Neural field model to reconcile structure with function in primary visual cortex

Voltage-sensitive dye imaging experiments in primary visual cortex (V1) have shown that local, oriented visual stimuli elicit stable orientation-selective activation within the stimulus retinotopic footprint. The cortical activation dynamically extends far beyond the retinotopic footprint, but the peripheral spread stays non-selective—a surprising finding given a number of anatomo-functional studies showing the orientation specificity of long-range connections. Here we use a computational model to investigate this apparent discrepancy by studying the expected population response using known published anatomical constraints. The dynamics of input-driven localized states were simulated in a planar neural field model with multiple sub-populations encoding orientation. The realistic connectivity profile has parameters controlling the clustering of long-range connections and their orientation bias. We found substantial overlap between the anatomically relevant parameter range and a steep decay in orientation selective activation that is consistent with the imaging experiments. In this way our study reconciles the reported orientation bias of long-range connections with the functional expression of orientation selective neural activity. Our results demonstrate this sharp decay is contingent on three factors, that long-range connections are sufficiently diffuse, that the orientation bias of these connections is in an intermediate range (consistent with anatomy) and that excitation is sufficiently balanced by inhibition. Conversely, our modelling results predict that, for reduced inhibition strength, spurious orientation selective activation could be generated through long-range lateral connections. Furthermore, if the orientation bias of lateral connections is very strong, or if inhibition is particularly weak, the network operates close to an instability leading to unbounded cortical activation.

[1]  D. Hubel,et al.  Uniformity of monkey striate cortex: A parallel relationship between field size, scatter, and magnification factor , 1974, The Journal of comparative neurology.

[2]  F. Chavane,et al.  Cortical response field dynamics in cat visual cortex. , 2007, Cerebral cortex.

[3]  T. Wiesel,et al.  Morphology and intracortical projections of functionally characterised neurones in the cat visual cortex , 1979, Nature.

[4]  T. Bonhoeffer,et al.  Relationship Between Lateral Inhibitory Connections and the Topography of the Orientation Map in Cat Visual Cortex , 1994, The European journal of neuroscience.

[5]  A. Sillito The contribution of inhibitory mechanisms to the receptive field properties of neurones in the striate cortex of the cat. , 1975, The Journal of physiology.

[6]  G. Mitchison,et al.  Long axons within the striate cortex: their distribution, orientation, and patterns of connection. , 1982, Proceedings of the National Academy of Sciences of the United States of America.

[7]  D. Hubel,et al.  Receptive fields and functional architecture of monkey striate cortex , 1968, The Journal of physiology.

[8]  R. Yuste,et al.  Feedforward Inhibition Contributes to the Control of Epileptiform Propagation Speed , 2007, The Journal of Neuroscience.

[9]  Brendon O. Watson,et al.  Modular Propagation of Epileptiform Activity: Evidence for an Inhibitory Veto in Neocortex , 2006, The Journal of Neuroscience.

[10]  K. Martin,et al.  Superficial layer pyramidal cells communicate heterogeneously between multiple functional domains of cat primary visual cortex , 2014, Nature Communications.

[11]  G. Blasdel,et al.  Orientation selectivity, preference, and continuity in monkey striate cortex , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[12]  Tobias Bonhoeffer,et al.  Orientation topography of layer 4 lateral networks revealed by optical imaging in cat visual cortex (area 18) , 1999, The European journal of neuroscience.

[13]  David J. B. Lloyd,et al.  Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disc , 2013 .

[14]  Peter E Latham,et al.  Welcome to Neural Systems and Circuits: bridging the gap between theory and experiment , 2011, Neural systems & circuits.

[15]  A. Grinvald,et al.  Relationship between intrinsic connections and functional architecture revealed by optical imaging and in vivo targeted biocytin injections in primate striate cortex. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[16]  T. Wiesel,et al.  Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex , 1989, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[17]  S. Amari Dynamics of pattern formation in lateral-inhibition type neural fields , 1977, Biological Cybernetics.

[18]  E. G. Jones,et al.  Numbers and proportions of GABA-immunoreactive neurons in different areas of monkey cerebral cortex , 1987, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[19]  P. Somogyi,et al.  Quantitative distribution of GABA-immunoreactive neurons in the visual cortex (area 17) of the cat , 2004, Experimental Brain Research.

[20]  David Fitzpatrick,et al.  Optogenetic Assessment of Horizontal Interactions in Primary Visual Cortex , 2014, The Journal of Neuroscience.

[21]  W. Singer,et al.  Functional Specificity of Long-Range Intrinsic and Interhemispheric Connections in the Visual Cortex of Strabismic Cats , 1997, The Journal of Neuroscience.

