Traveling waves enhance hippocampal-parahippocampal couplings in human episodic and working memory

The human medial temporal lobe (MTL) is an important brain region that plays important roles in memory, spatial navigation, emotions and motivations1 (Squire et al., 2004). The MTL consists of several structures including the hippocampus, entorhinal cortex (EC), and parahippocampus 2 (Eichenbaum and Lipton, 2008). The EC occupies most of the parahippocampal gyrus (PHG) and is the largest source of the input into the hippocampus. The PHG or parahippocampal cortex (PHC), lying adjacent to the hippocampal formation and bordering the subiculum , consists of several other subregions in addition to the EC 3 (van Strien et al., 2009 ). To date, hippocampal- entorhinal couplings at various frequencies have been implied in associative learning 4 (Igarashi et al., 2014), encoding temporal structure of experience 5 (Tacikowski et al., 2024), and working memory load 6 (Li et al., 2024 ). However, hippocampal-parahippocampal couplings were less studied7,8 (Aminoff et al., 2013; Fell et al., 2001 ). It remains unclear how the hippocampus coordinates information with its upstream or downstream structures during memory encoding and retrieval. Traveling waves (TWs), appearing in a form of spatiotemporal patterns of neural oscillations or spiking activity, provide a mechanism to coordinate information transfer in cognition and memory processing 9-12(Muller et al., 2018; Davis et al., 2020; Bhattacharya et al., 2022; Mohan et al., 2024). In the context of episodic memory, low-frequency (2-13 Hz) TWs have been reported in the human and rodent hippocampus and EC regions13-16 (Zhang and Jacobs, 2015; Lubennov and Siapas, 2009; Patel et al., 2012; Hernandez-Perez et al., 2020). Hippocampal TWs often propagate in a dominant direction in the MTL, along the dorso-ventral axis or the posterior- anterior axis, but bidirectional hippocampal TW patterns may also occur depending on the brain state or the electrode recording location 17-19 (Kleen et al., 2021; Patel et al., 2013; Smith et al., 2022). While the roles of hippocampal TWs in cognitive tasks remain incompletely understood, a working hypothesis is that changes in the propagation directions of TWs may provide a mechanism to flexibly organize large -scale brain activity to support different behavioral processes12 (Mohan et al., 2024). To date, a growing number of large -scale intracranial EEG (iEEG) or electrocorticogram (ECoG) studies have examined hippocampal mechanisms of memory encoding and retrieval in epileptic patients20-23 (Lega et al., 2016; Zhang et al., 2018; Kunz et al., 2019; Griffiths et al., 2021). In this study, based on direct multielectrode recordings from neurosurgical patients in a verbal memory task12,24-26(Mohan et al., 2024; Kragel et al., 2021; Sakon et al., 2022; Goyal et al., 2020), we detected bidirectional TW patterns from multiple recording electrodes implanted in either the hippocampus or the parahippocampus, and confirmed that low-frequency TWs were predominant in both the human hippocampus and parahippocampus (Supplementary Tables 1 and 2) during various memory task phases . We further tested whether TWs can modulate hippocampal - parahippocampal couplings in a task -dependent manner. Between -region coordination was characterized by both undirected and directed functional connectivity measures, including coherence, phase-locking value (PLV), and spectral Granger causality (SGC). Our results .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 4 revealed functional significance of TWs in coordinating hippocampal-parahippocampal and intra- hippocampal communications in episodic and working memory.

Detecting traveling waves in the human hippocampus and parahippocampal gyrus All experimental subjects who had various numbers or locations of electrodes implanted in the MTL of their brains were instructed to perform an episodic and working memory task. The memory task consists of countdown, encoding, distraction task and retrieval phases (Fig. 1a), and subjects learned and recalled sequences of English words. After viewing each list followed by a distraction task delay, subjects tried to freely verbally recall as many words as possible. We selected subjects (Methods and Supplementary Tables 1 and 2) with electrode implants simultaneously in both the hippocampus and PHG, at one or two hemispheres ( Fig. 1b,c ) and also included additional subjects with recording electrodes from the hippocampus or PHG alone . To detect TWs and accommodate more qualified subjects for the subsequent analyses, we set up at least a minimum of 3 channels (maximum: 6) within one brain area. We used an established criterion to detect the TWs (Methods and Supplementary Note) and projected the TWs along the posterior-anterior axis or plane (Supplementary Fig. 1). We first identified a dominant oscillatory frequency by removing the 1/f background ( Fig. 1d) and obtained the bandpass -filtered signals (Fig. 1e). We observed consistent phase shift at a n arrow theta frequency band across electrodes, forming a TW propagating in either a posterior-to-anterior (‘A-to-P’, or ‘front-to-back’) or the opposite anterior- to-posterior ( ‘P-to-A’ or ‘back -to-front’) direction ( Fig. 1f ). When the electrode layout was not perpendicular to the posterior -anterior axis, we examined the dominant wave propagation projected onto the posterior-anterior axis. However, because of the sparse electrode sampling of the hippocampus, the TW propagation axis could deviate from the implanted electrodes and we were underpower to provide a complete assessment. We independently detected hippocampal TWs (n= 30 subjects, N=50,551 events) or parahippocampal TWs (n=22 subjects, N=30,217 events) from all task periods (see Fig. 1 and Supplementary Fig. 2 for two subjects with representative hippocampal TWs, as well as Supplementary Fig. 3 for another subject with representative parahippocampal TWs). Bidirectional TWs, in either the hippocampus or the parahippocampus, were omnipresent across task phases in the verbal memory task. The propagation direction of detected TWs followed a bimodal distribution (Fig. 1g,h). The duration percentage of TWs also varied across task periods (Fig. 1 i). The overall number of detected hippocampal TW events were greater in memory encoding (N=15,343) and retrieval (N=14,193) than countdown (N=5,158) and distraction-task (N=12,441) periods. We computed the TW characteristics by their direction, speed, and spatial frequency. Among all detected TWs regardless of the propagation axis or direction, their spatial frequencies varied within a broad range with a median value of 0.05 mm-1 (Fig. 1j). In a rare iEEG recording (subject #R1032D), we detected bidirectional hippocampal TW patterns in both left and .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 5 right hemispheres, but these TWs were not always synchronized between hemispheres, in either timing or direction (Supplementary Fig. 4a,b). Changes in hippocampal TW propagation directions at timing or latency also varied between hemispheres (Supplementary Fig. 4c), and we did not find consistent TW direction patterns across two hemispheres between successful and unsuccessful trials . Additionally, hippocampal TWs enhanced the amplitude and phase synchronization between the EC and the parahippocampus located at the opposite hemispheres (Supplementary Fig. 4d). Traveling waves elevate intra-hippocampal and hippocampal-parahippocampal coordination in amplitude and phase Next, we examined whether TWs play a coordinating role for hippocampal -parahippocampal activity. In the representative subject (#R1032D), we found that hippocampal TWs significantly enhanced the phase synchronization between hippocampi as well as between the hippocampus and the EC or parahippocampus (Fig. 2a), with the most pronounced effect at the theta frequency band. Furthermore, TWs enhanced the coherence ( Fig. 2b) across a broad range of frequency bands not only between the left and right hippocampi, but also between the hippocampus and the EC or parahippocampus. The relative gain (i.e., statistic with TWs minus statistic without TWs) in both amplitude and phase couplings at the theta band between the left and right hippocampi suggest that TWs could facilitate long -range brain communications. Notably, the PLV statistics were relatively stable across the task phases ( Fig. 2 c). As the coherence statistic does not address the question of the predictability of activity between two brain regions , we further used SGC, in the Granger