What geometric visual hallucinations tell us about the visual cortex

Cortical spatiotemporal dimensionality reduction for visual grouping

The visual systems of many mammals, including humans, are able to integrate the geometric information of visual stimuli and perform cognitive tasks at the first stages of the cortical processing. This is thought to be the result of a combination of mechanisms, which include feature extraction at the single cell level and geometric processing by means of cell connectivity. We present a geometric model of such connectivities in the space of detected features associated with spatiotemporal visual stimuli and show how they can be used to obtain low-level object segmentation. The main idea is to define a spectral clustering procedure with anisotropic affinities over data sets consisting of embeddings of the visual stimuli into higher-dimensional spaces. Neural plausibility of the proposed arguments will be discussed.

Recent advances in the neuropsychopharmacology of serotonergic hallucinogens

Serotonergic hallucinogens, such as (+)-lysergic acid diethylamide, psilocybin, and mescaline, are somewhat enigmatic substances. Although these drugs are derived from multiple chemical families, they all produce remarkably similar effects in animals and humans, and they show cross-tolerance. This article reviews the evidence demonstrating the serotonin 5-HT2A receptor is the primary site of hallucinogen action. The 5-HT2A receptor is responsible for mediating the effects of hallucinogens in human subjects, as well as in animal behavioral paradigms such as drug discrimination, head twitch response, prepulse inhibition of startle, exploratory behavior, and interval timing. Many recent clinical trials have yielded important new findings regarding the psychopharmacology of these substances. Furthermore, the use of modern imaging and electrophysiological techniques is beginning to help unravel how hallucinogens work in the brain. Evidence is also emerging that hallucinogens may possess therapeutic efficacy.

Hallucinogen persisting perception disorder and the serotonergic system: a comprehensive review including new MDMA-related clinical cases

Hallucinogen persisting perception disorder (HPPD) is a drug-induced condition associated with inaccurate visual representations. Since the underlying mechanism(s) are largely unknown, this review aims to uncover aspects underlying its etiology. Available evidence on HPPD and drug-related altered visual processing was reviewed and the majority of HPPD cases were attributed to drugs with agonistic effects on serotonergic 5-HT₂A receptors. Moreover, we present 31 new HPPD cases that link HPPD to the use of ecstasy (MDMA), which is known to reverse serotonin reuptake and acts as agonist on 5-HT₂A receptors. The available evidence suggests that HPPD symptoms may be a result from a misbalance of inhibitory-excitatory activity in low-level visual processing and GABA-releasing inhibitory interneurons may be involved. However, high co-morbidities with anxiety, attention problems and derealization symptoms add complexity to the etiology of HPPD. Also, other perceptual disorders that show similarity to HPPD cannot be ruled out in presentations to clinical treatment. Taken together, evidence is still sparse, though low-level visual processing may play an important role. A novel finding of this review study, evidenced by our new cases, is that ecstasy (MDMA) use may also induce symptoms of HPPD.

From image processing to computational neuroscience: a neural model based on histogram equalization

There are many ways in which the human visual system works to reduce the inherent redundancy of the visual information in natural scenes, coding it in an efficient way. The non-linear response curves of photoreceptors and the spatial organization of the receptive fields of visual neurons both work toward this goal of efficient coding. A related, very important aspect is that of the existence of post-retinal mechanisms for contrast enhancement that compensate for the blurring produced in early stages of the visual process. And alongside mechanisms for coding and wiring efficiency, there is neural activity in the human visual cortex that correlates with the perceptual phenomenon of lightness induction. In this paper we propose a neural model that is derived from an image processing technique for histogram equalization, and that is able to deal with all the aspects just mentioned: this new model is able to predict lightness induction phenomena, and improves the efficiency of the representation by flattening both the histogram and the power spectrum of the image signal.

The ripple pond: enabling spiking networks to see

We present the biologically inspired Ripple Pond Network (RPN), a simply connected spiking neural network which performs a transformation converting two dimensional images to one dimensional temporal patterns (TP) suitable for recognition by temporal coding learning and memory networks. The RPN has been developed as a hardware solution linking previously implemented neuromorphic vision and memory structures such as frameless vision sensors and neuromorphic temporal coding spiking neural networks. Working together such systems are potentially capable of delivering end-to-end high-speed, low-power and low-resolution recognition for mobile and autonomous applications where slow, highly sophisticated and power hungry signal processing solutions are ineffective. Key aspects in the proposed approach include utilizing the spatial properties of physically embedded neural networks and propagating waves of activity therein for information processing, using dimensional collapse of imagery information into amenable TP and the use of asynchronous frames for information binding.

