Cross-regional phase amplitude coupling supports the encoding of episodic memories

Abstract

Phase amplitude coupling (PAC) between theta and gamma oscillations represents a key neurophysiological mechanism that promotes the temporal organization of oscillatory activity. For this reason, PAC has been implicated in item/context integration for episodic processes, including coordinating activity across multiple cortical regions. While data in humans has focused principally on PAC within a single brain region, data in rodents has revealed evidence that the phase of the hippocampal theta oscillation modulates gamma oscillations in the cortex (and vice versa). This pattern, termed cross-regional PAC (xPAC), has not previously been observed in human subjects engaged in mnemonic processing. We use a unique dataset with intracranial electrodes inserted simultaneously into the hippocampus and seven cortical regions across 40 human subjects to (1) test for the presence of significant cross-regional PAC (xPAC), (2) to establish that the magnitude of xPAC predicts memory encoding success, (3) to describe specific frequencies within the broad 2–9 Hz theta range that govern hippocampal-cortical interactions in xPAC, and (4) compare anterior versus posterior hippocampal xPAC patterns. We find that strong functional xPAC occurs principally between the hippocampus and other mesial temporal structures, namely entorhinal and parahippocampal cortices, and that xPAC is overall stronger for posterior hippocampal connections. We also show that our results are not confounded by alternative factors such as inter-regional phase synchrony, local PAC occurring within cortical regions, or artifactual theta oscillatory waveforms.

1 |. INTRODUCTION

The organization of high-frequency oscillatory activity according to the phase of a low-frequency oscillation is known as phase amplitude coupling (PAC). This pattern of brain oscillations has been established in both rodents and humans and is thought to be critical for properties of episodic memory such as temporal ordering (Squire, 1992), ensemble organization in working memory, and the phenomenon of phase coding (Buschman, Denovellis, Diogo, Bullock, & Miller, 2012; Jensen & Lisman, 2000). In humans, PAC within brain regions has been demonstrated in the hippocampus and neocortex, and the magnitude of coupling appears to predict memory encoding success (Canolty et al., 2006; Lega, Burke, Jacobs, & Kahana, 2014). In rodents, PAC has been extended to include interregional relationships between the hippocampus and extra-hippocampal regions (specifically, coupling between the hippocampus and striatum/PFC) by which the phase of the hippocampal theta oscillation modulates gamma oscillatory activity in the striatum and vice versa (Onslow, Bogacz, & Jones, 2011; Tort, Komorowski, Manns, Kopell, & Eichenbaum, 2009). Reported findings suggest that inter-regional phase amplitude coupling (xPAC) may be a mechanism by which an integrated representation of a memory is formed through precise coordination of local high-frequency oscillations.

Precise theta–gamma relationships have also been reported for entorhinal-hippocampal communication. In rats, the precisely timed arrival of entorhinal information (measured by gamma band activity) relative to the hippocampal theta oscillation in CA1 is associated with behavioral changes (Buzsáki, 2002; Hasselmo, 2005). Another study showed that the precise timing of ERC input into CA3 helps distinguish encoding versus retrieval-related activity and suggests that this temporal relationship is necessary for reversal of learning (Hasselmo, Bodelón, & Wyble, 2002). These findings highlight a point of clarification: xPAC-type relationships do not, in and of themselves, imply causality or directional information flow. Rather, xPAC implies a relative coordination relationship between brain regions.

To determine whether xPAC supports human episodic memory, we quantified inter-regional phase amplitude coupling using theta oscillations recorded in the hippocampus and gamma oscillations recorded in the cortex during episodic memory encoding. We utilized a unique dataset of 40 human subjects with intracranial electrodes implanted in both the anterior hippocampus (AH) and posterior hippocampus (PH) and in seven cortical regions in both hemispheres: entorhinal cortex (ERC), parahippocampal cortex (PHC), lateral prefrontal cortex (LPF), lateral middle temporal gyrus (LMT), posterior cingulate cortex (PC), basal temporal cortex (fusiform and inferior temporal gyrus, BTL), and lateral parietal cortex (LP). Anatomical details governing how electrodes were aggregated into regions is available in the Methods section. The demarcation between the ERC and PHC followed established methods, incorporating the coronal plane of the gyrus intralimbicus along the parahippocampal gyrus.

Using the modulation index method described by Canolty (Canolty et al., 2006), we identified hippocampal-cortical connections for which (1) significant xPAC is present (i.e., there is significantly nonuniform distribution of gamma power across hippocampal theta phase) and (2) xPAC predicts memory encoding success (functional xPAC). This method is relatively robust to signal noise over the time segments available in the free recall task (Onslow et al., 2011). Across cortical regions, we examined the preferred theta frequencies for hippocampal coupling and compared anterior versus posterior hippocampal coupling strength. The parahippocampal cortex and entorhinal cortex in particular showed significant functional xPAC; therefore, we sought to characterize hippocampal-ERC/PHC xPAC in more detail. We examined the preferred theta phase angle at which xPAC occurs and compared this to local PAC measured in these regions, revealing regional and hemispheric differences. To further add confidence to our results employing this new measure of functional connectivity, we wanted to ensure that estimation of xPAC was not confounded by other oscillatory patterns that characterize successful memory encoding, especially changes in cortical gamma power, interregional phase synchrony, and locally measured PAC. We therefore integrated these measurements into a multivariate model to understand the relative impact of these oscillatory patterns on xPAC magnitude and functional effects. We place our findings in the context of existing theories of PAC regarding the organization of oscillatory activity during the representation of episodic memories.

