Topographical Estimation of Visual Population Receptive Fields by fMRI

Visual cortex is retinotopically organized so that neighboring populations of cells map to neighboring parts of the visual field. Functional magnetic resonance imaging allows us to estimate voxel-based population receptive fields (pRF), i.e., the part of the visual field that activates the cells within each voxel. Prior, direct, pRF estimation methods¹ suffer from certain limitations: 1) the pRF model is chosen a-priori and may not fully capture the actual pRF shape, and 2) pRF centers are prone to mislocalization near the border of the stimulus space. Here a new topographical pRF estimation method² is proposed that largely circumvents these limitations. A linear model is used to predict the Blood Oxygen Level-Dependent (BOLD) signal by convolving the linear response of the pRF to the visual stimulus with the canonical hemodynamic response function. PRF topography is represented as a weight vector whose components represent the strength of the aggregate response of voxel neurons to stimuli presented at different visual field locations. The resulting linear equations can be solved for the pRF weight vector using ridge regression³, yielding the pRF topography. A pRF model that is matched to the estimated topography can then be chosen post-hoc, thereby improving the estimates of pRF parameters such as pRF-center location, pRF orientation, size, etc. Having the pRF topography available also allows the visual verification of pRF parameter estimates allowing the extraction of various pRF properties without having to make a-priori assumptions about the pRF structure. This approach promises to be particularly useful for investigating the pRF organization of patients with disorders of the visual system.     

Evaluating Population Receptive Field Estimation Frameworks in Terms of Robustness and Reproducibility

Within vision research retinotopic mapping and the more general receptive field estimation approach constitute not only an active field of research in itself but also underlie a plethora of interesting applications. This necessitates not only good estimation of population receptive fields (pRFs) but also that these receptive fields are consistent across time rather than dynamically changing. It is therefore of interest to maximize the accuracy with which population receptive fields can be estimated in a functional magnetic resonance imaging (fMRI) setting. This, in turn, requires an adequate estimation framework providing the data for population receptive field mapping. More specifically, adequate decisions with regard to stimulus choice and mode of presentation need to be made. Additionally, it needs to be evaluated whether the stimulation protocol should entail mean luminance periods and whether it is advantageous to average the blood oxygenation level dependent (BOLD) signal across stimulus cycles or not. By systematically studying the effects of these decisions on pRF estimates in an empirical as well as simulation setting we come to the conclusion that a bar stimulus presented at random positions and interspersed with mean luminance periods is generally most favorable. Finally, using this optimal estimation framework we furthermore tested the assumption of temporal consistency of population receptive fields. We show that the estimation of pRFs from two temporally separated sessions leads to highly similar pRF parameters.     

Perisaccadic Remapping and Rescaling of Visual Responses in Macaque Superior Colliculus

Visual neurons have spatial receptive fields that encode the positions of objects relative to the fovea. Because foveate animals execute frequent saccadic eye movements, this position information is constantly changing, even though the visual world is generally stationary. Interestingly, visual receptive fields in many brain regions have been found to exhibit changes in strength, size, or position around the time of each saccade, and these changes have often been suggested to be involved in the maintenance of perceptual stability. Crucial to the circuitry underlying perisaccadic changes in visual receptive fields is the superior colliculus (SC), a brainstem structure responsible for integrating visual and oculomotor signals. In this work we have studied the time-course of receptive field changes in the SC. We find that the distribution of the latencies of SC responses to stimuli placed outside the fixation receptive field is bimodal: The first mode is comprised of early responses that are temporally locked to the onset of the visual probe stimulus and stronger for probes placed closer to the classical receptive field. We suggest that such responses are therefore consistent with a perisaccadic rescaling, or enhancement, of weak visual responses within a fixed spatial receptive field. The second mode is more similar to the remapping that has been reported in the cortex, as responses are time-locked to saccade onset and stronger for stimuli placed in the postsaccadic receptive field location. We suggest that these two temporal phases of spatial updating may represent different sources of input to the SC.     

A geometric model of orientation tuning dynamics in visual neurons]

A geometrical model for the dynamics of orientation tuning of visual neurones was proposed, which makes it possible to study the dynamics of configuration, localization, and weight of excitatory and inhibitory subzones of the receptive field. The model reproduces typical patterns of orientation tuning dynamics, observed in neurophysiological experiments on cat visual cortex neurones. The parameters of the model (size and mutual position of excitatory and inhibitory zones of the receptive field, their weight, and dynamics type) were estimated that correspond to the main types of orientation tuning dynamics in natural conditions. It is shown that selective and acute tuning of neurones can be formed and/or sharpened by intracotrical inhibition, while the dynamics of preferred orientation is due to changes in the geometry of the inhibitory subzone of the receptive field.     

