Integrate-and-fire vs Poisson models of LGN input to V1 cortex: noisier inputs reduce orientation selectivity

One of the reasons the visual cortex has attracted the interest of computational neuroscience is that it has well-defined inputs. The lateral geniculate nucleus (LGN) of the thalamus is the source of visual signals to the primary visual cortex (V1). Most large-scale cortical network models approximate the spike trains of LGN neurons as simple Poisson point processes. However, many studies have shown that neurons in the early visual pathway are capable of spiking with high temporal precision and their discharges are not Poisson-like. To gain an understanding of how response variability in the LGN influences the behavior of V1, we study response properties of model V1 neurons that receive purely feedforward inputs from LGN cells modeled either as noisy leaky integrate-and-fire (NLIF) neurons or as inhomogeneous Poisson processes. We first demonstrate that the NLIF model is capable of reproducing many experimentally observed statistical properties of LGN neurons. Then we show that a V1 model in which the LGN input to a V1 neuron is modeled as a group of NLIF neurons produces higher orientation selectivity than the one with Poisson LGN input. The second result implies that statistical characteristics of LGN spike trains are important for V1’s function. We conclude that physiologically motivated models of V1 need to include more realistic LGN spike trains that are less noisy than inhomogeneous Poisson processes.     

Modeling Magnification and Anisotropy in the Primate Foveal Confluence

A basic organizational principle of the primate visual system is that it maps the visual environment repeatedly and retinotopically onto cortex. Simple algebraic models can be used to describe the projection from visual space to cortical space not only for V1, but also for the complex of areas V1, V2 and V3. Typically a conformal (angle-preserving) projection ensuring local isotropy is regarded as ideal and primate visual cortex is often regarded as an approximation of this ideal. However, empirical data show systematic deviations from this ideal that are especially relevant in the foveal projection. The aims of this study were to map the nature of anisotropy predicted by existing models, to investigate the optimization targets faced by different types of retino-cortical maps, and finally to propose a novel map that better models empirical data than other candidates. The retino-cortical map can be optimized towards a space-conserving homogenous representation or a quasi-conformal mapping. The latter would require a significantly enlarged representation of specific parts of the cortical maps. In particular it would require significant enlargement of parafoveal V2 and V3 which is not supported by empirical data. Further, the recently published principal layout of the foveal singularity cannot be explained by existing models. We suggest a new model that accurately describes foveal data, minimizing cortical surface area in the periphery but suggesting that local isotropy dominates the most foveal part at the expense of additional cortical surface. The foveal confluence is an important example of the detailed trade-offs between the compromises required for the mapping of environmental space to a complex of neighboring cortical areas. Our models demonstrate that the organization follows clear morphogenetic principles that are essential for our understanding of foveal vision in daily life.     

Correction of Distortion in Flattened Representations of the Cortical Surface Allows Prediction of V1-V3 Functional Organization from Anatomy

Several domains of neuroscience offer map-like models that link location on the cortical surface to properties of sensory representation. Within cortical visual areas V1, V2, and V3, algebraic transformations can relate position in the visual field to the retinotopic representation on the flattened cortical sheet. A limit to the practical application of this structure-function model is that the cortex, while topologically a two-dimensional surface, is curved. Flattening of the curved surface to a plane unavoidably introduces local geometric distortions that are not accounted for in idealized models. Here, we show that this limitation is overcome by correcting the geometric distortion induced by cortical flattening. We use a mass-spring-damper simulation to create a registration between functional MRI retinotopic mapping data of visual areas V1, V2, and V3 and an algebraic model of retinotopy. This registration is then applied to the flattened cortical surface anatomy to create an anatomical template that is linked to the algebraic retinotopic model. This registered cortical template can be used to accurately predict the location and retinotopic organization of these early visual areas from cortical anatomy alone. Moreover, we show that prediction accuracy remains when extrapolating beyond the range of data used to inform the model, indicating that the registration reflects the retinotopic organization of visual cortex. We provide code for the mass-spring-damper technique, which has general utility for the registration of cortical structure and function beyond the visual cortex.     

