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# Sense of self impacts spatial navigation and hexadirectional coding in human entorhinal cortex

## Abstract

Grid cells in entorhinal cortex (EC) encode an individual’s location in space and rely on environmental cues and self-motion cues derived from the individual’s body. Body-derived signals are also primary signals for the sense of self and based on integrated sensorimotor signals (proprioceptive, tactile, visual, motor) that have been shown to enhance self-centered processing. However, it is currently unknown whether such sensorimotor signals that modulate self-centered processing impact grid cells and spatial navigation. Integrating the online manipulation of bodily signals, to modulate self-centered processing, with a spatial navigation task and an fMRI measure to detect grid cell-like representation (GCLR) in humans, we report improved performance in spatial navigation and decreased GCLR in EC. This decrease in entorhinal GCLR was associated with an increase in retrosplenial cortex activity, which was correlated with participants’ navigation performance. These data link self-centered processes during spatial navigation to entorhinal and retrosplenial activity and highlight the role of different bodily factors at play when navigating in VR.

## Introduction

The discovery of grid cells in rodent entorhinal cortex (EC) has shed new light on the neural mechanisms of spatial representation1,2. Grid cells are place-modulated neurons believed to represent the location of an individual and are defined by characteristic spatial firing field maps corresponding to hexagonal grid patterns that tile a given environment3,4. Entorhinal grid cell activity is modulated by sensory cues from the environment as well as by motion-related cues from the individual (i.e., self-motion cues)1,2,5,6. While the field maps of grid cells have been shown to depend on distal landmarks and field boundaries1,7, their periodicity is maintained in darkness and across different environments and landmark changes1,8. This suggests that movement-related signals from the body also provide a considerable input to grid cells. Indeed, subsequent studies demonstrated the primary importance of such self-motion cues from the body for generating and maintaining grid representations9,10,11. Overall, these findings support the proposal that grid cells keep track of an individual’s location in space by relying on both self-motion cues and environmental sensory information5,12.

Self-motion cues are body-derived cues based on sensory and motor signals from the individual’s body during spatial navigation and include proprioceptive, tactile, vestibular, and motor signals2,5,13. Under normal conditions, the self is bound to the location of the physical body and experienced at the place occupied by the body. Although this association between self and body is a central feature of self-consciousness, captured by the concept of bodily self-consciousness (BSC)14,15,16, it can be modulated experimentally. Thus, recent research using virtual reality (VR) has shown that non-ordinary BSC states, such as illusory self-identification for an avatar or virtual body, can be induced by employing the online manipulation of sensory and motor signals from the individual’s body15,17. In some BSC paradigms18,19,20, participants receive tactile stimulation while viewing an avatar as seen from behind and projected in front of them that receives the same tactile stimulation (third-person viewpoint). In other BSC paradigms, the avatar is shown from a first-person viewpoint, while participants are exposed to visuotactile stimulation on the chest21,22. Both types of BSC studies showed that such enhanced self-centered processing results from integrated body-derived stimuli (proprioception, vision, touch) that are spatially and temporally congruent. Recent BSC studies further demonstrated that such enhanced self-centered processing associated with BSC changes also impact egocentric spatial processes (size perception23,24,25,26, spatial semantic distance27), linking BSC not just to self-centered processing, but also to spatial processing. However, whereas the key importance of body-derived sensorimotor signals in grid cells is well documented, it is currently unknown whether and how online sensorimotor bodily stimulations in VR, which have been shown to enhance self-centered processing linked to BSC, impact entorhinal grid cell activity. Here, we sought to investigate whether sensorimotor signals that enhance self-centered processing in a BSC paradigm implemented during spatial navigation in VR would modulate grid cell-like activity in EC.

