Grid cells are neurons in the entorhinal cortex that are thought to perform computations in support of spatial navigation. As direct recordings of grid cells from the human brain are only rarely possible, functional magnetic resonance imaging (fMRI) studies proposed and described an indirect measure of entorhinal grid-cell activity, which is quantified as a hexadirectional modulation (HM) of fMRI activity as a function of the subject’s movement direction through a virtual environment. However, the contributing role of the aggregated activity of grid cells to this modulation remains unclear. Our research addresses the unresolved question concerning the origin of HM of activity in the entorhinal cortex, as observed in fMRI, iEEG, and MEG studies (e.g. Doeller et al., Nature, 2010; Staudigl et al., Curr Biol, 2018; Convertino et al., Brain, 2023). Here, we explored three hypotheses through both numerical simulations and analytical calculations: head-direction tuning (conjunctive grid by head-direction cell hypothesis); firing-rate adaptation (repetition suppression hypothesis); or a bias towards a certain grid phase offset (structure-function mapping hypothesis). We defined the neural hexasymmetry as a new measure of HM, while introducing a novel method of quantifying the path hexasymmetry, which is the contribution of the subject's trajectory to the hexasymmetry. We observed that the effect sizes depended on i) the simulated subjects' trajectory through the environment, and ii) the exact properties of grid cells. Motivated by these findings, our simulated agent explored the environment using three types of navigation designed to resemble trajectories in human and rodent experiments involving grid cells. We also defined two sets of parameters for each hypothesis: an `ideal' set maximizing the effect size and a `realistic' set which we obtained from existing empirical studies of human grid cells. Our findings indicate that all three hypotheses can account for HM of sum grid-cell activity in ideal conditions. However, when including grid-cell properties found in the literature, our simulations most strongly support the conjunctive grid by head-direction cell hypothesis. In contrast, our simulations do not support the structure-function mapping hypothesis. With respect to the repetition-suppression hypothesis, our simulations are insufficient to substantiate or refute it, and further experiments on the adaptation properties of single grid cells are required.