Laminar Distribution of Phase-Amplitude Coupling of Spontaneous Current Sources and Sinks

Abstract

Although resting-state functional connectivity is a commonly used neuroimaging paradigm, the underlying mechanisms remain unknown. Thalamo-cortical and cortico-cortical circuits generate oscillations at different frequencies during spontaneous activity. However, it remains unclear how the various rhythms interact and whether their interactions are lamina-specific. Here we investigated intra- and inter-laminar spontaneous phase-amplitude coupling (PAC). We recorded local-field potentials using laminar probes inserted in the forelimb representation of rat area S1. We then computed time-series of frequency-band- and lamina-specific current source density (CSD), and PACs of CSD for all possible pairs of the classical frequency bands in the range of 1-150 Hz. We observed both intra- and inter-laminar spontaneous PAC. Of 18 possible combinations, 12 showed PAC, with the highest measures of interaction obtained for the pairs of the theta/gamma and delta/gamma bands. Intra- and inter-laminar PACs involving layers 2/3-5a were higher than those involving layer 6. Current sinks (sources) in the delta band were associated with increased (decreased) amplitudes of high-frequency signals in the beta to fast gamma bands throughout layers 2/3-6. Spontaneous sinks (sources) of the theta and alpha bands in layers 2/3-4 were on average linked to dipoles completed by sources (sinks) in layer 6, associated with high (low) amplitudes of the beta to fast-gamma bands in the entire cortical column. Our findings show that during spontaneous activity, delta, theta, and alpha oscillations are associated with periodic excitability, which for the theta and alpha bands is lamina-dependent. They further emphasize the differences between the function of layer 6 and that of the superficial layers, and the role of layer 6 in controlling activity in those layers. Our study links theories on the involvement of PAC in resting-state functional connectivity with previous work that revealed lamina-specific anatomical thalamo-cortico-cortical connections.

Keywords: cortical layers; cross-frequency coupling; current-source density (CSD); local-field potentials (LFP); phase-amplitude coupling; primary somatosensory cortex; resting state functional connectivity; spontaneous activity.

Figure 1

Experimental paradigm and alignment of probes. (A) LFP obtained from one channel positioned approximately 800 μm below the surface of the gray matter during a single stimulation trial. The red curve presents triggers used for forepaw stimulation. The evoked response appears shortly after each forepaw stimulus pulse. (B) Precise localization of laminar probes relative to the cortical surface: high-resolution image showing the part of a laminar probe close to the surface of cortex. Gray regions and dark curves around the probe are gray matter and pial blood vessels, respectively. Four contacts can be observed above the cortical surface, as indicated by the orange arrow. In this experiment and all other experiments conducted to create the prototypical CSD response presented in (D), we used linear probes with 32 contacts densely spaced at 50 μm intervals covering layers 1–5. (C) The mean CSD response obtained from one run immediately after the image presented in (B) was acquired. The dark horizontal lines mark the approximate depth of the borders between the cortical layers, labeled on the right. Note that in this experiment we used a linear probe with 32 contacts densely spaced at 50-μm intervals covering layers 1–5. CSD values are in micro-Amperes per cubic millimeter. (D) The spatiotemporal pattern of mean CSD responses, used as a template for localizing CSD responses relative to the cortical surface. CSD responses from 12 runs in 4 animals were aligned relative to the cortical surface as determined by their corresponding images of contacts above the surface. The image represents the average CSD response computed following this alignment procedure. The prototype pattern used to align the results from the other experiments was extracted from within the dark rectangle. (E) A 50-μm-thick section of the brain cut from the recording site shown in (B) and stained with Cresyl violet. The image to the left shows a lesion induced through the bottom-most contact (red arrow), traces left by the probe (blue arrow), and delineation to the cortical layers. The image to the right presents the position of all 32 contacts spaced at 50-μm intervals, including the 4 observed above the cortical surface (orange arrow). (F) CSD responses averaged over forepaw stimulations in a single run. The horizontal and vertical axes represent the time from stimulation in milliseconds and the cortical depth in millimeters. The highest dark horizontal line marks the cortical surface based on the spatiotemporal covariance computed on the right. CSD values are in micro-Amperes per cubic millimeter. The image to the right presents spatiotemporal covariance as a function of time and space. The maximal covariance is marked with a white cross. The position of the cortical surface relative to the maximal covariance is marked with a horizontal dark line.

