Comparing statistical performance of iES with minimum-norm imaging for mapping induced oscillations.

<p><i>a) Subspace scanning results:</i> (left) significant average <i>subcorr</i> map (<i>p</i> < .05, see text for procedure). Note that results were obtained from the subgroup of participants that presented the hypothesized effect (n = 8, see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005990#pcbi.1005990.g004" target="_blank">Fig 4</a>). (right) histogram from observed data and permutation tests to derive a <i>subcorr</i> threshold corresponding to <i>p</i> < .05. <i>b) Minimum-norm imaging results:</i> average maps of log-transformed power ratios (stimulus/baseline, <i>p</i> < .05). Note that the distinction between positive and negative effects is not possible. The results were derived from the same subgroup (n = 8) to allow comparison with a), the results obtained with the full group (n = 17) are shown as an outline. Contrary to iES, no increase in beta power could be detected over the right post-central gyrus region, with the same subgroup of subjects. Unthresholded maps are shown in the supplementary material. (right) histograms of observed data and permutation tests to determine significance of minimum-norm maps at <i>p</i> < .05. Note how the strong negative effects inflated the permutation distribution and prevented the detection of the smaller positive effects. As shown using iES, positive and negative effects could be evaluated separately and specifically.</p

Basic principles of iES.

<p><i>a) Examples of designs:</i> The experimental design (shown as a black trace) determines the quality function <i>f</i>(<b>s</b>), so that this latter takes high values for signals consistent with the hypothesis (in orange; the signals that do not correspond to the tested hypothesis are shown in blue). <i>b) MEG data:</i> the multichannel MEG recordings are captured in the matrix <b>X</b> = {<b>x</b>[<i>t</i> = 1], …, <b>x</b>[<b>t</b> = <b>T</b>]}. <i>c) Computing the signal subspace:</i> spatial patterns <b>P</b> = {<b>p</b>₁, …, <b>p</b>_<i>D</i>} are extracted from the MEG data by optimizing the quality function with respect to spatial filters <b>W</b> = {<b>w</b>₁, …, <b>w</b>_<i>D</i>}. Whereas <b>W</b> is used to extract the signals of interest from the multichannel MEG data, <b>P</b> are the forward fields of these signals as they contribute to the measured MEG data. <i>d) Computing the forward model:</i> shown are the MEG spatial patterns <b>G</b>(<i>ρ</i>) generated by two tangential dipoles at location <i>ρ</i> in a single subject. <i>e) Subspace correlation as a scanning metric:</i> The spatial patterns from c) and d) span a subspace of the MEG sensor space. A grid of source locations is scanned with a subspace correlation metric [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005990#pcbi.1005990.ref006" target="_blank">6</a>], quantifying the smallest possible angle between the data and source subspaces. This yields a distributed map of scores, which highlights possible source locations consistent with the hypothesis.</p

Illustration of the field-spread effect on the detection of weak MEG sources.

<p>Point-like sources are typically recovered using beamforming or minimum-norm estimation (MNE) imaging at the expense of exaggerated spatial smearing in the source space. The Source 1 and Source 2 maps are examples of such effect when active separately. When both sources are active simultaneously, their relative strengths impact the ability of source imaging to spatially resolve between the two active regions. When both source magnitudes are similar (Source strength 1 = 2), the map can display their respective contributions. When one source is weaker than the other (Source strength 1 < 2), its presence in the resulting source map may be masked by that of the strongest source (here Source 2).</p

Regularization methods for covariance estimates.

<p>For illustration we show GEP results from the single-subject data of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005990#pcbi.1005990.g003" target="_blank">Fig 3a</a> comparing gamma power between stimulus and baseline periods. The top panels display the power ratio <i>f</i>_{<i>induced</i>}, the bottom panels display the power associated with each component, computed as in the baseline and stimulus period. In <i>a)</i> component-wise power computed from regularized and unregularized covariance matrices are compared using the <i>diagonal loading</i> method. In <i>b)</i>, regularized results using the <i>truncated SVD</i> method, which results in a smaller number of components.</p

Effects in a subgroup of participants: Mapping induced oscillations in the beta band (13-30 Hz) during visual stimulation.

<p>The data are that of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005990#pcbi.1005990.g003" target="_blank">Fig 3</a>, and the present figure layout is identical. <i>a) Subspace computation, example subject:</i> in this participant, only one significant spatial dimension was retained for the signal subspace contributing to stronger power in the beta band. <i>b) Subspace computation, group level:</i> <i>γ</i> = .22 was the highest population prevalence that could be rejected at a <i>p</i> = 0.05, thus the majority null hypothesis could not be rejected. The analysis was pursued with the subgroup (n = 8) of participants that showed the hypothesized effect. The purpose was to appreciate the spatial concordance across subjects and compare iES to standard source imaging approaches. <i>c) Spatially filtered signals, example subject:</i> induced power changes in the band of interest (beta, but also in alpha band) are clearly visible in 3 example trials. <i>d) Spatially filtered signals, group level:</i> induced power changes in the band of interest were found in the participant subgroup (n = 8). <i>e) Subspace correlation maps, example subject:</i> the hypothesized effect localized to the right post-central/parietal cortex. <i>f) Subspace correlation maps, subgroup level:</i> the effect localized to the right post-central gyrus. Note that this effect cannot be generalized to the majority of the population that the subjects were drawn from (see b) but only to a subset, which may present interesting capacity for identifying subtypes in participants.</p

iES mapping amplitude correlations of a seed region with the rest of the brain during rest.

