Spatiotemporal organization of simple-cell receptive fields in area 18 of cat’s cortex

Spatiotemporal structures of receptive-fields (RF) have been studied for simple cells in area 18 of eat by measuring the temporal transfer function (TTF) over different locations (subregions) within the RF. The temporal characteristics of different subregions differed from each other in the absolute phase shift (APS) to visual stimuli. Two types of relationships can be seen: (i)The APS varied continuously from one subregion to the next: (ii) A 180°-phase jump was seen as the stimulus position changed somewhere within the receptive field. Spatiotemporal receptive field profiles have been determined by applying reverse Fourier analysis to responses in the frequency domain. For the continuous type, spatial and temporal characteristics cannot be dissociated (space time inseparable) and the spatiotemporal structure is oriented. On the contrary, the spatial and temporal characteristics for the jumping type can be dissociated (space-time separable) and the structure is not oriented in the space-time plane. Based on the APSs measured at different subregions, the optimal direction of motion and optimal spatial frequency of neurons can be predicted.     

Receptive field types in the lateral geniculate body and their frequency characteristics]

Time amplitude -- frequency characteristics of the I and II types of receptive fields (RF) of lateral geniculate and their dependence on the contrast and spatial parameters of the light stimulus were studied. It is shown that the frequency characteristics of the RF I type depends on the contrast and area of the light stimulus, the higher being the contrast at a small area the smaller are the low frequencies. However at a large area of the stimulus the inhibition of low frequencies is greater at a small contrast. The transmitting band of frequency characteristics of RF II type does not depend on the contrast at a small area of the stimulus, at a large area a fall of low frequencies takes place at high contrasts of the stimulus. Such different behaviour of the receptive fields is explained by the models, which take into account RF spatial characteristics.     

A linear model for symmetric receptive fields: implications for classification tests with flashed and moving images

The purpose of this study was to explore the effects of spatial and temporal properties on the expected responses of visual neurons that have linear receptive fields (RFs), particularly those having a mirror symmetric distribution of spatial subregions. Receptive fields that are symmetric in at least one spatial dimension occur in neurons of the retina, the lateral geniculate nucleus (LGN), and the visual cortex of mammals. Responses to flashing bars, moving bars, and moving edges were studied for different configurations of an analog RF model in which spatial and temporal aspects were varied independently. Responses of the model at intermediate stimulus speeds were found to agree with responses in the literature for X and Y units of the LGN and often for simple units of the visual cortex. In particular, having separated regions of response to light and dark edges, an identifying property of simple cells, was found to be a linear consequence of RF regions responding inversely to stimuli of opposite polarity. Model differences from responses of cortical complex units show that a linear model cannot mimic their responses, and imply that complex units employ major nonlinearities in coding image polarity (light vs dark), which signifies a nonlinearity in coding intensity. Because sudden flux changes inherent in flashing bars test mainly temporal RF properties, and slowly moving edges test mainly spatial properties, these two tests form a useful minimal set with which to describe and classify RFs. The usefulness of this set derives both from its sensitivity to spatial and temporal variables, and from the correlation between the linearity of a cell's processing of stimulus intensity and its RF classification.     

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.     

Spatiotemporal frequency responses of cat retinal ganglion cells

Spatiotemporal frequency responses were measured at different levels of light adaptation for cat X and Y retinal ganglion cells. Stationary sinusoidal luminance gratings whose contrast was modulated sinusoidally in time or drifting gratings were used as stimuli. Under photopic illumination, when the spatial frequency was held constant at or above its optimum value, an X cell's responsivity was essentially constant as the temporal frequency was changed from 1.5 to 30 Hz. At lower temporal frequencies, responsivity rolled off gradually, and at higher ones it rolled off rapidly. In contrast, when the spatial frequency was held constant at a low value, an X cell's responsivity increased continuously with temporal frequency from a very low value at 0.1 Hz to substantial values at temporal frequencies higher than 30 Hz, from which responsivity rolled off again. Thus, 0 cycles X deg-1 became the optimal spatial frequency above 30 Hz. For Y cells under photopic illumination, the spatiotemporal interaction was even more complex. When the spatial frequency was held constant at or above its optimal value, the temporal frequency range over which responsivity was constant was shorter than that of X cells. At lower spatial frequencies, this range was not appreciably different. As for X cells, 0 cycles X deg-1 was the optimal spatial frequency above 30 Hz. Temporal resolution (defined as the high temporal frequency at which responsivity had fallen to 10 impulses X s-1) for a uniform field was approximately 95 Hz for X cells and approximately 120 Hz for Y cells under photopic illumination. Temporal resolution was lower at lower adaptation levels. The results were interpreted in terms of a Gaussian center-surround model. For X cells, the surround and center strengths were nearly equal at low and moderate temporal frequencies, but the surround strength exceeded the center strength above 30 Hz. Thus, the response to a spatially uniform stimulus at high temporal frequencies was dominated by the surround. In addition, at temporal frequencies above 30 Hz, the center radius increased.     