sense of directed predictability, to evaluate the relative strengths of mutual influence between the two brain regions. Interestingly, the spectral information flow between the two brain regions was asymmetric: greater in the parahippocampus àhippocampus (or ECàhippocampus) direction than in the opposite direction (Fig. 2d). The GC strength was peaked at the beta frequency (20-30 Hz). For subject #R1032D, we also observed a GC peak at the high theta frequency (~9-10 Hz) in the hippocampusàEC direction. At the population level, we computed the coherence and PLV statistics during hippocampal TWs and compared them with the initial countdown period where a minimum level of memory processing was assumed. Notably, TWs enhanced coherence and PLV at two most prominent frequency bands: theta (5-9 Hz, Fig. 3a) and low gamma (35-55 Hz, Fig. 3b) oscillations. Additionally, hippocampal TWs modulated hippocampal theta phase-gamma amplitude couplings or PAC (Fig. 3c for subject #R1032D and Fig. 3d for a population summary). The duration fraction of detection hippocampal TWs positively correlated with hippocampal theta power (Fig. 3e,f). The hippocampal PAC modulation index was also positively correlated with the hippocampal theta power ( Fig. 3 g). Similarly, the summary statistics of parahippocampal TWs is shown in Supplementary Fig. 5. Task-dependent hippocampal-parahippocampal and intra-hippocampal couplings .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 6 We further investigated whether hippocampal-parahippocampal and intra-hippocampal couplings vary across memory task phases. We found that coherence at the gamma-band (35-55 Hz) was greater during memory retrieval than during encoding (p=0.001, rank-sum test, Fig. 4a), and the hippocampal PAC modulation index was greater during memory encoding than during retrieval (p=0.017, rank-sum test, Fig. 4b). However, we didn’t observe statistical difference in the peak- normalized SGC at the population level (Fig. 4c). Interestingly, we found that hippocampal theta (5-9 Hz) power was greater in unsuccessful than successful trials (p <10-5, signed-rank test; Fig. 4, left panel). Similarly, the hippocampal gamma (35-55 Hz) power was also lower in successful trials than unsuccessful trials (p=0.021; Fig. 4d , right panel). Between successful and unsuccessful trials in memory encoding, we observed that SGC at the gamma band (35-50 Hz) during unsuccessful trials was significantly greater than during successful trials in both the hippocampalàparahippocampal direction (p=0.0206, signed-rank test, n=30, Fig. 4e, left panel), and the parahippocampal àhippocampal direction (p=0.0 343, Fig. 4e , right panel). However, undirected PLV and coherence measures were not significantly different between successful and unsuccessful trials (data not shown), possibly due to trial imbalance and performance variability of subjects.

The human hippocampus can be subdivided into posterior and anterior parts, which correspond to the dorsal and ventral hippocampus in the rodent , respectively. Their functions also differ in structure, function and their connections to cortical and subcortical structures27,28 (Strange et al., 2014; Dandolo and Schwabe, 2018 ). The upstream and downstream structures of the hippocampus, including the EC and parahippocampus (or PHG in general), are believed to play a coordinated role in episodic memory processing and spatial navigation3 (van Strien et al., 2009). To date, there have been a growing number of human hippocampus studies based on electrophysiological recordings of clinical patients29-31 (Saint et al., 2023; Li et al., 2022; Axmacher et al., 2010 ). Human hippocampal TWs have been found based on grid or depth iEEG recordings13 (Zhang and Jacobs, 2015), but the nature of bidirectional wave propagation patterns was recently noticed 17 (Kleen et al. , 2 021). Here we found omnipresent hippocampal and parahippocampal TWs within a narrow theta band during a verbal memory task, wh ose propagation direction dominated in the posterior -anterior axis but could vary according to the electrode implant. Our findings suggest that hippocampal TWs may be broadly related to memory- driven behaviors, but may not be evoked by task events. The hippocampal TW direction could change during the same task epoch and the hippocampal TWs at both hemispheres were not necessarily synchronized. It has been known that the feedforward information flow through the cerebral cortex, PHG, and hippocampus can be described as a hierarchy of connectivity in which the cerebral cortex funnel information onto multiple areas within the parahippocampal region, whose outputs converge on the hippocampus 2 (Eichenbaum and Lipton, 2008 ). During .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 7 information feedback, the outputs of hippocampal processing are directed back down the hierarchy to the PHG, and then to the cerebral cortex. It has been suggested that posterior -to- anterior TWs correspond to feedforward processing while anterior -to-posterior TWs correspond to feedback processing in visual processing32,33 (Canales-Johnson et al., 2023; Fritch et al., 2021). Since bidirectional theta/alpha (2 -13 Hz) cortical TWs modulate human memory processing 12 (Mohan et al., 2024 ), i t is not totally unreasonable that changes in hippocampal or parahippocampal TWs are coordinated with other cortical processing. Recent iEEG data in human working memory (WM) tasks have shown that correct WM trials were associated with theta/alpha- coordinated unidirectional influence from the posterior to the anterior hippocampus, whereas WM errors were associated with bidirectional interactions between the anterior and posterior hippocampus30 (Li et al., 2022). While we reported both hippocampal and parahippocampal TWs, a question still remains whether hippocampal TWs are coordinated with parahippocampal TWs or other cortical TWs in a task-dependent manner. Our study provides several new insights into the mechanism of hippocampal TWs during memory processing. First, TWs elevated intra-hippocampal and hippocampal-parahippocampal couplings in amplitude (e.g., coherence) and phase (e.g., PLV) especially at theta and low gamma frequencies in the verbal memory task, which consists of both episodic memory and WM components. It has been known that h ippocampal theta oscillations play a key role in episodic memory34 (Buzsaki and Moser, 2013 ), and that hippocampal gamma oscillations may facilitate dynamic routing of information35 (Colgin and Moser, 2010) and modulate according to the working memory load36 (van Vugt et al., 2010 ). A potential mechanism of TWs is to promote long -range brain communications and neural plasticity 9 (Muller et al., 20 18). Second, the widely reported hippocampal theta phase -gamma amplitude couplings were enhanced during TWs. The enhancement occurred not only within the same hippocampal region but also between two opposite hippocampal regions. Our results are conceptually in line with the literature findings20,30,37 (Lega et al., 2016; Li et al., 2022; Wang et al., 2021). Third, we observed a consistent SGC peak at the beta frequency between the hippocampus and parahippocampus during the memory task, with stronger SGC strengths in the parahippocampus àhippocampus direction, where the feedback is crucial for top -down prediction38 (Engel et al., 2001 ). Since beta oscillations have been implied in the inhibitory control in WM and cognitive processing39 (Wessel and Anderson, 2024), our finding may suggest that the feedback information flow is important for maintaining episodic memory. Additionally, beta coupling s between the hippocampus and many sensory or non-sensory cortices also play a role in learning and memory 40 (Miles et al., 2023 ). N ovelty exploration in rodents is not only accompanied with enhanced hippocampal-cortical coherence at the theta and beta frequency bands, but also accompanied with increased SGC gain between the hippocampus and the frontal cortex41 (Franca et al., 2021). The human hippocampal-parahippocampal coupling and decoupling have been reported during memory formation 8 (Fell et al., 2001 ). Specifically, gamma -band phase synchronization (32-40 Hz) was suggested to be a mechanism of transiently connecting neural assemblies, and it .