Fig 1.
Single-pulse electrical stimulation with stereoelectroencephalography (sEEG).
A. A cartoon schematic of an axial MRI with two sEEG leads. B. Single-pulse biphasic electrical stimulation is delivered through adjacent sEEG electrode contacts (200μs, 6mA), separated by 3–7s between pulses. C. Cartoon voltage traces that might be elicited at two different sites in response to stimulation at a third site (i.e. with a stimulation artifact followed by a characteristic evoked potential deflection). D. An example set of actual evoked potentials showing the stimulation-locked evoked potential matrix V, with columns Vk(t)) shown as individual traces. E. Average stimulation-evoked potential from (D). F. Examples of some of the different measured average response shapes seen in these studies (as in E). These selected responses were produced from 5 different stimulation sites across two patients (over the interval 15ms-1s post-stimulation, where the gray line indicates 0 μV). The variety of different shapes seen in just this small subset shows that there is no one typical form of stimulation evoked potential shape.
Fig 2.
Quantifying single-trial cross-projections.
A. Stimulation and recording sites for this example, shown in an axial MRI section. B. 15 single trials of stimulation response (gray) produced the averaged evoked potential shape (black). C. Trial #1 (light blue) was unit-normalized and projected into the other 14 trials, omitting self-projection. D. As in (C), but for normalized trial #10 (orange). E. All 210 projections are shown sorted, note the obvious sub-sets corresponding to the projections of unit-normalized single trials. The projections of each trial into the others can reflect how representative each trial is of the canonical evoked potential response shape. F. The projections from (E), aggregated into a single column (i.e. imposing the assumption that the order of trials doesn’t matter, which will be false under some circumstances).
Fig 3.
Using time-resolved projection weight to quantify response duration, τR.
A. Stimulation and recording sites for this example, shown in a sagittal MRI section. B. 10 single trials of stimulation response (gray) produced the averaged evoked potential shape (black). C. Abbreviated timeseries are calculated from t1 to a range of t2s to obtain time-resolved projection weights (individual dots). The traces above indicate a subset of the projections (for the normalized trace of 9th trial) at times t2 = 20ms, t2 = 80ms = τR, t2 = .5s, and t2 = 1s, with distributions of at each of these timepoints highlighted in the light red background. In this example, the blue dots are projection of the normalized trace of 9th trial (illustrated in traces above). The thick black line is
. Calculated response duration, τR, is indicated by a red circle. Small vertical red lines indicate thresholds where
exceeds 98% of
(providing an estimate of the error in calculating τR). Note that blue dots in bottom portion are the projections illustrated for the 9th trial from the traces on the top. D. The projection weight temporal profile, from the black line in the lower portion of (C), is shown with a gray line. The averaged voltage response, from the black line in (B), is shown with a black line, and the significant portion of the response is highlighted (i.e. up to τR). E. As in (D), but for the example response from Fig 2.
Fig 4.
Parameterizing the evoked response for single trials.
A. An example evoked response, as in Figs 2B and 3B. B. The voltage response Vk(t) from trial k (black) is parameterized by how strongly the canonical response shape (C(t), red trace, time interval t1 to τR) is represented (scaling factor αk) plus the “residual” εk(t) (green): Vk(t) = αkC(t) + εk(t). C. Overlaid Vk(t), αkC(t), and εk(t) for example trial #6. D. As in (C), for all 10 trials.
Fig 5.
Examples of shapes, durations, projections, and parameterizations.
Five example responses illustrate projection magnitude profiles, parameterization values, and significance metrics. Note that the bottom response does not meet signficance at any time. The four top examples all met extraction significance at τR of p≪ 10−16 (t-test of vs 0). The bottom example is not significant (p = 0.37). Single trial parameters are averaged across trials for the 3 right-most columns. Note that the second trace might be called the classic N1/N2 response.
Fig 6.
Illustrative examples of extraction significance.
A. An example of a high noise, but highly significant voltage response. B. An example of no significant response to stimulation. C. Early significance is detected in an apparently insignificant response. D. Examination of the voltages prior to t1 shows a clear (presumably artifactual) offset, explaining the observation in (C). E. An example of significance throughout a response that appears to be insignificant, though does have a non-zero offset. F. Correcting (E) for the 20μV offset in baseline removes the artifactual significance. Note that p-values determined by t-test of vs 0.
Table 1.
Discovered parameters for single stimulation-recording pair.
Fig 7.
Examples of projection magnitudes and profiles obtained with synthetic data.
A. A 100ms, 100μV synthetic square wave response (zero noise). B. 50ms/100μV square. C. Two 50ms/100μV square. D. 100ms/100μV square (low noise). E. 100ms/100μV square (intermediate noise). F. 100ms/100μV square (high noise). G. Ramp up to 100μV over 100ms (zero noise). H. Ramp down from 100μV over 100ms. I. Ramp up to 100μV over 50ms then down to 0μV over 50ms. J. Sinusoid (peak ±100μV) over 100ms. K. Inverted sinusoid. L. Absolute value of sinusoid.
Fig 8.
Illustrations of different normalizations of single-trial cross projections.
As discussed in the manuscript, different trials Vk(t) and Vl(t) may be compared with each other directly, or after normalization with . A. Un-normalized projections Vk(t)Vl(t) are sub-optimal because trials with large amplitude are over-emphasized in comparison with trials of lower amplitude but more characteristic structure. B. The time-resolved structure of fully-normalized projections
are sub-optimal because they dramatically favor early transients and cannot resolve temporally-sustained structure. C. Semi-normalized projections are optimal in that they balance emphasis of amplitude and sustained structure between trials. Panels D-F show the same sample data as A-C, and illustrate the effect of extracting the canonical response from different epochs of time. In the “standard” extraction approach we have illustrated so far, C(t) is discovered using linear kernel PCA from V(t) over the isolated time interval from t1 to τR (black line with yellow highlight). We can also unit normalize the average voltage
over the t1 to τR interval, though the explained variance and signal-to-noise are slightly worse. D. If a C(t) is extracted using linear kernel PCA from t1 to t2 = 3 s (blue+red compound trace), the explained variance and signal-to-noise is very poor due to the introduction into the algorithmic process of a large amount of unnecessary noise from the time following τR, even if the extracted form is truncated at τR for parameterization (red trace). E and F. As in (D), but for t2 = 2 s (E) and t2 = 1 s (F). Note how the shapes converge as t2 decreases.
Fig 9.
Voltage deflections in the scalp EEG from intracranial sEEG electrical stimulation pulses, and automated artifactual trial identification.
A. Schematic, showing sEEG stimulation and EEG recording. B. Ten single-pulse EEG trials (gray) and average trace across trials (black). Note the clearly artifactual trial. C. Time-resolved projection magnitudes for trials from (B). D. Projection magnitudes at τR = 0.23s, suggesting that trial #6 is artifactual (p = 1.8⋅10−6, unpaired t-test comparing red+green vs black). Green dots indicate projections of normalized trial #6 into other trials, and red dots indicate normalized projections of other trials into trial #6. E and F. As in (B and C), with trial #6 removed. Note the change in τR from 0.23 to 0.28s and from 8.5 to 14.5μV
.