resolution of the minimum norm model will blur this source using the dipoles that are available in the head model (red and blue arrows). Because of the dipoles’ orientations, the minimum norm images produces positive values (red arrows) on one side of the sulcus and negative on the other side (blue arrows).
When displaying the cortical maps at one time point, we are usually not interested in the sign of the minimum norm values but rather by their amplitude. This is why we always display them by default with the colormap option "absolute values" selected.
However, we cannot simply discard the sign of these values because we need these for other types of analysis, typically time-frequency decompositions and connectivity analysis. For estimating frequency measures on the source maps it is essential that we retain the sign of the time course at each location so that the correct oscillatory frequencies are identified.
In cases where the orientation constraint imposed on the dipole orientations produces implausible results, it is possible to relax it partially (option "loose constraints") or completely (option "unconstrained"). This produces a vector (3 component) current source at each location which can complicate interpretation, but avoids some of the noisy and discontinuous features in the current map that are often seen in the constrained maps. Unconstrained solutions are particularly appropriate when using the MNI template instead of the subject's anatomy, or when studying deeper or non-cortical brain regions for which the normal to the cortical surface obtained with FreeSurfer or BrainSuite is unlikely to match any physiological reality.
Select the options: Minimum norm imaging, Current density map, Unconstrained.
S = sqrt(Sx2 + Sy2 + Sz2)
The maps we observe here look a lot smoother than the constrained sources we computed earlier. This can be explained by the fact that there is no sharp discontinuity in the forward model between two adjacent points of the grid for a vector dipole represented in Cartesian coordinates while the normal to the surface for two nearby points can be very different, resulting in rapidly changing forward models for the constrained case.
Source map normalization
The current density values returned by the minimum norm method have a few problems:
- The values tend to be higher at the surface of the brain (close to the sensors).
- The maps are sometimes patchy and difficult to read.
Normalizing the current density maps with respect to a reference level (estimated from noise recordings, pre-stimulus baseline or resting state recordings) can help with all these issues at the same time. In the case of dSPM and sLORETA, the normalizations are computed as part of the inverse routine and based on noise and data covariances, respectively. While dSPM does produce a Z-score map, we also provide an explicit Z-score normalization that offers the user more flexibility in defining a baseline period over which Brainstorm computes the standard deviation for normalization.
The normalization options do not change the temporal dynamics of your results when considering a single location but they do alter the relative scaling of each point in the min norm map. If you look at the time series associated with one given source, it will be exactly the same for all normalizations, except for a scaling factor. Only the relative weights change between the sources, and these weights do not change over time.
Select successively the two normalization options: dSPM, sLORETA, (constrained).
Double-click on all of them to compare them (screen capture at 143ms):
Current density maps: Tends to highlight the top of the gyri and the superficial sources.
sLORETA: Produces smoother maps where all the potentially activated area of the brain (given to the low spatial resolution of the source localization with MEG/EEG) is shown as connected, regardless of the depth of the sources. The maps are unitless, but unlike dSPM cannot be interpreted as Z-scores so are more difficult to interpret.
The Z-transformation converts the current density values to a score that represents the number of standard deviations with respect to a baseline period. We define a baseline period in our file (in this case, the pre-stimulus baseline) and compute the average and standard deviation for this segment. Then for every time point we subtract the baseline average and divide by the baseline standard deviation. Z = (Data - μ) / σ
- This measure tells how much a value deviates from the baseline average, in number of times the standard deviation. This is done independently for each source location, so the sources with a low variability during baseline will be more salient in the cortical maps post-stimulus.
In Process1: Select the constrained current density maps (file MN: MEG(Constr)).
Do not select "Use absolute values": We want the sign of the current values.
Double-click on the new normalized file to display it on the cortex (file with the "| zscore" tag).
You can see that the cortical maps obtained in this way are very similar to the other normalization approaches, especially with the dSPM maps.
Use non-normalized current density maps for:
- Computing shared kernels applied to single trials.
- Averaging files across MEG runs.
- Computing time-frequency decompositions or connectivity measures on the single trials.
Use normalized maps (dSPM, sLORETA, Z-score) for:
- Estimating the sources for an average response.
- Exploring visually the average response (ERP/ERF) at the source level.
- Normalizing the subject averages before a group analysis.
- Recommended normalization approach:
- It is difficult to declare that one normalization technique is better than another. They have different advantages and may be used in different cases. Ideally, they should all converge to similar observations and inferences. If you obtain results with one method that you cannot reproduce with the others, you should question your findings.
- dSPM and sLORETA are linear measures and can expressed as imaging kernels, therefore they are easier to manipulate in Brainstorm. sLORETA maps can be smoother but they are difficult to interpret. dSPMs, as z-score maps, are much easier to understand and interpret.
