Bias in Human Path Integration Is Predicted by Properties of Grid Cells

Taking a shortcut: what mechanisms do fish use?

Path integration is a powerful navigational mechanism whereby individuals continuously update their distance and angular vector of movement to calculate their position in relation to their departure location, allowing them to return along the most direct route even across unfamiliar terrain. While path integration has been investigated in several terrestrial animals, it has never been demonstrated in aquatic vertebrates, where movement occurs through volumetric space and sensory cues available for navigation are likely to differ substantially from those in terrestrial environments. By performing displacement experiments with Lamprologus ocellatus, we show evidence consistent with fish using path integration to navigate alongside other mechanisms (allothetic place cues and route recapitulation). These results indicate that the use of path integration is likely to be deeply rooted within the vertebrate phylogeny irrespective of the environment, and suggests that fish may possess a spatial encoding system that parallels that of mammals.

Grid codes underlie multiple cognitive maps in the human brain

Grid cells fire at multiple positions that organize the vertices of equilateral triangles tiling a 2D space and are well studied in rodents. The last decade witnessed rapid progress in two other research lines on grid codes-empirical studies on distributed human grid-like representations in physical and multiple non-physical spaces, and cognitive computational models addressing the function of grid cells based on principles of efficient and predictive coding. Here, we review the progress in these fields and integrate these lines into a systematic organization. We also discuss the coordinate mechanisms of grid codes in the human entorhinal cortex and medial prefrontal cortex and their role in neurological and psychiatric diseases.

Dissociating effects of aging and genetic risk of sporadic Alzheimer's disease on path integration

Path integration is a spatial navigation ability that requires the integration of information derived from self-motion cues and stable landmarks, when available, to return to a previous location. Path integration declines with age and Alzheimer's disease (AD). Here, we sought to separate the effects of age and AD risk on path integration, with and without a landmark. Overall, 279 people participated, aged between 18 and 80 years old. Advanced age impaired the appropriate use of a landmark. Older participants furthermore remembered the location of the goal relative to their starting location and reproduced this initial view without considering that they had moved in the environment. This lack of adaptative behavior was not associated with AD risk. In contrast, participants at genetic risk of AD (apolipoprotein E ε4 carriers) exhibited a pure path integration deficit, corresponding to difficulty in performing path integration in the absence of a landmark. Our results show that advanced-age impacts landmark-supported path integration, and that this age effect is dissociable from the effects of AD risk impacting pure path integration.

A map of spatial navigation for neuroscience

Spatial navigation has received much attention from neuroscientists, leading to the identification of key brain areas and the discovery of numerous spatially selective cells. Despite this progress, our understanding of how the pieces fit together to drive behavior is generally lacking. We argue that this is partly caused by insufficient communication between behavioral and neuroscientific researchers. This has led the latter to under-appreciate the relevance and complexity of spatial behavior, and to focus too narrowly on characterizing neural representations of space-disconnected from the computations these representations are meant to enable. We therefore propose a taxonomy of navigation processes in mammals that can serve as a common framework for structuring and facilitating interdisciplinary research in the field. Using the taxonomy as a guide, we review behavioral and neural studies of spatial navigation. In doing so, we validate the taxonomy and showcase its usefulness in identifying potential issues with common experimental approaches, designing experiments that adequately target particular behaviors, correctly interpreting neural activity, and pointing to new avenues of research.

Spatial uncertainty and environmental geometry in navigation

Variations in the geometry of the environment, such as the shape and size of an enclosure, have profound effects on navigational behavior and its neural underpinning. Here, we show that these effects arise as a consequence of a single, unifying principle: to navigate efficiently, the brain must maintain and update the uncertainty about one's location. We developed an image-computable Bayesian ideal observer model of navigation, continually combining noisy visual and self-motion inputs, and a neural encoding model optimized to represent the location uncertainty computed by the ideal observer. Through mathematical analysis and numerical simulations, we show that the ideal observer accounts for a diverse range of sometimes paradoxical distortions of human homing behavior in anisotropic and deformed environments, including 'boundary tethering', and its neural encoding accounts for distortions of rodent grid cell responses under identical environmental manipulations. Our results demonstrate that spatial uncertainty plays a key role in navigation.