Spatial stereoresolution for depth corrugations may be set in primary visual cortex

Stereo "3D" depth perception requires the visual system to extract binocular disparities between the two eyes' images. Several current models of this process, based on the known physiology of primary visual cortex (V1), do this by computing a piecewise-frontoparallel local cross-correlation between the left and right eye's images. The size of the "window" within which detectors examine the local cross-correlation corresponds to the receptive field size of V1 neurons. This basic model has successfully captured many aspects of human depth perception. In particular, it accounts for the low human stereoresolution for sinusoidal depth corrugations, suggesting that the limit on stereoresolution may be set in primary visual cortex. An important feature of the model, reflecting a key property of V1 neurons, is that the initial disparity encoding is performed by detectors tuned to locally uniform patches of disparity. Such detectors respond better to square-wave depth corrugations, since these are locally flat, than to sinusoidal corrugations which are slanted almost everywhere. Consequently, for any given window size, current models predict better performance for square-wave disparity corrugations than for sine-wave corrugations at high amplitudes. We have recently shown that this prediction is not borne out: humans perform no better with square-wave than with sine-wave corrugations, even at high amplitudes. The failure of this prediction raised the question of whether stereoresolution may actually be set at later stages of cortical processing, perhaps involving neurons tuned to disparity slant or curvature. Here we extend the local cross-correlation model to include existing physiological and psychophysical evidence indicating that larger disparities are detected by neurons with larger receptive fields (a size/disparity correlation). We show that this simple modification succeeds in reconciling the model with human results, confirming that stereoresolution for disparity gratings may indeed be limited by the size of receptive fields in primary visual cortex.     

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.     

Pooling strategies in V1 can account for the functional and structural diversity across species

Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of orientation maps in higher mammals’ V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a theoretical model based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence in V1 of complex cells with or without that of orientation maps, as observed in distinct species of mammals. In particular, we observed that pooling in the feature space is directly related to the orientation map formation while pooling in the retinotopic space is responsible for the emergence of a complex cells population. Introducing different forms of pooling in a predictive model of early visual processing as implemented in SDPC can therefore be viewed as a theoretical framework that explains the diversity of structural and functional phenomena observed in V1.     

MEG responses to the perception of global structure within glass patterns

Background

The perception of global form requires integration of local visual cues across space and is the foundation for object recognition. Here we used magnetoencephalography (MEG) to study the location and time course of neuronal activity associated with the perception of global structure from local image features. To minimize neuronal activity to low-level stimulus properties, such as luminance and contrast, the local image features were held constant during all phases of the MEG recording. This allowed us to assess the relative importance of striate (V1) versus extrastriate cortex in global form perception.

Methodology/Principal Findings

Stimuli were horizontal, rotational and radial Glass patterns. Glass patterns without coherent structure were viewed during the baseline period to ensure neuronal responses reflected perception of structure and not changes in local image features. The spatial distribution of task-related changes in source power was mapped using Synthetic Aperture Magnetometry (SAM), and the time course of activity within areas of maximal power change was determined by calculating time-frequency plots using a Hilbert transform. For six out of eight observers, passive viewing of global structure was associated with a reduction in 10–20 Hz cortical oscillatory power within extrastriate occipital cortex. The location of greatest power change was the same for each pattern type, being close to or within visual area V3a. No peaks of activity were observed in area V1. Time-frequency analyses indicated that neural activity was least for horizontal patterns.

Conclusions

We conclude: (i) visual area V3a is involved in the analysis of global form; (ii) the neural signature for perception of structure, as assessed using MEG, is a reduction in 10–20 Hz oscillatory power; (iii) different neural processes may underlie the perception of horizontal as opposed to radial or rotational structure; and (iv) area V1 is not strongly activated by global form in Glass patterns.     