2 |. METHODS

2.1 |. Data acquisition and preprocessing

The intracranial electroencephalogram (iEEG) data were collected at UT Southwestern medical center while subjects performed the free recall task after seizure mapping surgery (stereo EEG electrode implantation). The free recall task we used consisted of 25 lists, each comprised of 12 common nouns. Each word was presented on the monitor for 1,800 ms followed by 400 ms of blank screen. A 30 s interval in between every two lists was given for the subject to recall as many of the words as possible in any order. In the study, seven regions of interest (ROIs) comprising of ERC, PHC, LPF, LMT, PC, BTL, and LP were selected to construct xPAC connectivity for both AH and PH in both left and right hemispheres. Electrode localization was achieved by co-registration of the postoperative computer tomography scans with preoperative magnetic resonance images, which were evaluated by a member of the neuroradiology team to determine the final electrode locations. Demarcation between the ERC and PHC in the parahippocampal gyrus was the gyrus intralimbicus, following established methods. This demarcation is shown in Figure 3a, showing coronal plane T2 slices immediately to the front and back of the gyrus intralimbicus for ERC and PHC, respectively. (Insausti et al., 2019; Maass, Berron, Libby, Ranganath, & Düzel, 2015).¹ We utilized an iEEG database including 40 subjects, which contributed to 3,767 hippocampus-to-ROI electrode pairs. All electrode pairs reflect signal recorded from the same subject. The iEEG recordings were down-sampled to 250 Hz, notch filtered at 60 Hz, time-aligned into individual trials (stimulus onset at 0 ms, 1,800 ms per trial), and labeled as successful encoding (SuE, recalled items) or unsuccessful encoding (UnsuE, unrecalled items) based upon behavioral performance.

FIGURE 3.

(a) Example trace of coronal plane T2 MR slices immediately to the front and back of the gyrus intralimbicus for ERC (upper, in red) and PHC (lower, in blue), respectively. (b) Functional effects of xPAC in the theta-gamma spectrum, shown as the t-statistic at each frequency–frequency pixel from a mixed effects model. Red indicates greater magnitude during SuE, and blue indicates greater magnitude during UnsuE. Areas outlined in white indicate the significant xPAC patterns after FDR correction across theta/gamma spectrum (q = 0.05). (c) Functional effects of xPAC at each theta frequency determined by mixed effects modeling. Results reflect aggregate values across regions of interest. Functional effects are represented by t-statistics extracted from the MEM, where positive values indicate greater xPAC magnitudes during SuE than UnsuE, and vice versa. (d) Distribution of preferred phases of xPAC during successful encoding. Preferred phases were averaged (angular mean) across trials for each significant electrode pair. Color-mapping denotes the hippocampal theta frequencies, and ** indicates p <.01 via Watson–Williams test

2.2 |. Phase-amplitude coupling

The modulation index (MI, Canolty et al., 2006) is a cross-frequency coupling measure of nested oscillations applied principally to theta and gamma bands. xPAC expands the application of this measure by utilizing hippocampal theta phase with cortical gamma amplitude. The instantaneous theta phase of hippocampus and gamma amplitude (envelope) of the ROI can be obtained by ${\alpha }_{{\text{ROI}}_{\gamma }}\left[n\right]=\left|\mathcal{H}\left(x_{{\text{ROI}}_{\gamma }}\left[n\right]\right)\right|$, and ${\phi }_{\text{H}\theta }\left[n\right]=\text{arg}\left(\mathcal{H}\left(x_{\text{H}\theta }\left[n\right]\right)\right)$, where $\mathcal{H}$ denotes the Hilbert transform, and $x_{{\text{ROI}}_{\gamma }}\left[n\right]$ and x_Hθ[n] denote the bandpass filtered signals of hippocampus in theta band and ROI in gamma band, respectively. Notably, to include the side peaks produced by theta, the bandwidth of bandpass filters (for gamma) should be twice the theta frequency (Aru et al., 2015). The analytical signal of the two is obtained by:

$$z\left[n\right]={\alpha }_{{\text{ROI}}_{\gamma }}\left[n\right]\text{exp}\left(i{\phi }_{\text{H}\theta }\left[n\right]\right)$$ (1)

The magnitude of the mean vector, M_raw, denotes the coupling strength, whereas the phase angle of the mean, φ_pf, represents the preferred phase for coupling. They are obtained by:

$$M_{\text{raw}}=\left|\frac{1}{n}\sum _{n=1}^{N}z\left[n\right]\right|$$ (2)

and

$${\phi }_{\text{pf}}=\text{arg}\left(\frac{1}{n}\sum _{n=1}^{N}z\left[n\right]\right)$$ (3)