[22]  Laurent U. Perrinet,et al.  Complex dynamics in recurrent cortical networks based on spatially realistic connectivities , 2012, Front. Comput. Neurosci..

[23]  David J. B. Lloyd,et al.  Continuation of Localized Coherent Structures in Nonlocal Neural Field Equations , 2013, SIAM J. Sci. Comput..

[24]  A. Grinvald,et al.  Spatial Relationships among Three Columnar Systems in Cat Area 17 , 1997, The Journal of Neuroscience.

[25]  Helmut Schmidt,et al.  Snakes and ladders in an inhomogeneous neural field model , 2014, 1403.1037.

[26]  T. Powell,et al.  The intrinsic, association and commissural connections of area 17 on the visual cortex. , 1975, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[27]  D. Coppola,et al.  Response to Comment on “Universality in the Evolution of Orientation Columns in the Visual Cortex“ , 2012, Science.

[28]  J. Lund,et al.  Widespread periodic intrinsic connections in the tree shrew visual cortex. , 1982, Science.

[29]  V. Mountcastle Modality and topographic properties of single neurons of cat's somatic sensory cortex. , 1957, Journal of neurophysiology.

[30]  Jérôme Ribot,et al.  Roles of visual experience and intrinsic mechanism in the activity-dependent self-organization of orientation maps: theory and experiment , 2004, Neural Networks.

[31]  Z. Kisvárday,et al.  Axon topography of layer IV spiny cells to orientation map in the cat primary visual cortex (area 18). , 2011, Cerebral cortex.

[32]  Stephen Coombes,et al.  Waves, bumps, and patterns in neural field theories , 2005, Biological Cybernetics.

[33]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[34]  Paul C. Bressloff,et al.  Spatiotemporal Dynamics of Neural Fields on Product Spaces , 2014, SIAM J. Appl. Dyn. Syst..

[35]  H. Sompolinsky,et al.  Theory of orientation tuning in visual cortex. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[36]  Tanya I. Baker,et al.  Spontaneous pattern formation and pinning in the primary visual cortex , 2009, Journal of Physiology-Paris.

[37]  F. Chavane,et al.  The stimulus-evoked population response in visual cortex of awake monkey is a propagating wave , 2014, Nature Communications.

[38]  V. Braitenberg,et al.  A note on myeloarchitectonics , 1962, The Journal of comparative neurology.

[39]  Amiram Grinvald,et al.  VSDI: a new era in functional imaging of cortical dynamics , 2004, Nature Reviews Neuroscience.

[40]  Fred Wolf,et al.  Can Retinal Ganglion Cell Dipoles Seed Iso-Orientation Domains in the Visual Cortex? , 2013, PloS one.

[41]  François Grimbert Mesoscopic models of cortical structures , 2008 .

[42]  Alain Destexhe,et al.  Improving voltage-sensitive dye imaging: with a little help from computational approaches , 2017, Neurophotonics.

[43]  Jonathan Touboul,et al.  Pinwheel-dipole configuration in cat early visual cortex , 2016, NeuroImage.

[44]  D. Hubel,et al.  Ferrier lecture - Functional architecture of macaque monkey visual cortex , 1977, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[45]  O. Creutzfeldt,et al.  The distribution of degenerating axons after small lesions in the intact and isolated visual cortex of the cat , 1977, Experimental Brain Research.

[46]  U. Eysel,et al.  Orientation-specific relationship between populations of excitatory and inhibitory lateral connections in the visual cortex of the cat. , 1997, Cerebral cortex.

[47]  Ad Aertsen,et al.  A modeler's view on the spatial structure of intrinsic horizontal connectivity in the neocortex , 2010, Progress in Neurobiology.

[48]  R. Shapley,et al.  A neuronal network model of macaque primary visual cortex (V1): orientation selectivity and dynamics in the input layer 4Calpha. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[49]  Carlo R. Laing,et al.  PDE Methods for Nonlocal Models , 2003, SIAM J. Appl. Dyn. Syst..

[50]  Fred Wolf,et al.  Coverage, continuity, and visual cortical architecture , 2011, Neural systems & circuits.

[51]  U. Eysel,et al.  Topography of orientation centre connections in the primary visual cortex of the cat , 2001, Neuroreport.

[52]  R. Shapley,et al.  Orientation Selectivity in Macaque V1: Diversity and Laminar Dependence , 2002, The Journal of Neuroscience.

[53]  Amiram Grinvald,et al.  Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns , 1991, Nature.

[54]  Jean-Luc R Stevens,et al.  Mechanisms for Stable, Robust, and Adaptive Development of Orientation Maps in the Primary Visual Cortex , 2013, The Journal of Neuroscience.