Redundancy and Reducibility in the Formats of Spatial Representations

Mental representations are the essence of cognition. Yet to understand how the mind works, one must understand not just the content of mental representations (i.e., what information is stored) but also the format of those representations (i.e., how that information is stored). But what does it mean for representations to be formatted? How many formats are there? Is it possible that the mind represents some pieces of information in multiple formats at once? To address these questions, I discuss a "case study" of representational format: the representation of spatial location. I review work (a) across species and across development, (b) across spatial scales, and (c) across levels of analysis (e.g., high-level cognitive format vs. low-level neural format). Along the way, I discuss the possibility that the same information may be organized in multiple formats simultaneously (e.g., that locations may be represented in both Cartesian and polar coordinates). Ultimately, I argue that seemingly "redundant" formats may support the flexible spatial behavior observed in humans and that researchers should approach the study of all mental representations with this possibility in mind.

Microcircuits for spatial coding in the medial entorhinal cortex

The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism's spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.

Bayesian decision theory and navigation

Spatial navigation is a complex cognitive activity that depends on perception, action, memory, reasoning, and problem-solving. Effective navigation depends on the ability to combine information from multiple spatial cues to estimate one's position and the locations of goals. Spatial cues include landmarks, and other visible features of the environment, and body-based cues generated by self-motion (vestibular, proprioceptive, and efferent information). A number of projects have investigated the extent to which visual cues and body-based cues are combined optimally according to statistical principles. Possible limitations of these investigations are that they have not accounted for navigators' prior experiences with or assumptions about the task environment and have not tested complete decision models. We examine cue combination in spatial navigation from a Bayesian perspective and present the fundamental principles of Bayesian decision theory. We show that a complete Bayesian decision model with an explicit loss function can explain a discrepancy between optimal cue weights and empirical cues weights observed by (Chen et al. Cognitive Psychology, 95, 105-144, 2017) and that the use of informative priors to represent cue bias can explain the incongruity between heading variability and heading direction observed by (Zhao and Warren 2015b, Psychological Science, 26[6], 915-924). We also discuss (Petzschner and Glasauer's , Journal of Neuroscience, 31(47), 17220-17229, 2011) use of priors to explain biases in estimates of linear displacements during visual path integration. We conclude that Bayesian decision theory offers a productive theoretical framework for investigating human spatial navigation and believe that it will lead to a deeper understanding of navigational behaviors.

Structuring Knowledge with Cognitive Maps and Cognitive Graphs

Humans and animals use mental representations of the spatial structure of the world to navigate. The classical view is that these representations take the form of Euclidean cognitive maps, but alternative theories suggest that they are cognitive graphs consisting of locations connected by paths. We review evidence suggesting that both map-like and graph-like representations exist in the mind/brain that rely on partially overlapping neural systems. Maps and graphs can operate simultaneously or separately, and they may be applied to both spatial and nonspatial knowledge. By providing structural frameworks for complex information, cognitive maps and cognitive graphs may provide fundamental organizing schemata that allow us to navigate in physical, social, and conceptual spaces.

Environmental deformations dynamically shift human spatial memory

Place and grid cells in the hippocampal formation are commonly thought to support a unified and coherent cognitive map of space. This mapping mechanism faces a challenge when a navigator is placed in a familiar environment that has been deformed from its original shape. Under such circumstances, many transformations could plausibly serve to map a navigator's familiar cognitive map to the deformed space. Previous empirical results indicate that the firing fields of rodent place and grid cells stretch or compress in a manner that approximately matches the environmental deformation, and human spatial memory exhibits similar distortions. These effects have been interpreted as evidence that reshaping a familiar environment elicits an analogously reshaped cognitive map. However, recent work has suggested an alternative explanation, whereby deformation-induced distortions of the grid code are attributable to a mechanism that dynamically anchors grid fields to the most recently experienced boundary, thus causing history-dependent shifts in grid phase. This interpretation raises the possibility that human spatial memory will exhibit similar history-dependent dynamics. To test this prediction, we taught participants the locations of objects in a virtual environment and then probed their memory for these locations in deformed versions of this environment. Across three experiments with variable access to visual and vestibular cues, we observed the predicted pattern, whereby the remembered locations of objects were shifted from trial to trial depending on the boundary of origin of the participant's movement trajectory. These results provide evidence for a dynamic anchoring mechanism that governs both neuronal firing and spatial memory.