Shuffled data is then created by inserting a randomly generated time lag between the time series of theta phase and gamma amplitude when forming the analytical signal. With iterations of this randomization procedure, a normalized magnitude is calculated:

$$M_{\text{norm}}=\frac{M_{\text{raw}}-\mu }{\sigma }$$ (4)

where μ and σ are, respectively, the mean and the standard deviations of surrogate magnitudes. In this study, 250 surrogates are implemented for each trial (as presented in Figure 1b). The surrogate procedure normalizes the MI among different subjects and regions which most likely have various power levels. An MI has a magnitude of M_norm at the angle of preferred phase, denoting the asymmetry of the analytical signal in the complex plane. If an analytical signal is circularly symmetric, it indicates that no coupling is found, while significant coupling occurs at the phase at which the magnitude is larger. We also measured local cortical PAC (both phase and amplitude information from the same brain region) as part of our control model described in Figure 4. The computation of PAC remained the same but both theta phase and gamma amplitude were from the same target region. We used the shuffled data to impose the requirement that all functionally significant xPAC connections exceeded a threshold MI value of 1.96, indicating that the MI value exceeded that expected by chance. We did this to ensure that all connections shown as functionally relevant also exhibited a minimum xPAC magnitude.

FIGURE 1.

Example trace of an xPAC computing procedure. (a) Instantaneous phase and amplitude from hippocampal and parahippocampal cortex (PHC) recordings. The unfiltered trace from the PHC is shown in row A1. iEEG data obtained during memory encoding were bandpass filtered in the slow gamma range (30–70 Hz, PHC, row A2) and slow theta (2–5 Hz, hippocampus, row A3) ranges. The amplitude of PHC gamma oscillations (row A2) and the phase of hippocampal slow theta (row A3) were obtained via Hilbert transform. The real and imaginary components of the signal were used in the MI calculation (row A4). (b) Analytical signals: complex-valued analytic signal in complex plane where red dot is the mean. Raw coupling magnitude M_raw is 9.8638 and preferred phase φ_pf is 268°. Then, 250 surrogate (shuffled) samples of the analytical signal were computed to normalize the coupling magnitude by z-scoring the M_raw with the mean and s.d. of surrogate magnitudes. The green dot denotes the MI, whose magnitude M_norm is 0.8217

FIGURE 4.

(a) Schematic illustrations for the control analysis of xPAC, phase synchrony (PLV), cortical local PAC, and oscillatory power (gamma for cortices and theta for hippocampus). Functional effect (SuE vs. UnsuE) of each connectivity/functional measure was computed by an independent mixed effects model. (b) Predicting models of xPAC magnitude during successful encoding. R² for each predictor indicates the independent model of the predictor using its magnitude during SuE, whereas R² for PAC: PLV denotes the combined effects (magnitude) of phase synchrony (PLV) and cortical local PAC in predicting xPAC. The variance of xPAC magnitude explained by these predictors (including the PLV:PAC interaction model) were all less than 5% (red line). (c) Predicting models of xPAC functional effects. R² for each predictor indicates the independent model of the predictor using its functional effects, whereas R² for baseline denotes the combined effects (functional effects) of PLV, PAC, cortical gamma power (gPower), and hippocampal theta power (tPower) in predicting xPAC. The variance of xPAC functional effects explained by these predictors (including two interaction models) were all less than 1% (red line)

2.3 |. Phase synchrony and power differences

We sought to develop a model that tested for functionally significant xPAC while accounting for possible functional effects of phase synchrony and differences in gamma oscillatory power (the analysis described in Figure 4). For each hippocampal-cortical connection, we computed phase locking value (PLV, Lachaux, Rodriguez, Martinerie, & Varela, 1999; Siapas, Lubenov, & Wilson, 2005). Instantaneous phases for hippocampus and target cortex are obtained by the Hilbert transform of the bandpass filtered local signals. The PLV is given by:

$$PLV=\left|\frac{1}{n}\sum _{n=1}^N\text{exp}\left(i\left({\phi }_{\text{H}\theta }\left[n\right]-{\phi }_{\text{ROI}\theta }\left[n\right]\right)\right)\right|$$ (5)

We measured functional effects related to differences in oscillatory power by incorporating the normalized power for the frequency range of interest relative to the entire spectral power via the power spectral density estimation (PSD), such that:

$${\mathit{\text{Power}}}_{\gamma }=\frac{{\sum }_{\gamma }{\widehat{P}}_{xx}\left(\gamma \right)}{{\sum }_f{\widehat{P}}_{xx}\left(f\right)}$$ (6)

where ${\widehat{P}}_{xx}$ is the PSD estimation via periodogram over the entire spectrum, γ denotes the gamma band in interests, and f is the entire bandwidth such that 0 ≤ f ≤ f_s/2, where f_s denotes the sampling frequency of iEEG signals. These estimations were performed separately for successful and unsuccessful encoding events and incorporated into our mixed effects models (MEMs) described below.

2.4 |. Mixed effects models

We used MEM to assess for functional significance of observed SuE/UnsuE differences in observed xPAC (as extracted by MI). Measured MI values were separately entered for the SuE and UnsuE conditions for each observed electrode pair (which for xPAC included theta phase information measured in the hippocampus and gamma amplitude information measured in the cortical region of interest). Subject was included as a random effect in the model. Such a model can be written as:

$$y=X\beta +Zu+\epsilon$$ (7)

where y is the responding variable (e.g., encoding successes for functional effects and xPAC for predicting), β is a coefficient vector of fixed effects, u is a vector of random effects, ε is a vector of random errors, X is the regressor matrix (a.k.a. design matrix) associated with the independent variables, and Z is the regressor matrix associated with subject labels. We followed best linear unbiased estimates (BLUE) and predictors (BLUP) to solve the mixed effects equations (MME, as in Henderson, 1973; Pinheiro & Bates, 1996).