<p><i>a)</i> We show example traces of co-occurring oscillatory bursts in the alpha band (8-13 Hz) in the resting-state, from the same MEG sessions as presented in previous sections. The two examples have different phase lags, around 270° and 180° respectively [which would be discarded in other approaches, see e.g., <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005990#pcbi.1005990.ref023" target="_blank">23</a>]. <i>b)</i> Correlation of alpha amplitudes between the seed region (circle) and the rest of the brain, using minimum-norm imaging in an example subject. <i>c)</i> (left) iES <i>subcorr</i> map showing source locations whose amplitudes correlated with the seed region’s at <i>r</i> > .4. The homologous contralateral region is emphasized in this map. (right) the same map with the data projected away from the spatial pattern of the seed region. <i>d)</i> Same as b) but averaged over the group <i>e)</i> same as c) but averaged over the group and statistically thresholded using the permutation approach explained above.</p

Simulation results comparing sensitivity of iES and standard approach.

<p><i>a)</i> Examples of simulated time-series that follow a 1/f spectral distribution (grey trace) or target a pre-specified <i>f</i>_{<i>narrow</i>}, which is the ratio between narrow-band and broadband power (blue traces). <i>b)</i> Simulation setup: Two sources of interest in blue targeting pre-specified <i>f</i>_{<i>narrow</i>} (blue traces) are embedded in background brain noise composed of 1/f signals evenly distributed across 66 locations. <i>c)</i> Metric of detection probability: We quantified the probability that the two sources of interest were detected in a source map by using a range of different thresholds: the two sources were detected, if they were contained in two separate clusters after thresholding. Here we show 4 different thresholds in two simulation scenarios using the standard imaging approach. In the first scenario, sources were detected with 2 out of 4 (detection probability: 0.5) threshold values. In the second scenario, sources were detected only with 1 out 4 (detection probability: 0.25) threshold values. This configuration illustrates the issue of concurrent sources with different strengths on the detection of separate clusters of activity. <i>d)</i> Comparison of methods: the maps from each simulation run were thresholded using 50 different values to estimate a detection probability as in c). Since the range of data values for both MNE and iES were different, we normalized the detection probability by the maximum value obtained in each method. Thus we did not compare the absolute detection probability between the two methods, but rather how it varied with respect to the difference in <i>f</i>_{<i>narrow</i>}, between the sources of interest.</p

iES group analysis: Mapping induced gamma oscillations during visual stimulation.

<p><i>a) Subspace computation, example subject:</i> (left) values of the quality function <i>f</i>_{<i>induced</i>} for all the spatial patterns in the MEG data, ranked in decreasing order. The components with the 5 largest values of the quality function were deemed consistent with the tested hypothesis (highlighted with black dots—left, and their sensor topographies shown to the right). This was determined via permutation tests, which yielded , a threshold indicating the minimum value of the quality function for significance (<i>p</i> < 0.05). Note that the number of significant components may vary per subject, as illustrated hereafter. <i>b) Effect prevalence, group level:</i> (left) number of significant spatial components for each subject (<i>K</i>_<i>obs</i> = 17 is the number of participants in this example). The subject illustrated in Panel A is shown in blue; (right) prevalence testing results (as detailed in Materials and Methods) showing the likelihood of the data under a population prevalence <i>γ</i>. <i>γ</i> = .83 is the highest value that can be rejected at <i>p</i> < 0.05 (horizontal dashed line). <i>c) Spatially-filtered signals, example subject:</i> (left) three example trials: the increase in gamma oscillations after stimulus presentation can be readily appreciated visually in the spatially-filtered signals; (right) average time-frequency map across 220 trials: here too, the strong induction of gamma activity is clearly visible. <i>d) Spatially-filtered signals, group level:</i> (left) average wavelet power of spatially-filtered signals in the two time periods of interest (baseline and visual stimulus). Values are expressed in decibels with respect to empty-room MEG recordings, shaded regions are standard errors over subjects; (right) power spectra of the stimulus period in decibels with respect to the baseline period. Thin lines represent single-subject data. <i>e) Subspace correlation maps, example subject:</i> (top) Map of <i>subcorr</i> values in the 3-D source grid, indicating the location of brain regions generating stimulus-induced gamma activity, (bottom) Fisher-z transformed map. <i>f) Subspace correlation maps, group level:</i> (left) a permutation procedure to determine a statistical threshold to apply on the average <i>subcorr</i> scores. The figure shows the histograms of the permuted and observed <i>subcorr</i> values; (right) group-level average <i>subcorr</i> map, thresholded at <i>p</i> < 0.05. The effect confirms the single-subject data shown, and localizes to the occipital visual cortex.</p

Mapping of narrow-band oscillations.

<p>The sources of narrow-band signals were mapped for the theta, alpha and beta frequency bands using <i>a) iES subspace scanning</i> and <i>b) power ratios from minimum norm imaging (narrow-band over broadband 2-100 Hz)</i>. iES allows for statistical thresholding across the group using permutation procedures that are equivalent for all use cases. The theta band results showed marked differences between the two approaches in deeper, medial temporal regions. iES revealed bilateral sources whereas MNE power ratio maps pointed at predominant source activity in the right hemisphere.</p

Mapping correlation of a peripheral signal with neural oscillation amplitudes.

<p><i>a)</i> video frames from an eye tracker camera during a MEG recording at rest, pupil diameter was extracted using a fitted ellipse. <i>b)</i> pupil diameter time-series time-locked to a visual stimulus onset (overlaid trials). The gray bar indicates the baseline time period for analysis. <i>c)</i> <i>subcorr</i> map showing sources whose amplitudes correlate with pupil diameter across trials during the visual task. The signal subspace for this analysis contained one significant component which signal correlated at <i>r</i> = −0.44 with changes in pupil diameter. The maps were threshold at 75% of the maximum value).</p