Path integration in large-scale space and with novel geometries: Comparing vector addition and encoding-error models

Path integration is thought to rely on vestibular and proprioceptive cues yet most studies in humans involve primarily visual input, providing limited insight into their respective contributions. We developed a paradigm involving walking in an omnidirectional treadmill in which participants were guided on two sides of a triangle and then found their back way to origin. In Experiment 1, we tested a range of different triangle types while keeping the distance of the unguided side constant to determine the influence of spatial geometry. Participants overshot the angle they needed to turn and undershot the distance they needed to walk, with no consistent effect of triangle type. In Experiment 2, we manipulated distance while keeping angle constant to determine how path integration operated over both shorter and longer distances. Participants underestimated the distance they needed to walk to the origin, with error increasing as a function of the walked distance. To attempt to account for our findings, we developed configural-based computational models involving vector addition, the second of which included terms for the influence of past trials on the current one. We compared against a previously developed configural model of human path integration, the Encoding-Error model. We found that the vector addition models captured the tendency of participants to under-encode guided sides of the triangles and an influence of past trials on current trials. Together, our findings expand our understanding of body-based contributions to human path integration, further suggesting the value of vector addition models in understanding these important components of human navigation.

How do we remember where we have been? One important mechanism for doing so is called path integration, which refers to the computation of one’s position in space with only self-motion cues. By tracking the direction and distance we have walked, we can create a mental arrow from the current location to the origin, termed the homing vector. Previous studies have shown that the homing vector is subject to systematic distortions depending on previously experienced paths, yet what influences these patterns of errors, particularly in humans, remains uncertain. In this study, we compare two models of path integration based on participants walking two sides of a triangle without vision and then completing the third side based on their estimate of the homing vector. We found no effect of triangle shape on systematic errors, while the systematic errors scaled with path length logarithmically, similar to Weber-Fechner law. While we show that both models captured participants’ behavior, a model based on vector addition best captured the patterns of error in the homing vector. Our study therefore has important implications for how humans track their location, suggesting that vector-based models provide a reasonable and simple explanation for how we do so.

Efficient and flexible representation of higher-dimensional cognitive variables with grid cells

We shed light on the potential of entorhinal grid cells to efficiently encode variables of dimension greater than two, while remaining faithful to empirical data on their low-dimensional structure. Our model constructs representations of high-dimensional inputs through a combination of low-dimensional random projections and "classical" low-dimensional hexagonal grid cell responses. Without reconfiguration of the recurrent circuit, the same system can flexibly encode multiple variables of different dimensions while maximizing the coding range (per dimension) by automatically trading-off dimension with an exponentially large coding range. It achieves high efficiency and flexibility by combining two powerful concepts, modularity and mixed selectivity, in what we call "mixed modular coding". In contrast to previously proposed schemes, the model does not require the formation of higher-dimensional grid responses, a cell-inefficient and rigid mechanism. The firing fields observed in flying bats or climbing rats can be generated by neurons that combine activity from multiple grid modules, each representing higher-dimensional spaces according to our model. The idea expands our understanding of grid cells, suggesting that they could implement a general circuit that generates on-demand coding and memory states for variables in high-dimensional vector spaces.

Grid coding, spatial representation, and navigation: Should we assume an isomorphism?