## Results

### Avatar-related changes in BSC enhance spatial navigation performance

We adopted a spatial navigation task from previous fMRI studies30,31 to assess spatial navigation performance and BSC, and to calculate GCLR (Fig. 1a; see Methods). Each session started with an encoding phase, in which participants had to memorize the locations of three objects. Following encoding, for each trial, a cue indicated a specific target object that participants had to recall and reach by navigating to it in the arena. At the end of each retrieval trial, the distance between the recalled location and its correct location (i.e., “distance error”) was determined. Navigation trace length and navigation time were also recorded in order to quantify spatial navigation performance. To assess the influence of BSC (self-identification) on grid cell-like activity as reflected in GCLR, we designed two experimental conditions and induced different levels of self-identification with the avatar by providing different online sensorimotor stimulation during the task. In the Body condition, supine participants saw, from their first-person viewpoint, a supine virtual avatar, which was spatially congruent with their own body position. As shown in Fig. 1a, we also showed the virtual right hand of the avatar (and a virtual joystick) that carried out the same movements as the participant’s right hand on the physical joystick in the scanner. Such spatial congruency between the participant’s body and the avatar’s body (or alignment of bodily reference frames; see methods for further detail) has been investigated in previous BSC research and shown to induce higher levels of self-identification with the avatar37,38. By contrast, the No-body condition did neither contain an avatar nor the right-hand movements and served as a control condition, for which we expected no or less self-identification as compared to the Body condition. Importantly, the No-body condition is identical to most previous human GCLR studies30,31.

We assessed BSC by asking participants to rate their self-identification with the avatar (Q1: Self-Identification), to rate experienced threat (in response to a virtual knife that was seen as approaching the part of the arena where the virtual avatar was located) (Q2: Threat; see Methods and Supplementary Fig. 1c), and also assessed two control items (Q3, Q4; see Methods). As predicted, ratings to Q1 and Q2 were higher in the Body vs. No-body condition (paired two-sided Wilcoxon signed-rank test, Q1: Z = 3.02, r = 0.60, p = 2.53e-03; Q2: Z = 3.80, r = 0.76, p = 1.42e-04, n = 25; Fig. 2a), indicating that our manipulation was effective in modulating BSC. Although we cannot exclude the influence of the demand characteristics while our participants were responding to the questionnaire, they did not give different ratings in the control questions, making it less likely that the observed effects were merely driven by the biases (i.e., no difference across conditions in control questions; Q3: Z = 0.57, r = 0.11, p = 0.569 Q4: Z = 1.05, r = 0.21, p = 0.293; see Methods; Supplementary Fig. 1a). Post-experiment debriefing confirmed these results (see Methods; Supplementary Fig. 1b).

To assess the influence of the BSC modulation on spatial navigation and memory, we compared spatial navigation/memory performance during both conditions. All participants were able to navigate in the virtual environment and complete the task while being scanned in the MRI scanner (Fig. 2b). Interestingly, participants showed better spatial memory precision as indexed by lower distance errors in the Body vs. No-body condition (mixed-effects regression; df = 1, F = 11.18, p = 8.25e-04, n = 27; Fig. 2d). Navigation efficiency was also improved, as participants carried out shorter paths in the Body condition vs. the No-body condition (df = 1, F = 8.46, p = 3.81e-03; Supplementary Fig. 2a), while average navigation time did not differ across conditions (df = 1, F = 0.21, p = 0.648; Supplementary Fig. 2b). These results demonstrate that the Body condition induces higher self-identification with the virtual avatar (as indexed by Q1 and Q2), as well as higher spatial navigation/memory performance in the virtual environment.

Of note, participants stopped navigating significantly farther from the arena’s border in the Body condition (i.e., the condition where they see a self-identified avatar in front of them) compared to the No-body condition (df = 1, F = 52.29, p = 4.80e-13, n = 27; Fig. 2e, f). This navigational difference was consistently observed in 22 out of 27 participants. Our finding is compatible with spatial changes, referred to as a drift in self-location toward a self-identified avatar, reported by previous research on BSC using different behavioral measures18,19,39,40. Thus, when self-identifying with the avatar seen in front of them, our participants stopped before reaching the intended destination, in turn, farther from the border (Fig. 2e). This link between the drift in spatial navigation and BSC was further confirmed by the significant relationship between the drift and BSC ratings (i.e., Threat; Q2): the more participants felt threatened by the virtual knife directed to where the avatar was, the farther they stopped away from the arena’s border before reaching the target (1.00 ± 0.27 vm; predicted by mixed-effects regression; df = 1, F = 11.23, p = 0.0263 without the multiple testing correction for two questions (Q1&Q2), n = 25; Fig. 2g). Of note, we did not find a significant correlation between Q1 and the drift. We reiterate that spatial memory precision was higher in the Body condition, despite the fact that, on average, participants stopped farther from the optimal target point (5 vm) in the Body condition (6.38 ± 0.70 vm away from the border; Fig. 2f-red) compared to the No-body condition (5.38 ± 0.67 vm; Fig. 2f-blue). Thus, although it could be argued that the drift may worsen the distance error in the Body condition (participants stopped too early), the opposite was the case for overall spatial navigation performance. Two types of angular errors were calculated in order to further assess spatial memory, eliminating the influence of the drift in self-location effect on the spatial memory precision. The results show that both types of the angular errors were also significantly lower in the Body condition (type 1: mixed-effects regression; df = 1, F = 5.397, p = 0.020, n = 27; type 2: df = 1, F = 7.21; p = 7.25e-3; Supplementary Fig. 2c).