Activation of serotonin 2A receptors underlies the psilocybin-induced effects on α oscillations, N170 visual-evoked potentials, and visual hallucinations

Visual illusions and hallucinations are hallmarks of serotonergic hallucinogen-induced altered states of consciousness. Although the serotonergic hallucinogen psilocybin activates multiple serotonin (5-HT) receptors, recent evidence suggests that activation of 5-HT2A receptors may lead to the formation of visual hallucinations by increasing cortical excitability and altering visual-evoked cortical responses. To address this hypothesis, we assessed the effects of psilocybin (215 μg/kg vs placebo) on both α oscillations that regulate cortical excitability and early visual-evoked P1 and N170 potentials in healthy human subjects. To further disentangle the specific contributions of 5-HT2A receptors, subjects were additionally pretreated with the preferential 5-HT2A receptor antagonist ketanserin (50 mg vs placebo). We found that psilocybin strongly decreased prestimulus parieto-occipital α power values, thus precluding a subsequent stimulus-induced α power decrease. Furthermore, psilocybin strongly decreased N170 potentials associated with the appearance of visual perceptual alterations, including visual hallucinations. All of these effects were blocked by pretreatment with the 5-HT2A antagonist ketanserin, indicating that activation of 5-HT2A receptors by psilocybin profoundly modulates the neurophysiological and phenomenological indices of visual processing. Specifically, activation of 5-HT2A receptors may induce a processing mode in which stimulus-driven cortical excitation is overwhelmed by spontaneous neuronal excitation through the modulation of α oscillations. Furthermore, the observed reduction of N170 visual-evoked potentials may be a key mechanism underlying 5-HT2A receptor-mediated visual hallucinations. This change in N170 potentials may be important not only for psilocybin-induced states but also for understanding acute hallucinatory states seen in psychiatric disorders, such as schizophrenia and Parkinson's disease.

Coordinated optimization of visual cortical maps (I) symmetry-based analysis

In the primary visual cortex of primates and carnivores, functional architecture can be characterized by maps of various stimulus features such as orientation preference (OP), ocular dominance (OD), and spatial frequency. It is a long-standing question in theoretical neuroscience whether the observed maps should be interpreted as optima of a specific energy functional that summarizes the design principles of cortical functional architecture. A rigorous evaluation of this optimization hypothesis is particularly demanded by recent evidence that the functional architecture of orientation columns precisely follows species invariant quantitative laws. Because it would be desirable to infer the form of such an optimization principle from the biological data, the optimization approach to explain cortical functional architecture raises the following questions: i) What are the genuine ground states of candidate energy functionals and how can they be calculated with precision and rigor? ii) How do differences in candidate optimization principles impact on the predicted map structure and conversely what can be learned about a hypothetical underlying optimization principle from observations on map structure? iii) Is there a way to analyze the coordinated organization of cortical maps predicted by optimization principles in general? To answer these questions we developed a general dynamical systems approach to the combined optimization of visual cortical maps of OP and another scalar feature such as OD or spatial frequency preference. From basic symmetry assumptions we obtain a comprehensive phenomenological classification of possible inter-map coupling energies and examine representative examples. We show that each individual coupling energy leads to a different class of OP solutions with different correlations among the maps such that inferences about the optimization principle from map layout appear viable. We systematically assess whether quantitative laws resembling experimental observations can result from the coordinated optimization of orientation columns with other feature maps.

Generalized spin models for coupled cortical feature maps obtained by coarse graining correlation based synaptic learning rules

We derive generalized spin models for the development of feedforward cortical architecture from a Hebbian synaptic learning rule in a two layer neural network with nonlinear weight constraints. Our model takes into account the effects of lateral interactions in visual cortex combining local excitation and long range effective inhibition. Our approach allows the principled derivation of developmental rules for low-dimensional feature maps, starting from high-dimensional synaptic learning rules. We incorporate the effects of smooth nonlinear constraints on net synaptic weight projected from units in the thalamic layer (the fan-out) and on the net synaptic weight received by units in the cortical layer (the fan-in). These constraints naturally couple together multiple feature maps such as orientation preference and retinotopic organization. We give a detailed illustration of the method applied to the development of the orientation preference map as a special case, in addition to deriving a model for joint pattern formation in cortical maps of orientation preference, retinotopic location, and receptive field width. We show that the combination of Hebbian learning and center-surround cortical interaction naturally leads to an orientation map development model that is closely related to the XY magnetic lattice model from statistical physics. The results presented here provide justification for phenomenological models studied in Cowan and Friedman (Advances in neural information processing systems 3, 1991), Thomas and Cowan (Phys Rev Lett 92(18):e188101, 2004) and provide a developmental model realizing the synaptic weight constraints previously assumed in Thomas and Cowan (Math Med Biol 23(2):119-138, 2006).

