Development of Maps of Simple and Complex Cells in the Primary Visual Cortex

Hubel and Wiesel (1962) classified primary visual cortex (V1) neurons as either simple, with responses modulated by the spatial phase of a sine grating, or complex, i.e., largely phase invariant. Much progress has been made in understanding how simple-cells develop, and there are now detailed computational models establishing how they can form topographic maps ordered by orientation preference. There are also models of how complex cells can develop using outputs from simple cells with different phase preferences, but no model of how a topographic orientation map of complex cells could be formed based on the actual connectivity patterns found in V1. Addressing this question is important, because the majority of existing developmental models of simple-cell maps group neurons selective to similar spatial phases together, which is contrary to experimental evidence, and makes it difficult to construct complex cells. Overcoming this limitation is not trivial, because mechanisms responsible for map development drive receptive fields (RF) of nearby neurons to be highly correlated, while co-oriented RFs of opposite phases are anti-correlated. In this work, we model V1 as two topographically organized sheets representing cortical layer 4 and 2/3. Only layer 4 receives direct thalamic input. Both sheets are connected with narrow feed-forward and feedback connectivity. Only layer 2/3 contains strong long-range lateral connectivity, in line with current anatomical findings. Initially all weights in the model are random, and each is modified via a Hebbian learning rule. The model develops smooth, matching, orientation preference maps in both sheets. Layer 4 units become simple cells, with phase preference arranged randomly, while those in layer 2/3 are primarily complex cells. To our knowledge this model is the first explaining how simple cells can develop with random phase preference, and how maps of complex cells can develop, using only realistic patterns of connectivity

Unified developmental model of maps, complex cells and surround modulation in the primary visual cortex

For human and animal vision, the perception of local visual features can depend on the spatial arrangement of the surrounding visual stimuli. In the earliest stages of visual processing this phenomenon is called surround modulation, where the response of visually selective neurons is influenced by the response of neighboring neurons. Surround modulation has been implicated in numerous important perceptual phenomena, such as contour integration and figure-ground segregation. In cats, one of the major potential neural substrates for surround modulation are lateral connections between cortical neurons in layer 2/3, which typically contains ”complex” cells that appear to combine responses from ”simple” cells in layer 4C. Interestingly, these lateral connections have also been implicated in the development of functional maps in primary visual cortex, such as smooth, well-organized maps for the preference of oriented lines. Together, this evidence suggests a common underlying substrate the lateral interactions in layer 2/3—as the driving force behind development of orientation maps for both simple and complex cells, and at the same time expression of surround modulation in adult animals. However, previously these phenomena have been studied largely in isolation, and we are not aware of a computational model that can account for all of them simultaneously and show how they are related. In this thesis we resolve this problem by building a single, unified computational model that can explain the development of orientation maps, the development of simple and complex cells, and surround modulation. First we build a simple, single-layer model of orientation map development based on ALISSOM, which has more realistic single cell properties (such as contrast gain control and contrast invariant orientation tuning) than its predecessor. Then we extend this model by adding layer 2/3, and show how the model can explain development of orientation maps of both simple and complex cells. As the last step towards a developmental model of surround modulation, we replace Mexican-hat-like lateral connectivity in layer 2/3 of the model with a more realistic configuration based on long-range excitation and short-range inhibitory cells, extending a simpler model by Judith Law. The resulting unified model of V1 explains how orientation maps of simple and complex cells can develop, while individual neurons in the developed model express realistic orientation tuning and various surround modulation properties. In doing so, we not only offer a consistent explanation behind all these phenomena, but also create a very rich model of V1 in which the interactions between various V1 properties can be studied. The model allows us to formulate several novel predictions that relate the variation of single cell properties to their location in the orientation preference maps in V1, and we show how these predictions can be tested experimentally. Overall, this model represents a synthesis of a wide body of experimental evidence, forming a compact hypothesis for much of the development and behavior of neurons in the visual cortex

Linking Visual Cortical Development to Visual Perception

Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333); Office of Naval Research (N00014-95-1-0657

A Neural Network Model for the Development of Simple and Complex Cell Receptive Fields Within Cortical Maps of Orientation and Ocular Dominance