To summarize, these behavioral results show that the Body condition was characterized by higher self-identification with the avatar and drift in self-location influencing navigational behavior, and, importantly, by an improvement in spatial navigation performance.

### Grid cell-like representation decreases when spatial navigation is performed with a self-identified avatar

We next assessed whether these changes in BSC and spatial navigation were associated with changes in grid cell activity as reflected by GCLR in EC. As a first step, we confirmed the recruitment of GCLR in our task regardless of the experimental condition, applying previously established methods30,32,35. A putative grid orientation ($$\varphi$$) of each session was estimated with the other five sessions of fMRI images matched with heading direction$$\,(\theta )$$ information. Based on the calculated grid orientation, the GCLR of each session was determined by the magnitude of the sixfold symmetric fluctuation as a function of the heading direction (see Methods). This analysis revealed a significant hexadirectional BOLD signal modulation, GCLR, in EC when our participants navigated in the virtual environment (sinusoidal regressor: Z = 2.23, r = 0.45, p = 0.0128, Fig. 3b; aligned vs. misaligned contrast: Z = 2.00, r = 0.40, p = 0.0226, n = 25, Fig. 3c), replicating earlier data30 (also see Supplementary Fig. 3).

Next, we determined GCLR differences between the two conditions by calculating condition-wise GCLR using cross-validation, which was designed to be independent of the other sessions and, in turn, each condition (see Methods). These results confirmed that GCLR was present in the No-body condition (the condition that is similar to conditions used by previous human spatial navigation and GCLR studies; Z = 2.83, r = 0.57, p = 2.30e-03, n = 25; Fig. 3d). GCLR was absent in the Body condition (Z = 0.69, r = 0.14, p = 0.245; Fig. 3d), which is the condition with enhanced BSC and spatial navigation performance. Within-subject comparisons between both conditions confirmed significantly lower GCLR in the Body vs. No-body condition (Z = 2.26, r = 0.45, p = 0.0236). We further assessed whether the difference in GCLR between the conditions is related to the difference in the behavioral parameters (e.g., navigated trace length, distance to the border). In-depth control analyses with the resampled datasets that have the inverted or non-significant condition-wise differences in those behavioral parameters again corroborated our results, showing that GCLR was prominent only in the No-body condition regardless of the behavioral parameters (see Supplementary Note 3 and Supplementary Figs. 8, 9).

## Discussion

Here we show that signals that are of relevance for BSC impact grid cell-like activity by inducing a state of enhanced self-centered processing (enhanced self-identification with an avatar during spatial navigation; i.e., Body condition) during a spatial navigation task. The Body condition was associated with improved spatial navigation performance and decreased GCLR in EC, which has been proposed to reflect the activity of grid cell populations30,31,32,33,34,35. This unexpected decrease in entorhinal GCLR was associated with an increase in RSC activity, another major spatial navigation region45,54,55. Moreover, RSC activity, stronger during the Body condition, was correlated with our participants’ navigation performance. These data link self-centered processes during spatial navigation to entorhinal and retrosplenial activity.

We report that enhanced self-related processing, induced by sensorimotor congruency between our participants’ physical body and the seen corresponding avatar during spatial navigation improved spatial navigation performance. Participants committed smaller distance errors and navigated in shorter paths when seeing the avatar associated with synchronous sensorimotor stimulation (Fig. 2c, d). Previous work has revealed that modulations of BSC not only alter body- and self-related processes39,56,57, but also affect spatial representation and episodic memory24,27,58,59. The present data extend BSC to spatial navigation.