- Z-normalized current density maps are also easy to interpret. They represent explicitly a "deviation from experimental baseline" as defined by the user. In contrast, dSPM indicates the deviation from the data that was used to define the noise covariance used in computing the min norm map.
Delete your experiments
Select all the source files you computed until now and delete them.
Computing sources for single trials
Select: Minimum norm imaging, Current density map, Constrained: Normal to cortex
Averaging in source space
Computing the average
In Run#02, right-click on the head model or the folder > Compute sources .
Select: Minimum norm imaging, Current density map, Constrained: Normal to cortex
Now we have the source maps available for all the recordings, we can average them in source space across runs. This allows us to average MEG recordings that were recorded with different head positions (in this case Run#01 and Run#02 have different channel files so they could potentially have different head positions preventing the direct averaging at the sensor level).
The two following approaches are equivalent:
- Averaging the sources of all the individual trials across runs,
- Averaging the sources for the sensor averages that we already computed for each run.
Select "By trial group (subject average)" to average together files with similar names.
Select "Weighted average" to account for the different numbers of trials in both runs.
Right-click on each of them > File > View file contents, and check the nAvg field:
78 trials for the deviant condition, 378 trials for the standard condition.
Double-click on the source averages to display them (deviant=top, standard=bottom).
Open the sensor-level averages as a time reference.
Use the predefined view "Left, Right" for looking at the two sides at the same time (shortcut: "7").
- Clear the Process1 list, then drag and drop the new averages in it.
Run process "Pre-process > Band-pass filter": [0,40] Hz
Epochs are too short: Look at the filter response, the expected transient duration is at least 78ms. The first and last 78ms of the average should be discarded after filtering. However, doing this would get rid of almost all the 100ms baseline, which we need for normalization. As mentioned here, we should have been importing longer epochs in order to filter and normalize the averages properly.
- In Process1, select the two filtered averages.
Run process "Standardize > Baseline normalization", baseline=[-100,-1.7]ms, Z-score.
Four new files are accessible in the database: two filtered and two filtered+normalized.
Double-click on the source averages to display them (deviant=top, standard=bottom).
Delete the non-normalized filtered files, we will not use them in the following tutorials.
Note for beginners
Everything below is advanced documentation, you can skip it for now.
Averaging normalized values
Averaging normalized source maps within a single subject requires more attention than averaging current density maps. The amplitude of the normalized measures increase with the SNR of the signal, the higher the SNR the higher the normalized score. For instance, the average of the dSPM for the single trials is lower than the dSPM of the averaged trials (by a factor of sqrt(N), where N is the number of trials).
- From the expression of the dSPM, we know exactly what factor should be applied to compensate for this effect so that new value reflects the enhanced SNR that results from averaging over trials. When computing the average of dSPM or other normalized values, we have to also multiply the average with the square root of the number of files averaged together.
dSPM(Average(trials)) = sqrt(Ntrials) * Average(dSPM(trials))
Average the current density maps, then normalize.
- sLORETA(Average(trials)) = Average(sLORETA(trials))
Display: Contact sheets and movies
Contact sheet: Right-click on any figure > Snapshot > Time contact sheet: Figure
MEG_simulated [Nmeg x Ntime] = Forward_model [Nmeg x Nsources] * MN_sources [Nsources x Ntime]
Then you can compare visually the original MEG recordings with the simulated ones. More formally, you can compute an error measure from the residuals (recordings - simulated).
Open side-by-side the original and simulated MEG recordings for the same condition:
Advanced options: Minimum norm [TODO]
Click on the button [Show details] to bring up all the advanced minimum norm options.
Briefly, the use of various depth weightings was far more debated in the 1990s, before the introduction of MNE normalization via dSPM, sLORETA, and other "z-scoring" methods, which mostly cancel the effects of depth weighting (put another way, after normalization min norm results tend to look quite similar whether depth weighting is used or not).
By modifying the source covariance model at each point in the source grid, deeper sources are "boosted" to increase their signal strength relative to the shallower dipoles; otherwise, the resulting MNE current density maps are too dominated by the shallower sources. If using dSPM or sLORETA, little difference in using depth weighting should be noted. To understand how to set these parameters, please refer to the MNE manual. (options --depth, --weightexp and --weightlimit).
Noise covariance regularization [TODO]
MNE and dipole modeling are best done with an accurate model of the noise covariance, which is generally computed from experimental data. As such, these estimates are themselves prone to errors that arise from relatively too few data points, weak sensors, and strange data dependencies that can cause the eigenspectrum of the covariance matrix to be illconditioned (i.e. a large eigenvalue spread or matrix condition number). In Brainstorm, we provide several means to "stabilize" or "regularize" the noise covariance matrix, so that source estimation calculations are more robust to small errors.