Figure 2

Spontaneous current source density (CSD) from one hemisphere. The 3 upper panels present the time courses obtained with the iCSD method for 3 diameters of sources and sinks: 0.5, 1, and 2 mm. The bottom panel presents the spontaneous CSD obtained using the standard method, which assumes infinite diameters of sources and sinks.

Figure 3

Band-limited spontaneous current-source density. The 7 panels show spontaneous current source density in the delta (top), theta, alpha, beta, low-gamma, middle-gamma, and high-gamma (bottom) bands. The color look-up table was scaled linearly according to the maximal absolute value, separately for each band.

Figure 4

Results of testing the null hypothesis that the average phase-amplitude coupling (PAC) is not different from 0. The figure shows the average Z score, $\overline{Z}$, computed over 12 hemispheres (one Z-score per hemisphere) using iCSD and assumed 0.5-mm diameters of current sources and sinks. Seven frequency bands, delta (1–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz), low gamma (30–50 Hz), middle gamma (50–100 Hz), and fast gamma (100–150 Hz), were considered. The PACs from the 18 different pairs of frequency bands we considered are presented in 18 different matrices. Each of the entries presents $\overline{Z}$, conditioned that it passed the statistical test, proving to be different from 0 (2-tailed t-test, while considering multiple comparisons with false discovery rate q < 0.01). White entries represent pairs of contacts that did not show statistically significant PAC.

Figure 5

Alignment of amplitudes with the CSD of delta oscillations. In (A) the amplitudes of the higher rhythms (from beta to fast-gamma) in each contact were aligned with the CSD of the delta rhythm from the same contact. The reference signal, electrode contact-specific CSD in the delta band, is shown in the bottom panel. The CSD was calculated using the iCSD method with 0.5 mm diameter. In (B) the amplitudes presented in (A) were normalized contact-wise by subtracting the mean amplitude and dividing the result by the standard deviation of the amplitudes. White entries represent represent values that were not different than zero (n = 12 data-sets; two-tailed t-test corrected for FDR, q < 0.01).

Figure 6

Alignment of amplitudes with the CSD of the theta oscillations. In (A,B) amplitudes and normalized amplitudes, respectively, of higher rhythms (from beta to fast-gamma) in each contact were aligned with the CSD of the theta rhythm from the same contact. The CSD was calculated using the iCSD method with 0.5 mm diameter. The normalization and format of presentation are identical to those used for Figure 5.

Figure 7

Alignment of amplitudes with the CSD of the alpha oscillations. In (A,B) the amplitudes and normalized amplitudes, respectively, of higher rhythms (from beta to fast-gamma) in each contact were aligned with the CSD of the alpha rhythm from the same contact. The CSD was calculated using the iCSD method with 0.5 mm diameter. The normalization and format of presentation are identical to those used for Figures 5, 6.

Figure 8

Alignment of amplitudes with the CSD of the delta oscillations obtained from 3 specific contacts. In the left-most columns, the amplitudes of higher rhythms (from beta to fast-gamma, top 4 panels) in each contact were aligned with the CSD of the delta rhythm from layer 2/3 (contact 6). The reference signal, the CSD in the delta band from contact 6, is shown at the bottom. The 2nd panel from the bottom presents the average of the CSD in the delta band aligned with the CSD of the same rhythm from contact 6. White entries in the panels that present amplitudes represent values that were not different than zero (n = 12 data-sets; two-tailed t-test corrected for FDR, q < 0.01). In the middle columns, the amplitudes of higher rhythms were aligned with the CSD of the delta rhythm from layer 5a (contact 10). In the right-most columns, the amplitudes of higher rhythms were aligned with the CSD of the delta rhythm from layer 6 (contact 19).

Figure 9

Alignment of amplitudes with the CSD of theta oscillations obtained from 3 specific contacts. The format of presentation is identical to that used for Figure 8.

Figure 10

Alignment of amplitudes with the CSD of alpha oscillations obtained from 3 specific contacts. The format of presentation is identical to that used for Figures 8, 9.