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 8 was also found that hippocampal gamma power reduced in successful recalls than unsuccessful recalls. Therefore, gamma activity was interpreted as a hippocampal resting rhythm or as a correlate of specificity of local assembly activation, and certain components of hippocampal - parahippocampal circuits might be shut off or rest during successful memory encoding 8 (Fell et al., 2001 ). Our result of hippocampal theta and gamma power reduction during successful memory encoding seems to support this interpretation. Additionally, bidirectional hippocampal- parahippocampal information flow was reduced in the gamma band. A continuing puzzle and important question of interest for TWs is their predictability to task behaviors. To date, several reports have shown that the characteristics of cortical TWs in episodic or working memory tasks could discriminate successful from unsuccessful trials12,42 (Zhang et al., 2018; Mohan et al., 2024), whereas others also reported contradictory results43 (Sreekumar et al., 2021). Our investigations showed variable results at the individual level and some inconclusive population statistics (e.g., PLV and coherence metrics) . This can be possibly ascribed to many factors, such as a small sample size, imbalanced successful/unsuccessful trials, and variable hippocampal-parahippocampal electrode locations. Because of both technical and data constraints, we suspect that a holistic TW view based on multi-site recordings with additional task controls are required to fully answer this question. The mechanistic role of hippocampal or parahippocampal TWs remains to be determined in the context of organizing the timing and direction of interactions between different brain regions during memory processing or memory - guided behaviors. There are several technical limitations in our findings. First, detection of hippocampal or parahippocampal TWs was limited by the location and number of recording electrodes within the MTL, therefore our detection was likely subject to errors (false negatives and false positives) . Spatial aliasing may also occur due to inadequate spatial sampling, resulting in ambiguous wave direction12 (Mohan et al., 2024), Second, the difference in the duration of task phases may cause us to miss potential differences of TW characteristics in a task-dependent manner. Third, there was no real “control” experiments, therefore it remains unclear whether our bidirectional TWs are specific to this memory task or are universal across many other cognitive processes. Follow-up experiments and systematic investigations may help resolve these puzzles in the future. Biophysically-realistic circuit -level modeling may also play complementary role in making experimental predictions44 (Wu and Chen, 2023). .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 9

Subjects and protocols A large multi -institutional cohort of dr ug-resistant epilepsy patients (N=259) participated in an episodic memory study. All patients were surgically implanted with grids and strips of electrodes for the purpose of identifying epileptogenic regions. The detailed protocol has been previously published task12,24-26 (Mohan et al., 2024; Kragel et al., 2021; Sakon et al., 2022; Goyal et al., 2020). All participants provided informed written consent upon obtaining experimental protocol approval from the institutional review board (IRB) at each hospital . Based on the recording iEEG channel location coverage in the hippocampus and the parahippocampus or both, a total of 81 subjects (48 men, 33 women; mean±SD age, 39.1±12 years) were used in our current study , and a further subset of 48 subjects were qualified for TW analyses (Supplementary Tables 1 and 2). Verbal memory task In the episodic memory task, the subjects were instructed to perform a verbal free-recall task of memorizing a list of words ( Fig. 1a). Each session started with 10-s count down, followed by Word-encoding (with alternating Word ON and Word OFF), Distraction and Word-retrieval periods. During the encoding phase, each trial consisted of 12 English words presented sequentially as text on the computer screen. Each word was presented for 1 .6 s, followed by a blank screen for 0.75-1 s. The lists consisted of high -frequency nouns (http://memory.psych.upenn.edu/Word_Pools). After the list, the subjects were presented with a 20 s math distractor task prior to free recall. During retrieval, the participants were given 30 s to verbally recall the words in any order. The verbal responses were recorded on a microphone and then manually scored after the task. iEEG channel re-referencing and preprocessing In this public dataset, human iEEG recordings had various sampling rates (e.g., 500 Hz, 1000 Hz, 1024 Hz, and 1600 Hz). Additionally, bipolar and monopolar referencing methods were noticed among the recordings. For all TW analyses, we only focused on recordings with the monopolar referencing method. To rule out the effect of volume conduction, we adopted re-referencing using the average reference. We conducted Hz high-pass filtering (>0.2 Hz) and band-stop filtering to remove the power interference at 60 Hz and 120 Hz (each with 2 Hz bandwidth) for the raw iEEG signals. Detection of traveling waves A traveling wave (TW) is defined as a “single” oscillation defined within one narrow frequency band that appears across electrodes with a progressive spatial and temporal phase shift. In theory, TWs can simultaneously occur at multiple oscillations, making the detection of a wave pattern more challenging. We adopted a published method 12 (Mohan et al., 2024 ) and modify it to detect TWs and calculate the TW direction and phase velocity along a specific two-dimensional (2D) plane or one-dimensional (1D) axis. At the first step, we found clustering electrodes that can fit within a 15 mm radius sphere, containing at least three electrodes with power spectrum peaks (after removing 1/f background signal) approximately at the same frequency 𝜔. It is well known that the EEG or iEEG power spectrum follows a power law45,46 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 10 (Gao, 2015; Gyurkovics et al., 2021). To identify the peak oscillation, we removed the 1/f background signal and identified peaks that were local maxima that were at least one standard deviation above the mean, which produced the normalized power spectrum. From this peak frequency, we defined a narrowband oscillation within a narrow bandwidth of 2 Hz (i.e., [low frequency, high frequency], where high frequency- low frequency = 2 Hz). At the second step, we applied a finite impulse response (FIR) filter to extract the signal of interest and used a Hilbert transform to extract phase information at each time point. To find the duration with stable phase difference, we calculated time -varying phase differences using an average reference, in which their time derivatives were analyzed to identify periods where all channels’ time derivatives remained below a specified threshold. We retained durations that contain ed at least three complete cycles at the peak frequency 𝜔. At the third step, we identified wave packets where the signal envelope exceeds one standard deviation of the narrowband signal of interest. For each time region, we checked if at least 80% of the duration was occupied by wave packets across all channels. If this criterion was met, we considered the instance as a TW event candidate. In calculating the number of TW events during task periods, if a TW event covered more than one task periods (e.g., encoding plus distraction), then the event would be double-counted in both task periods. Avoid spatial aliasing and remove bad TW candidates As demonstrated previously12 (Mohan et al., 2024), the use of grid and strip electrodes to record TWs could introduce inaccuracies in estimating their directions and phase velocities due to insufficient spatial sampling. To address this issue, we employ ed a method to filter out TW candidates where the model predict ed a maximum phase difference exceeding 2𝜋. Additionally, we excluded candidates with an 𝑅! value below 0.1 from linear regression (see below) to ensure the reliability of the fitted model. Measuring TW direction and phase velocity We proposed an approach for calculating spatial propagation of TWs. We assumed that for a plane wave, the phase at the 𝑖-th electrode changing over time 𝑡 is described by the following equation 𝜙" = 𝜔𝑡 − 𝒌 ⋅ 𝒓", where 𝒌 is the wave vector (spatial frequency) and 𝜔 is the frequency, 𝒓" is the spatial position of electrode 𝑖. When using a center reference, the relative phase at the 𝑖-th electrode, denoted by Δ𝜙", can be written as Δ𝜙" = − 𝒌 ⋅ 𝒓" + 𝐶, where 𝐶 denotes a constant. Rewriting this equation in a scalar form by summing up the spatial dimensions from 1 to 𝑛 Δ𝜙" = − 3 𝑘#𝑟#" $ #%& + C, where 𝑛 denotes the dimension of space and 𝑘# is wave vector component along axis 𝑗, and 𝑟#" denotes the position of electrode 𝑖 along axis 𝑗. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 11 To avoid overfitting, we applied principal component analysis (PCA) to identify the main axes of the electrode cluster. Axes with the ratio of explained variance greater than 0.05 were retained, reducing the dimensionality of the electrode positions. For example, if two axes exceed the threshold, the reduced dimensionality will be 𝑛 = 2, indicating a model of order 2. Since most recording electrodes were spatially close, we assumed that the maximum phase difference between any two electrodes should not exceed 2π. This constraint helped us adjust the phase difference range. A linear regression model was then used to fit the data. For electrodes reduced to a 2D plane ( 𝑛 = 2), we excluded the wave vector component 𝑘' and the fitting equation becomes Δ𝜙" = −𝑘&𝑟&" − 𝑘!𝑟!" + C, Upon completion of fitting, we determined the wave vector components 𝒌" = (𝑘&, 𝑘!) and calculated the 𝑅! value of the linear model to assess the goodness of fit. The direction of 𝒌" characterizes the direction of TWs in this 2D plane. Accordingly, the wave vector component 𝒌" and the phase velocity 𝑣( ) *+,! in a specific direction are related by the equation 𝑘 = 𝜔 𝑣( ) *+,! , where 𝜔 denotes the frequency measured in radian. This relationship allows us to calculate the phase velocity in the chosen direction. However, it's important to note that the phase velocity in a specific direction is always greater than or equal to the actual phase speed of the actual propagating wave (see Supplementary Note). This discrepancy arises because the phase velocity depends on the projection of the wave vector onto a chosen direction, which can lead to overestimation of the true wave speed. Coherence analysis In a frequency domain, coherence measures amplitude-amplitude coupling between two random signals across a wide range of frequencies. We calculated the magnitude-squared coherence between pairwise iEEG signals using the following formula: Coh-.(𝜔) = = /0"#(2)/ $ 0""(2)⋅0##(2) where 𝑃-. (𝜔) denotes the cross-power spectral density of 𝑥 and 𝑦, 𝑃-- (𝜔) and 𝑃..(𝜔) denote the power spectral densities of variables 𝑥 and 𝑦, respectively. The mean theta coherence was computed by Coh5 = & 2$62% ∫ 𝐶-.(𝜔)𝑑𝜔 2$ 2% where 𝜔& = 5 Hz, 𝜔! = 9 Hz. In TW-specific analyses, to calculate coherence between the hippocampus and the parahippocampus (or EC), we selected two channels, one located from each region, with the farthest distance apart . In task -dependent coherence analyses, we computed coherence among all possible pairs and presented the largest coherence value. Phase-locking value (PLV) analysis .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 12 PLV is commonly used for characteriz ing phase synchronization between two band -limited signals. It provides the information regarding phase coupling between two iEEG signals. The amplitude 𝐴(𝑡) and the instantaneous phase 𝜙(𝑡) of a signal 𝑠(𝑡) can be estimated using the Hilbert transform ℋ{⋅} as follows: 𝑧(𝑡) = 𝐴(𝑡) expN𝑖𝜙(𝑡)O = 𝑠(𝑡) + 𝑖ℋ{𝑠(𝑡)} = Re{𝑧(𝑡)} + 𝑖Im{𝑧(𝑡)} where 𝑖 = √−1 denotes the imaginary unit. The analytic signal 𝑧(𝑡) can be considered as an embedding of the one-dimensional time-series in the 2D complex plane. From the analytic signal, we can compute the instantaneous phase 𝜙(𝑡) = arctan \ 78{:(;)} =>{:(;)}], 𝜙 ∈ [−𝜋, 𝜋] The phase synchronization is defined as the locking of phases of two oscillators 𝜙&(𝑡) and 𝜙!(𝑡) , and 𝛿𝜙(𝑡) is defined as their relative phase 𝛿𝜙(𝑡) = 𝜙&(𝑡) − 𝜙!(𝑡). Accordingly, PLV is defined as: PLV = ef1 𝑁 3 sin (𝛿𝜙(𝑗∆𝑡)) ?6& #%@ k ! + f 1 𝑁 3 cos (𝛿𝜙(𝑗∆𝑡)) ?6& #%@ k ! l &/! where N denotes the total number of samples and ∆𝑡 denotes the time between two successive samples. The PLV value is bounded between 0 and 1, where 0 indicates completely unsynchronized phases and 1 indicates perfect synchronization. To calculate PLV between the hippocampus and parahippocampus (or EC), we selected two channels with the farthest locations for computation. Phase-amplitude coupling (PAC) analysis PAC has been widely recognized as an important mechanism in memory processing47,37 (Bergmann et al., 2018; Wang et al., 2021). We first band-pass filtered the raw iEEG signal to obtain the instantaneous power and phase representations of a priori defined (theta or gamma) frequency band using the Hilbert transform. From the derived complex -valued signals, we extracted the instantaneous theta phase and gamma amplitude (envelope), and further constructed the phase -amplitude histogram (15 bins within 0–2𝜋). The modulation index (MI) of PAC was computed using an established method48 (Tort et al., 2010): 𝐴" = Amplitude" ∑ Amplitude## 𝐻 = − 3 𝐴" log(𝐴" ) " 𝐻8BC = log(𝑁) MI = (𝐻8BC − 𝐻) 𝐻8BC where Amplitude" denotes the instantaneous amplitude for the i-th sample, and 𝐴" denotes the corresponding normalized amplitude, and 𝑁=15 denotes the total number of bins. Spectral Granger causality (SGC) analysis .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 13 Given a bivariate iEEG time series 𝚯 ∈ ℝ!, we resampled the iEEG signals to 200 Hz and modeled them using a r-order linear vector autoregressive system, VAR(r) 𝜣; = 3 𝑨D𝜣;6D E D%& + 𝒆; where 𝐞; denotes two-dimensional white Gaussian noise, 𝑨D denotes 2-by-2 coefficient matrix for the 𝜏- th lag. If the VAR(r) process is stable, then all the roots of the reverse characteristic polynomial are bigger than 1 in terms of the Euclidean norm (i.e., outside the unit circle). Once {𝑨D} are known or fully identified, the SGC can be analytically computed49 (Barnett and Seth, 2014). The VAR(r) parameters can be identified from the least-squared estimation, following a model order selection for 𝑟. The maximum model order was set to be 15, with a default model order of 10. The SGC estimate and statistics were computed using an established MATLAB toolbox (www.sussex.ac.uk/sackler/mvgc/). For each subject, we computed the mean SGC and the confidence intervals based on a leave -one-out strategy. To allow population-level comparisons, we also normalized SGC for each subject (normalized by the peak of SGC from both directions) and computed the group -averaged normalized SGC. All selected hippocampal and parahippocampal channel locations are summarized in Supplementary Fig. 6. Statistics We used two shuffling methods to evaluate the significance of PAC. In the first method, the phase array's sequence was preserved, while the amplitude array was randomly shuffled. In the second method, the phase array sequence was also maintained, but the amplitude array was shuffled by circularly rotating its start and end points. We imposed that the time shift for this rotation must exceed the duration of an encoding trial (1.6 s). For each method, we perform ed 500 shuffling tests, and the p -value for both tests must be below 0.05 to achieve statistical significance. For statistical tests , we employed non-parametric Wilconxon rank-sum test (for unpaired comparisons) and Wilcoxon signed-rank test (for paired comparisons), respectively. Data Availability The raw electrophysiological data in this study are publicly available and available upon request at https://memory.psych.upenn.edu/Data_Request. Code Availability The computer codes developed in this study are available upon the request from the corresponding author and will be soon available in the GitHub repository. Acknowledgments We thank M. Kahana for sharing the experimental data, and thank G. Buzsaki and J. Jacobs for valuable comments on the manuscript. We thank R. Wang for discussion. This work was initiated when X.C. conducted a summer research internship at NYU. The work was supported by grants RF1-DA056394, R01- .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 14 MH118928, P50-MH132642, R01-NS121776, and R01-MH139352 (Z.S.C.) from the US National institutes of Health. The views, opinions and/or findings expressed are those of the authors and should not be interpreted as representing the official views or policies of the US government. The funders had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript. Author contributions Z.S.C. conceived and supervised experiments, developed the methods, interpreted the data, and wrote the paper. X.C. developed the methods, performed experiments, analyzed and interpreted the data. Z.S.C. acquired funding. Competing interests The authors declare no competing interests. Supplementary information Supplementary Note, Supplementary Fig. S1-S6 and Supplementary Tables S1-S2.