Regularize noise covariance: The L2 matrix norm is defined as the largest eigenvalue of its eigenspectrum. This option adds to the covariance matrix a diagonal matrix whos entries are a fraction of the matrix norm. The default is 0.1, such that covariance matrix is stabilized by adding to it an identity matrix that is scaled to 10% of the largest eigenvalue.
Median eigenvalue: The eigenspectrum of MEG data can often span many decades, due to highly colored spatial noise, but this broad spectrum is generally confined to the first several modes only. Thus the L2 norm is many times greater than the majority of the eigenvalues, and it is difficult to prescribe a conventional regularization parameter. Instability in the inverse is dominated by defects found in the smallest eigenvalues. This approach stabilizes the eigenspectrum by replicating the median (middle) eigenvalue for the remainder of the small eigenvalues.
Diagonal noise covariance: Deficiencies in the eigenspectrum often arise from numerical inter-dependencies found among the channels, particularly in covariance matrices computed from relatively short sequences of data. One common method of stabilization is to simply take the diagonal of the covariance matrix and zero-out the cross-covariances. Each channel is therefore modeled as independent of the other channels. The eigenspectrum is now simply the (sorted) diagonal values.
No covariance regularization: We simply use the noise covariance matrix as computed or provided by the user.
Automatic shrinkage: Stabilization method of Ledoit and Wolf (2004), still under testing in the Brainstorm environment. Basically tries to estimate a good tradeoff between no regularization and diagonal regularization, using a "shrinkage" factor. See Brainstorm code "bst_inverse_linear_2016.m" for notes and details.
Recommended option: This author (Mosher) votes for the median eigenvalue as being generally effective. The other options are useful for comparing with other software packages that generally employ similar regularization methods. [TODO]
Regularization parameter [TODO]
In minimum norm estimates, as mentioned above in the comparisons among methods, the data covariance matrix is essentially synthesized by adding the noise covariance matrix to a modeled signal covariance matrix. The signal covariance matrix is generated by passing the source prior through the forward model. The source prior is in turn prescribed by the source model orientation and the depth weighting.
A final regularization parameter, however, determines how much weight the signal model should be given relative to the noise model, i.e. the "signal to noise ratio" (SNR). In Brainstorm, we follow the definition of SNR as first defined in the original MNE software of Hamalainen. The signal covariance matrix is "whitened" by the noise covariance matrix, such that the whitened eigenspectrum has elements in terms of SNR (power). We find the mean of this spectrum, then take the square root to yield the average SNR (amplitude). The default in MNE and in Brainstorm is "3", i.e. the average SNR (power) is 9.
Signal-to-noise ratio: Use SNR of 3 as the classic recommendation, as discussed above.
RMS source amplitude: An alternative definition of SNR, but still under test and may be dropped. [TODO]
As mentioned above, these methods create a convenient linear imaging kernel that is "tall" in the number of elemental dipoles (one or three per grid point) and "wide" only in the number of sensors. At subsequent visualization time, we efficiently multiply the kernel with the data matrix to compute the min norm images.
For some custom purposes, however, a user may find it convenient to pre-multiply the data matrix and generate the full source estimation matrix. This would only be recommended in small data sets, since the full results can become quite large.
- Full results [15000x361] = Inverse kernel [15000x274] * Recordings [274x361]
Advanced options: LCMV beamformer
As mentioned in the introduction above, two other methods can be selected for source estimation, a beamformer and dipole modeling. In this section, we review the options for the beamformer. You need to estimate a data covariance matrix in order to enable the option "LCMV beamformer" in the interface.
The only option "Pseudo Neural Activity Index" (PNAI), is named after the definition of the Neural Activity Index (NAI). We have modified Van Veen’s definition to rely strictly on the data covariance, without need for a separate noise covariance matrix, but the basic premise is the same as in dSPM, sLORETA, and other normalizations. Viewing the resulting "map," in an identical manner to that with MNE, dSPM, and sLORETA described above, reveals possibly multiple sources as peaks in the map. The PNAI scores analogously to z-scoring.
We recommend you choose "unconstrained" and let the later Dipole scanning process, which finds the best fitting dipole at each time point, optimize the orientation with respect to the data.
Data covariance regularization
Same definitions as in MNE, only applied to the data covariance matrix, rather than the noise covariance matrix. Our recommendation is to use median eigenvalue.
Advanced options: Dipole modeling
Dipole modeling fits a single dipole at each potential source location to produce a dipole scanning map. This map can be viewed as a indication of how well, and where, the dipole fits at each time point. However, we recommend using the subsequent best-dipole fitting routine (dipole scanning) to determine the final location and orientation of the dipole (one per time point). Please note that this function does not fit multiple simultaneous dipoles.