Entorhinal grid cell activity in animals and humans has been consistently shown to depend on self-motion-related cues, originating from the individual’s body, as well as sensory cues from the environment1,2,5,6,11. Prior human studies have also observed GCLR linked to various cognitive functions related to spatial representation30,33,34,35,62,63. However, it is not known how GCLR in humans depends on self-centered processes related to BSC and self-identification with a body in particular. In the present study, we provide fresh insights into this relationship. Interestingly, contrary to our initial prediction, we observed a decrease of GCLR in EC in the Body condition, while the typical hexadirectional modulation in EC was observed during the condition that was similar to previous spatial navigation studies (i.e., the No-body condition)30,31,32. Accordingly, the present data link GCLR reduction to enhanced self-centered processing characterized by enhanced self-identification with an avatar.

EC is not the sole brain region that determines spatial navigation performance. For example, Kunz et al. (2015) reported that compensatory mechanisms in the hippocampus account for GCLR reduction despite maintained spatial navigation performance31. Spatial navigation is based on activity within a large distributed network, involving IPS/PPC, RSC, and several other regions44,45,46,48,72,73,74, also supported by the whole-brain analysis in the present study revealing activations in bilateral retrosplenial cortex (RSC), bilateral parahippocampal gyrus and right lingual gyrus42,43,44,45. From these regions, only RSC activity was significantly enhanced in the Body condition, where we also observed reduced GCLR. Moreover, we further associated higher RSC activation with improved spatial navigation performance (i.e., smaller distance error). These data are compatible with a compensatory role of RSC activity for the decreased GCLR in EC. This is in line with the recent work by Bierbrauer et al. (2020), which suggests that RSC is involved in compensatory navigational mechanisms when GCLR is affected (i.e., in a genetic risk group for Alzheimer’s disease)70. Thus, in the present study, increased right RSC activity in the BSC condition may reflect compensatory mechanisms for decreases in entorhinal GCLR.

Thus, the attenuation of entorhinal GCLR could also be related to decreased reliance on allocentric spatial processing associated with the boosted egocentric processing by the BSC modulation, further corroborated by increased activity in posterior parietal regions (i.e., IPS, RSC) associated with the decreased GCLR (see Fig. 4). In support of our proposal, previous work consistently linked human RSC activation to spatial navigation45,47,54,55,75,76,77 and RSC has been proposed to be important for orienting to landmarks70, a central feature of our experimental design as distal landmarks only provided orientation cues. Moreover, clinical research consistently linked human RSC damage (especially of right RSC) to orientation impairments in spatial navigation47,78,79. Hence, the correlation we observed between RSC activation and spatial memory precision (i.e., distance error) extends previous findings on the role of RSC in spatial navigation and adds the important finding that spatial navigation-related activity in RSC, depends on the level of BSC. RSC has been regarded as a mediator between self-centered (egocentric) and environmental (allocentric) processes in PPC and medial EC, respectively54,55. RSC integrates body-derived self-motion cues while mapping one’s location in the environment80,81. Moreover, RSC has also prominently been associated with several self-related cognitive processes beyond spatial navigation, such as self-orientation in time82, across social dimensions83, integration of self-referential stimuli84, autobiographical memory85,86, and BSC15,49,50.

Finally, the present IPS data further extend the BSC-related changes we observed in RSC and EC. IPS, and more generally PPC, is regarded as a core region for egocentric spatial representation in humans46,52,87,88. Supporting this human work, rodent studies reported that neurons in PPC encode self-centered cues independent of the external environment (e.g., self-motion and acceleration) during navigation89,90. In addition, many human BSC studies reported IPS activation when key components of BSC (e.g., self-location and self-identification) were modulated by multisensory stimuli, and IPS is considered a key BSC region14,15,49,50,51. Reporting increased IPS activity associated with solid behavioral evidence of drift in self-location during spatial navigation when our participants navigated with a self-identified avatar, these IPS and RSC data extend previous BSC neuroimaging findings to the field of spatial navigation. In the Body condition, we observed increased IPS activation that has been linked with BSC and egocentric spatial processing. Many previous studies showed that body-referenced cues (e.g., vestibular, motor, and proprioceptive signals) are processed in PPC and provide crucial inputs to grid cells10,11,28,91. We argue that the present data link BSC-related processing as manipulated by online sensorimotor stimulation to egocentric processes in IPS and to allocentric grid cells in EC, suggesting that human grid cell-like activity in EC reflects ego- and allocentric processing demands. Enhanced RSC activity in the Body condition and the mediating role of RSC between ego- and allocentric processes in spatial navigation, as well as between PPC and EC54,55, is compatible with this suggestion. Accordingly, we propose that the BSC changes, characterized by strengthened self-centered processing referenced to the avatar, associate enhanced egocentric, self-centered, processing in IPS, with altered ego- and allocentric processing in RSC, and with reduced allocentric spatial representation, GCLR in EC.