In our focused analysis of xPAC at each frequency-frequency pixel as in Figure 3b, hippocampal-ERC/PHC xPAC was computed using continuous frequency values, by which theta oscillations were split into bins with 1 Hz resolution and gamma activity was divided into bins with 2 Hz resolutions. Functional effects were modeled (using the same MEM approach) at each frequency-frequency pixel, and the t-stats of the fixed effects were represented as functional patterns of the xPAC.

For the analysis presented in Figure 4 (testing for the impact of inter-regional synchrony, locally measured PAC, and gamma power differences on xPAC), we used two methods, one of which used the functional xPAC effects (Sue/UnsuE differences) and the other that used the measured values (local and inter-regional xPAC, power values, and PLV values) themselves. First, we modeled xPAC using magnitudes observed for these values across recording locations using the same mixed effects approach. The explained variance using these magnitudes is plotted in Figure 4b. Then, we also modeled the functional effects of xPAC differences using the functional effects for these other predictors (i.e., local PAC, inter-regional PLV, and cortical gamma and hippocampal theta oscillatory power) using the mixed effects approach. We show the explained variance for each predictor in Figure 4c. The purpose of this analysis was to test whether and how these other factors explained the magnitude and functional effects of xPAC using explained variance.

We used an n-way ANOVA to test for differences in the magnitude of xPAC (across all cortical locations) when the theta signal was recorded from the AH versus PH. The purpose of this analysis was to test whether anterior or posterior xPAC exhibits a larger functional effect across all connections. This was done separately for the left and right hemisphere. The predicting models were built region by region via xPAC information in all four theta/gamma combinations (as presented in Figure 2). We used the t-statistics describing the functional xPAC effect (SuE vs. UnsuE) from the MEM and aggregated these across electrode pairs. We tested for a primary effect of frequency band and hippocampal location.

FIGURE 2.

(a) iEEG electrode maps: numbers of electrodes in each region from 40 subjects, with a minimum of 60 electrodes and a maximum of 201 electrodes contributing to 3,767 hippocampal-cortical electrode pairs overall. (b) Significant functional (SuE vs. UnsuE) xPAC connections, identified by mixed effects models. For all significant connections, xPAC also had significantly greater magnitude than expected by chance (MI Z >1.96). Left and right hemispheric connections are shown on each side of circle connectivity plots. AH, anterior hippocampus; ERC, entorhinal cortex; LMT, lateral middle temporal gyrus; LP, lateral parietal cortex; LPF, lateral prefrontal cortex; PC, posterior cingulate cortex; PH, posterior hippocampus; PHC, parahippocampal cortex; BTL, basal temporal cortex (fusiform and inferior temporal gyrus). (c) MI functional effects for the ERC/PHC versus other regions. The observed MI functional effect (red line) was obtained by comparing the distributions of MI differences (MI during SuE–MI during UnsuE) for ERC/PHC and other five regions, and the null distribution H₀ was obtained by 1,000 random shuffles. (d) Mean t-stats describing the functional xPAC effects for slow and fast theta bands in anterior versus posterior hippocampus in two hemispheres via ANOVA. * and ** denote p <.05 and p <.01, respectively

In a separate convergent analysis approach meant to demonstrate the robustness of our principal findings, functional effects were also examined by comparing the distribution of t-statistics between SuE and UnsuE incorporating 1,000 permutations, followed by false discovery rate (FDR) correction (q = 0.05) across connections. The individual t-stats from the hypothesis testing are included in Supporting Information. This method did not utilize the MEM to assess significance—but rather a t-test applied to the distribution of MI values for the SuE and UnsuE conditions across electrodes comprising the data for each region of interest.

3 |. RESULTS

Our analysis aimed to understand how the organization of gamma band activity in the cortex relative to hippocampal theta oscillations (as quantified by PAC) can predict memory encoding success, hypothesizing that this hippocampal-cortical relationship represents another form of interregional coordination along with phase–phase and amplitude–amplitude coupling that has been described in human systems (Aru et al., 2015; Lachaux et al., 1999). We calculated interregional phase-amplitude coupling (xPAC) using intracranial data across 40 patients who performed the free recall episodic memory task. Subjects recalled 23.62 ± 12.12% of items with a rate of list intrusions of 4.82%. The phase of theta frequency oscillation was recorded in the hippocampus while the amplitude of gamma oscillation was obtained from one of seven cortical regions (ERC, PHC, LPF, LMT, PC, BTL, and LP) in each hemisphere. We quantified the magnitude of xPAC present in these signals with the modulation index developed by Canolty (Canolty et al., 2006). Example data showing the implementation of this method are shown in Figure 1. We also performed a confirmatory analysis using the KL-distance method, included in the Supporting Information section (Tort, Komorowski, Eichenbaum, & Kopell, 2010).