Grid cells provide a compelling example of a link between cellular activity and an abstract and difficult to define concept like space. Accordingly, a representational perspective on grid coding argues that neural grid coding underlies a fundamentally spatial metric. Recently, some theoretical proposals have suggested extending such a framework to nonspatial cognition as well, such as category learning. Here, we provide a critique of the frequently employed assumption of an isomorphism between patterns of neural activity (e.g., grid cells), mental representation, and behavior (e.g., navigation). Specifically, we question the strict isomorphism between these three levels and suggest that human spatial navigation is perhaps best characterized by a wide variety of both metric and nonmetric strategies. We offer an alternative perspective on how grid coding might relate to human spatial navigation, arguing that grid coding is part of a much larger conglomeration of neural activity patterns that dynamically tune to accomplish specific behavioral outputs.

Deforming the metric of cognitive maps distorts memory

Environmental boundaries anchor cognitive maps that support memory. However, trapezoidal boundary geometry distorts the regular firing patterns of entorhinal grid cells, proposedly providing a metric for cognitive maps. Here we test the impact of trapezoidal boundary geometry on human spatial memory using immersive virtual reality. Consistent with reduced regularity of grid patterns in rodents and a grid-cell model based on the eigenvectors of the successor representation, human positional memory was degraded in a trapezoid environment compared with a square environment-an effect that was particularly pronounced in the narrow part of the trapezoid. Congruent with changes in the spatial frequency of eigenvector grid patterns, distance estimates between remembered positions were persistently biased, revealing distorted memory maps that explained behaviour better than the objective maps. Our findings demonstrate that environmental geometry affects human spatial memory in a similar manner to rodent grid-cell activity and, therefore, strengthen the putative link between grid cells and behaviour along with their cognitive functions beyond navigation.

Mesoscopic Neural Representations in Spatial Navigation

Recent evidence suggests that mesoscopic neural oscillations measured via intracranial electroencephalography exhibit spatial representations, which were previously only observed at the micro- and macroscopic level of brain organization. Specifically, theta (and gamma) oscillations correlate with movement, speed, distance, specific locations, and goal proximity to boundaries. In entorhinal cortex (EC), they exhibit hexadirectional modulation, which is putatively linked to grid cell activity. Understanding this mesoscopic neural code is crucial because information represented by oscillatory power and phase may complement the information content at other levels of brain organization. Mesoscopic neural oscillations help bridge the gap between single-neuron and macroscopic brain signals of spatial navigation and may provide a mechanistic basis for novel biomarkers and therapeutic targets to treat diseases causing spatial disorientation.

Spatial Updating Strategy Affects the Reference Frame in Path Integration

This study investigated how spatial updating strategies affected the selection of reference frames in path integration. Participants walked an outbound path consisting of three successive waypoints in a featureless environment and then pointed to the first waypoint. We manipulated the alignment of participants' final heading at the end of the outbound path with their initial heading to examine the adopted reference frame. We assumed that the initial heading defined the principal reference direction in an allocentric reference frame. In Experiment 1, participants were instructed to use a configural updating strategy and to monitor the shape of the outbound path while they walked it. Pointing performance was best when the final heading was aligned with the initial heading, indicating the use of an allocentric reference frame. In Experiment 2, participants were instructed to use a continuous updating strategy and to keep track of the location of the first waypoint while walking the outbound path. Pointing performance was equivalent regardless of the alignment between the final and the initial headings, indicating the use of an egocentric reference frame. These results confirmed that people could employ different spatial updating strategies in path integration (Wiener, Berthoz, & Wolbers Experimental Brain Research 208(1) 61-71, 2011), and suggested that these strategies could affect the selection of the reference frame for path integration.

Path integration maintains spatial periodicity of grid cell firing in a 1D circular track

Entorhinal grid cells are thought to provide a 2D spatial metric of the environment. In this study we demonstrate that in a familiar 1D circular track (i.e., a continuous space) grid cells display a novel 1D equidistant firing pattern based on integrated distance rather than travelled distance or time. In addition, field spacing is increased compared to a 2D open field, probably due to a reduced access to the visual cue in the track. This metrical modification is accompanied by a change in LFP theta oscillations, but no change in intrinsic grid cell rhythmicity, or firing activity of entorhinal speed and head-direction cells. These results suggest that in a 1D circular space grid cell spatial selectivity is shaped by path integration processes, while grid scale relies on external information.