The present results associate enhanced spatial navigation performance with decreased GCLR in EC when participants were navigating during an enhanced BSC state (i.e., navigating with a self-identified avatar), showing that enhanced self-centered bodily processing boosted navigation behavior and decreased entorhinal GCLR. These decreases in entorhinal GCLR were associated with increases in RSC activity, another major spatial navigation region that has been shown to mediate between ego- and allocentric spatial representation. Moreover, RSC activity, stronger during the Body condition, was correlated with our participants’ navigation performance. These data link the sense of self behaviorally and neurally to spatial navigation and opposing activations in the entorhinal and retrosplenial cortex.

## Methods

### Participants

Twenty-seven healthy right-handed participants (13 males and 14 females; mean age 25.3 ± 1.96) with normal or corrected-to-normal vision were recruited from the general population. The number of participants, 27, was chosen according to the minimum sample size calculated from Nau et al. (2018) to reproduce conventional grid cell-like representation. Participants were naive to the purpose of the study, gave informed consent in accordance with the institutional guidelines (IRB #: GE 15-273) and the Declaration of Helsinki (2013), and received monetary compensation (CHF20/hour). Two participants who entered random answers to the questionnaire were excluded from the questionnaire analysis (i.e., both pressed the response button repeatedly at incorrect moments during the experiment; further confirmed by post-experiment debriefing). A participant whose structural image was examined as abnormal by a medical investigator was excluded from the fMRI analysis. Another participant was excluded from the grid cell-like representation analyses due to severe image distortions and signal drop in EC (~2.3% of voxels in the EC were above the global average of mean EPI). A session with head drift greater than 3 mm was also excluded from fMRI analyses.

Stereoscopic visual stimuli were provided via MRI-compatible goggles (VisualSystem, Nordic NeuroLab: 800 × 600 resolution, 40 Hz refresh rate). An MRI-compatible joystick (Tethyx, Current Designs) was used to perform the task inside the MRI scanner. The task program including the virtual arena and virtual objects was implemented with Unity Engine (Unity Technologies, https://unity3d.com).

In total, the experiment consisted of six sessions divided into three blocks, aimed at comparing the two conditions (Fig. 1b) in terms of both brain activity and spatial navigation performances. The order of the conditions was pseudo-randomized within each block and counterbalanced between participants (N-B/B-N/N-B or B-N/N-B/B-N). As the task was self-paced, the duration of each session varied depending on the participant’s performance (mean round duration: 9.0 ± 0.70 min), but didn’t differ between the conditions (t-test: p = 0.92).

### BSC modulation with the virtual body

The Body condition with a neutral body-shaped avatar was designed to experimentally modulate BSC, more specifically, to enhance self-identification with the virtual avatar in the VR environment compared to the baseline: the No-body condition. The avatar was designed to be gender-neutral and gray-skinned without hair. The virtual body was in the same posture as a participant—supine—and its right hand was shown as congruent with respect to the participant’s hand movements controlling the joystick. These settings of avatar were chosen to achieve sensorimotor congruency between the participant’s body and the avatar, which has been reported to lead to self-identification with the avatar37,38,92,93.

### Questionnaire

At the end of each session, participants were asked to answer four questions using a Likert scale ranging from −3 (strongly disagree) to 3 (strongly agree). The questions were randomly ordered across sessions and participants answered with the joystick. Q1 (“I felt as if what I saw in the middle of the scene was my body”) was intended to measure self-identification with the avatar. Q2 (“I felt as if the threat (knife) was toward me”) was also designed to measure the degree of threat towards the participant. Q3 (“I felt dizzy”) sought to measure cybersickness (Supplementary Fig. 1a). Q4 (“I felt as if I had three bodies”) served as a general control question. A short debriefing was carried out after participants had completed the experiment.

