Fig 1.
Neural recording, vibratory stimulation and our analysis scheme.
(A) Photo of anterior parietal cortex with outlines of sulci (white lines) superimposed. The planar array was inserted into the paw representation region of S1 (yellow square). A linear array was inserted into S2 region located in the suprasylvian sulci (yellow rectangle). (B) Time course of the depth modulation of the vibratory stimulation. The stimulator presses 500μm into the skin over 0.1s of ramping, followed by a pause of 0.1s. At t = 0, the vibration stimulation starts. Here, 159μm of 23Hz sinusoid is superimposed on a step indentation. We represent a combination of the depth modulation for F1 and F2, such as X [μm] and Y [μm], as [F1, F2] = [X, Y]. (C) Time domain representation of LFP signal from bipolar channel 156 in S1 (Session 2–2). Here, we computed the mean of the pre-stimulus LFP from -0.5 to -0.1s and used it as a baseline per trial, which is subtracted from LFP per trial. The mean trace from 15 trials is shown ([F1, F2] = [159, 16]). Shade represents the standard deviation across 15 trials, indicating extremely robust and clean SSEP. (D) Power spectrum of the LFP signal from 0.5 to 2.5s after stimulus onset in (C). Again, shading represents standard deviation. Vertical lines show frequencies of interest. (Red for 23Hz and its harmonics, green for 200Hz and blue for intermodulation.) (E and F) Frequency domain representation of logSNR (E) and vibration evoked logPower (VELogP) (F). Note that raw log values are multiplied by 10 and values are shown in [dB].
Table 1.
Summary of the experiments.
Fig 2.
Proportion of significant channels (two-way ANOVA) in S1 and S2.
Statistical results from logP and VELogP are identical and shown in black. Results from logSNR are shown in brown. Vertical lines beneath x-axis indicate F1 fundamental and harmonic (red), F2 fundamental (green), and intermodulation frequencies (blue). (A-C) % of channels that were deemed as significant according to two-way ANOVA only for the main effects of the amplitude of F1 (but not F2 main effect nor F1-F2 interaction; A), F2 = 200Hz main effect only (but not F1 main effect nor F1-F2 interaction; B) and both main effects of F1 and F2 as well as F1-F2 interaction (C). We also tried to see a ‘gain control’ type effect by showing logSNR as functions of stimulus amplitudes (S1–S3 Figs). Unfortunately, the results were not clear possibly due to 1) variations in experimental conditions (Table 1) and 2) spatial specificity in the neural response (See Figs 3–5, below).
Fig 3.
Exemplar logSNR at f1 = 23Hz depend on the vibration amplitude of F1 = 23Hz.
16 panels are arranged so that the row and column encodes the input amplitude of F1 = 23Hz (from 0 to 159μm) and F2 = 200Hz (from 0 to 16μm), respectively. (A) logSNR of S1 bipolar channel 131, whose location in the Utah array in (B) is identified with a blue diamond, (Session 2–2). This channel’s responses at f1 = 23Hz showed a significant main effect of F1 = 23Hz amplitude, but neither the main effect of F2 = 200Hz nor their interaction. p-value (F1, F2, interaction) = (<10−5, 0.054, 0.52) with the corrected threshold 0.00019. y-axis of each subplot is the mean logSNR with standard deviation across 15 trials. x-axis is the response frequency f, around f = 23Hz. Note that, as we considered a set of frequencies F’ = {f | f-3<f’<f-1 or f+1<f’<f+3} as the neighboring frequencies for the logSNR computation, logSNR is smoothed and has a lower spectral resolution than the half bandwidth of 0.5Hz. (B) Spatial mapping of logSNR at f1 = 23Hz across all channels in S1 (Session 2–2). Each square represents one of the bipolar re-referenced channels. The center of the square is plotted at the middle point between the original unipolar recordings of the 10x10 array. Squares with gray indicate channels, which were removed from the analysis (see Methods).
Fig 4.
Exemplar logSNR at f2 = 200Hz depends on the vibration amplitude of F2 = 200Hz.
This figure is shown with the same format as Fig 3. (A) logSNR of bipolar channel 36 in S1 (Session 2–2). This channel’s responses at f2 = 200Hz showed a significant main effect of F2 = 200Hz amplitude, but neither the main effect of F1 = 23Hz nor their interaction. x-axis is the response frequency f, around f = 200Hz. p-value (F1, F2, interaction) = (0.00043, <10−5, 0.14) with the corrected threshold 0.00019. (B) Spatial mapping of logSNR at f2 = 200Hz across all channels in S1 (Session 2–2).
Fig 5.
Exemplar logSNR at f1 = 23Hz depend on the vibration amplitude of F1 = 23Hz, F2 = 200Hz, and their interaction.