The local and non-local components of the local field potential in awake primate visual cortex

The Local Field Potential (LFP) is the analog signal recorded from a microelectrode inserted into cortex, typically in the frequency band of approximately 1 to 200 Hz. Here visual stimuli were flashed on in the receptive fields of primary visual cortical neurons in awake behaving macaques, and both isolated single units (neurons) and the LFP signal were recorded from the same unipolar microelectrode. The fall-off of single unit activity as a visual stimulus was moved from near the center to near the edge of the receptive field paralleled the fall-off of the stimulus-locked (evoked) LFP response. This suggests that the evoked LFP strongly reflects local neuronal activity. However, the evoked LFP could be significant even when the visual stimulus was completely outside the receptive field and the single unit response had fallen to zero, although this phenomenon was variable. Some of the non-local components of the LFP may be related to the slow distributed, or non-retinotopic, LFP signal previously observed in anesthetized animals. The induced (not time-locked to stimulus onset) component of the LFP showed significant increases only for stimuli within the receptive field of the single units. While the LFP primarily reflects local neuronal activity, it can also reflect neuronal activity at more distant sites, although these non-local components are typically more variable, slower, and weaker than the local components.     

Eye movements modulate visual receptive fields of V4 neurons

The receptive field, defined as the spatiotemporal selectivity of neurons to sensory stimuli, is central to our understanding of the neuronal mechanisms of perception. However, despite the fact that eye movements are critical during normal vision, the influence of eye movements on the structure of receptive fields has never been characterized. Here, we map the receptive fields of macaque area V4 neurons during saccadic eye movements and find that receptive fields are remarkably dynamic. Specifically, before the initiation of a saccadic eye movement, receptive fields shrink and shift towards the saccade target. These spatiotemporal dynamics may enhance information processing of relevant stimuli during the scanning of a visual scene, thereby assisting the selection of saccade targets and accelerating the analysis of the visual scene during free viewing.     

Visual receptive field organization

Increasingly systematic approaches to quantifying receptive fields in primary visual cortex, combined with inspired ideas about functional circuitry, non-linearities, and visual stimuli, are bringing new interest to classical problems. This includes the distinction and hierarchy between simple and complex cells, the mechanisms underlying the receptive field surround, and debates about optimal stimuli for mapping receptive fields. An important new problem arises from recent observations of stimulus-dependent spatial and temporal summation in primary visual cortex. It appears that the receptive field can no longer be considered unique, and we might have to relinquish this cherished notion as the embodiment of neuronal function in primary visual cortex.     

Adaptation-dependent synchronous activity contributes to receptive field size change of bullfrog retinal ganglion cell

Nearby retinal ganglion cells of similar functional subtype have a tendency to discharge spikes in synchrony. The synchronized activity is involved in encoding some aspects of visual input. On the other hand, neurons always continuously adjust their activities in adaptation to some features of visual stimulation, including mean ambient light, contrast level, etc. Previous studies on adaptation were primarily focused on single neuronal activity, however, it is also intriguing to investigate the adaptation process in population neuronal activities. In the present study, by using multi-electrode recording system, we simultaneously recorded spike discharges from a group of dimming detectors (OFF-sustained type ganglion cells) in bullfrog retina. The changes in receptive field properties and synchronization strength during contrast adaptation were analyzed. It was found that, when perfused using normal Ringer's solution, single neuronal receptive field size was reduced during contrast adaptation, which was accompanied by weakening in synchronization strength between adjacent neurons' activities. When dopamine (1 μM) was applied, the adaptation-related receptive field area shrinkage and synchronization weakening were both eliminated. The activation of D1 receptor was involved in the adaptation-related modulation of synchronization and receptive field. Our results thus suggest that the size of single neuron's receptive field is positively related to the strength of its synchronized activity with its neighboring neurons, and the dopaminergic pathway is responsible for the modulation of receptive field property and synchronous activity of the ganglion cells during the adaptation process.     

The Gaussian derivative model for spatial-temporal vision: I. Cortical model

How do we see the motion of objects as well as their shapes? The Gaussian Derivative (GD) spatial model is extended to time to help answer this question. The GD spatio-temporal model requires only two numbers to describe the complete three-dimensional space-time shapes of individual receptive fields in primate visual cortex. These two numbers are the derivative numbers along the respective spatial and temporal principal axes of a given receptive field. Nine transformation parameters allow for a standard geometric association of these intrinsic axes with the extrinsic environment. The GD spatio-temporal model describes in one framework the following properties of primate simple cell fields: motion properties, number of lobes in space-time, spatial orientation. location, and size. A discrete difference-of-offset-Gaussians (DOOG) model provides a plausible physiological mechanism to form GD-like model fields in both space and time. The GD model hypothesizes that receptive fields at the first stage of processing in the visual cortex approximate 'derivative analyzers' that estimate local spatial and temporal derivatives of the intensity profile in the visual environment. The receptive fields as modeled provide operators that can allow later stages of processing in either a biological or machine vision system to estimate the motion as well as the shapes of objects in the environment.     