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It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 18 Figure 1. Detecting of hippocampal traveling waves (TWs) in human intracranial EEG recordings (a) Schematic of the verbal memory task. a b c d e 200 ms 100 ms 100 ms -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 -20 -10 0 10 20 a b c d e b a c d e -20 -10 0 10 20 1.25 1.00 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 Phase (rad) Phase (rad) Displacement (mm) Displacement (mm) P-to-A direction A-to-P direction HIPP Traveling Waves (TWs) Subject R1032D Filtered Filtered d(i) AP PP PA A A Countdown Encoding Distraction task Retrieval Duration {A-to-P} Duration {P-to-A} = 81ɿ19 = 67ɿ33 = 73:27 = 79:21 N=88 N=136N=120N=46 EC Left Right 200 ms HIPP Traveling Waves (TWs) PH 100 ms Filtered 100 ms Filtered a b c d-0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 -15 -10 -5 0 5 10 15 A-to-P direction P-to-A directionPhase (rad) Displacement (mm) Countdown Encoding Distraction task Retrieval 1e-9 3.0 2.5 2.0 1.5 1.0 0.5 0.0 2 4 6 8 10 12 14 Freq (Hz) 1e-10 0.5 1.0 1.5 2.0 1.1 1.0 0.9 6 7 8 e d c b a PSD (V/Hz) Left HIPP iEEG Normalized power PSD (V/Hz) Freq (Hz) d c b a 2 4 6 8 10 12 14 0 1 2 3 4 5 6 1e-9 1e-10 5 4 3 2 1 1.05 1.00 0.95 6 7 8 PSD (V/Hz) Right HIPP iEEG Freq (Hz) Freq (Hz) PETUNIA CHAIR PHONE ENCODING (~30 s) 5 + 3 +2 5 +8 + 4 4 + 1 + 9 DISTRACTION TASK (~20 s) “CHAIR” “PHONE” RETRIEVAL (~30 s) (12 words) COUNTDOWN (~10 s) 10 9 2 1 a EC HIPP PH D V A P L M Left Right N=206N=133N=222N=77 Time {A-to-P} Time {P-to-A} = 36:64 = 29:71 = 22:78 = 23:77 Time {A-to-P} Time {P-to-A} Time {A-to-P} Time {P-to-A} Time {A-to-P} Time {P-to-A} a b c d -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 -15 -10 -5 0 5 10 15 Phase (rad) Displacement (mm) PSD (V/Hz) a b c d b d(ii) c(ii) c(i) e(i) e(ii) f(i) f(ii) f(i) f(ii) g(ii) g(i)Anterior Posterior h Superior Inferior P to A A to P 0 1000 2000 3000 1000 2000 A P PPA A No. total detected TW events Countdown Encoding Distraction Task Retrieval 0.0 0.1 0.2 0.3 0.4 0.5 A P i Duration fraction of TWs 30 subjects, 46 channel clusters j N=20 subjects Duration {A-to-P} Duration {P-to-A} Duration {A-to-P} Duration {P-to-A} Duration {A-to-P} Duration {P-to-A} a b c d e e d c b a a a b b c c d d Norm. power 0 2 4 6 8 10 12 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Spatial frequency (mm -1) Distribution TW speed = theta freq / spatial freq j .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 19 (b) Cartoon illustration of the hippocampus (HIPP), entorhinal cortex (EC) and parahippocampus (PH). Electrode implants in the left (6 in total) and right (5 in total) hemispheres from one representative subject (#R1032D) were shown. (c) Illustration of implanted electrode locations covering the left hippocampus and EC (i, symbol ‘ ’) as well as the right hippocampus and parahippocampus (ii, symbol ‘ ’). (d) Power spectral density (PSD) of hippocampal intracranial EEG (iEEG) signals at the left ( i) and right ( ii) hemispheres. Shade area denotes the theta band (5 -9 Hz). Normalized power by removing 1/f background is shown in the inset. (e) Illustrated bidirectional hippocampal TW snapshots with both posterior-to-anterior (‘P-to-A’) and anterior-to-posterior (‘A-to-P’) propagation directions. Arrows show the propagation direction. (f) Regression analysis showed consistent phase shift relative to electrode displacement distance. This is true for both P-to-A and A-to-P propagation directions. (g) Distribution of hippocampal TW propagation directions across four different task phases, where N denotes the number of detected TW events. The duration percentage of two propagation directions (P-to-A vs. A-to-P) is shown at the bottom of polar histogram. (h) The number of total detected hippocampal TW events in both P -to-A and A -to-P propagation directions for a subset of subjects (N=20). The inset shows the distribution of bidirectional hippocampal TW propagation direction. (i) Duration fraction of hippocampal TWs (with all propagation directions) at four different task phases among 30 subjects and 46 channel clusters. Each dot represents a channel cluster. (j) Distribution of detected TW spatial frequency (events pooled from all subjects). The TW speed or phase velocity is defined as the ratio between the median theta frequency (i.e., 7 Hz or 44 radian) and spatial frequency. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 20 Figure 2. Hippocampal-parahippocampal couplings in one representative subject (#R1032D). (a) Phase locking value (PLV) profiles between the left and right hippocampi, the left hippocampus and EC, the right hippocampus and parahippocampus. Hippocampal TWs (in either P -to-A or A-to-P propagation direction) significantly enhanced PLV compared to the countdown period. (b) Coherence profiles between the left and right hippocampi, the left hippocampus and EC, the right hippocampus and parahippocampus. Hippocampal TWs (in either P -to-A or A -to-P propagation direction) significantly enhanced coherence compared to the countdown period. (c) Comparison of theta-band PLV across four memory task periods and during TWs. Comparison was made between two hipp ocampal channels in the anterior part (left panel) versus between hippocampal channels in the posterior part (right panel). Symbols ‘ ’ and ‘ ’ denote the channel locations at the EC and the parahippocampus, respectively. (d) Similar to panel c, except for theta-band coherence comparison. (e) Directed spectral Granger causality between the right hippocampus and the right parahippocampus. Error bar denotes the confidence intervals. (f) Similar to panel e, except for between the left hippocampus and the left EC. 0.5 0.6 0.7 0.8 0.9 5 10 15 20 25 30 35 40 Freq. (Hz) Phase locking value (PLV) 0.95 0.90 0.85 0.80 0.75 0.70 0.65 0.60 0.55 5 10 15 20 25 30 35 40 Freq. (Hz) Phase locking value (PLV) P to A A to P Countdown P to A A to P Countdown 0.7 0.6 0.5 0.4 0.3 0.2 0.1 5 10 15 20 25 30 35 40 Freq. (Hz) Phase locking value (PLV) P to A A to P Countdown Left HIPP #e to Right HIPP #d Left HIPP #e to Left EC Right HIPP #d to Right PH 0.0 0.2 0.4 0.6 0.8Theta-band phase locking value (PLV) CountdownEncoding Distraction Task Retrieval P to A A to P Left HIPP #a to