Cortical maps: where theory meets experiments

Primary visual cortex (V1) has remarkably systematic functional maps. One commonly used class of computational models proposes that such maps are generated by a mechanism that projects the multiple dimensions of neuronal responses smoothly onto the two dimensions of cortex. In this issue of Neuron, Mriganka Sur and colleagues find a close match between such model predictions and measurements from ferret V1.     

Dimensional reduction of a V1 ring model with simple and complex cells

In this paper, we extend a framework for constructing low-dimensional dynamical systems models of mammalian primary visual cortex to a cortical network model that incorporates the full nonlinear effects of complex cells. The procedure consists of capturing the essential dynamics in a low-dimensional subspace using empirical methods, then recasting the equations in the reduced vector space. Previously, we considered visual cortical network models consisting of only simple cells with nearly linear responses to external stimuli. Here we show that fully nonlinear effects can be incorporated by examining the dimensional reduction of an idealized ring model of V1 with both simple and complex cells. We found it expedient to divide the subspace into four separate neuronal populations: excitatory simple, excitatory complex, inhibitory simple and inhibitory complex. In order to reproduce the fluctuation-driven dynamics in this reduced space, we incorporated (1) white noises with different intensities into individual neuronal populations, and (2) firing rate estimates to capture the probability of firing due to subthreshold fluctuations. With a more accurate, fitted connectivity, our modified dimensional reduced models can reproduce the firing rates, circular variances and modulation ratios observed in the original ring model.     

Emergence of orientation-selective inhibition in the primary visual cortex: a Bayes–Markov computational model

The recent consensus is that virtually all aspects of response selectivity exhibited by the primary visual cortex are either created or sharpened by cortical inhibitory interneurons. Experimental studies have shown that there are cortical inhibitory cells that are driven by geniculate cells and that, like their cortical excitatory counterparts, are orientation selective, though less sharply tuned. The main goal of this article is to demonstrate how orientation-selective inhibition might be created by the circuitry of the primary visual cortex (striate cortex, V1) from its nonoriented geniculate inputs. To fulfill this goal, first, a Bayes–Markov computational model is developed for the V1 area dedicated to foveal vision. The developed model consists of three parts: (i) a two-layered hierarchical Markov random field that is assumed to generate the activity patterns of the geniculate and cortical inhibitory cells, (ii) a Bayesian computational goal that is formulated based on the maximum a posteriori (MAP) estimation principle, and (iii) an iterative, deterministic, parallel algorithm that leads the cortical circuitry to achieve its assigned computational goal. The developed model is not fully LGN driven and it is not implementable by the neural machinery of V1. The model, then, is transformed into a fully LGN-driven and physiologically plausible form. Computer simulation is used to demonstrate the performance of the developed models.     

Different processing phases for features, figures, and selective attention in the primary visual cortex

Our visual system imposes structure onto images that usually contain a diversity of surfaces, contours, and colors. Psychological theories propose that there are multiple steps in this process that occur in hierarchically organized regions of the cortex: early visual areas register basic features, higher areas bind them into objects, and yet higher areas select the objects that are relevant for behavior. Here we test these theories by recording from the primary visual cortex (area V1) of monkeys. We demonstrate that the V1 neurons first register the features (at a latency of 48 ms), then segregate figures from the background (after 57 ms), and finally select relevant figures over irrelevant ones (after 137 ms). We conclude that the psychological processing stages map onto distinct time episodes that unfold in the visual cortex after the presentation of a new stimulus, so that area V1 may contribute to all these processing steps.     

Primary visual cortex and visual awareness

The primary visual cortex (V1) is probably the best characterized area of primate cortex, but whether this region contributes directly to conscious visual experience is controversial. Early neurophysiological and neuroimaging studies found that visual awareness was best correlated with neural activity in extrastriate visual areas, but recent studies have found similarly powerful effects in V1. Lesion and inactivation studies have provided further evidence that V1 might be necessary for conscious perception. Whereas hierarchical models propose that damage to V1 simply disrupts the flow of information to extrastriate areas that are crucial for awareness, interactive models propose that recurrent connections between V1 and higher areas form functional circuits that support awareness. Further investigation into V1 and its interactions with higher areas might uncover fundamental aspects of the neural basis of visual awareness.     

