Rules for the Cortical Map of Ocular Dominance and Orientation Columns

Three computational rules are sufficient to generate model cortical maps that simulate the interrelated structure of cortical ocular dominance and orientation columns: a noise input, a spatial band pass filter, and competitive normalization across all feature dimensions. The data of Blasdel from optical imaging experiments reveal cortical map fractures, singularities, and linear zones that are fit by the model. In particular, singularities in orientation preference tend to occur in the centers of ocular dominance columns, and orientation contours tend to intersect ocular dominance columns at right angles. The model embodies a universal computational substrate that all models of cortical map development and adult function need to realize in some form.Air Force Office of Scientific Research (F49620-92-J- 0499, F49620-92-J-0334); Office of Naval Research (N00014-92-J-4015, N00014-91-J-4100); National Science Foundation (IRI-90-24877); British Petroleum (BP 89A-1204

Reorganization of columnar architecture in the growing visual cortex

Many cortical areas increase in size considerably during postnatal development, progressively displacing neuronal cell bodies from each other. At present, little is known about how cortical growth affects the development of neuronal circuits. Here, in acute and chronic experiments, we study the layout of ocular dominance (OD) columns in cat primary visual cortex (V1) during a period of substantial postnatal growth. We find that despite a considerable size increase of V1, the spacing between columns is largely preserved. In contrast, their spatial arrangement changes systematically over this period. While in young animals columns are more band-like, layouts become more isotropic in mature animals. We propose a novel mechanism of growth-induced reorganization that is based on the `zigzag instability', a dynamical instability observed in several inanimate pattern forming systems. We argue that this mechanism is inherent to a wide class of models for the activity-dependent formation of OD columns. Analyzing one member of this class, the Elastic Network model, we show that this mechanism can account for the preservation of column spacing and the specific mode of reorganization of OD columns that we observe. We conclude that neurons systematically shift their selectivities during normal development and that this reorganization is induced by the cortical expansion during growth. Our work suggests that cortical circuits remain plastic for an extended period in development in order to facilitate the modification of neuronal circuits to adjust for cortical growth.Comment: 8+13 pages, 4+8 figures, paper + supplementary materia

Understanding visual map formation through vortex dynamics of spin Hamiltonian models

The pattern formation in orientation and ocular dominance columns is one of the most investigated problems in the brain. From a known cortical structure, we build spin-like Hamiltonian models with long-range interactions of the Mexican hat type. These Hamiltonian models allow a coherent interpretation of the diverse phenomena in the visual map formation with the help of relaxation dynamics of spin systems. In particular, we explain various phenomena of self-organization in orientation and ocular dominance map formation including the pinwheel annihilation and its dependency on the columnar wave vector and boundary conditions.Comment: 4 pages, 15 figure

How does the Cerebral Cortex Work? Learning, Attention, and Grouping by the Laminar Circuits of Visual Cortex

The organization of neocortex into layers is one of its most salient anatomical features. These layers include circuits that form functional columns in cortical maps. A major unsolved problem concerns how bottom-up, top-down, and horizontal interactions are organized within cortical layers to generate adaptive behaviors. This article models how these interactions help visual co1tex to realize: (I) the binding process whereby cortex groups distributed data into coherent object representations; (2) the attentional process whereby cortex selectively processes important events; and (3) the developmental and learning processes whereby cortex shapes its circuits to match environmental constraints. New computational ideas about feedback systems suggest how neocortex develops and learns in a stable way, and why top-down attention requires converging bottom-up inputs to fully activate cortical cells, whereas perceptual groupings do not.Defense Advanced Research Projects Agency; National Science Foundation (IRI-97-20333); Office of Naval Research (N00014-95-1-0409, N00014-95-1-0657

Global Perturbation of Initial Geometry in a Biomechanical Model of Cortical Morphogenesis

Cortical folding pattern is a main characteristic of the geometry of the human brain which is formed by gyri (ridges) and sulci (grooves). Several biological hypotheses have suggested different mechanisms that attempt to explain the development of cortical folding and its abnormal evolutions. Based on these hypotheses, biomechanical models of cortical folding have been proposed. In this work, we compare biomechanical simulations for several initial conditions by using an adaptive spherical parameterization approach. Our approach allows us to study and explore one of the most potential sources of reproducible cortical folding pattern: the specification of initial geometry of the brain.Comment: 4 pages 2 columns (IEEE style), 41st EMB Conferenc

tDCS changes in motor excitability are specific to orientation of current flow

BACKGROUND: Measurements and models of current flow in the brain during transcranial Direct Current Stimulation (tDCS) indicate stimulation of regions in-between electrodes. Moreover, the folded cortex results in local fluctuations in current flow intensity and direction, and animal studies suggest current flow direction relative to cortical columns determines response to tDCS. METHODS: Here we test this idea by using Transcranial Magnetic Stimulation Motor Evoked Potentials (TMS-MEP) to measure changes in corticospinal excitability following tDCS applied with electrodes aligned orthogonal (across) or parallel to M1 in the central sulcus. RESULTS: Current flow models predicted that the orthogonal electrode montage produces consistently oriented current across the hand region of M1 that flows along cortical columns, while the parallel electrode montage produces non-uniform current directions across the M1 cortical surface. We find that orthogonal, but not parallel, orientated tDCS modulates TMS-MEPs. We also show modulation is sensitive to the orientation of the TMS coil (PA or AP), which is thought to select different afferent pathways to M1. CONCLUSIONS: Our results are consistent with tDCS producing directionally specific neuromodulation in brain regions in-between electrodes, but shows nuanced changes in excitability that are presumably current direction relative to column and axon pathway specific. We suggest that the direction of current flow through cortical target regions should be considered for targeting and dose-control of tDCS

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

Coordinated optimization of visual cortical maps : 2. Numerical studies

In the juvenile brain, the synaptic architecture of the visual cortex remains in a state of flux for months after the natural onset of vision and the initial emergence of feature selectivity in visual cortical neurons. It is an attractive hypothesis that visual cortical architecture is shaped during this extended period of juvenile plasticity by the coordinated optimization of multiple visual cortical maps such as orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we introduced a class of analytically tractable coordinated optimization models and solved representative examples, in which a spatially complex organization of the OP map is induced by interactions between the maps. We found that these solutions near symmetry breaking threshold predict a highly ordered map layout. Here we examine the time course of the convergence towards attractor states and optima of these models. In particular, we determine the timescales on which map optimization takes place and how these timescales can be compared to those of visual cortical development and plasticity. We also assess whether our models exhibit biologically more realistic, spatially irregular solutions at a finite distance from threshold, when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. We show that, although maps typically undergo substantial rearrangement, no other solutions than pinwheel crystals and stripes dominate in the emerging layouts. Pinwheel crystallization takes place on a rather short timescale and can also occur for detuned wavelengths of different maps. Our numerical results thus support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the architecture of the visual cortex. We discuss several alternative scenarios that may improve the agreement between model solutions and biological observations