Right HIPP #a Left HIPP #a to Left EC Right HIPP #a to Right PH 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7Theta-band phase locking value (PLV) CountdownEncoding Distraction Task Retrieval P to A A to P a d e 0 20 40 60 80 100 Freq (Hz) 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 0.1 0.2 0.3 0.4 0.5Spectral Granger causality 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 Right HIPP --> PH PH --> Right HIPP Freq (Hz) Freq (Hz) Freq (Hz) Spectral Granger causality Spectral Granger causality Spectral Granger causality Countdown Encoding Distraction task Retrieval Right HIPP --> PH PH --> Right HIPP Right HIPP --> PH PH --> Right HIPP Right HIPP --> PH PH --> Right HIPP 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 100 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 Spectral Granger causality Spectral Granger causality Spectral Granger causality Spectral Granger causality Freq (Hz) Freq (Hz) Freq (Hz) Freq (Hz) Left HIPP --> EC EC --> Left HIPP Left HIPP --> EC EC --> Left HIPP Left HIPP --> EC EC --> Left HIPP Left HIPP --> EC EC --> Left HIPP Left Right edc ba dc b a 0.3 0.5 0.6 0.7 0.4 5 10 15 20 25 30 35 40 Freq. (Hz) Coherence right HIPP #d vs. PH Left HIPP#e vs. EC 0.75 0.70 0.65 0.60 0.55 0.50 0.45 5 10 15 20 25 30 35 40 Coherence Freq. (Hz) P to A A to P Countdown P to A A to P Countdown b Left HIPP #e vs. Right HIPP #d 5 10 15 20 25 30 35 40 45 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 P to A A to P Countdown Coherence Freq. (Hz) 45 45 right HIPP #d vs. PH Left HIPP#e vs. EC Left HIPP #e vs. Right HIPP #d c Left HIPP #e to Right HIPP #d Left HIPP #e to Left EC Right HIPP #d Right PH 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Countdown Encoding Distraction Task Retrieval P to A A to P Theta-band coherence 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Left HIPP #a to Right HIPP #d Left HIPP #a to Left EC Right HIPP #a Right PH Countdown Encoding Distraction Task Retrieval P to A A to P Theta-band coherence Countdown Encoding Distraction task Retrieval f .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 21 Figure 3. Summary statistics regarding hippocampal-parahippocampal couplings. (a) Scatter plot comparisons of PLV (blue) and coherence (green) between the left hippocampus and right hippocampus during TWs and the countdown period. Left: theta band (5 -9 Hz). Right: low gamma band (35-55 Hz). (b) Scatter plot comparisons of PLV (blue) and coherence (green) between the hippocampus and parahippocampus during TWs and the countdown period. Left: theta band (5 -9 Hz). Right: low gamma band (35-55 Hz). (c) Representative e xamples (Subject #R1032D ) of hippocampal theta -phase gamma -amplitude couplings. The PAC modulation index was greater with TWs (0.0031) than without TWs (0.0014). (d) Population statistics of hippocampal PAC without TWs and with TWs. PAC modulation index was greater with TWs than without TWs (p=0.001, signed-rank test, n=27). (e) The duration fraction of detected TWs from hippocampal iEEG signals positively correlated with hippocampal theta power, as shown from a representative subject #R1083J (Pearson correlation 0.49, p<10-23). Each dot represents the statistic computed from a 20 -s moving window with 50% overlap across the complete task recordings. (f) Population summary of Pearson correlation statistics between hippocampal theta power and duration fraction of detected TWs (similar to panel e). Each dot represents the result from one subject, the ones with solid black color was marked statistically significant (p<0.05). (g) The derived hippocampal PAC modulation index positively correlated with the hippocampal theta power (Pearson correlation 0.34, p=0.026, n=26). Each dot represents one subject. 0.0 0.1 0.2 0.3 0.4 4.0 3.5 3.0 2.5 2.0 1e-5 Theta power (RMS) (V) Duration fraction of detecting TW Pearson corr. 0.49 (p < 1e-23) Population Pearson correlation significant corr. p < 0.05 d e gf PAC modulation index 0.14 0.12 0.10 0.08 0.06 0.04 0.02 0.00 1e-3 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 Theta power (RMS) (V) Pearson corr. 0.34 (p=0.026, n=26) 0 6 12 phase (rad) Amplitude 0.001 Countdown TW left HIPP vs right HIPP (5-9 Hz) left HIPP vs right HIPP (35-55 Hz) TW Countdown HIPP vs PH (5-9 Hz) Countdown TW HIPP vs PH (35-55 Hz) Countdown TW 0 2 4 6 8 10 12 Phase (rad) 0 1 2 3 4 5 6 1e-6 Amplitude (V) PAC Modulation Index 0.0014 without TW 0 2 4 6 8 10 12 0 1 2 3 4 5 6 1e-6 PAC Modulation Index 0.0031 with TW Phase (rad) Amplitude (V) c a b 1e-2 1e-3 1e-4 1e-5 1e-4 1e-3 1e-2 PAC modulation index (w/ TW) PAC modulation index (w/o TW) p = 0.001, n= 27 0 6 12phase (rad) Amplitude0.015 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 PLV Coherence 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 PLV Coherence n=19 n=19 PLV Coherence 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 n=23 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 PLV Coherence n=23 -0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 n=45 channel clusters 30 patients .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 22 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Gamma band (35-55 Hz) coherence (Encoding) Gamma band coherence (Retrieval) p = 0.001, n=47 1e-2 1e-3 1e-4 1e-4 1e-3 1e-2 PAC modulation index (Retrieval) PAC modulation index (Encoding) a b p = 0.017, n=69 c Freq (Hz) Countdown Encoding Distraction task Retrieval Freq (Hz)Freq (Hz) Freq (Hz) theta (5-9 Hz), gamma (35-55 Hz) HIPP vs PH 1e-5 5 4 3 2 1 0 1e-5 0 1 2 3 4 5 HIPP iEEG mean power (V) HIPP iEEG mean power (V) Successful Unsuccessful theta (5-9 Hz) p < 1e-5, n=81 1e-5 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1e-5 p = 0.021, n=81 gamma (35-55 Hz) HIPP iEEG mean power (V) Successful HIPP iEEG mean power (V) Unsuccessful d e 0.04 0.06 0.08 0.10 0.12 0.14 0.04 0.06 0.08 0.10 0.12 0.14 GC (Successful) GC (Unsuccessful) gamma band (35-50 Hz) p =0.0206, n=30 HIPP-->PH PH-->HIPP 0.05 0.10 0.15 0.20 0.25 0.05 0.10 0.15 0.20 0.25 GC (Successful) GC (Unsuccessful) gamma band (35-50 Hz) p =0.0343, n=30 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 Normalized SGC HIPP-->PH PH-->HIPP (n=30 patients) HIPP-->PH PH-->HIPP (n=30 patients) HIPP-->PH PH-->HIPP (n=30 patients) HIPP-->PH PH-->HIPP (n=30 patients) .