Out of the Randomness: Correlating Noise in Biological Systems

The study of the dynamics of biological systems requires one to follow relaxation processes in time with micron-size spatial resolution. This need has led to the development of different fluorescence correlation techniques with high spatial resolution and a tremendous (from nanoseconds to seconds) temporal dynamic range. Spatiotemporal information can be obtained even on complex dynamic processes whose time evolution is not forecast by simple Brownian diffusion. Our discussion of the most recent applications of image correlation spectroscopy to the study of anomalous sub- or superdiffusion suggests that this field still requires the development of multidimensional image analyses based on analytical models or numerical simulations. We focus in particular on the framework of spatiotemporal image correlation spectroscopy and examine the critical steps in getting information on anomalous diffusive processes from the correlation maps. We point out how a dual space-time correlative analysis, in both the direct and the Fourier space, can provide quantitative information on superdiffusional processes when these are analyzed through an empirical model based on intermittent active dynamics. We believe that this dual space-time analysis, potentially amenable to mathematical treatment and to the exact fit of experimental data, could be extended to include the rich phenomenology of subdiffusive processes, thereby quantifying relevant parameters for the various motivating biological problems of interest.     

Orientation and spatiotemporal tuning of cells in the primary visual cortex of an Australian marsupial,the wallaby<Emphasis Type="Italic"> Macropus eugenii</Emphasis>

The metatherians (marsupials) have been separated from eutherians (placentals) for approximately 135 million years. It might, therefore, be expected that significant independent evolution of the visual system has occurred. The present paper describes for the first time the orientation, direction and spatiotemporal tuning of neurons in the primary visual cortex of an Australian marsupial, the wallaby Macropus eugenii. The stimuli consisted of spatial sinusoidal gratings presented within apertures covering the classical receptive fields of the cells. The neurons can be classified as those with clear ON and OFF zones and those with less well-defined receptive field structures. Seventy-percent of the total cells encountered were strongly orientation selective (tuning functions at half height were less than 45 degrees ). The preferred orientations were evenly distributed throughout 360 degrees for cells with uniform receptive fields but biased towards the vertical and horizontal for cells with clear ON-OFF zones. Many neurons gave directional responses but only a small percentage of them (4%) showed motion opponent properties (i.e. they were excited by motion in one direction and actively inhibited by motion in the opposite direction). The median peak temporal tuning for cells with clear ON-OFF zones and those without were 3 Hz and 6 Hz, respectively. The most common peak spatial frequency tuning for the two groups were 2 cycles per degree and 0.5 cycles per degree, respectively. Spatiotemporal tuning was not always the same for preferred and antipreferred direction motion. In general, the physiology of the wallaby cortex was similar to well studied eutherian mammals suggesting either convergent evolution or a highly conserved architecture that stems from a common therian ancestor.     

Spike-based synaptic plasticity and the emergence of direction selective simple cells: mathematical analysis

In the companion paper we presented extended simulations showing that the recently observed spike-timing dependent synaptic plasticity can explain the development of simple cell direction selectivity (DS) when simultaneously modifying the synaptic strength and the degree of synaptic depression. Here we estimate the spatial shift of the simple cell receptive field (RF) induced by the long-term synaptic plasticity, and the temporal phase advance caused by the short-term synaptic depression in response to drifting grating stimuli. The analytical expressions for this spatial shift and temporal phase advance lead to a qualitative reproduction of the frequency tuning curves of non-directional and directional simple cells. In agreement with in vivo recordings, the acquired DS is strongest for test gratings with a temporal frequency around 1–4 Hz. In our model this best frequency is determined by the width of the learning function and the time course of depression, but not by the temporal frequency of the training stimuli. The analysis further reveals the instability of the initially symmetric RF, and formally explains why direction selectivity develops from a non-directional cell in a natural, directionally unbiased stimulation scenario.     