### Prescreening and training in the Mock scanner

The participants were trained to perform the spatial navigation task in a mock scanner. The training consisted of one session of the No-body condition and lasted around 10 min, keeping them naive to the experimental condition. To avoid potential carryover effects, we used different virtual objects and environments than those used in the main experiment. This training also allowed us to exclude participants experiencing a severe cybersickness caused by navigation in the VR environment94.

### MRI data acquisition

MRI data were acquired at the Human Neuroscience Platform of the Campus Biotech (Geneva, Switzerland), with a 3 T MRI scanner (SIEMENS, MAGNETOM Prisma) equipped with a 64-channel head-and-neck coil. The task-related functional images covering the entire brain were acquired with a T2*-weighted Echo Planar Imaging (EPI) sequence with the following parameters: TR = 1000 ms, TE = 32 ms, Slice thickness = 2 mm (no gap), In-plane resolution = 2 mm × 2 mm, Number of slices = 66, Multiband factor = 6, FoV = 225 mm, Flip angle = 50˚, slice acquisition order = interleaved. The structural image per participant was recorded with a T1-weighted MPRAGE sequence with the following parameters: TR = 2300 ms, TE = 2.25 ms, TI = 900 ms, Slice thickness = 1 mm, In-plane resolution = 1 mm × 1 mm, Number of slices = 208, FoV = 256 mm, Flip angle = 8˚. In addition to that, B0 field map (magnitude and phase information, respectively) was acquired to correct EPI distortion by inhomogeneous magnetic fields (especially, near the medial temporal lobe).

### fMRI data preprocessing

MRI data were preprocessed with SPM12 (http://www.fil.ion.ucl.ac.uk/spm). Functional images were slice-time corrected, realigned, unwarped using a B0 field map, and coregistered with the individual T1-weighted structural image. For the conventional generalized linear model(GLM) analysis (e.g., region-of-interest (ROI) analysis of task-related regions and IPS), the images were normalized to Montreal Neurological Institute (MNI) space, to allow a second-level GLM analysis designed to localize commonly activated brain regions across participants. Following previous studies, other analyses regarding grid cell-like hexadirectional modulation with the EC as a main ROI were conducted in the native space without normalization to avoid additional signal distortion31,32. All preprocessed functional images were smoothed with a 5 mm full-width-half-maximum Gaussian smoothing kernel as the final preprocessing step.

### Definition of the EC ROI in participants’ native space

Participant-wise EC ROIs for the analysis of grid cell-like representations(GCLR) were defined using Freesurfer (v6.0.0, http://surfer.nmr.mgh.harvard.edu) as described in previous studies31,95. Briefly, a cortical parcellation was automatically conducted by the software with the individual T1 structural images based on the Desikan-Killiany Atlas96. The bilateral EC labels generated from the parcellation were taken as an individual ROI and were examined manually by overlapping them on the corresponding structural image. Subsequently, the ROIs in the “freesurfer conformed space” were transformed into volume ROIs in the participant’s native space and, then, coregistered and resliced to the mean EPI images.

### Analysis of grid cell-like representation (GCLR)

The Grid Code Analysis Toolbox (GridCAT v1.03, https://www.nitrc.org/projects/gridcat) under MATLAB 2018b (The Mathworks) was used to analyze GCLR97, following a seminal method which was proposed by Doeller et al. (2010). The analysis was comprised of two steps with mutually exclusive datasets. As a first step, with one of the partitioned datasets, a first GLM (GLM 1) was used to calculate $${\beta }_{1}$$ and $${\beta }_{2}$$, using two parametric modulation regressors: $${\cos }\left(6{\theta }_{t}\right)$$ and $${\sin }(6{\theta }_{t})$$ respectively, where $${\theta }_{t}$$ is heading direction during the navigation in time(t). Then, using the betas, voxel-wise amplitude($$A$$) and grid orientations($$\varphi$$) were respectively estimated by

$$A=\sqrt{{\beta }_{1}^{\,2}+{\beta }_{2}^{\,2}}$$
(1)
$$\varphi ={{\tan }}^{-1}({\beta }_{2}/{\beta }_{1})/6$$
(2)