In an open field, the preferential firing of grid cells on a hexagonal lattice is formed by integrating external as well as self-motion cues. Here, the authors show that on a 1D circular track, path integration cues shape the spatial selectivity of grid cells while external cues determine the scale of the grid.

Environmental deformations dynamically shift the grid cell spatial metric

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics.

Navigation in Real-World Environments: New Opportunities Afforded by Advances in Mobile Brain Imaging

A central question in neuroscience and psychology is how the mammalian brain represents the outside world and enables interaction with it. Significant progress on this question has been made in the domain of spatial cognition, where a consistent network of brain regions that represent external space has been identified in both humans and rodents. In rodents, much of the work to date has been done in situations where the animal is free to move about naturally. By contrast, the majority of work carried out to date in humans is static, due to limitations imposed by traditional laboratory based imaging techniques. In recent years, significant progress has been made in bridging the gap between animal and human work by employing virtual reality (VR) technology to simulate aspects of real-world navigation. Despite this progress, the VR studies often fail to fully simulate important aspects of real-world navigation, where information derived from self-motion is integrated with representations of environmental features and task goals. In the current review article, we provide a brief overview of animal and human imaging work to date, focusing on commonalties and differences in findings across species. Following on from this we discuss VR studies of spatial cognition, outlining limitations and developments, before introducing mobile brain imaging techniques and describe technical challenges and solutions for real-world recording. Finally, we discuss how these advances in mobile brain imaging technology, provide an unprecedented opportunity to illuminate how the brain represents complex multifaceted information during naturalistic navigation.

Human spatial representation: what we cannot learn from the studies of rodent navigation

Studies of human and rodent navigation often reveal a remarkable cross-species similarity between the cognitive and neural mechanisms of navigation. Such cross-species resemblance often overshadows some critical differences between how humans and nonhuman animals navigate. In this review, I propose that a navigation system requires both a storage system (i.e., representing spatial information) and a positioning system (i.e., sensing spatial information) to operate. I then argue that the way humans represent spatial information is different from that inferred from the cellular activity observed during rodent navigation. Such difference spans the whole hierarchy of spatial representation, from representing the structure of an environment to the representation of subregions of an environment, routes and paths, and the distance and direction relative to a goal location. These cross-species inconsistencies suggest that what we learn from rodent navigation does not always transfer to human navigation. Finally, I argue for closing the loop for the dominant, unidirectional animal-to-human approach in navigation research so that insights from behavioral studies of human navigation may also flow back to shed light on the cellular mechanisms of navigation for both humans and other mammals (i.e., a human-to-animal approach).

Spatial Representations in the Human Brain

While extensive research on the neurophysiology of spatial memory has been carried out in rodents, memory research in humans had traditionally focused on more abstract, language-based tasks. Recent studies have begun to address this gap using virtual navigation tasks in combination with electrophysiological recordings in humans. These studies suggest that the human medial temporal lobe (MTL) is equipped with a population of place and grid cells similar to that previously observed in the rodent brain. Furthermore, theta oscillations have been linked to spatial navigation and, more specifically, to the encoding and retrieval of spatial information. While some studies suggest a single navigational theta rhythm which is of lower frequency in humans than rodents, other studies advocate for the existence of two functionally distinct delta-theta frequency bands involved in both spatial and episodic memory. Despite the general consensus between rodent and human electrophysiology, behavioral work in humans does not unequivocally support the use of a metric Euclidean map for navigation. Formal models of navigational behavior, which specifically consider the spatial scale of the environment and complementary learning mechanisms, may help to better understand different navigational strategies and their neurophysiological mechanisms. Finally, the functional overlap of spatial and declarative memory in the MTL calls for a unified theory of MTL function. Such a theory will critically rely upon linking task-related phenomena at multiple temporal and spatial scales. Understanding how single cell responses relate to ongoing theta oscillations during both the encoding and retrieval of spatial and non-spatial associations appears to be key toward developing a more mechanistic understanding of memory processes in the MTL.