3.1 |. Significant xPAC occurs between the hippocampus and multiple cortical regions, especially the parahippocampal cortex and entorhinal cortex

For the initial quantification of xPAC, we utilized two different theta and gamma frequency bands based upon previous observations (Lega et al., 2014; Lega, Jacobs, & Kahana, 2012). We separately extracted phase information for the slow-theta (2–5 Hz) and fast-theta (5–9 Hz) frequency bands in the hippocampus and amplitude information for the high gamma (70–100 Hz) and low gamma (30–70 Hz) bands in the cortex then calculated xPAC separately for successfully and unsuccessfully encoded memory items for each hippocampal-cortical electrode pair. We used a MEM (subject as random effect) to contrast xPAC measured during SuE and UnsuE. Results in Figure 2b show significant connections (FDR corrected p <.05 in MEM). We additionally required that all connections shown in Figure 2b remain significant when including only individual connections for which the larger magnitude condition (e.g., SuE for red connections in 2B) exhibited MI values significantly greater than chance (z value of 1.96). This criterion was used to ensure functional effects were not driven by nonsignificant xPAC. Plots of MI values by region are available in Supporting Information. The functional effects for hippocampal-ERC/PHC identified by our MEM, are shown in the bar plots in Figure 2b, split for AH and PH. Additionally, we used another, convergent method to characterize xPAC patterns across the cortex. Functional xPAC between hippocampus and ERC/PHC were also shown to be significant using this alternative approach in which we compared distributions of MI values for SuE versus UnsuE at the subject level using a t-test with associated shuffle procedure (FDR corrected p <.05). These results are found in Supporting Information.

We further tested the functional xPAC effects for the ERC/PHC as compared to other brain regions. We computed the MI difference (MI during SuE–MI during UnsuE) for ERC and PHC versus the five other regions across all theta-gamma connections using a permutation procedure. Results showed hippocampal-ERC/PHC connections had significantly greater functional MI difference as compared to all other regions (p = .002, MI differences with shuffle procedure). This result is visible in Figure 2c. Moreover, we calculated the proportion of hippocampal-ERC/PHC electrode pairs that exhibited significant effects when contrasting SuE/UnsuE distributions within each electrode pair (FDR correct p <.05, comparing distribution of trial-level xPAC values between encoding conditions). On average, 62.17 ± 17.04% of the subjects had at least one electrode pair that exhibited significant hippocampus-ERC/PHC xPAC effects. Results for all connections and frequency bands are included in the Supporting Information section.

3.2 |. Detailed examination of xPAC in the ERC and PHC

Given the robust functional xPAC we observed between the hippocampus and ERC/PHC, we performed a more detailed analysis of the frequency/frequency interactions during successful and unsuccessful encoding as well as of the distribution of the preferred theta phase at which coupling occurs for these connections. We computed the xPAC magnitude (modulation index value) during the SuE and UnsuE conditions at each frequency–frequency pixel and compared these between memory conditions. The resulting pattern of functional effects was identified using a MEM. This is shown in in Figure 3b. We then summarized the functional effects across the 2–9 Hz frequency spectrum, which suggest that (in aggregate) lower theta frequencies centered at 3–6 Hz exhibited decreased connectivity, as quantified by lower xPAC magnitude, for the SuE condition, while higher theta frequencies exhibited greater xPAC connectivity for SuE (in Figure 3c). We show these more detailed data to provide a comprehensive picture of xPAC for the ERC/PHC, though these specific frequency-frequency interactions remain exploratory as compared to our principal, hypothesis-driven results which were obtained using band-limited data, as presented in Figure 2.

We further described ERC/PHC xPAC by identifying the preferred phase angle for cross-frequency coupling (Figure 3d). We observed significant nonuniformity of the preferred phase angles for hippocampal xPAC (FDR corrected p <.05, Rayleigh test applied to the distribution of phase angles across all theta frequencies). In all cases, the phase distributions were nonuniform. Figure 3d shows the phase distribution for significant ERC/PHC xPAC electrode pairs during SuE with both the AH and PH. We then compared the distributions of preferred phase for AH versus PH using the Watson-Williams test. Results showed phase distributions were significantly different between AH/PH for all ERC and PHC connections in both hemispheres. (p <.01, FDR corrected). In the right hemisphere, the mean preferred phase angles for AH versus PH were 0.5485π versus 0.1995π for ERC connections, and −0.1655π versus 0.8296π for PHC connections. In the left hemisphere, AH coupling with the ERC clustered at phases around 2/3π and 5/3π while PH-ERC coupling clustered at phases around 3/2π, and the mean preferred phase angles for PHC connections in the left hemisphere were clustered similarly in AH and PH (−0.6511π for AH vs. −0.4900π for PH).

3.3 |. AH versus PH exhibit different xPAC properties during item encoding

Based upon models suggesting different roles for AH versus PH in episodic memory, we compared functional xPAC values along the longitudinal locations of hippocampus via an n-way ANOVA, separately for each hemisphere and for the slow and fast theta frequency band, testing for an interaction between hippocampal location and memory condition (Lin, Umbach, Rugg, & Lega, 2019; Poppenk, Evensmoen, Moscovitch, & Nadel, 2013). We found that posterior hippocampal xPAC values were stronger for successful encoding, which was significant in the left but not right hemisphere, (F_(1,562) = 7.65 p = .0059 and F_(1,351) = 1.27, p = .26, respectively). Mean t-statistics (across regions) from the MEM are shown for anterior/posterior locations in Figure 2d. We discuss implications of this finding below as they pertain to models of hippocampal longitudinal specialization.

