Abstract
Recent human functional magnetic resonance imaging (fMRI) and animal electrophysiology studies suggest that grid cells in entorhinal cortex are an efficient neural mechanism for encoding knowledge about the world, not only for spatial location but also for more abstract cognitive information. The world, be it physical or abstract, is often high-dimensional, but grid cells have been mainly studied on a simple two-dimensional (2D) plane. Recent theoretical studies have proposed how grid cells encode three-dimensional (3D) physical space, but it is unknown whether grid codes can be examined non-invasively in humans. Here, we investigated whether it was feasible to test different 3D grid models using fMRI based on the direction-modulated property of grid signals. In doing so, we developed interactive software to help researchers visualize 3D grid fields and predict grid activity in 3D as a function of movement directions. We found that a direction-modulated grid analysis was sensitive to one type of 3D grid model – a face-centred cubic (FCC) lattice model. As a proof of concept, we searched for 3D grid-like signals in human entorhinal cortex using a novel 3D virtual reality paradigm and a new fMRI analysis method. We found that signals in the left entorhinal cortex were explained by the FCC model. This is preliminary evidence for 3D grid codes in the human brain, notwithstanding the inherent methodological limitations of fMRI. We believe that our findings and software serve as a useful initial stepping-stone for studying grid cells in realistic 3D worlds and also, potentially, for interrogating abstract high-dimensional cognitive processes.
Highlights
Grid cells in entorhinal cortex (EC) have received much attention from researchers in the field of spatial navigation because of their unique firing pattern
A principle for detecting 3D grid codes using functional magnetic resonance imaging (fMRI) Before we propose a method for detecting 3D grid codes, we will first summarise how 2D grid codes have been probed in previous fMRI studies. fMRI measures the gross activity of thousands of neurons via complex neural-hemodynamic coupling
Another explanation for the direction-modulated grid signal measured by fMRI is that when a participant's movement direction is aligned with the main grid axis, relatively few grid cells are repeatedly activated, whereas when the movement is not aligned with the main grid axis, more cells are irregularly activated
Summary
Grid cells in entorhinal cortex (EC) have received much attention from researchers in the field of spatial navigation because of their unique firing pattern. Human fMRI studies have observed grid-like signals that encode locations during mental imagery (Bellmund et al, 2016; Horner et al, 2016), features of abstract visual stimuli (Constantinescu et al, 2016) and eye position during 2D visual search (Nau et al, 2018; Julian et al, 2018). This suggests that grid cells may be suitable for more abstract “cognitive mapping” (Tolman, 1948). Grid cells should be able to efficiently encode 3D and higher dimensional space (unless the high dimensional cognitive problem can be projected into low dimensional space, e.g. context-dependent encoding)
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