A Dynamic Bayesian Observer Model Reveals Origins of Bias in Visual Path Integration

Path integration is a strategy by which animals track their position by integrating their self-motion velocity. To identify the computational origins of bias in visual path integration, we asked human subjects to navigate in a virtual environment using optic flow and found that they generally traveled beyond the goal location. Such a behavior could stem from leaky integration of unbiased self-motion velocity estimates or from a prior expectation favoring slower speeds that causes velocity underestimation. Testing both alternatives using a probabilistic framework that maximizes expected reward, we found that subjects' biases were better explained by a slow-speed prior than imperfect integration. When subjects integrate paths over long periods, this framework intriguingly predicts a distance-dependent bias reversal due to buildup of uncertainty, which we also confirmed experimentally. These results suggest that visual path integration in noisy environments is limited largely by biases in processing optic flow rather than by leaky integration.

Contracted time and expanded space: The impact of circumnavigation on judgements of space and time

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Certain locations in the world can only be reached by circumnavigating obstacles.

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All travel times are underestimated and all distances are overestimated.

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Travel times are further compressed when circumnavigation is required.

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Distances are further expanded when circumnavigation is required.

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Temporal and spatial cognitive biases may be dissociable.

The ability to estimate distance and time to spatial goals is fundamental for survival. In cases where a region of space must be navigated around to reach a location (circumnavigation), the distance along the path is greater than the straight-line Euclidean distance. To explore how such circumnavigation impacts on estimates of distance and time, we tested participants on their ability to estimate travel time and Euclidean distance to learned destinations in a virtual town. Estimates for approximately linear routes were compared with estimates for routes requiring circumnavigation. For all routes, travel times were significantly underestimated, and Euclidean distances overestimated. For routes requiring circumnavigation, travel time was further underestimated and the Euclidean distance further overestimated. Thus, circumnavigation appears to enhance existing biases in representations of travel time and distance.

Ten Years of Grid Cells

The medial entorhinal cortex (MEC) creates a neural representation of space through a set of functionally dedicated cell types: grid cells, border cells, head direction cells, and speed cells. Grid cells, the most abundant functional cell type in the MEC, have hexagonally arranged firing fields that tile the surface of the environment. These cells were discovered only in 2005, but after 10 years of investigation, we are beginning to understand how they are organized in the MEC network, how their periodic firing fields might be generated, how they are shaped by properties of the environment, and how they interact with the rest of the MEC network. The aim of this review is to summarize what we know about grid cells and point out where our knowledge is still incomplete.

The Role of the Human Entorhinal Cortex in a Representational Account of Memory

Connectivity studies in animals form the basis for a representational view of medial temporal lobe (MTL) subregions. In this view, distinct subfields of the entorhinal cortex (EC) relay object-related and spatial information from the perirhinal and parahippocampal cortices (PRC, PHC) to the hippocampus (HC). Relatively recent advances in functional magnetic resonance imaging (fMRI) methodology allow examining properties of human EC subregions directly. Antero-lateral and posterior-medial EC subfields show remarkable consistency to their putative rodent and nonhuman primate homologs with regard to intra- and extra-MTL functional connectivity. Accordingly, there is now evidence for a dissociation of object-related vs. spatial processing in human EC subfields. Here, variance in localization may be integrated in the antero-lateral vs. posterior-medial distinction, but may additionally reflect process differences. Functional results in rodents further suggest material-specific representations may be more integrated in EC compared to PRC/PHC. In humans, however, evidence for such a dissociation between EC and PRC/PHC is lacking. Future research may elucidate on the unique contributions of human EC to memory, especially in light of its high degree of intrinsic and extrinsic connectivity. A thorough characterization of EC subfield function may not only advance our understanding of human memory, but also have important clinical implications.