Prenatal development of the primary visual cortex leads to simple cells with spatially distinct and oriented ON and OFF subregions. These simple cells are organized into spatial maps of orientation and ocular dominance that exhibit singularities, fractures, and linear zones. On a finer spatial scale, simple cells occur that are sensitive to similar orientations but opposite contrast polarities, and exhibit both even-symmetric and odd-symmetric receptive fields. Pooling of outputs from oppositely polarized simple cells leads to complex cells that respond to both contrast polarities. A neural network model is described which simulates how simple and complex cells self-organize starting from unsegregated and unoriented geniculocortical inputs during prenatal development. Neighboring simple cells that are sensitive to opposite contrast polarities develop from a combination of spatially short-range inhibition and high-gain recurrent habituative excitation between cells that obey membrane equations. Habituation, or depression, of synapses controls reset of cell activations both through enhanced ON responses and OFF antagonistic rebounds. Orientation and ocular dominance maps form when high-gain medium-range recurrent excitation and long-range inhibition interact with the short-range mechanisms. The resulting structure clarifies how simple and complex cells contribute to perceptual processes such as texture segregation and perceptual grouping.Air Force Office of Scientific Research (F49620-92-J-0334); British Petroleum (BP 89A-1204); National Science Foundation (IRI-90-24877); Office of Naval Research (N00014-91-J-4100); Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409

Linking Visual Development and Learning to Information Processing: Preattentive and Attentive Brain Dynamics

National Science Foundation (SBE-0354378); Office of Naval Research (N00014-95-1-0657

A geometric model of multi-scale orientation preference maps via Gabor functions

In this paper we present a new model for the generation of orientation preference maps in the primary visual cortex (V1), considering both orientation and scale features. First we undertake to model the functional architecture of V1 by interpreting it as a principal fiber bundle over the 2-dimensional retinal plane by introducing intrinsic variables orientation and scale. The intrinsic variables constitute a fiber on each point of the retinal plane and the set of receptive profiles of simple cells is located on the fiber. Each receptive profile on the fiber is mathematically interpreted as a rotated Gabor function derived from an uncertainty principle. The visual stimulus is lifted in a 4-dimensional space, characterized by coordinate variables, position, orientation and scale, through a linear filtering of the stimulus with Gabor functions. Orientation preference maps are then obtained by mapping the orientation value found from the lifting of a noise stimulus onto the 2-dimensional retinal plane. This corresponds to a Bargmann transform in the reducible representation of the $\text{SE}(2)=\mathbb{R}^2\times S^1$ group. A comparison will be provided with a previous model based on the Bargman transform in the irreducible representation of the $\text{SE}(2)$ group, outlining that the new model is more physiologically motivated. Then we present simulation results related to the construction of the orientation preference map by using Gabor filters with different scales and compare those results to the relevant neurophysiological findings in the literature

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

A Neural Model of How Horizontal and Interlaminar Connections of Visual Cortex Develop into Adult Circuits that Carry Out Perceptual Grouping and Learning

A neural model suggests how horizontal and interlaminar connections in visual cortical areas Vl and V2 develop within a laminar cortical architecture and give rise to adult visual percepts. The model suggests how mechanisms that control cortical development in the infant lead to properties of adult cortical anatomy, neurophysiology, and visual perception. The model clarifies how excitatory and inhibitory connections can develop stably by maintaining a balance between excitation and inhibition. The growth of long-range excitatory horizontal connections between layer 2/3 pyramidal cells is balanced against that of short-range disynaptic interneuronal connections. The growth of excitatory on-center connections from layer 6-to-4 is balanced against that of inhibitory interneuronal off-surround connections. These balanced connections interact via intracortical and intercortical feedback to realize properties of perceptual grouping, attention, and perceptual learning in the adult, and help to explain the observed variability in the number and temporal distribution of spikes emitted by cortical neurons. The model replicates cortical point spread functions and psychophysical data on the strength of real and illusory contours. The on-center off-surround layer 6-to-4 circuit enables top-clown attentional signals from area V2 to modulate, or attentionally prime, layer 4 cells in area Vl without fully activating them. This modulatory circuit also enables adult perceptual learning within cortical area Vl and V2 to proceed in a stable way.Defense Advanced Research Projects Agency and the Office of Naval Research (N00014-95-1-0409); National Science Foundation (IRI-97-20333); Office of Naval Research (N00014-95-1-0657

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