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.

Fluctuation-driven Turing patterns

Models of diffusion-driven pattern formation that rely on the Turing mechanism are utilized in many areas of science. However, many such models suffer from the defect of requiring fine tuning of parameters or an unrealistic separation of scales in the diffusivities of the constituents of the system in order to predict the formation of spatial patterns. In the context of a very generic model of ecological pattern formation, we show that the inclusion of intrinsic noise in Turing models leads to the formation of "quasipatterns" that form in generic regions of parameter space and are experimentally distinguishable from standard Turing patterns. The existence of quasipatterns removes the need for unphysical fine tuning or separation of scales in the application of Turing models to real systems.

Analysis of a hyperbolic geometric model for visual texture perception

We study the neural field equations introduced by Chossat and Faugeras to model the representation and the processing of image edges and textures in the hypercolumns of the cortical area V1. The key entity, the structure tensor, intrinsically lives in a non-Euclidean, in effect hyperbolic, space. Its spatio-temporal behaviour is governed by nonlinear integro-differential equations defined on the Poincaré disc model of the two-dimensional hyperbolic space. Using methods from the theory of functional analysis we show the existence and uniqueness of a solution of these equations. In the case of stationary, that is, time independent, solutions we perform a stability analysis which yields important results on their behavior. We also present an original study, based on non-Euclidean, hyperbolic, analysis, of a spatially localised bump solution in a limiting case. We illustrate our theoretical results with numerical simulations.Mathematics Subject Classification: 30F45, 33C05, 34A12, 34D20, 34D23, 34G20, 37M05, 43A85, 44A35, 45G10, 51M10, 92B20, 92C20.

Investigating the mechanisms of hallucinogen-induced visions using 3,4-methylenedioxyamphetamine (MDA): a randomized controlled trial in humans

BACKGROUND

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.

METHODOLOGY/PRINCIPAL FINDINGS

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.

CONCLUSIONS/SIGNIFICANCE

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.

TRIAL REGISTRATION

Clinicaltrials.gov NCT00823407.

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.

Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields

The work studies the spatiotemporal activity propagation in a two-dimensional spatial system involving a finite transmission speed. We derive a numerical scheme in detail to integrate the corresponding evolution equation and validate the derived algorithm by a study of a spatially periodic system. Finally, the work demonstrates numerically transmission delay-induced breathers subjected to anisotropic external input.

Epilepsy as a dynamic disease: a tutorial of the past with an eye to the future

How can clinical epileptologists and computational neuroscientists learn to function together within the confines of interdisciplinary teams to develop new and more effective treatment strategies for epilepsy? Here we introduce epileptologists to the way modelers think about epilepsy as a dynamic disease. Not only is there terminology to be learned, but also it is necessary to identify those areas where clinical input might be expected to have the greatest impact. It is concluded that both groups have major roles to play in educating, evaluating, and shaping the direction of the efforts of each other.

Effects of the anesthetic agent propofol on neural populations

The neuronal mechanisms of general anesthesia are still poorly understood. Besides several characteristic features of anesthesia observed in experiments, a prominent effect is the bi-phasic change of power in the observed electroencephalogram (EEG), i.e. the initial increase and subsequent decrease of the EEG-power in several frequency bands while increasing the concentration of the anaesthetic agent. The present work aims to derive analytical conditions for this bi-phasic spectral behavior by the study of a neural population model. This model describes mathematically the effective membrane potential and involves excitatory and inhibitory synapses, excitatory and inhibitory cells, nonlocal spatial interactions and a finite axonal conduction speed. The work derives conditions for synaptic time constants based on experimental results and gives conditions on the resting state stability. Further the power spectrum of Local Field Potentials and EEG generated by the neural activity is derived analytically and allow for the detailed study of bi-spectral power changes. We find bi-phasic power changes both in monostable and bistable system regime, affirming the omnipresence of bi-spectral power changes in anesthesia. Further the work gives conditions for the strong increase of power in the δ-frequency band for large propofol concentrations as observed in experiments.