Parietal neurons encoding visual space in a head-frame of reference.

Neurons of the visual system are known to have receptive fields organized in retinotopic coordinates. We wanted to test whether visual neurons existed whose receptive fields were organized in spatial coordinates. Extracellular recordings from single cells were carried out in one area of the posterior parietal cortex (area V6) of a behaving macaque monkey. Among a great majority of retinotopically organized visual cells, neurons whose visual receptive field did not shift with gaze were also found. These cells responded to the visual stimulation of the same spatial position independently of the animal's direction of gaze, that is, their receptive field was anchored to an absolute spatial location. We suggest that these neurons directly encode visual space and are involved in programming visually-guided motor actions in space.     

Inhibitory components in the neuronal response of the lateral suprasylvian cortical area in the cat

Inhibitory components in the response evoked by presentation of mobile visual stimuli in neurons belonging to the lateral suprasylvian area of the cerebral cortex were investigated in cats. It was demonstrated by comparing poststimulus histograms of neuronal response to movement in two opposite directions that the location of discharge centers within the receptive fields changed in relation to movement direction. No spatial area giving rise to the inhibitory component of response could be found in any of the neurons with monotone stationary structure of their receptive fields. Findings from experiments involving techniques of stimulating a test area of the receptive field separately indicated that inhibitory components of response in neurons of the lateral suprasylvian area with monotone organization of the receptive field could represent inhibitory after-response following the neuronal excitation produced by the visual stimulus traveling across this field.L. A. Orbeli Institute of Physiology, Academy of Sciences of the Armenian SSR, Erevan. Translated from Neirofiziologiya, Vol. 19, No. 3, pp. 299–308, May–June, 1987.     

Properties of neurons of the tectal portion of the visual system of the axolotl Ambystoma mexicanum]

In the tectum opticum of the adult neotenic A. mexicanum, responses of single neuronal units to diffuse illumination and moving visual stimuli have been investigated. Of 111 unites investigated, 27 are presented by tectal neurons, their maximum distribution being observed at a depth of 500-600 mu. In superficial layers 9 ipsi-elements were found; their receptive fields are located in the antero-dorsal part of the visual field, at both sides of the body axis. Among the units identified as the terminals of visual fibers, 70% have receptive fields of 5-10 degrees, being localized in general more close to the surface as compared to the units with the receptive field diameter of 40 and more degrees (11%). Visual neurons and ganglionic retinal cells with axons terminating in the tectum, exhibit poor specificity to the size of a stimulus within 5-30 degrees and do not react to stimuli of 2 degrees.     

End-to-end neural system identification with neural information flow

Neural information flow (NIF) provides a novel approach for system identification in neuroscience. It models the neural computations in multiple brain regions and can be trained end-to-end via stochastic gradient descent from noninvasive data. NIF models represent neural information processing via a network of coupled tensors, each encoding the representation of the sensory input contained in a brain region. The elements of these tensors can be interpreted as cortical columns whose activity encodes the presence of a specific feature in a spatiotemporal location. Each tensor is coupled to the measured data specific to a brain region via low-rank observation models that can be decomposed into the spatial, temporal and feature receptive fields of a localized neuronal population. Both these observation models and the convolutional weights defining the information processing within regions are learned end-to-end by predicting the neural signal during sensory stimulation. We trained a NIF model on the activity of early visual areas using a large-scale fMRI dataset recorded in a single participant. We show that we can recover plausible visual representations and population receptive fields that are consistent with empirical findings.     

