Matthew C. Wiener

What geometric visual hallucinations tell us about the visual cortex

Many observers see geometric visual hallucinations after taking hallucinogens such as LSD, cannabis, mescaline or psilocybin; on viewing bright flickering lights; on waking up or falling asleep; in near-death experiences; and in many other syndromes. Klver organized the images into four groups called form constants: (I) tunnels and funnels, (II) spirals, (III) lattices, including honeycombs and triangles, and (IV) cobwebs. In most cases, the images are seen in both eyes and move with them. We interpret this to mean that they are generated in the brain. Here, we summarize a theory of their origin in visual cortex (area V1), based on the assumption that the form of the retinocortical map and the architecture of V1 determine their geometry. (A much longer and more detailed mathematical version has been published in Philosophical Transactions of the Royal Society B, 356 [2001].) We model V1 as the continuum limit of a lattice of interconnected hypercolumns, each comprising a number of interconnected iso-orientation columns. Based on anatomical evidence, we assume that the lateral connectivity between hypercolumns exhibits symmetries, rendering it invariant under the action of the Euclidean group E(2), composed of reflections and translations in the plane, and a (novel) shift-twist action. Using this symmetry, we show that the various patterns of activity that spontaneously emerge when V1s spatially uniform resting state becomes unstable correspond to the form constants when transformed to the visual field using the retino-cortical map. The results are sensitive to the detailed specification of the lateral connectivity and suggest that the cortical mechanisms that generate geometric visual hallucinations are closely related to those used to process edges, contours, surfaces, and textures.

Response Features Determining Spike Times

Interpreting messages encoded in single neuronal responses requires knowing which features of the responses carry information. That the number of spikes is an important part of the code has long been obvious. In recent years, it has been shown that modulation of the firing rate with about 25 ms precision carries information that is not available from the total number of spikes across the whole response. It has been proposed that patterns of exactly timed (1 ms precision) spikes, such as repeating triplets or quadruplets, might carry information that is not available from knowing about spike count and rate modulation. A model using the spike count distribution, the low pass filtered PSTH (bandwidth below 30 Hz), and, to a small degree, the interspike interval distribution predicts the numbers and types of exactly-timed triplets and quadruplets that are indistinguishable from those found in the data. From this it can be concluded that the coarse (<30 Hz) sequential correlation structure over time gives rise to the exactly timed patterns present in the recorded spike trains. Because the coarse temporal structure predicts the fine temporal structure, the information carried by the fine temporal structure must be completely redundant with that carried by the coarse structure. Thus, the existence of precisely timed spike patterns carrying stimulus-related information does not imply control of spike timing at precise time scales.

Model based decoding of spike trains

Reliably decoding neuronal responses requires knowing what aspects of neuronal responses are stimulus related, and which aspects act as noise. Recent work shows that spike trains can be viewed as stochastic samples from the rate variation function, as estimated by the time dependent spike density function (or normalized peristimulus time histogram). Such spike trains are exactly described by order statistics, and can be decoded millisecond-by-millisecond by iterative application of order statistics.