3.4 |. xPAC is not confounded by either PLV, power differences, local PAC, or theta waveforms

We tested the impact of other oscillatory properties known to affect memory encoding that could explain our observations of xPAC, both in terms of raw magnitude and observed functional effects (SuE vs. UnsuE differences). Schematic illustrations showing the procedures for these connectivity/functional measures are shown in Figure 4a, and the details are found in Section 2. With this goal in mind, we constructed a multivariate model to test how much the factors of phase synchrony between the hippocampus and ERC/PHC and local PAC within the ERC/PHC predicted xPAC magnitude. Results are shown in Figure 4b, where a model was built for each cortical region (ERC/PHC in both hemispheres) with aggregation across AH and PH. Figure 4b reports the R² for each predictor in each region by constructing independent models along with an interaction model (shown as PAC: PLV). Results (a minimum R² of .0009 for PLV in ERC-L, and a maximum R² of .0286 for PAC: PLV in PHC-R) showed that (1) local PAC and synchrony each account for a small fraction of the variance of xPAC across all significant connections and (2) these factors were mostly independent, as the interaction model reflects the sum of the variance explained by each factor separately. This finding suggests that, in terms of xPAC magnitude, our observations of xPAC are not readily explained by the factors of phase synchrony and local PAC.

Additionally, we tested how well the functional effects (SuE vs. UnsuE differences) of PLV, local PAC, cortical gamma power differences (in the ERC/PHC), and hippocampal theta power differences (in the AH/PH) predicted our functional xPAC observations for the ERC and PHC (xPAC SuE vs. UnsuE differences). Models were built for individual cortical regions with data (xPAC, PLV, and theta power differences) aggregation across hippocampi. Results are shown in Figure 4c, where baseline R² indicates the coefficient of determination of the full model (including all predictors), and R² for each predictor was computed by an independent predicting model (also including a local PAC/PLV interaction model). As with prediction of xPAC magnitude described above, the variance explained by these factors was quite modest (a minimum R² of .0001 for PAC in ERC-L, and a maximum R² of .0071 for the full model in ERC-L), for both full and individual models.

We also tested for the impact of spurious xPAC attributable to the nature of the underlying theta waveform (in the hippocampus) used for computing xPAC. Lozano-Soldevilla et al. recently raised concerns about the effect of nonsinusoidal (clipping distorted theta) waveforms on measured PAC (Lozano-Soldevilla, ter Huurne, & Oostenveld, 2016). We note that for xPAC, this effect is diminished (assuming a lack of hippocampal-ERC/PHC theta phase synchrony for xPAC recording locations, as demonstrated above) because gamma oscillatory measurements are performed at a separate brain location than theta measurements, meaning that spuriously detected theta/gamma relationships, due to theta harmonics, are less likely to occur. Stated another way, local PAC is more susceptible to this issue than xPAC, since the signal from which phase is calculated (theta oscillations) and the signal from which amplitude is calculated (gamma oscillations) are not recorded from the same place. Nonetheless, we implemented a recently published method for morphological characterization of input oscillatory data by computing the sample entropy as described in Vaz, Yaffe, Wittig Jr, Inati, and Zaghloul (2017) and Richman and Moorman (2000), to test how often our data include “sharp oscillations” that can lead to spurious PAC measurement (characterized by low sample entropy). We found that 86.83% of our trials had a sample entropy greater than 0.4, and 3.41% of trials had a sample entropy less than 0.25 (in practical terms, a sample entropy exceeding 0.4 is likely to indicate nested oscillations while less than 0.25 indicates sharp oscillations in Vaz et al. (2017). The sample entropy for our trials were 0.7782 ± 0.3100. We then recalculated our xPAC results excluding 20% of electrode pairs (17.5 ± 5.9 out of 86.8750 ± 29.06) that had lowest sample entropy. Using a linear regression model for comparing the recomputed xPAC with our original xPAC, we found that the functional effects of xPAC in the theta-gamma spectrum were minimally impacted. Resulting R² was .8388 ± .0577 (a minimum of 0.7248 for AH-PHC in the right, and a maximum of 0.8961 for PH PH-ERC in the left) for the relationship between our original results and the xPAC excluding lower sample entropy pairs. Thus, we believe our quantification of xPAC was primarily based on hippocampal-cortical nested oscillatory relationships rather than sharp oscillations or any higher order harmonics of theta frequencies in the gamma band.

4 |. DISCUSSION

We describe the phenomenon of cross regional phase amplitude coupling (xPAC) between the hippocampus and seven neocortical regions as human subjects encode episodic memories. Our key findings are that: (1) significant xPAC occurs between the hippocampus and cortex, especially for other mesial temporal regions (ERC and PHC), (2) xPAC supports successful memory encoding, including when using methods that account for potential confounding effects such as phase synchronization, gamma power changes, and within-region PAC, (3) in the left hemisphere, posterior hippocampal xPAC with the ERC and PHC was stronger than for the AH, and (4) the preferred phase of coupling for xPAC differs between the AH and PH for several connections.

