Empirically validated theoretical analysis of visual-spatial perception under change of nervous system arousal

Abstract

Introduction: Visual-spatial perception is a process for extracting the spatial relationship between objects in the environment. The changes in visual-spatial perception due to factors such as the activity of the sympathetic nervous system (hyperactivation) or parasympathetic nervous system (hypoactivation) can affect the internal representation of the external visual-spatial world. We formulated a quantitative model of the modulation of visual-perceptual space under action by hyperactivation or hypoactivation-inducing neuromodulating agents. We showed a Hill equation based relationship between neuromodulator agent concentration and alteration of visual-spatial perception utilizing the metric tensor to quantify the visual space.

Methods: We computed the dynamics of the psilocybin (hyperactivation-inducing agent) and chlorpromazine (hypoactivation-inducing agent) in brain tissue. Then, we validated our quantitative model by analyzing the findings of different independent behavioral studies where subjects were assessed for alterations in visual-spatial perception under the action of psilocybin and under chlorpromazine. To validate the neuronal correlates, we simulated the effect of the neuromodulating agent on the computational model of the grid-cell network, and also performed diffusion MRI-based tractography to find the neural tracts between the cortical areas involved: V2 and the entorhinal cortex.

Results: We applied our computational model to an experiment (where perceptual alterations were measured under psilocybin) and found that for n (Hill-coefficient) = 14.8 and k = 1.39, the theoretical prediction followed experimental observations very well (χ2 test robustly satisfied, p > 0.99). We predicted the outcome of another psilocybin-based experiment using these values (n = 14.8 and k = 1.39), whereby our prediction and experimental outcomes were well corroborated. Furthermore, we found that also under hypoactivation (chlorpromazine), the modulation of the visual-spatial perception follows our model. Moreover, we found neural tracts between the area V2 and entorhinal cortex, thus providing a possible brain network responsible for encoding visual-spatial perception. Thence, we simulated the altered grid-cell network activity, which was also found to follow the Hill equation.

Conclusion: We developed a computational model of visuospatial perceptual alterations under altered neural sympathetic/parasympathetic tone. We validated our model using analysis of behavioral studies, neuroimaging assessment, and neurocomputational evaluation. Our quantitative approach may be probed as a potential behavioral screening and monitoring methodology in neuropsychology to analyze perceptual misjudgment and mishaps by highly stressed workers.

Keywords: Hill equation; autonomic nervous system; diffusion tensor imaging; grid cell; metric tensor; psilocybin; spatial perception; visual cortex.

FIGURE 1

Conceptual illustration of the physical space and perceived visual space under the influence of th drug-induced activation of the autonomic nervous system.

FIGURE 2

(A) Grid cells encode the navigational space by integrating the self-motion information for path integration. (B) Our formulation of the metric representation of the visual space by grid cells by integrating the information about the eye movements for path integration like process.

FIGURE 3

(A) Rotated ellipse represents the geometry of the perceived space under psilocybin administration. (B) The spherical coordinate system for locating a point in three-dimensional visual space. (C) Left panel: Alteration of Gaussian curvature of the perceptual space, the curvature being estimated at the fixation point O. Right panel: Alteration of the rotation angle of the perceptual space, the rotation being estimated from the perspective of the subject at the center of the ellipse. For both panels, the change in the alteration is shown at different time points after psilocybin ingestion.

FIGURE 4

(Lower left panel) The ellipse represents the geometry of the perceived space in the horizontal plane where “a” and “b” are the length of the major axis and minor axis (the ellipse is in the horizontal plane). Here, the subject is sitting at the center of the ellipse and looking along the y-axis, i.e., looking directly forward, while sitting in the experimental chair with a chin-rest. Before the experiment starts, the vertical rods are arranged in the vertical fronto-parallel plane. (Lower right panel) The coordinate system for measuring the angular coordinate of a point on the ellipse. [Upper right panel (Inset box)] The alteration of the metric tensor at point O (fixation point), at four successive time points: time t = 0 (just before the experiment, no psilocybin given), then at time points t = 90, 180, and 270 min after psilocybin ingestion.

FIGURE 5

Psilocybin concentration in the brain’s extracellular space after oral ingestion.