A Feedback Model of Attention Explains the Diverse Effects of Attention on Neural Firing Rates and Receptive Field Structure

Visual attention has many effects on neural responses, producing complex changes in firing rates, as well as modifying the structure and size of receptive fields, both in topological and feature space. Several existing models of attention suggest that these effects arise from selective modulation of neural inputs. However, anatomical and physiological observations suggest that attentional modulation targets higher levels of the visual system (such as V4 or MT) rather than input areas (such as V1). Here we propose a simple mechanism that explains how a top-down attentional modulation, falling on higher visual areas, can produce the observed effects of attention on neural responses. Our model requires only the existence of modulatory feedback connections between areas, and short-range lateral inhibition within each area. Feedback connections redistribute the top-down modulation to lower areas, which in turn alters the inputs of other higher-area cells, including those that did not receive the initial modulation. This produces firing rate modulations and receptive field shifts. Simultaneously, short-range lateral inhibition between neighboring cells produce competitive effects that are automatically scaled to receptive field size in any given area. Our model reproduces the observed attentional effects on response rates (response gain, input gain, biased competition automatically scaled to receptive field size) and receptive field structure (shifts and resizing of receptive fields both spatially and in complex feature space), without modifying model parameters. Our model also makes the novel prediction that attentional effects on response curves should shift from response gain to contrast gain as the spatial focus of attention drifts away from the studied cell.     

A network that uses few active neurones to code visual input predicts the diverse shapes of cortical receptive fields

Computational models of primary visual cortex have demonstrated that principles of efficient coding and neuronal sparseness can explain the emergence of neurones with localised oriented receptive fields. Yet, existing models have failed to predict the diverse shapes of receptive fields that occur in nature. The existing models used a particular "soft" form of sparseness that limits average neuronal activity. Here we study models of efficient coding in a broader context by comparing soft and "bard" forms of neuronal sparseness. As a result of our analyses, we propose a novel network model for visual cortex. The model forms efficient visual representations in which the number of active neurones, rather than mean neuronal activity, is limited. This form of hard sparseness also economises cortical resources like synaptic memory and metabolic energy. Furthermore, our model accurately predicts the distribution of receptive field shapes found in the primary visual cortex of cat and monkey.     

A model study of the dynamic mechanisms of the double orientation tuning of the visual cortex neurons]

The dynamics of double orientation tuning of neurons in the visual cortex of cat was studied by means of computer simulation. It was possible to test the role of shape, relative localization and weight of the inhibitory and excitatory zones of a receptive field and the dynamics of these characteristics. It was shown that selective and acute double orientation tuning can be achieved only through changes in the weight of zones in the receptive fields with the end-stopping and lateral inhibitory zones whereas only the presence of the end-stopping inhibitory zone in the receptive field is sufficient during changes in zone localization and area.     

Receptive field families

It is generally agreed upon that size invariance and the absence of spurious resolution are two requirements that characterize well behaved spatial samping in visual systems. We show that these properties taken together constrain the structure of receptive fields to a very large degree. Only those field structures that arise as solutions of a certain linear partial differential equation of the second order prove to satisfy these general constraints. The equation admits of complete, orthonormal families of solutions. These families have to be regarded as the possible receptive field families subject to certain symmetry conditions. They can be transformed into each other via unitary transformations. Thus a single representation suffices to construct all the others. This theory permits us to classify the possible linear receptive field structures exhaustively, and to define their internal and external interrelations. This induces a principled taxonomy of linear receptive fields.     

Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity.     

Studies of functional connectivity in the developing and mature visual cortex

We have investigated several aspects of cortical organization in adult cats and in young kittens. First, we determined receptive field (RF) maps of correlated discharge between pairs of cortical cells. Unique bicellular RFs appear to convey high resolution information. Second, we studied the dynamics of neural interaction between pairs of cells. Using cross-correlation analysis, we studied monosynaptic and polysynaptic interactions in both kittens and cats. A somewhat surprising finding is that there were no cases of monosynaptic excitation from simple to complex cells as would be predicted by a simple hierarchical processing theory. Third, we studied length and side tuning characteristics of cortical cells and worked out the relationships between them. Fourth, we carried out an investigation of binocular processing in which we compared monocular and binocular sensitivity of cortical cells with respect to contrast. Our results are comparable to those found in psychophysical work. Fifth, we examined how stereoscopic depth information is encoded by simple cells in the visual cortex. We show that structural differences in RFs of left and right eyes may be expressed in terms of phase. Phase-based encoding appears to be a very plausible alternative to the standard position-based notion. Sixth, we attempted to induce plastic changes in connections between cell pairs by long-term activation (up to 2 h) in kittens and cats. Although connection strength between some cell pairs was increased during long-term activation, there was no consistent pattern of this effect. Seventh, we attempted to study the functional basis of reported claims of RF expansion following use of an artificial scotoma. However, we found no receptive field size change from this procedure. For some cells, there is an apparent change of gain in the form of base (spontaneous) rates and absolute response levels. Finally, we have examined RF dynamics in the central visual pathways. The standard treatment of RFs is to consider only spatial aspects. But the RF is inherently both temporal and spatial in nature and we have examined the dynamics of spatiotemporal organization of RFs in central visual pathways.