The appeal of the xPAC phenomenon is that it provides a mechanism for the organization of activity across brain regions. PAC within the hippocampus and neocortex has been reported in numerous rodent and human studies, with an important distinction between slow and fast gamma activity observed during memory behavior (Colgin, 2015). PAC in general is thought to be important partially because the timing of spiking activity relative to the theta cycle influences long term potentiation (Dan & Poo, 2006; Feldman, 2012) and so xPAC between regions may promote the appropriate integration of item information into context or facilitate the “indexing” function central to the hypothesized role of the hippocampus in memory formation (Backus, Schoffelen, Szebényi, Hanslmayr, & Doeller, 2016; Preston & Eichenbaum, 2013; Schlichting & Preston, 2015). This conception of xPAC matches rodent data demonstrating that hippocampal theta phase may organize memory-related prefrontal spiking activity (Hyman, Zilli, Paley, & Hasselmo, 2005; Jones & Wilson, 2005). For this reason, the identification of xPAC represents an important contribution to the study of human memory. We believe it is noteworthy that we observed strong xPAC for ERC/PHC with the hippocampus because of the direct anatomical pathways that facilitate communication between these regions (Canto, Wouterlood, & Witter, 2008; Witter, Wouterlood, Naber, & Van Haeften, 2000). Hippocampal-cortical xPAC beyond these regions may be less apparent in our results secondary to the inclusion of these regions for which coupling was quite strong, but the robust ERC/PHC xPAC fits with a priori expectations based on predicted interactions between these regions. Indeed, the characterization of ERC/PHC to cortical xPAC in subsequent investigations will further elucidate how this mechanism supports episodic memory (Basu & Siegelbaum, 2015; Eichenbaum, Schoenbaum, Young, & Bunsey, 1996; Preston & Eichenbaum, 2013). We note that the existence of xPAC does not necessarily imply directional causal control. The version of inter-regional xPAC described by Knight and Canolty (Canolty & Knight, 2010) proposes a model by which synchronous theta oscillations and local PAC organize cortical activity relative to the hippocampus, with interregional xPAC observed as a subsidiary consequence of this organization. However, we did not observe especially strong overlap between functionally synchronous connections in the cortex and the magnitude of xPAC (Figure 4). More selective filtering of cortical contacts based upon PLV values may however reveal such connectivity (consistent with the Knight and Canolty model). The ERC/PHC xPAC relationships we observed in the absence of functionally significant synchrony may be consistent with a model in which xPAC reflects the previously reported mechanism of memory encoding modulation via the precise timing of the arrival of information from the ERC (as represented by gamma band activity) relative to the hippocampal theta oscillation (Hasselmo et al., 2002; Schomburg et al., 2014). Further characterization of this hypothesis includes extension of our xPAC analysis to the period of memory retrieval, potentially incorporating alternative (cued) paradigms better suited to the analysis of retrieval-related oscillations. This may reveal differential preferred phase values for coupling, consistent with the separate phases at encoding and retrieval, or SPEAR model, articulated by Hasselmo et al. (2002) and supported by evidence in rodents (Colgin et al., 2009; Manns, Zilli, Ong, Hasselmo, & Eichenbaum, 2007). Further data from an animal model point to hippocampal modulation of memory-relevant spiking activity in the frontal cortex, a result suggesting that testing for xPAC in prefrontal regions (which were not well represented in our sample) may provide more definitive evidence consistent with the SPEAR model (Hyman et al., 2005).

One of the key limitations of our study is the relatively coarse regional aggregation we performed. Further investigations using more precise anatomical localization may reveal more subtle xPAC patterns. We note however that this aggregation did not influence results for the ERC/PHC as strongly given the smaller volume occupied by these regions (with presumably less inter-subject heterogeneity in the underlying signals). This may explain why we observed stronger effects for those regions. Our dataset did not contain sufficient anatomical specificity to examine medial versus lateral ERC/PHC effects, which rodent data suggest may reveal important functional differences (Furtak, Wei, Agster, & Burwell, 2007; Kerr, Agster, Furtak, & Burwell, 2007). This is an important point to address in future experimentation, as rodent findings suggest differential lateral versus medial ERC modulation of spiking activity by theta oscillations (Deshmukh, Yoganarasimha, Voicu, & Knierim, 2010), which may have implications for the integration of item (LEC) and contextual (MEC) information in the hippocampus (Knierim, 2015).

Our analysis separated the theta band into two sub-bands (termed 2–5 Hz “slow theta” and 5–9 Hz “fast theta”) to account for potential differences across this spectrum seen in previous human investigations (Fell et al., 2011; Lega, Kahana, Jaggi, Baltuch, & Zaghloul, 2011; Rutishauser, Ross, Mamelak, & Schuman, 2010; Steinvorth, Wang, Ulbert, Schomer, & Halgren, 2010; Watrous et al., 2013). Memory-related effects in the 2–5 Hz range have previously been reported during episodic memory encoding (Lega et al., 2012; Lin et al., 2017), spatial memory encoding and retrieval (Ekstrom et al., 2005), and recognition memory tasks (Rutishauser et al., 2010). However, phase locking of single unit activity in the 5–9 Hz range reportedly may differ according to rated confidence in a recognition memory paradigm (Rutishauser et al., 2015), and oscillatory differences in this band (such as phase reset and cross frequency coupling) may support working memory (Axmacher et al., 2010; Chaieb et al., 2015; Mormann et al., 2005). A slow/fast theta distinction is further supported by recent findings incorporating spatial memory data, which specifically delineate separate functional properties for oscillations in the slow versus fast theta frequency range (Goyal et al., 2020), as well as hippocampal connectivity data supporting the existence of distinct fast versus slow theta oscillation networks (Choi et al., 2020). However, not all previous studies have used a demarcation exactly at 5 Hz; Goyal, for example, uses 4.5 Hz as a cutoff and extends the fast theta range to 11 Hz, while others do not segregate data into bands. We note that, the slow theta frequency range, including for example the oscillations as shown in Figure 1, are lower in frequency than typical PAC measurements in rodents. Our results can help further explicate inter-species differences in memory-relevant hippocampal theta activity (Jacobs, 2014).