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 previous work 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.

Our visual perception of the world is remarkably stable despite the fact that we move our gaze and body. This must be the effect of the neuronal organization of the visual areas of our brains that succeed in maintaining in our consciouness a representation that seems to be protected from brutal variations. We propose a theory to account for an invariance that pertains to such image features as edges and textures. It is based on the simple assumption that the spatial variations of the image intensity, its derivatives, are extracted and represented in some visual brain areas by populations of neurons that excite and inhibit each other according to the values of these derivatives. Geometric transformations of the retinal image, caused say by eye movements, affect these derivatives. Assuming that their representations are invariant to these transformations, we predict the appearance of specific patterns of activity which we call hyperbolic planforms. It is surprising that the geometry that emerges from our investigations is not the usual Euclidean geometry but the much less familiar hyperbolic, non-Euclidean, geometry. We also propose some preliminary ideas for putting our theory to the test by actual measurements of brain activity.

Natural scene statistics and the structure of orientation maps in the visual cortex

Visual activity after eye-opening influences feature map structure in primary visual cortex (V1). For instance, rearing cats in an environment of stripes of one orientation yields an over-representation of that orientation in V1. However, whether such changes also affect the higher-order statistics of orientation maps is unknown. A statistical bias of orientation maps in normally raised animals is that the probability of the angular difference in orientation preference between each pair of points in the cortex depends on the angle of the line joining those points relative to a fixed but arbitrary set of axes. Natural images show an analogous statistical bias; however, whether this drives the development of comparable structure in V1 is unknown. We examined these statistics for normal, stripe-reared and dark-reared cats, and found that the biases present were not consistently related to those present in the input, or to genetic relationships. We compared these results with two computational models of orientation map development, an analytical model and a Hebbian model. The analytical model failed to reproduce the experimentally observed statistics. In the Hebbian model, while orientation difference statistics could be strongly driven by the input, statistics similar to those seen in experimental maps arose only when symmetry breaking was allowed to occur spontaneously. These results suggest that these statistical biases of orientation maps arise primarily spontaneously, rather than being governed by either input statistics or genetic mechanisms.

Inverse problems in dynamic cognitive modeling

Inverse problems for dynamical system models of cognitive processes comprise the determination of synaptic weight matrices or kernel functions for neural networks or neural/dynamic field models, respectively. We introduce dynamic cognitive modeling as a three tier top-down approach where cognitive processes are first described as algorithms that operate on complex symbolic data structures. Second, symbolic expressions and operations are represented by states and transformations in abstract vector spaces. Third, prescribed trajectories through representation space are implemented in neurodynamical systems. We discuss the Amari equation for a neural/dynamic field theory as a special case and show that the kernel construction problem is particularly ill-posed. We suggest a Tikhonov-Hebbian learning method as regularization technique and demonstrate its validity and robustness for basic examples of cognitive computations.

Transient Turing patterns in a neural field model

We investigate Turing bifurcations in a neural field model with one spatial dimension. For some parameter values the resulting Turing patterns are stable, while for others the patterns appear transiently. We show that this difference is due to the relative position in parameter space of the saddle-node bifurcation of a spatially periodic pattern and the Turing bifurcation point. By varying parameters we are able to observe transient patterns whose duration scales in the same way as type-I intermittency. Similar behavior occurs in two spatial dimensions.

Nonlocal Ginzburg-Landau equation for cortical pattern formation

We show how a nonlocal version of the real Ginzburg-Landau (GL) equation arises in a large-scale recurrent network model of primary visual cortex. We treat cortex as a continuous two-dimensional sheet of cells that signal both the position and orientation of a local visual stimulus. The recurrent circuitry is decomposed into a local part, which contributes primarily to the orientation tuning properties of the cells, and a long-range part that introduces spatial correlations. We assume that (a) the local network exists in a balanced state such that it operates close to a point of instability and (b) the long-range connections are weak and scale with the bifurcation parameter of the dynamical instability generated by the local circuitry. Carrying out a perturbation expansion with respect to the long-range coupling strength then generates a nonlocal coupling term in the GL amplitude equation. We use the nonlocal GL equation to analyze how axonal propagation delays arising from the slow conduction velocities of the long-range connections affect spontaneous pattern formation.

