On the neural origin of hexadirectional fMRI modulations

When human beings navigate through an environment, a conceptual space, memories or even imagined spaces, fMRI signals in select brain regions vary with movement direction, alternating in strength with a periodicity of 60 degrees. At the cellular level, certain neurons called grid-cells form a hexagonal lattice representation of physical space. Given that the axes of the lattices align across neurons, the concerted directional and spatial firing of populations of these neurons may form the basis of the hexadirectional modulation of the fMRI signal. However, the exact link between the two remains unclear. Multiple mechanisms have been proposed that could couple neuronal activity to the fMRI signal. These include (1) preferential neuronal discharge when the direction of motion coincides with the lattice axes, (2) repetition suppression when multiple fields are traversed in succession, or alternatively, (3) a nonlinear transduction step. Here, we propose targeted experiments that can distinguish these mechanisms, for which we assess the expected effect sizes via simulations. In particular, by introducing calibrated pauses between linear path segments, it is possible to differentiate the repetition-suppression hypothesis from the nonlinear transduction model. By additionally varying the subjects movement speed and path lengths, the proposed protocol can distinguish conjunctive neuronal tuning (in which neurons respond to both speed and location or direction and location) from the other hypotheses. Crucially, if either the repetition-suppression or the nonlinear-transduction hypothesis holds, then the scale of the lattices will play a role. According to our analysis, hexadirectional signals should emerge only when a linear path segment is longer than half of the spatial lattice period. As grid cells with different scales are grouped into distinct modules along the dorso-ventral axis of the entorhinal cortex, this may make it possible to non-invasively measure the hierarchy of grid scales in the human brain.