In our results, functional xPAC occurs across the theta frequency spectrum. We believe this further supports the idea that human memory requires the dynamic interaction of both slow and fast theta oscillations, influenced by regional and hemispheric factors (Axmacher et al., 2010; Backus et al., 2016; Canolty et al., 2006; Lega et al., 2014). This finding of theta heterogeneity is also supported by findings from Tort indicating that hippocampal-striatal xPAC occurs at multiple frequencies from 3 to 11 Hz (Tort et al., 2009). Certainly, we acknowledge that the choice to demarcate fast versus slow theta oscillations at 5 Hz risks missing more subtle patterns that may be observable using a case-by-case identification of preferred theta frequencies for memory-related activity. Future investigations of xPAC may incorporate updated oscillation detection algorithms to delineate frequency ranges for fast and slow theta oscillations on an electrode-by-electrode basis, which could uncover more subtle patterns (Cole & Voytek, 2019).

Using a multivariate model, we attempted to differentiate memory-related effects attributable to xPAC versus those attributable to local PAC. We note that the existence of local PAC in the absence of phase synchrony does not explain xPAC, and if local PAC and hippocampal xPAC occur at slightly different frequencies, this finding may provide an explanatory mechanism for observed divergence between preferred hippocampal theta frequencies exhibiting mnemonically-relevant properties (2–5 Hz) and cortical regions exhibiting properties across a broader range of theta frequencies (Axmacher et al., 2010; Backus et al., 2016; Canolty & Knight, 2010; Foster & Parvizi, 2012; Lega et al., 2014). Overall, the specific interactions between local PAC and xPAC remains a fruitful avenue for further investigation, especially for noteworthy xPAC connections seen in Figure 2b such as hippocampus-PHC.

We specifically compared xPAC for the AH versus PH. In the left hemisphere, the stronger functional xPAC effects in the PH may reflect more spatially coherent theta oscillations within the PH (leading to clearer identification of xPAC across electrodes) or a preferred septo-temporal propagation for these oscillations. The latter idea is further supported by the phase offset for preferred PAC coupling phase shown in Figure 3, as AH coupling mostly occurred later in the theta cycle (although the phase offset was greater than previously seen for coherent AH versus PH theta oscillations (Zhang & Jacobs, 2015). We note also that the lack of AH/PH distinction in the right hemisphere may reflect the verbal memory task we used, although hemispheric differences in hippocampal activity have mostly not been observed in free recall (Burke et al., 2014; Sederberg, Kahana, Howard, Donner, & Madsen, 2003) and therefore further examination of xPAC using spatial memory paradigms may prove insightful to explicate these differences. A recently articulated model of memory processing, the posterior medial/anterior temporal model (PMAT), posits that the PRC and ERC participate in different cortical networks, and if one extends this model to AH/PH distinctions, our findings of functionally significant PH/ERC coupling would seem surprising as the ERC is clearly identified within the AT but not PM network (Ranganath & Ritchey, 2012; Ritchey, Libby, & Ranganath, 2015). However, it is also possible that the entire hippocampus, both AH and PH, participate in both networks given its central role in mnemonic processing (Choi et al., 2020) Furthermore, this model relies mostly on noninvasive data collected during item retrieval and therefore may not apply as strictly to data collected during memory encoding, as we present here.

The quantification of PAC has been the topic of extensive discussion in the human electrophysiology literature. Several different methods have been used in high profile publications. While our main findings follow the MI calculation described by Canolty et al. (2006), we also tested our results using other methods for PAC quantification, namely MI by KL-distance as a measure of the dependence of hippocampal theta and cortical gamma, and implemented recommended steps in PAC calculations such as filter bandwidth (Aru et al., 2015; Lozano-Soldevilla et al., 2016; Richman & Moorman, 2000; Tort et al., 2010; Vaz et al., 2017). Our main findings regarding xPAC between hippocampal theta oscillations and ERC/PHC gamma oscillations were mostly supported by results performed using KL distance. We found that the coupling phase observed using KL-distance was difficult to track precisely due to the estimation of amplitude-phase distribution. Furthermore, we attempted to directly test and control for the impact of theta waveforms leading to spurious detection of PAC activity in our data. As discussed in the Results section, in xPAC the underlying waveform in theta does not influence the measurement of the phase dependence of gamma oscillations in the non-hippocampal region (ERC/PHC). Therefore, we believe xPAC is less sensitive to this concern than local PAC as long as one accounts for possible effect of phase synchrony (established in Figure 4). However, using published criteria for exclusion of sharp oscillations and clipping distortion in the hippocampus, we still observed significant xPAC. Certainly, methods to account for nonsinusoidal underlying waveforms remain an active area of investigation.