FIGURE 6

(A) Variation of the sum of squared residual with the Hill coefficient (n) and the Half-effect drug concentration (k). At n = 14.8 units (left panel) and k = 1.39 picomoles/cm³ (right panel), the sum of squared residual is minimum, showing the optimum fit. (B) The curve shows the mathematically calculated alterations in the metric tensor component of the perceptual space (solid line) while the psilocybin concentration changes. The filled circles show the experimentally derived metric tensor components along with the corresponding value of the modulation index (M) and the time duration since the start of psilocybin ingestion (in minutes). Note the close correspondence of the experimental data-points to the theoretical curve. Indeed, the mathematical model is well validated by the experimentally measured observations, which is further corroborated by robust satisfaction of the goodness-of-fit criterion (χ² statistical test firmly satisfied, p > 0.99).

FIGURE 7

(A) Metric tensor of the perceived space obtained from corresponding experimentally measured spatial distortion threshold at four successive time points: time t = 0 (just before experiment, no psilocybin given), then at time points t = 60, 110 and 280 min after psilocybin ingestion. (B) The metric tensor of perceptual space under the psilocybin induced hyperactivation condition. The theoretically computationally predicted values are shown in blue filled circle, while the experimentally derived values are shown by the red cross. Observe the strong congruence of the experimental points with the theoretical points. Actually, the theoretical model is soundly validated by the empirical data as substantiated by strong satisfaction of goodness-of-fit criterion (there is robust satisfaction of the χ²-squared statistical test).

FIGURE 8

(A) Numerical values of the metric tensor components of the perceived space obtained from experimentally recorded spatial distortion threshold at time t = 0, 210, and 450 min after ingestion of 50 mg oral intake of chlorpromazine. (B) Predicted chlorpromazine concentration (picomoles/cm³) in the brain’s extracellular fluid as calculated from the theoretical computational model (chlorpromazine input is 50 mg). (C) The curve shows the predicted alteration in the mathematically calculated metric tensor component of the perceptual space (solid line) while the chlorpromazine concentration changes. The filled circles show the experimentally derived data-points estimating the metric tensor components. For each experimental data-point, there is shown the time duration since the start of chlorpromazine ingestion (in minutes). Note the close correspondence of the experimental data-points to the theoretical computational curve. Indeed the mathematical model is well corroborated by the experimentally measured observations.

FIGURE 9

Anatomical connectivity (neural tracts) between the entorhinal cortex and visual cortex (area V2) in the sixteen subjects obtained after performing the tractography experiment. The neural tracts in the remaining fourteen subjects are shown in Supplementary Figure S7.

FIGURE 10

Activity of the neuronal nodes under no-drug condition (A) when eyes are not moving and fixating in the visual field (B) when eyes are making a constant movement in the visual field (C) when eyes are randomly scanning in the visual field. (D) Variation in the angular position of the eyeball movements during constant eye movement (upper) and random eye movement (lower).

FIGURE 11

Activity of the neuronal nodes under drug-induced activation: (A) activation pattern of the nodes under the different values of the △I = 0.05, 0.15, 0.25, and 0.30. (B) Variation in the activity of node number 47 as the △I changes from 0 to 0.30.

FIGURE 12

(A) Change in the periodic activation of the neuronal nodes for different values of the △I. (B) Activity of the neuronal node 47 for the different values of the △I and time. (C) Variation in the angular coordinates of the moving fixation point. At the origin, t = 0 s: θ = 0 and Φ = 0; thereafter, θ and Φ are increasing linearly with time, indicating that eyes move with a constant velocity across both angular directions.

FIGURE 13

(A) Activity pattern of the neuronal nodes for the different values of the △I, as the eyeball is moving randomly in the visual field. (B) Temporal variation in the activity of neuronal node 47 for the different values of △I. (C) Variation in the angular coordinates of the randomly moving fixation point.

FIGURE 14

(A) Spatiotemporal distance (L) for a particular value of the △I. We calculated L for the different values of the △I. (B) Experimentally calculated activity index (filled circles) using the neural network-based model of grid cell network, and the corresponding Hill equation curve is also shown. (C,D) Variation of the sum of squared residual with the Hill coefficient (n) and k. At n = 1.8 and k = 0.07, the sum of squared residuals is minimum and optimally fits the observed data points.