In the second part of the analysis, a putative grid orientation was calculated by the weighted average of the voxel-wise grid orientations($$\varphi$$) in the ROI (i.e., EC) with the voxel-wise amplitude($$A$$) of each voxel as its weight. Subsequently, based on the putative grid orientation($$\varphi$$) and moving direction information($${\theta }_{t}$$), a second GLM (GLM2) estimates an amplitude of GCLR in the EC, selectively (1) by contrasting regressors for navigation toward grid-aligned ($$\varphi$$ + 0,60,120,…,300) vs. misaligned ($$\varphi$$ + 30,90,150,…,330) direction or (2) by applying a sixfold symmetric sinusoidal parametric modulation regressor:

$${\cos }\left(6\left({\theta }_{t}-\varphi \right)\right)$$
(3)

We calculated GCLRs with both methods respectively, to confirm that our result does not depend on either of the methods. In order to optimally utilize all available data and improve the signal-to-noise ratio, a cross-validation method with multiple partitions was adopted35, instead of dividing the data into two equal halves. An amplitude of sixfold representation for a given session was calculated based on the grid orientation estimated with the other five sessions and the process was repeated for every session. The session-wise results were summed together to estimate the overall grid cell-like representation of the participant.

### Calculation of condition-wise GCLR

The classical GCLR in the previous step was calculated with all six sessions without taking into account the experimental condition of each session, which implies that each estimate does not purely represent a magnitude of the hexadirectional modulation in the corresponding experimental condition. Besides, as two different experimental conditions were timely intermingled, grid orientations across sessions even within the same condition could be unstable, which critically affects the GCLR estimation31,32. Hence, we calculated session-wise BOLD contrasts between aligned vs. misaligned movement independently from the other sessions, using data from the single session only. Leave-one-out cross-validation with ten partitions was performed for each session to optimally utilize the dataset and maximize the signal-to-noise ratio (See the Methods section above)35. In more detail, each session was divided into multiple three-second (3 s) bins. The first out of each of these ten bins became the first partition (where the bin index modulo 10 equals 1) and each second bin from every ten bins became the second partition (bin index modulo 10 equals 2), and so forth until the tenth partition. Notably, this method was dedicated to the comparison of GCLR between the Body and No-body condition, rather than the demonstration of hexadirectional modulation in contrast to the controls (e.g., four/five/seven-fold symmetry) which was already fulfilled. Calculated session-wise results were averaged by condition to get the condition-wise GCLR, which is robust to potential temporal instability of grid orientations across sessions.

### Temporal and spatial stabilities of grid orientations

Spatial stability was defined as the homogeneity of voxel-wise grid orientations within EC. To assess the spatial stability of a session, Rayleigh’s test for non-uniformity of circular data was calculated with the voxel-wise grid orientations within EC. Rayleigh’s z-value was taken as an index of the spatial stability of the session31,32. Temporal stability was defined as the stability of grid orientations over time. For each session, it was computed by the circular standard deviation of ten grid orientations estimated during each of the ten cross-validations of GCLR described above. Of note, the ten grid orientations were calculated with ten different data portions from different time points. Therefore temporally stable grid orientations should remain similar across folds, resulting in a small standard deviation (Supplementary Note 1).

### Generalized linear model (GLM) analysis to detect task-related brain regions

Whole-brain GLM analysis using normalized functional images was performed to detect brain regions, possibly accounting for changes in spatial navigation performance. Beta values during the task phase were extracted using GLM analysis with the tailored regressors using SPM12 (Supplementary Table 1). First, with the parametric modulation regressor, we searched for brain regions where its activation during the ‘Retrieval’ phase was correlated with the “distance error”. However, this analysis did not reveal any significant clusters after the voxel-level family-wise error correction (FWE). Second, we assessed contrasts (Body > No-body) during the task phases before participants finished the retrieval procedure (i.e., Cue + Retrieval), as such responses could be responsible for the spatial navigation performance of the trial. However, again, no cluster (extent threshold >20 voxels) survived after voxel-level FWE correction (p < 0.05).