Although not widely recognized, dipole modeling and beamforming are more alike than they are different – when comparing the inverse operators required to compute the dipole scanning map (dipole modeling) and the beamformer output map (LCMV), we see that they differ only in that the former uses an inverse noise covariance matrix while the latter replaces this with the inverse of the data covariance.
This field is now missing, but the resulting imaging kernel file is directly analogous to the PNAI result from LCMV beamforming. The user can display this scanning measure just as with the LCMV case, where again the normalization and units are a form of z-scoring.
Use "unconstrained source" modeling and let the process "dipole scanning" optimize the orientation of the dipole for every time instance.
Noise covariance regularization
Similarly, use "median eigenvalue".
The tutorial "MEG current phantom (Elekta)" demonstrates dipole modeling of 32 individual dipoles under realistic experimental noise conditions.
On the hard drive
Constrained shared kernel
Right-click on a shared inverse file in the database explorer > File > View file contents.
Structure of the source files: results_*.mat
Time: [1 x Ntime] Time values for each sample recorded in F, in seconds.
HeadModelType: Type of source space used for this head model ('surface', 'volume', 'mixed').
HeadModelFile: Relative path to the head model used to compute the sources.
SurfaceFile: Relative path to the cortex surface file related with this head model.
Atlas: Used only by the process "Sources > Downsample to atlas".
GridAtlas: Atlas "Source model" used with mixed source models.
GoodChannel: [1 x Nchannels] Array of channel indices used to estimate the sources.
Comment: String displayed in the database explorer to represent this file.
History: Operations performed on the file since it was create (menu "View file history").
Whitener: Noise covariance whitener computed in bst_inverse_linear_2016.m
DataWhitener: Data covariance whitener computed in bst_inverse_linear_2016.m
SourceDecompVa: [3 x Nsources] Concatenated right singular vectors from the SVD decomposition of the whitened leadfield for each source (only for unconstrained sources).
SourceDecompSa: [3 x Nvertices] Vector diagonal of the singular values from the SVD decomposition of the whitened leadfield for each source (only for unconstrained sources).
Std: For averaged files, number of trials that were used to compute this file.
DisplayUnits: String, force the display of this file using a specific type of units.
ChannelFlag: [Nchannels x 1] Copy of the ChannelFlag field from the original data file.
Full source maps
In Intra-subject, right-click on one of the normalized averages > File > View file contents.
This file has the same structure as a shared inverse kernel, with the following differences:
It contains the full time series (ImageGridAmp) instead of an inverse operator (ImagingKernel).
The Z-score process updated the field Function ('mn' => 'zscore')
Minimum norm: Baillet S, Mosher JC, Leahy RM
Electromagnetic brain mapping, IEEE SP MAG 2001.
dSPM: Dale AM, Liu AK, Fischl BR, Buckner RL, Belliveau JW, Lewine JD, Halgren E
Dynamic statistical parametric mapping: combining fMRI and MEG for high-resolution imaging of cortical activity. Neuron 2000 Apr, 26(1):55-67
sLORETA: Pascual-Marqui RD
Standardized low-resolution brain electromagnetic tomography (sLORETA): technical details, Methods Find Exp Clin Pharmacol 2002, 24 Suppl D:5-12
Tutorial: Volume source estimation
Tutorial: Deep cerebral structures
Tutorial: Computing and displaying dipoles
Tutorial: Dipole fitting with FieldTrip
Tutorial: Maximum Entropy on the Mean (MEM)
Forum: Minimum norm units (pA.m): http://neuroimage.usc.edu/forums/showthread.php?1246
Forum: Imaging resolution kernels: http://neuroimage.usc.edu/forums/showthread.php?1298
Forum: Spatial smoothing: http://neuroimage.usc.edu/forums/showthread.php?1409
Forum: Units for dSPM/sLORETA: http://neuroimage.usc.edu/forums/showthread.php?1535
Forum: EEG reference: http://neuroimage.usc.edu/forums/showthread.php?1525#post6718
Forum: Sign of the MNE values: http://neuroimage.usc.edu/forums/showthread.php?1649
Forum: Combine mag+gradiometers: http://neuroimage.usc.edu/forums/showthread.php?1900
Forum: Combine EEG+fMRI: http://neuroimage.usc.edu/forums/showthread.php?2679
Forum: Residual ocular artifacts: http://neuroimage.usc.edu/forums/showthread.php?1272
Forum: Dipole fitting: http://neuroimage.usc.edu/forums/showthread.php?2400
Forum: Simulate recordings from sources: http://neuroimage.usc.edu/forums/showthread.php?2563