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.     

Mathematical modeling and parameter estimation of axonal cargo transport

This paper is about how cortical recurrent interactions in primary visual cortex (V1) together with feedback from extrastriate cortex can account for spectral peaks in the V1 local field potential (LFP). Recent studies showed that visual stimulation enhances the γ-band (25–90 Hz) of the LFP power spectrum in macaque V1. The height and location of the γ-band peak in the LFP spectrum were correlated with visual stimulus size. Extensive spatial summation, possibly mediated by feedback connections from extrastriate cortex and long-range horizontal connections in V1, must play a crucial role in the size dependence of the LFP. To analyze stimulus-effects on the LFP of V1 cortex, we propose a network model for the visual cortex that includes two populations of V1 neurons, excitatory and inhibitory, and also includes feedback to V1 from extrastriate cortex. The neural network model for V1 was a resonant system. The model’s resonance frequency (ResF) was in the γ-band and varied up or down in frequency depending on cortical feedback. The model’s ResF shifted downward with stimulus size, as in the real cortex, because increased size recruited more activity in extrastriate cortex and V1 thereby causing stronger feedback. The model needed to have strong local recurrent inhibition within V1 to obtain ResFs that agree with cortical data. Network resonance as a consequence of recurrent excitation and inhibition appears to be a likely explanation for γ-band peaks in the LFP power spectrum of the primary visual cortex.     

The symplectic structure of the primary visual cortex

We propose to model the functional architecture of the primary visual cortex V1 as a principal fiber bundle where the two-dimensional retinal plane is the base manifold and the secondary variables of orientation and scale constitute the vertical fibers over each point as a rotation–dilation group. The total space is endowed with a natural symplectic structure neurally implemented by long range horizontal connections. The model shows what could be the deep structure for both boundary and figure completion and for morphological structures, such as the medial axis of a shape.     

基于初级视觉皮层的同步振荡目标检测模型

提出一种基于初级视觉皮层的目标检测模型,该模型只采用方位选择性细胞和皮层内水平连接等Ｖ１基本单元,它以链码表示的目标轮廓作为知识,允许该知识以时间脉冲的形式控制Ｖ１区内神经细胞的动态活动,使与知识轮廓形状相符合的轮廓内的细胞进入同步振荡状态,实现对视野中特定目标轮廓的识别。计算机仿真结果表明,在较高级皮层的“知识”控制之下,初级视觉皮层结构上实现简单的目标检测是可行的。     

Computational Modeling of Orientation Tuning Dynamics in Monkey Primary Visual Cortex

In the primate visual pathway, orientation tuning of neurons is first observed in the primary visual cortex. The LGN cells that comprise the thalamic input to V1 are not orientation tuned, but some V1 neurons are quite selective. Two main classes of theoretical models have been offered to explain orientation selectivity: feedforward models, in which inputs from spatially aligned LGN cells are summed together by one cortical neuron; and feedback models, in which an initial weak orientation bias due to convergent LGN input is sharpened and amplified by intracortical feedback. Recent data on the dynamics of orientation tuning, obtained by a cross-correlation technique, may help to distinguish between these classes of models. To test this possibility, we simulated the measurement of orientation tuning dynamics on various receptive field models, including a simple Hubel-Wiesel type feedforward model: a linear spatiotemporal filter followed by an integrate-and-fire spike generator. The computational study reveals that simple feedforward models may account for some aspects of the experimental data but fail to explain many salient features of orientation tuning dynamics in V1 cells. A simple feedback model of interacting cells is also considered. This model is successful in explaining the appearance of Mexican-hat orientation profiles, but other features of the data continue to be unexplained.     