Characterization of spatial and temporal properties of monkey LGN Y-cells

LGN Y-cells in 3 anaesthetized (N₂O/O₂) and paralyzed rhesus monkeys were investigated with stimuli, intensity modulated by gaussian white noise, and with moving and counterphase modulated spatial sine wave gratings. The results support the model, postulated on the base of electrophysiological recordings in the retina of cat and mudpuppy, which consists of a linear centre and surround mechanism whose responses are modified in a frequency-selective multiplicative way by a nonlinear mechanism in the receptive field. This nonlinear mechanism is also held responsible for the second-order harmonic responses, which are the defining characteristic of Y-cells. The temporal and spatial characteristics of these mechanisms were determined. The responses obtained with the GWN stimulation and with modulated spatial sine wave gratings both indicate that the optimal temporal frequency of the linear mechanisms is near 7 Hz at 70 td and near 5 Hz for the nonlinear mechanism. The optimal spatial frequency for the linear mechanism is between 0.5–2 cycles/deg and between 6–12 cycles/deg for the nonlinear mechanism.     

Spatial properties of goldfish ganglion cells

We systematically classified goldfish ganglion cells according to their spatial summation properties using the same techniques and criteria used in cat and monkey research. Results show that goldfish ganglion cells can be classified as X-, Y-, or W-like based on their responses to contrast-reversal gratings. Like cat X cells, goldfish X-like cells display linear spatial summation. Goldfish Y-like cells, like cat Y cells, respond with frequency doubling at all spatial positions when the contrast-reversal grating consists of high spatial frequencies. There is also a third class of neurons, which is neither X- nor Y-like; many of these cells' properties are similar to those of the "not-X" cells found in the eel retina. Spatial filtering characteristics were obtained for each cell by drifting sinusoidal gratings of various spatial frequencies and contrasts across the receptive field of the cell at a constant temporal rate. The spatial tuning curves of the cell depend on the temporal parameters of the stimulus; at high drift rates, the tuning curves lose their low spatial frequency attenuation. To explore this phenomenon, temporal contrast response functions were derived from the cells' responses to a spatially uniform field whose luminance varied sinusoidally in time. These functions were obtained for the center, the surround, and the entire receptive field. The results suggest that differences in the cells' spatial filtering across stimulus drift rate are due to changes in the interaction of the center and surround mechanisms; at low temporal frequencies, the center and surround responses are out-of-phase and mutually antagonistic, but at higher temporal rates their responses are in-phase and their interaction actually enhances the cell's responsiveness.     

Receptive field properties of near neighbor orientation selective neurons in the visual cortex: a modeling study

The primary visual cortex is organized into clusters of cells having similar receptive fields (RFs). A purely feedforward model has been shown to produce realistic simple cell receptive fields. The modeled cells capture a wide range of receptive field properties of orientation selective cortical cells. We have analyzed the responses of 78 nearby cell pairs to study which RF properties are clustered. Orientation preference shows strongest clustering. Orientation tuning width (hwhh) and tuning height (spikes/sec) at the preferred orientation are not as tightly clustered. Spatial frequency is also not as tightly clustered and RF phase has the least clustering. Clustering property of orientation preference, orientation tuning height and width depend on the location of cells in the orientation map. No such location dependence is observed for spatial frequency and RF phase. Our results agree well with experimental data.     

Emergence of spatiotemporal receptive fields and its application to motion detection

A model of motion sensitivity as observed in some cells of area V1 of the visual cortex is proposed. Motion sensitivity is achieved by a combination of different spatiotemporal receptive fields, in particular, spatial and temporal differentiators. The receptive fields emerge if a Hebbian learning rule is applied to the network. Similar to a Linsker model the network has a spatially convergent, linear feedforward structure. Additionally, however, delays omnipresent in the brain are incorporated in the model. The emerging spatiotemporal receptive fields are derived explicitly by extending the approach of MacKay and Miller. The response characteristic of the network is calculated in frequency space and shows that the network can be considered as a spacetime filter for motion in one direction. The emergence of different types of receptive field requires certain structural constraints regarding the spatial and temporal arborisation. These requirements can be derived from the theoretical analysis and might be compared with neuroanatomical data. In this way an explicit link between structure and function of the network is established.     

Temporal pattern discrimination within the receptive field of cat retinal ganglion cells

ON-center and OFF-center receptive fields of cat retinal ganglion cells can be divided into two categories: sensitive (type N) and insensitive (type L) to three statistical temporal visual stimuli with different second order statistics but identical first order statistics (Tsukada et al. 1982). The temporal pattern sensitivity of type N response is closely related to the nonlinear stage of Y cells depending on the interaction between center and surround mechanism. The temporal pattern sensitivity of type N responses has a spatial profile within the receptive field; it is highly sensitive in the center region of the receptive field and less sensitive toward the field periphery. The temporal pattern sensitivity in the center region of the receptive field to statistical properties (irregular or regular) of a surrounding flash annulus shows modulation like a switching element: when the surrounding area is stimulated by a more regular flash stimulus with normal distribution of inter-stimulus intervals the system is sensitive (switching on) to the temporal pattern, while a change to an irregular one with an exponential distribution makes it insensitive (switching off) to the temporal pattern.     