[55]  F. Chavane,et al.  Lateral Spread of Orientation Selectivity in V1 is Controlled by Intracortical Cooperativity , 2011, Front. Syst. Neurosci..

[56]  D. Coppola,et al.  Universality in the Evolution of Orientation Columns in the Visual Cortex , 2010, Science.

[57]  Paul C. Bressloff,et al.  Spontaneous symmetry breaking in self–organizing neural fields , 2005, Biological Cybernetics.

[58]  John H. R. Maunsell,et al.  Coding of image contrast in central visual pathways of the macaque monkey , 1990, Vision Research.

[59]  K. Albus A quantitative study of the projection area of the central and the paracentral visual field in area 17 of the cat , 1975, Experimental brain research.

[60]  D. Ringach,et al.  Retinal origin of orientation maps in visual cortex , 2011, Nature Neuroscience.

[61]  Christian Igel,et al.  A Dynamic Neural Field Model of Mesoscopic Cortical Activity Captured with Voltage-Sensitive Dye Imaging , 2010, PLoS Comput. Biol..

[62]  Misha Tsodyks,et al.  From , 2020, Definitions.

[63]  Boris S. Gutkin,et al.  Multiple Bumps in a Neuronal Model of Working Memory , 2002, SIAM J. Appl. Math..

[64]  U. Eysel,et al.  GABA-induced inactivation of functionally characterized sites in cat visual cortex (area 18): effects on orientation tuning , 1992, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[65]  F. Wolf Symmetry, multistability, and long-range interactions in brain development. , 2005, Physical review letters.

[66]  K. Naka,et al.  S‐potentials from colour units in the retina of fish (Cyprinidae) , 1966, The Journal of physiology.

[67]  Frédéric Chavane,et al.  A biophysical cortical column model to study the multi-component origin of the VSDI signal , 2010, NeuroImage.

[68]  P. Bressloff Spatiotemporal dynamics of continuum neural fields , 2012 .

[69]  U. Eysel,et al.  Evidence for a contribution of lateral inhibition to orientation tuning and direction selectivity in cat visual cortex: reversible inactivation of functionally characterized sites combined with neuroanatomical tracing techniques , 1998, The European journal of neuroscience.

[70]  Fredric M. Wolf,et al.  Random Wiring, Ganglion Cell Mosaics, and the Functional Architecture of the Visual Cortex , 2015, PLoS Comput. Biol..

[71]  A. Grinvald,et al.  Imaging Cortical Dynamics at High Spatial and Temporal Resolution with Novel Blue Voltage-Sensitive Dyes , 1999, Neuron.

[72]  V. Bringuier,et al.  Horizontal propagation of visual activity in the synaptic integration field of area 17 neurons. , 1999, Science.

[73]  G. Goodhill,et al.  Analysis of the elastic net model applied to the formation of ocular dominance and orientation columns. , 2000, Network.

[74]  Lai-Sang Young,et al.  Orientation Selectivity from Very Sparse LGN Inputs in a Comprehensive Model of Macaque V1 Cortex , 2016, The Journal of Neuroscience.

[75]  Frédéric Chavane,et al.  Effects of GABAA kinetics on cortical population activity: computational studies and physiological confirmations. , 2016, Journal of neurophysiology.

[76]  M. Golubitsky,et al.  Geometric visual hallucinations, Euclidean symmetry and the functional architecture of striate cortex. , 2001, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[77]  P. Adorján,et al.  Axonal topography of cortical basket cells in relation to orientation, direction, and ocular dominance maps , 2001, The Journal of comparative neurology.

[78]  F. Chavane,et al.  Voltage-sensitive dye imaging: Technique review and models , 2010, Journal of Physiology-Paris.

[79]  James Rankin,et al.  Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis , 2013, Journal of mathematical biology.

[80]  D. Fitzpatrick,et al.  Orientation Selectivity and the Arrangement of Horizontal Connections in Tree Shrew Striate Cortex , 1997, The Journal of Neuroscience.

[81]  Florentin Wörgötter,et al.  Design Principles of Columnar Organization in Visual Cortex , 1994, Neural Computation.

[82]  Stephen J Eglen,et al.  Parasol cell mosaics are unlikely to drive the formation of structured orientation maps in primary visual cortex. , 2012, Visual neuroscience.

[83]  Alex S. Ferecskó,et al.  Model‐based analysis of excitatory lateral connections in the visual cortex , 2006, The Journal of comparative neurology.

[84]  A. Grinvald,et al.  Functional Organization for Direction of Motion and Its Relationship to Orientation Maps in Cat Area 18 , 1996, The Journal of Neuroscience.