Compression and reflection of visually evoked cortical waves

Neuronal interactions between primary and secondary visual cortical areas are important for visual processing, but the spatiotemporal patterns of the interaction are not well understood. We used voltage-sensitive dye imaging to visualize neuronal activity in rat visual cortex and found visually evoked waves propagating from V1 to other visual areas. A primary wave originated in the monocular area of V1 and was "compressed" when propagating to V2. A reflected wave initiated after compression and propagated backward into V1. The compression occurred at the V1/V2 border, and local GABAA inhibition is important for the compression. The compression/reflection pattern provides a two-phase modulation: V1 is first depolarized by the primary wave, and then V1 and V2 are simultaneously depolarized by the reflected and primary waves, respectively. The compression/reflection pattern only occurred for evoked waves and not for spontaneous waves, suggesting that it is organized by an internal mechanism associated with visual processing.     

Surface-Based Analyses of Anatomical Properties of the Visual Cortex in Macular Degeneration

Introduction

Macular degeneration (MD) can cause a central visual field defect. In a previous study, we found volumetric reductions along the entire visual pathways of MD patients, possibly indicating degeneration of inactive neuronal tissue. This may have important implications. In particular, new therapeutic strategies to restore retinal function rely on intact visual pathways and cortex to reestablish visual function. Here we reanalyze the data of our previous study using surface-based morphometry (SBM) rather than voxel-based morphometry (VBM). This can help determine the robustness of the findings and will lead to a better understanding of the nature of neuroanatomical changes associated with MD.

Methods

The metrics of interest were acquired by performing SBM analysis on T1-weighted MRI data acquired from 113 subjects: patients with juvenile MD (JMD; n = 34), patients with age-related MD (AMD; n = 24) and healthy age-matched controls (HC; n = 55).

Results

Relative to age-matched controls, JMD patients showed a thinner cortex, a smaller cortical surface area and a lower grey matter volume in V1 and V2, while AMD patients showed thinning of the cortex in V2. Neither patient group showed a significant difference in mean curvature of the visual cortex.

Discussion

The thinner cortex, smaller surface area and lower grey matter volume in the visual cortex of JMD patients are consistent with our previous results showing a volumetric reduction in their visual cortex. Finding comparable results using two rather different analysis techniques suggests the presence of marked cortical degeneration in the JMD patients. In the AMD patients, we found a thinner cortex in V2 but not in V1. In contrast to our previous VBM analysis, SBM revealed no volumetric reductions of the visual cortex. This suggests that the cortical changes in AMD patients are relatively subtle, as they apparently can be missed by one of the methods.     

Visually Driven Activation in Macaque Areas V2 and V3 without Input from the Primary Visual Cortex

Creating focal lesions in primary visual cortex (V1) provides an opportunity to study the role of extra-geniculo-striate pathways for activating extrastriate visual cortex. Previous studies have shown that more than 95% of neurons in macaque area V2 and V3 stop firing after reversibly cooling V1 [1], [2], [3]. However, no studies on long term recovery in areas V2, V3 following permanent V1 lesions have been reported in the macaque. Here we use macaque fMRI to study area V2, V3 activity patterns from 1 to 22 months after lesioning area V1. We find that visually driven BOLD responses persist inside the V1-lesion projection zones (LPZ) of areas V2 and V3, but are reduced in strength by ∼70%, on average, compared to pre-lesion levels. Monitoring the LPZ activity over time starting one month following the V1 lesion did not reveal systematic changes in BOLD signal amplitude. Surprisingly, the retinotopic organization inside the LPZ of areas V2, V3 remained similar to that of the non-lesioned hemisphere, suggesting that LPZ activation in V2, V3 is not the result of input arising from nearby (non-lesioned) V1 cortex. Electrophysiology recordings of multi-unit activity corroborated the BOLD observations: visually driven multi-unit responses could be elicited inside the V2 LPZ, even when the visual stimulus was entirely contained within the scotoma induced by the V1 lesion. Restricting the stimulus to the intact visual hemi-field produced no significant BOLD modulation inside the V2, V3 LPZs. We conclude that the observed activity patterns are largely mediated by parallel, V1-bypassing, subcortical pathways that can activate areas V2 and V3 in the absence of V1 input. Such pathways may contribute to the behavioral phenomenon of blindsight.