Anesthetic-induced transitions by propofol modeled by nonlocal neural populations involving two neuron types

The present work derives the spatiotemporal field equation of neural populations considering two types of neurons. The model considers pyramidal cells, which may excite or inhibit other neurons, and GABAergic interneurons inhibiting terminal neurons. Additionally, taking into account excitatory and inhibitory synapses, the neural population obeys a vector-field equation involving nonlocal spatial interactions. The work studies the effect of the anesthetic agent propofol, which increases the decay time of inhibitory synapses. In addition, it explains the bifurcation mechanism in some detail and finds a saddle-node bifurcation subject to the propofol concentration. This bifurcation may model the transition between consciousness and nonconsciousness and vice versa during the administration of general anesthetics in medicine.

Kinetic theory for neuronal networks with fast and slow excitatory conductances driven by the same spike train

We present a kinetic theory for all-to-all coupled networks of identical, linear, integrate-and-fire, excitatory point neurons in which a fast and a slow excitatory conductance are driven by the same spike train in the presence of synaptic failure. The maximal-entropy principle guides us in deriving a set of three (1+1) -dimensional kinetic moment equations from a Boltzmann-like equation describing the evolution of the one-neuron probability density function. We explain the emergence of correlation terms in the kinetic moment and Boltzmann-like equations as a consequence of simultaneous activation of both the fast and slow excitatory conductances and furnish numerical evidence for their importance in correctly describing the coarse-grained dynamics of the underlying neuronal network.

A future for systems and computational neuroscience in France?

This special issue of the Journal of Physiology, Paris, is an outcome of NeuroComp'06, the first French conference in Computational Neuroscience. The preparation for this conference, held at Pont-à-Mousson in October 2006, was accompanied by a survey which has resulted in an up-to-date inventory of human resources and labs in France concerned with this emerging new field of research (see team directory in http://neurocomp.risc.cnrs.fr/). This thematic JPP issue gathers some of the key scientific presentations made on the occasion of this first interdisciplinary meeting, which should soon become recognized as a yearly national conference representative of a new scientific community. The present introductory paper presents the general scientific context of the conference and reviews some of the historical and conceptual foundations of Systems and Computational Neuroscience in France.

Neural interactions between flicker-induced self-organized visual hallucinations and physical stimuli

Spontaneous pattern formation in cortical activity may have consequences for perception, but little is known about interactions between sensory-driven and self-organized cortical activity. To address this deficit, we explored the relationship between ordinary stimulus-controlled pattern perception and the autonomous hallucinatory geometrical pattern formation that occurs for unstructured visual stimulation (e.g., empty-field flicker). We found that flicker-induced hallucinations are biased by the presentation of adjacent geometrical stimuli; geometrical forms that map to cortical area V1 as orthogonal gratings are perceptually opponent in biasing hallucinations. Rotating fan blades and pulsating circular patterns are the most salient biased hallucinations. Apparent motion and fractal (1/f) noise are also effective in driving hallucinatory pattern formation (the latter is consistent with predictions of spatiotemporal pattern formation driven by stochastic resonance). The behavior of these percepts suggests that self-organized hallucinatory pattern formation in human vision is governed by the same cortical properties of localized processing, lateral inhibition, simultaneous contrast, and nonlinear retinotopic mapping that govern ordinary vision.

Theoretical understanding of the early visual processes by data compression and data selection

Early vision is best understood in terms of two key information bottlenecks along the visual pathway -- the optic nerve and, more severely, attention. Two effective strategies for sampling and representing visual inputs in the light of the bottlenecks are (1) data compression with minimum information loss and (2) data deletion. This paper reviews two lines of theoretical work which understand processes in retina and primary visual cortex (V1) in this framework. The first is an efficient coding principle which argues that early visual processes compress input into a more efficient form to transmit as much information as possible through channels of limited capacity. It can explain the properties of visual sampling and the nature of the receptive fields of retina and V1. It has also been argued to reveal the independent causes of the inputs. The second theoretical tack is the hypothesis that neural activities in V1 represent the bottom up saliencies of visual inputs, such that information can be selected for, or discarded from, detailed or attentive processing. This theory links V1 physiology with pre-attentive visual selection behavior. By making experimentally testable predictions, the potentials and limitations of both sets of theories can be explored.