The same format as Fig 3. (A) logSNR of bipolar channel 158 in S1 (Session 2–2). This channel’s responses at f1 = 23Hz showed a significant main effect of F1 = 23Hz amplitude, the main effect of F2 = 200Hz, and their interaction. x-axis is the response frequency f, around f = 23Hz. p-values (F1, F2, interaction) are all p<10−5 with the corrected threshold 0.00019. (B) Spatial mapping of logSNR at f2 = 200Hz across all channels in S1 (Session 2–2).
Fig 6.
Nontagged frequencies between 50-150Hz in S2 are modulated by F2 = 200Hz vibratory amplitude.
(A)-(C) F1 main effect (A), F2 main effect (B), interaction (C) F-statistics from ANOVA performed on logP in S1 (shades of pale blue to blue) and S2 (shades of pale red to red). We plotted 95th percentile (top 5%), 90th (top 10%), and 50th (median). Some channels in S2 showed significant main effect of 200Hz vibratory amplitude in nontagged frequencies (+/-0.5Hz outside of the tagged, harmonic, and intermodulation frequencies, and outside of 50Hz, 100Hz, and 150Hz) from 50-150Hz. No main effects of 23Hz amplitude or interaction. We smoothed lines for a display purpose (1 data point per 1Hz). Note that [-] represents unitless.
Fig 7.
Exemplar nontagged frequencies responses between 50-150Hz modulated by F2 = 200Hz vibratory amplitude.
(A) Exemplar nontagged responses (VELogP) between 50-150Hz in bipolar channel 102 in S2 (Session 2–2). Note that the top left panel, which corresponds to the no- vibration condition, gives a flat line because VELogP is defined as the deviation of logPower from mean logPower of no vibration condition. It still has some variance across trials, shown as standard deviation (grey shading). (B) Spatial mapping of high gamma power (HGP) in S2 (Session 2–2). The location of bipolar channel 102 is located in the 8x8 array by a blue diamond. Color encodes the mean nontagged HGP in dB (our HGP measure, see Methods).
Fig 8.
Time course of the mean nontagged HGP and the frequencies of interest in S2.
(A) Evoked bandlimited power (half band width = 2Hz) around the stimulus onset. Mean log power is first averaged within the frequencies of interest for HGP (thick black), f1 harmonic (red), and intermodulation (blue) frequencies around HGB for each trial. Different line types for different frequencies (see the legend). Mean across trials per channel is further averaged across channels. The mean power during -0.5 to -0.25s for each frequency per trial is subtracted. (B) Summary of HGP, harmonic and intermodulation frequencies. Time courses for the harmonic (red) intermodulation (blue) in (A) are averaged for each category within each channel. Shading represents standard error of the mean across the top 10% channels selected as in Fig 6.
Fig 9.
Waveforms of modeled processes.
(A) Waveforms in the time domain (0 to 0.5s). X and Y are sinusoidal inputs at 23 and 200Hz, respectively. For the definitions of Rect and HSq, see the main text. (B) Spectra of each waveform in the frequency domain.
Table 2.
Models considered in analysis.
Fig 10.
Exemplar channel’s observed and modelled responses.
(A) Bipolar channel 43 in S1 (Session 2–2)’s logSNR (black) is compared to the optimally fitted models from four model architectures based on Rect functions. The best parameters for each model are the following. Rect-1 (red): -0.023Rect(X)+1.0Rect(Y), Rect-2 (blue): -0.98Rect(X)+58Rect(Y)-0.90Rect(XY), Rect-3 (purple): -0.98Rect(X)+30Rect(Y)+0.094Rect(X)Rect(Y) and Rect-4 (yellow): 1.8Rect(X)+55Rect(Y)+0.48Rect(XY)-2.4Rect(X)Rect(Y). (See S8 Fig for parameters from other channels.) The respective sums of logSNR differences from the observed logSNR across the frequencies of interest are 130, 105, 83 and 79. (B) Difference between the observed and the best model at the frequencies of interest. Color scheme is the same as in (A).
Fig 11.
Comparison of fitting performances across rectification models.
(A) Comparison of performance across four rectification models based on the cumulative probability distributions of the minimum difference for S1 and S2 separately. For a display purpose, we removed the worst 1% channels in S1 for two rectification models Rect(X)+Rec(Y) and Rect(X)+Rect(Y)+Rect(XY). (B) Comparison of each model’s performance between S1 and S2 based on the cumulative probability distributions of the minimum difference. *, **, and *** indicates p<0.05, p<0.01, and p<0.001 according to Kolmogorov-Smirnov tests.
Fig 12.
Akaike’s Information Criterion (AIC) for 8 models for S1 and S2.
The best model is the full rectification model for both S1 and S2.