Granger causality analysis of rat cortical functional connectivity in pain

Abstract

Objective: The primary somatosensory cortex (S1) and the anterior cingulate cortex (ACC) are two of the most important cortical brain regions encoding the sensory-discriminative and affective-emotional aspects of pain, respectively. However, the functional connectivity of these two areas during pain processing remains unclear. Developing methods to dissect the functional connectivity and directed information flow between cortical pain circuits can reveal insight into neural mechanisms of pain perception.

Approach: We recorded multichannel local field potentials (LFPs) from the S1 and ACC in freely behaving rats under various conditions of pain stimulus (thermal versus mechanical) and pain state (naive versus chronic pain). We applied Granger causality (GC) analysis to the LFP recordings and inferred frequency-dependent GC statistics between the S1 and ACC.

Main results: We found an increased information flow during noxious pain stimulus presentation in both S1[Formula: see text]ACC and ACC[Formula: see text]S1 directions, especially at theta and gamma frequency bands. Similar results were found for thermal and mechanical pain stimuli. The chronic pain state shares common observations, except for further elevated GC measures especially in the gamma band. Furthermore, time-varying GC analysis revealed a negative correlation between the direction-specific and frequency-dependent GC and animal's paw withdrawal latency. In addition, we used computer simulations to investigate the impact of model mismatch, noise, missing variables, and common input on the conditional GC estimate. We also compared the GC results with the transfer entropy (TE) estimates.

Significance: Our results reveal functional connectivity and directed information flow between the S1 and ACC during various pain conditions. The dynamic GC analysis support the hypothesis of cortico-cortical information loop in pain perception, consistent with the computational predictive coding paradigm.

Figure 1:

Schematic diagram of multichannel LFP data preprocessing and Granger causality (GC) analysis.

Figure 2:

Experimental LFP data. (A) Snapshot of Z-scored multichannel LFP signals during spontaneous baseline. Channels #1–32 were implanted in the ACC, and Channels #33–64 were implanted in the S1. (B) PCA and the eigenspectrum showed that the dominant energy was concentrated in the 1st principal component (PC). (C) Z-scored spectrogram of LFP signals (white traces) from one S1 and one ACC channels. Warm color indicates an increase in spectral power. Vertical dotted lines show the onset of stimulus presentation. In this example, we observed a clear power increase in the S1 at theta and high gamma frequency bands, and in the ACC at high gamma frequency band.

Figure 3:

Computer simulation results. (A) Network connectivity. Arrow indicates the directed statistical dependence between two random variables. (B) Impact of different levels of SNR on the conditional GC estimates based on the simulated data from Model 1. Shaded area denotes the standard error of the mean (SEM) across trials. The first row shows the ground truth. (C) Impact of the model mismatch on the conditional GC estimates based on the simulated data from Model 1. Shaded area denotes SEM. (D) True (top) and estimated (bottom) pairwise directed functional connectivity based on two arbitrary nodes. Fill-in entry indicates the presence of directed GC.

Figure 4:

Granger causality (GC) analysis during thermal stimuli (250 mW vs. 50 mW laser) stimulations in naive and CFA rats. (A) Spectral GC estimates in both S1→ACC and ACC→S1 directions. Shaded areas denote the 95% confidence intervals. (B) Similar to panel A, except for CFA rats. (C,D) Population statistics of GC measures at different frequency bands. Rank-sum test: *, p < 0.05; **, p < 0.01.

Figure 5:

Granger causality (GC) analysis during mechanical stimuli (PP vs. VF) stimulations in naive and CFA rats. (A) Spectral GC estimates in both S1→ACC and ACC→S1 directions. Shaded areas denote the 95% confidence intervals. (B) Similar to panel A, except for CFA rats. (C,D) Population statistics of GC measures at different frequency bands. Rank-sum test: *, p < 0.05.

Figure 6:

Assessment of channel selection and configuration for Granger causality analysis. The results of the first four columns were derived from a 2 × 2 system, with one channel from the S1 and the other from the ACC (channels #1 and #12 are ACC channels; channels #40 and #54 are S1 channels), whereas the result of the fifth column was derived from a 4 × 4 system. The result of the last column was derived from two PC1, each computed from PCA based on 32 channels within each region. (A) 250 mW laser stimulation. (B) PP stimulation.

Figure 7:

Illustration of dynamic Granger causality (GC) analysis based on one animal’s recordings before and after CFA. Time-varying GC estimates were derived from a moving window of 100 ms with a step size of 25 ms. Time 0 denotes the paw withdrawal onset. (A,B) Frequency-dependent GC measures in both S1→ACC and ACC→S1 directions at four frequency bands during 250 mW laser stimulations (A, naive condition before CFA; B, chronic pain condition after CFA). Shaded areas denote the 95% confidence intervals. (C,D) Similar to panels A and B, except for PP stimulations.

Figure 8:

Temporal coordination of cross-frequency Granger causality (GC) between the S1→ACC (61–80 Hz, yellow) and ACC→S1 (31–60 Hz, blue) directions. (A) Representative single-trial examples during four pain conditions shown in Fig. 7. Time 0 denotes the paw withdrawal onset. As seen, the rise time of yellow trace appeared slightly earlier than the rise time of blue trace in each example. (B) Corresponding trial average during four pain conditions shown in Fig. 7. In all but one plots, the blue trace lagged behind the yellow trace in the rise time.

Figure 9:

Left column: Two pairs of LFP signal trials (red and blue) from channels S1 and ACC (top part of every panel from A to E) with corresponding estimates of time-varying Granger causality (GC) (bottom part of every panel from A to E). In all panels the blue trials have a shorter withdrawal latency than the red trials. The vertical red and blue lines mark the animal’s paw withdrawal time from the respective trials. Note that time bar is different between the top and bottom plots. Right column: The scatter plot between the withdrawal latency and the log(GC) value computed within a specific moving window (i.e., the shaded area shown in the plots of time-varying GC). The Spearman’s rank correlation rho and p values (n = 54 trials) are shown. The results were illustrated for different frequency bands and directions: (A) GC_ACC→S1 at theta band. (B) GC_S1→ACC at beta band. (C) GC_ACC→S1 at beta band. (D) GC_S1→ACC at gamma band. (E) GC_ACC→S1 at gamma band.

Figure 10:

Comparison between the Granger causality (GC) and the transfer entropy (TE) method for computer simulated data (Model 1). (A) The estimated peak GC values with respect to the number of simulated samples. The horizontal dashed lines represent the respective ground truth values. With more samples, the GC estimates became more accurate. (B) The estimated TE with respect to the number of simulated samples.

Figure 11:

Comparison between the Granger causality (GC) and the transfer entropy (TE) method for experimental data. (A) The estimated TE in both S1→ACC and ACC→S1 directions during laser stimulations (50 mW, n = 46 trials; 250 mW, n = 72 trials). Signed-rank test: *, p < 0.05; **, p < 0.01. (B, C) Figure legend same as panel A, except for the narrowband signals filtered within the theta and gamma bands, respectively.