A computational perspective on migraine aura

The classical visual aura of migraine is characterized by a unilateral hallucination, composed of a zigzag fortification pattern followed by a trailing scotoma. This pattern usually starts in central vision, expands and spreads to the periphery, and then disappears. We review a number of historical attempts to explain the migraine aura in terms of brain events, then summarize recent theories of the pathophysiology of the aura. We describe an approach to the computational modeling of migraine aura, based on the principles of (a) cortical organization, and (b) active wave propagation in an excitable medium. We demonstrate correspondences between properties of the model system and aspects of the pathophysiology of the aura. The simulations produced by the model are in agreement with descriptions and drawings of visual aura from migraine patients. We outline several testable predictions stemming from the implementation of the model, and explain how model-based empirical research has the capacity to (a) improve recording of the phenomena of the visual aura, (b) improve understanding of the spatio-temporal dynamics of other types of aura, in particular somatosensory and dysphasic aurae, and (c) clarify the theoretical requirements for the initiation of aura in the brain.

The functional geometry of local and horizontal connections in a model of V1

A mathematical model of interacting hypercolumns in primary visual cortex (V1) is presented that incorporates details concerning the geometry of local and long-range horizontal connections. Each hypercolumn is modeled as a network of interacting excitatory and inhibitory neural populations with orientation and spatial frequency preferences organized around a pair of pinwheels. The pinwheels are arranged on a planar lattice, reflecting the crystalline-like structure of cortex. Local interactions within a hypercolumn generate orientation and spatial frequency tuning curves, which are modulated by horizontal connections between different hypercolumns on the lattice. The symmetry properties of the local and long-range connections play an important role in determining the types of spontaneous activity patterns that can arise in cortex.

Symmetry induced coupling of cortical feature maps

The mammalian visual cortex maps retinal position (retinotopy) and orientation preference (OP) across its surface. Simultaneous measurements in vivo suggest that positive correlation exists between the location of dislocations in these two maps, contradicting the predictions of classical dimension reduction models. Model symmetries exert a significant influence on pattern development. However, classical models for cortical map formation have inappropriate symmetry properties. By applying equivariant bifurcation theory we derive symmetry induced, model independent coupling of the OP and retinotopic maps and show that this coupling replicates observations.

Patterns of Ongoing Activity and the Functional Architecture of the Primary Visual Cortex

Ongoing spontaneous activity in the cerebral cortex exhibits complex spatiotemporal patterns in the absence of sensory stimuli. To elucidate the nature of this ongoing activity, we present a theoretical treatment of two contrasting scenarios of cortical dynamics: (1) fluctuations about a single background state and (2) wandering among multiple "attractor" states, which encode a single or several stimulus features. Studying simplified network rate models of the primary visual cortex (V1), we show that the single state scenario is characterized by fast and high-dimensional Gaussian-like fluctuations, whereas in the multiple state scenario the fluctuations are slow, low dimensional, and highly non-Gaussian. Studying a more realistic model that incorporates correlations in the feed-forward input, spatially restricted cortical interactions, and an experimentally derived layout of pinwheels, we show that recent optical-imaging data of ongoing activity in V1 are consistent with the presence of either a single background state or multiple attractor states encoding many features.

Mexican hats and pinwheels in visual cortex

Many models of cortical function assume that local lateral connections are specific with respect to the preferred features of the interacting cells and that they are organized in a Mexican-hat pattern with strong "center" excitation flanked by strong "surround" inhibition. However, anatomical data on primary visual cortex indicate that the local connections are isotropic and that inhibition has a shorter range than excitation. We address this issue in an analytical study of a neuronal network model of the local cortical circuit in primary visual cortex. In the model, the orientation columns specified by the convergent lateral geniculate nucleus inputs are arranged in a pinwheel architecture, whereas cortical connections are isotropic. We obtain a trade-off between the spatial range of inhibition and its time constant. If inhibition is fast, the network can operate in a Mexican-hat pattern with isotropic connections even with a spatially narrow inhibition. If inhibition is not fast, Mexican-hat operation requires a spatially broad inhibition. The Mexican-hat operation can generate a sharp orientation tuning, which is largely independent of the distance of the cell from the pinwheel center.

Modeling of automatic capture and focusing of visual attention

An explanation, based on simple analysis of the spatiotemporal variations of the visual environment, is given to the automatic capture and focusing of visual attention. It is assumed that the transmittance for the sensory signals is modulated by separate control circuits that sample input from the same area of the visual field but at a lower resolution. When these circuits detect significant spatial and/or temporal variations, they "open gates" for the more accurate information arising from the same area. If the variations are related to the spatial resolution, which varies within wide limits over the retina, the visual field is "opened" up to a radius where it captures the most salient structures of the image. If the temporal variations of the signals are further emphasized, the high spatial frequencies begin to dominate. If then the gaze is moved by a small amount, the transmittance of the foveal signal paths is activated strongest.