### ROI analysis of task-related BOLD activity by using the functional localizer

Next, we performed ROI analysis to investigate brain regions involved in spatial navigation performance. Functional ROIs relevant to the spatial navigation task were defined by the functional contrast (Task: Cue + Retrieval + Feedback + Collection > implicit baseline; i.e., orthogonal to the conditions of interest: the Body and No-body) in second-level GLM using a voxel-level threshold family-wise error-corrected for multiple comparisons of p < 0.05 and using an extent threshold of 20 voxels (Fig. 4a; Supplementary Fig. 5; and Supplementary Table 2). In order to search for task-related activity accounting for improved spatial navigation, mean beta values within the ROIs during the task phases before reaching the recalled location (i.e., Cue + Retrieval) were compared between the two experimental conditions.

### ROI analysis of intraparietal sulcus region (IPS)

We anatomically defined the ROI for the bilateral IPS based on the normalized functional images (in MNI space) by using SPM Anatomy Toolbox based on the Jülich probabilistic cytoarchitectonic maps98. Betas during the Retrieval phase in IPS were compared between the Body and No-body conditions.

### Statistics and reproducibility

Statistical assessments for behavioral and fMRI data were performed with R (v3.5.3 for Windows, https://www.r-project.org/) and RStudio (v1.2.1335, http://www.rstudio.com). Outlying data points outside of the standard deviation range, −3 to 3, were excluded from the statistical analysis. For the behavioral parameters having a value per trial (distance errors, navigation trace length and time, distance from the border), mixed-effects regressions (lme4_1.1-18-1, a package of R), which include condition as a fixed effect and random intercepts for individual participants, were used to assess statistical significance. Random slopes were included as far as there were no estimation failures. For the other parameters with no single-trial estimates (e.g., questionnaire ratings, spatial/temporal stability of the grid orientation, task-related BOLD activity), a non-parametric two-sided Wilcoxon signed-rank test was used. The conventional sixfold patterns of GCLR were assessed with a one-sided Wilcoxon signed-rank test, as expected from previous work30,35. However, the condition-wise comparison of the GCLRs was performed with a two-sided test. To indicate the effect size of the Wilcoxon signed-rank test, r values were calculated with the following formula:

$${{{{{\rm{r}}}}}}={{{{{\rm{Z}}}}}}/\sqrt{N}$$
(4)

Assessments of correlations were conducted using mixed-effect regression models so that the condition-induced effects within participants are properly taken into account by the random effect of a participant, in addition to the across-participants effect. In order to assume the best-fit distribution and apply proper parameters for each mixed-effects regression used, data distribution of each dependent variable was assessed using fitdistrplus(v1.0-11, a package of R).

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

The data underlying the results and the main figures of this study have been uploaded on the open science framework (https://doi.org/10.17605/OSF.IO/U8VHA) and are open to the public.

## Code availability

The customized codes that were used for this study are available on the open science framework (https://doi.org/10.17605/OSF.IO/U8VHA) and open to the public.

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## Acknowledgements

This work was supported by the Korean Government Scholarship Program for study overseas, the Korea Institute of Science and Technology (KIST) Institutional Program (2E31642), and the Bertarelli Foundation to H.-J.M. O.B. is supported by the Swiss National Science Foundation (No. 320030_188798) and by the Bertarelli Foundation. N.F. has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant 803122). Additional support was provided by the Fondation Campus Biotech Geneva (FCBG)—a foundation of the Swiss Federal Institute of Technology Lausanne (EPFL), the University of Geneva (UniGe), and the Hôpitaux Universitaires de Genève (HUG), the Institute of Translational Molecular Imaging (ITMI).

## Author information

Authors

### Contributions

Conceptualization, H.-J.M., B.G, H.-D.P., and O.B.; Methodology, H.-J.M., B.G., H.-D.P., and N.F.; Software, H.-J.M.; Formal analysis, H.-J.M., and N.F.; Investigation, H.-J.M.; Writing—original draft, H.-J.M.; Writing—review and editing, B.G., H.-D.P., N.F., and O.B.; Resources, H.-J.M.; Funding acquisition and supervision, O.B.

### Corresponding author

Correspondence to Olaf Blanke.

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Moon, HJ., Gauthier, B., Park, HD. et al. Sense of self impacts spatial navigation and hexadirectional coding in human entorhinal cortex. Commun Biol 5, 406 (2022). https://doi.org/10.1038/s42003-022-03361-5

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• DOI: https://doi.org/10.1038/s42003-022-03361-5