Types of receptive fields in the lateral geniculate body and their functional model

In the Type I receptive fields (RFs) changes of the luminance leads to a shift of the curve relating the response and the stimulus area along the abscissa, in the Type II RFs the maximum of a response does not shift with changes of the luminance (Types I and II on classification by Glezer et al., 1971, 1972). The transient responses were observed in the Type I RFs and sustained responses in the Type II RFs. In the Type I RFs variation of the stimulus area and intensity brings about the change in the temporal and spatial frequency characteristics. This is produced by functional reorganization of the RF. In the Type II RFs there is no functional reorganization. The data obtained indicate that the Type I RFs are non-linear. By contrast, the Type II RFs are linear systems. The analysis of the model has shown that the distinctions in the dynamic characteristics of the responses of RFs belonging to different types is mainly due to different time constants for excitation and inhibition as well as inhibition coefficients. Distinctions in the mode of dependence of the RF response on stimulus parameters have been found to result from different relationship between delay time and stimulus parameters as well as different forms of the spatial weighting functions. It is shown that the Type I RFs transmit higher frequency components of the image spectrum, i.e. they emphasise the temporal and spatial contrasts. The Type II RFs transmit low frequency components of the spectrum including information about the intensity of an input stimulus.     

Nonlinear characteristics in the Frog's visual system

The receptive fields of retinal fibers in the visual tectum of the frog are mapped with different techniques and the spatial summation characteristics are examined, by presenting stimuli of various shapes and sizes in the center of the receptive field. When the size is increased gradually from the center of the stimulus, for constant stimulus intensity, the maximum response is obtained for stimuli of approximately the size of the most responsive part of the RF. Using a clustering technique to obtain stimuli that are part of the RF and combinations of these parts, it is evident that the spatial summation characteristics are not linear. A model is developed that describes the nonlinear form of these results, based on a power law.     

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.     

Seeing objects in motion

This paper reports estimates of the conjoint spatiotemporal tuning functions of the neural mechanisms of the human vision system which detect image motion. The functions were derived from measurements of the minimum contrast necessary to detect the direction of drift of a sinusoidal grating, in the presence of phase-reversed masking gratings of various spatial and temporal frequencies. A mask of similar spatial and temporal frequencies to the test grating reduces sensitivity considerably, whereas one differing greatly in spatial or temporal frequency has little or no effect. The results show that for test gratings drifting at 8 Hz, the tuning function is bandpass in both space and time, peaked at the temporal and spatial frequency (SF) of the test (SFs were 0.1, 1 or 5 c deg-1; c represents cycles throughout). For a grating of 5 c deg-1 drifting at 0.3 Hz, the function is bandpass in space but lowpass in time. Fourier transform of the frequency results yields a function in space-time which we term the 'spatiotemporal receptive field'. For movement detectors (bandpass in space and time) the fields comprise alternating ridges of opposing polarity, elongated in space-time along the preferred velocity axis of the detector. We suggest that this organization explains how detectors analyse form and motion concurrently and accounts, at least in part, for a variety of perceptual phenomena, including summation, reduction of motion smear, metacontrast, stroboscopic motion and spatiotemporal interpolation.     

Spatio-temporal organization of receptive fields of the cat striate cortex

The responses of cortical cells to gratings and bars were compared. The excitatory and inhibitory on-and off-zones of a simple cell are composed of on- and off-subfields of CGL. Any zone is formed by an opponent pair of subfields one of which gives an excitatory effect, the other — inhibitory. Such organization assumes the linear properties of a simple field. The deviations from linearity are due to spatial dis-placements of the subfields, heterogeneity of subfields, or the absence of one subfield in the opponent pair. Subfields may be both phasic and tonic, even in the same RF. Analysis of the most common type of a complex cell with modulated responses against unmodulated background shows that a mask eliminating stimulation of any half of the RF causes (according to the theory of filtres) increasing the bandwidth due to the increase or the appearance of responses to side low and high frequencies. The modulated components of the responses from both halves of the RF are out of phase. Analysis of this fact and the responses to thin bars suggests that a complex field is formed by linear and nonlinear subsystems converging onto output neuron. Other types of complex fields are organized by different combinations of subsystems. Limited in area by masking the RF responds to much higher spatial frequencies than the whole RF. The optimal frequency in two-dimensional spatial frequency characteristics of the RF does not change with orientation. Simple RFs and a part of complex RF calculate the amplitude and the phase of the stimulus, the other part of complex RFs (with unmodulated response) calculate only amplitude. Given all this, the RFs are grating filters of spatial frequency.