Hyperbolic planforms in relation to visual edges and textures perception

We propose to use bifurcation theory and pattern formation as theoretical probes for various hypotheses about the neural organization of the brain. This allows us to make predictions about the kinds of patterns that should be observed in the activity of real brains through, e.g. optical imaging, and opens the door to the design of experiments to test these hypotheses. We study the specific problem of visual edges and textures perception and suggest that these features may be represented at the population level in the visual cortex as a specific second-order tensor, the structure tensor, perhaps within a hypercolumn. We then extend the classical ring model to this case and show that its natural framework is the non-Euclidean hyperbolic geometry. This brings in the beautiful structure of its group of isometries and certain of its subgroups which have a direct interpretation in terms of the organization of the neural populations that are assumed to encode the structure tensor. By studying the bifurcations of the solutions of the structure tensor equations, the analog of the classical Wilson and Cowan equations, under the assumption of invariance with respect to the action of these subgroups, we predict the appearance of characteristic patterns. These patterns can be described by what we call hyperbolic or H-planforms that are reminiscent of Euclidean planar waves and of the planforms that were used in [1, 2] to account for some visual hallucinations. If these patterns could be observed through brain imaging techniques they would reveal the built-in or acquired invariance of the neural organization to the action of the corresponding subgroups.Comment: 34 pages, 11 figures, 2 table

The constitution of visual perceptual units in the functional architecture of V1

Scope of this paper is to consider a mean field neural model which takes into account the functional neurogeometry of the visual cortex modelled as a group of rotations and translations. The model generalizes well known results of Bressloff and Cowan which, in absence of input, accounts for hallucination patterns. The main result of our study consists in showing that in presence of a visual input, the eigenmodes of the linearized operator which become stable represent perceptual units present in the image. The result is strictly related to dimensionality reduction and clustering problems

A Model for the Origin and Properties of Flicker-Induced Geometric Phosphenes

We present a model for flicker phosphenes, the spontaneous appearance of geometric patterns in the visual field when a subject is exposed to diffuse flickering light. We suggest that the phenomenon results from interaction of cortical lateral inhibition with resonant periodic stimuli. We find that the best temporal frequency for eliciting phosphenes is a multiple of intrinsic (damped) oscillatory rhythms in the cortex. We show how both the quantitative and qualitative aspects of the patterns change with frequency of stimulation and provide an explanation for these differences. We use Floquet theory combined with the theory of pattern formation to derive the parameter regimes where the phosphenes occur. We use symmetric bifurcation theory to show why low frequency flicker should produce hexagonal patterns while high frequency produces pinwheels, targets, and spirals

Investigating the Mechanisms of Hallucinogen-Induced Visions Using 3,4-Methylenedioxyamphetamine (MDA): A Randomized Controlled Trial in Humans

The mechanisms of drug-induced visions are poorly understood. Very few serotonergic hallucinogens have been studied in humans in decades, despite widespread use of these drugs and potential relevance of their mechanisms to hallucinations occurring in psychiatric and neurological disorders.We investigated the mechanisms of hallucinogen-induced visions by measuring the visual and perceptual effects of the hallucinogenic serotonin 5-HT2AR receptor agonist and monoamine releaser, 3,4-methylenedioxyamphetamine (MDA), in a double-blind placebo-controlled study. We found that MDA increased self-report measures of mystical-type experience and other hallucinogen-like effects, including reported visual alterations. MDA produced a significant increase in closed-eye visions (CEVs), with considerable individual variation. Magnitude of CEVs after MDA was associated with lower performance on measures of contour integration and object recognition.Drug-induced visions may have greater intensity in people with poor sensory or perceptual processing, suggesting common mechanisms with other hallucinatory syndromes. MDA is a potential tool to investigate mystical experiences and visual perception

Flicker-light induced visual phenomena: Frequency dependence and specificity of whole percepts and percept features

Flickering light induces visual hallucinations in human observers. Despite a long history of the phenomenon, little is known about the dependence of flicker-induced subjective impressions on the flicker frequency. We investigate this question using Ganzfeld stimulation and an experimental paradigm combining a continuous frequency scan (1–50 Hz) with a focus on re-occurring, whole percepts. On the single-subject level, we find a high degree of frequency stability of percepts. To generalize across subjects, we apply two rating systems, (1) a set of complex percept classes derived from subjects’ reports and (2) an enumeration of elementary percept features, and determine distributions of occurrences over flicker frequency. We observe a stronger frequency specificity for complex percept classes than elementary percept features. Comparing the similarity relations among percept categories to those among frequency profiles, we observe that though percepts are preferentially induced by particular frequencies, the frequency does not unambiguously determine the experienced percept

Quasicrystal patterns in a neural field model

Doubly periodic patterns in planar neural field models have been extensively studied since the 1970s for their role in explaining geometric visual hallucinations. The study of activity patterns that lack translation invariance has received little, if any, attention. Here we show that a scalar neural field model with a translationally invariant kernel can support quasicrystal solutions and that these can be understood using many of the theoretical tools developed previously for materials science. Our approach is constructive in that we consider constraints on the nonlocal kernel describing interactions in the neural field that lead to the simultaneous excitation of two periodic spatial patterns with incommensurate wavelengths. The resulting kernel has a shape that is a modulation of a Mexican-hat kernel. In the neighborhood of the degenerate bifurcation of a homogeneous steady state, we use a Fourier amplitude approach to determine the value of a Lyapunov functional for various periodic and quasicrystal states. For some values of the parameters defining a translationally invariant synaptic kernel of the model, we find that quasicrystal states have the lowest value of the Lyapunov functional. We observe patterns of 12-fold, 10-fold, and 6-fold rotational symmetry that are stable, but none with 8-fold symmetry. We describe some of the visual hallucination patterns that would be perceived from these quasicrystal cortical patterns, making use of the well known inverse retinocortical map from visual neuroscience

Neural patterns of conscious visual awareness in the Riddoch syndrome

The Riddoch syndrome is one in which patients blinded by lesions to their primary visual cortex can consciously perceive visual motion in their blind field, an ability that correlates with activity in motion area V5. Our assessment of the characteristics of this syndrome in patient ST, using multimodal MRI, showed that: 1. ST's V5 is intact, receives direct subcortical input, and decodable neural patterns emerge in it only during the conscious perception of visual motion; 2. moving stimuli activate medial visual areas but, unless associated with decodable V5 activity, they remain unperceived; 3. ST's high confidence ratings when discriminating motion at chance levels, is associated with inferior frontal gyrus activity. Finally, we report that ST's Riddoch Syndrome results in hallucinatory motion with hippocampal activity as a correlate. Our results shed new light on perceptual experiences associated with this syndrome and on the neural determinants of conscious visual experience