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 23 Figure 4. Characterizations of hippocampal-parahippocampal couplings in memory task. (a) Hippocampal-parahippocampal coherence at the gamma band (35-55 Hz) was greater during memory retrieval than during memory encoding (p=0.001, signed-rank test, n=47). (b) Hippocampal PAC statistics was greater during memory encoding than during memory retrieval (p=0.017, signed-rank test, n=69). (c) Comparisons of population-averaged (n=30) normalized spectral Granger causality (SGC) in four memory task periods. A peak at beta frequency (20-30 Hz) was noticeable in all SGC profiles. (d) Comparison of hippocampal iEEG power at theta (5-9 Hz) and gamma (35-55 Hz) bands between successful and unsuccessful trials during memory encoding. Unsuccessful memory trials had significantly greater theta (p<0.00001) and gamma (p=0.021) power than successful trials. (e) Population SGC statistics (n=30) within the gamma band between the hippocampus and the parahippocamus in memory encoding. The SGC strength during unsuccessful trials was significantly greater in the hippocampusàparahippocampus direction (p=0.0238, signed-rank test), and showed a greater trend in the hippocampusàparahippocampus direction (p=0.0570, signed-rank test). .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 24 Supplementary Information Hippocampal-parahippocampal coupling in human episodic and working memory Xinyu Chen and Zhe Sage Chen Supplementary Note Projection of wave vector in TW detection. Consider the wave propagation in a three-dimensional space (Supplementary Fig. 1a). When the recording electrodes are arranged in a line, the recorded wave vector will represent the projection of the actual wave vector onto the line. Similarly, if the electrodes are arranged on a plane, the recorded wave vector will correspond to the projection of the actual vector onto the plane. Overestimation of TW propagation speed. Because of the electrode layout may not completely align with the actual TW direction (from source to destination), we measured the wave speed via the “recorded” phase velocity in a specific direction constrained by the recording electrode locations, which is always greater than the actual phase velocity. As shown in Supplementary Fig. 1b, let’s consider a 2D plane wave with angle 𝜃 between the electrode axis and the actual wave vector. If the wave is recorded along one axis only, it will appear that the wave propagates directly from point a’ to point e, rather than propagating along its true path from point a to point e. Consequently, the perceived distance the wave propagates within the same time interval would be greater, resulting in overestimated phase velocity. This can be illustrated using the following equations: 𝑘" = 𝑘 cos𝜃, 𝑣 = 𝜔/𝑘 and 𝑣" = 𝜔/𝑘 cos𝜃 ≥ 𝑣, where 𝑣 denotes the phase velocity, 𝜔 denotes the oscillatory frequency, and 𝑘 denotes the spatial frequency. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 25 Supplementary Table 1. Summary of experimental subjects (n=30) containing hippocampal TWs used in the analysis. The dominant TW oscillation was centered at the midpoint within the range [Low freq, High freq]. Subject Age Sex Handed -ness # sess. Accuracy rate Low freq High freq # params Electrode channels R1032D 19 F R 2 0.29 6 8 1 LOTD2, LOTD3, LOTD4, LOTD5, LOTD6 ROTD2, ROTD3, ROTD4, ROTD5 R1035M 45 F A 1 0.29 8 10 1 LA4, LB1, LB2, LB3, LC2 R1045E 51 M R 2 0.40 5 7 1 LAHD3, LAHD4, LAHD5 LMHD1, LMHD2, LMHD3 R1056M 34 M A 1 0.75 6 8 1 RB1, RB2, RB3 R1061T 21 M R 1 0.29 7 9 1 LB1, LB2, LB3 RB1, RB2, RB3 R1065J 34 F R 4 0.65 8 10 1 LE1, LE2, LE3, LE4 LA1, LA2, LA3, LA4 LD1, LD2, LD3, LD4, LD5 LC1, LC2, LC3, LC4 RC1, RC2, RC3, RC4 R1066P 39 M R 3 0.26 8 10 1 RDA2, RDA3, RDH3 R1083J 49 F R 1 0.06 6.5 8.5 1 LC1, LC2, LC3, LD2, LD3 R1092J 44 M R 1 0.31 7 9 2 LAH1, LAH2, LH1, LH2, LH3 R1094T 47 M R 1 0.12 6 8 1 LB1, LB2, LB3, LB4 RB2, RB3, RB4 R1102P 34 M R 2 0.32 7 8 1 LDH1, LDH2, LDH3 RDA1, RDA2, RDA3 R1108J 23 F R 4 0.42 8 10 1 RC1, RC2, RC3, RC4, RD1 R1112M 29 F R 1 0.19 7 9 2 RMD1, RMD2, RMD3, RPD1, RPD2 R1174T 29 M R 1 0.28 7 8 1 LB1, LB2, LB3 LC2, LC3, LC4 R1190P 57 F R 2 0.16 10 12 1 LDH2, LDH3, LDH4 R1212P 46 M R 1 0.13 8 10 1 RDA1, RDA2, RDH1, RDH2, RDH3 R1228M 58 F R 1 0.29 5 7 2 LA2, LA3, LA4, LB1, LB2, LB3, LB4 R1239E 27 M R 2 0.30 7 9 1 3LD2, 3LD3, 3LD4 4RD1, 4RD2, 4RD3, 4RD4 R1254E 29 M R 1 0.14 7 9 1 3LD2, 3LD3, 3LD4 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 26 R1273D 48 F L 3 0.16 6 8 2 LAD2, LHD2, LHD3, LHD4 R1291M 35 M R 2 0.54 6 8 1 LMD1, LMD2, LMD3 R1293P 38 M R 1 0.47 7 8 1 LA1, LA2, LA3, LA4 R1303E 62 F R 1 0.25 7 9 1 4RD1, 4RD2, 4RD3, 4RD4 3LD1, 3LD2, 3LD3, 3LD4 6RD1, 6RD2, 6RD3 R1310J 20 M R 2 0.42 7 9 1 RD2, RD3, RD4 LB1, LB2, LB3 LD1, LD2, LD3 R1315T 22 M R 1 0.17 6 8 1 LB1, LB2, LB3 R1320D 56 M R 3 0.09 6 8 1 RAHD2, RAHD3, RAHD4, RAHDMICRO3 R1332M 26 M R 1 0.57 11 14 1 LH1, LH2, LH3, LH4 RM1, RM2, RM3 R1334T 38 F R 1 0.27 5 7 1 LB1, LB2, LB3, LB4 R1337E 55 M R 2 0.30 8 10 1 2RD1, 2RD2, 2RD3 R1342M 41 M R 1 0.20 6 8 1 LB1, LB2, LB3, LB4 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 27 Supplementary Table 2. Summary of experimental subjects (n=22) containing parahippocampal TWs used in the analysis. The dominant TW oscillation was centered at the midpoint within the range [Low freq, High freq]. Note that four subjects were also included in Supplementary Table 1. Subject Age Sex Handed -ness # sess. Accuracy rate Low freq High freq # params Electrode channels R1013E 36 F R 1 0.27 6 8 1 RP1, RP2, RP3, RP4 R1065J 34 F R 4 0.65 6 8 1 LE6, LE7, LD5 R1066P 39 M R 3 0.26 8 10 2 LDA1, LDA4, LDH1, LDH2, LDH3 R1086M 20 M L 1 0.12 5 6 2 LATD1, LATD2, LATD3, LMTD1, LMTD2 R1089P 36 M L 1 0.17 8 10 1 LDH1, LDH2, LDH3 R1107J 25 M R 2 0.57 8 10 1 LAIT1, LAIT2, LAIT3, LAIT4, LAIT5, LAIT6 R1111M 20 M R 2 0.58 7 9 1 LTD1, LTD2, LTD3, LTD4 R1119P 26 F L 1 0.09 11 12.5 1 LDH1, LDH2, LDH3, LDH4 R1138T 41 M R 2 0.17 6 8 1 RC1, RC2, RC3 RF1, RF3, RF4 R1157C 22 M R 3 0.31 8 10 1 MT1, MT2, MT3 R1188C 25 F R 1 0.55 6 8 2, 1 TP1, TP2, TP3, HB1 TO1, TO2, TO3, TO4 R1239E 27 M R 2 0.30 7 9 1 4RD6, 6RD3, 6RD4 R1266J 47 F L 1 0.15 8 10 2 LC1, LC2, LD1, LD2, LD3 R1278E 21 F R 2 0.30 8 10 1 6RD1, 6RD2, 6RD3 R1288P 53 M R 1 0.08 6 7 1 RC1, RC2, RC3 R1293P 38 M R 1 0.47 7 8 1 RA1, RA2, RA3 R1422T 24 F R 1 0.46 7 8 1 RF1, RF2, RF3, RF4 R1436J 33 F R 1 0.33 7 9 1 RC2, RC3, RC4, RC5 R1486J 38 M R 4 0.48 6 8 1 LA1, LA2, LA3 RA1, RA2, RA3, RA4 R1627T 55 F R 2 0.42 8 10 1 LF1, LF2, LF3 R1672T 52 M R 5 0.34 8 10 1 LF1, LF2, LF3 R1674A 24 F R 4 0.35 6 8 1 LBT1, LBT2, LBT3 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 28 Supplementary Figure 1. Illustration of wave vector projection and overestimation of wave speed. (a) In the 3D space, the recorded wave vector ki represents the projection of the actual wave vector k onto the line (left) if the recording electrodes (red dots) lie on a 1D line, or represents the projection of the actual wave vector k onto the plane if the recording electrodes lie on a 2D plane (right). (b) Cartoon illustration of the difference between the actual TW path (a-b-c-d-e) and the perceived TW path (a’-b’-c’-d’-e), where two paths have an angle 𝜃. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 29 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 30 Supplementary Figure 2. Hippocampal TW detection in one representative subject (#R1092J). (a) Illustration of implanted electrode locations covering the left hippocampus (blue) and the parahippocampus. (b) Power spectral density (PSD) of hippocampal iEEG signals. Shade area denotes the theta band (5-9 Hz). Normalized power by removing 1/f background is shown in the inset. (c) Illustrated bidirectional TW snapshots with both posterior -to-anterior (‘P -to-A’) and anterior -to- posterior (‘A-to-P’) projection directions. Arrows show the propagation direction. (d) 2D regression between the phase shift and electrode displacement, showing for P-to-A (i) and A- to-P (ii) projection directions. (e) Distribution of TW speed for P-to-A (i) and A-to-P (ii) projection directions. (f) Comparison of hippocampal theta power between two propagation directions. (g) Distribution of TW propagation directions across four different task phases , where N denotes the number of detected TW events. The duration percentage of two propagation directions (P-to-A vs. A-to-P) is shown at the bottom of polar histogram. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 31 Supplementary Figure 3. Parahippocampal TW detection in one representative subject (#R1107J). .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 32 (a) Illustration of implanted electrode locations covering the left parahippocampus. Note that recording electrode locations were arranged in a line along the L-R axis. (b) Power spectral density (PSD) of parahippocampal iEEG signals. Shade area denotes the theta band (5-9 Hz). Normalized power by removing 1/f background is shown in the inset. (c) Illustrated bidirectional TW snapshots with both L-to-R and R-to-L propagation directions. Arrows show the wave propagation direction. (d) Linear regression between the phase shift and the electrode displacement for two opposite propagation directions. (e) Distribution of TW direction across four different task phases , where N denotes the number of detected TW events. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 33 .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 34 Left hemisphereRight hemisphere 10 s unsuccessful successful P-to-A A-to-P A-to-P -> A-to-P P-to-A -> P-to-AP-to-A -> A-to-P A-to-P -> P-to-A Countdown Encoding Distraction task Retrieval b P-to A -> A-to-P A-to-P -> P-to-A Left hemisphere, dominant direction: P-to-A P-to-A -> P-to-A A-to-P -> A-to-P Time interval (s) 0 10 20 30 40 50 Right hemisphere, dominant direction: A-to-P 0 10 20 30 40Time interval (s) c a 250 ms Subject #R1032D HIPP Traveling Waves (TWs) EC HIPP Traveling Waves (TWs) PH P to A A to P CountDown 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Phase Locking Value 5 10 15 20 25 30 35 40 P-to A -> A-to-P A-to-P -> P-to-A P-to-A -> P-to-A A-to-P -> A-to-P d Freq (Hz) 5 10 15 20 25 30 35 40 45 0.5 0.4 0.3 0.2 0.1 0.0 Freq (Hz) Coherence P to A A to P CountDown EC (left) vs PH (right) EC (left) vs PH (right) .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 35 Supplementary Figure 4. Synchronization statistics of hippocampal TWs occurring at two hemispheres (subject #R1032D). (a) A snapshot of temporally overlapping hippocampal TW events simultaneously occurred at two hemispheres during memory retrieval. Shaded area denotes the detected TW events. (b) Illustration of the changes in hippocampal TWs directions at two hemispheres during a complete trial. (c) Summary statistics of time intervals between two consecutive hippocampal TWs from two hemispheres. (d) Hippocampal TWs enhanced phase synchronization (left) and coherence (right) between the EC and the parahippocampus located at the two opposite hemispheres. .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 36 Supplementary Figure 5. Population statistics of detected parahippocampal TWs. (a) Distribution of bidirectional parahippocampal TW propagation for all subjects (N=22). (b) The number of total detected parahippocampal TW events among P-to-A and A-to-P propagation directions for selected subjects (N=8). (c) Distribution of spatial frequency of detected parahippocampal TW events (pooled from all subjects). (d) Duration fraction of hippocampal TWs (for all propagation directions) at four different task phases among 22 subjects and 25 channel clusters. Each dot represents a channel cluster. P to A A to P 1000 500 0 500 1000 b Counts a A P c 0 2 4 6 8 10 12 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Distribution Spatial frequency (mm -1) N=8 subjects N=22 subjects 0.0 0.1 0.2 0.3 0.4 Countdown Encoding Distraction Task Retrieval Duration fraction of TWs d 22 subjects, 25 channel clusters Duration {A-to-P} Duration {P-to-A} = 52:48 Parahippocampal TWs .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint 37 Supplementary Figure 6. Summary of recording electrode locations in the hippocampus and parahippocampus regions used in Granger causality analysis (n=30 subjects). Left Left Right Right Parahippocampus/ Entorhinal Cortex channels Hippocampus channels .CC-BY-NC-ND 4.0 International licenseavailable under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprintthis version posted December 15, 2024. ; https://doi.org/10.1101/2024.12.10.627735doi: bioRxiv preprint