Striate cortex increases contrast gain of macaque LGN neurons.

Recurrent projections comprise a universal feature of cerebral organization. Here, we show that the corticofugal projections from the striate cortex (VI) to the lateral geniculate nucleus (LGN) robustly and multiplicatively enhance the responses of parvocellular neurons, stimulated by gratings restricted to the classical receptive field and modulated in luminance, by over two-fold in a contrast-independent manner at all but the lowest contrasts. In the equiluminant plane, wherein stimuli are modulated in chromaticity with luminance held constant, such enhancement is strongly contrast dependent. These projections also robustly enhance the responses of magnocellular neurons but contrast independently only at high contrasts. Thus, these results have broad functional significance at both network and neuronal levels by providing the experimental basis and quantitative constraints for a wide range of models on recurrent projections and the control of contrast gain.

Space-time spectra of complex cell filters in the macaque monkey: a comparison of results obtained with pseudowhite noise and grating stimuli.

White noise stimuli were used to estimate second-order kernels for complex cells in cortical area V1 of the macaque monkey, and drifting grating stimuli were presented to the sample of neurons to obtain orientation and spatial-frequency tuning curves. Using these data, we quantified how well second-order kernels predict the normalized tuning of the average response of complex cells to drifting gratings. The estimated second-order kernel of each complex cell was transformed into an interaction function defined over all spatial and temporal lags without regard to absolute position or delay. The Fourier transform of each interaction function was then computed to obtain an interaction spectrum. For a cell that is well modeled by a second-order system, the cell's interaction spectrum is proportional to the tuning of its average spike rate to drifting gratings. This result was used to obtain spatial-frequency and orientation tuning predictions for each cell based on its second-order kernel. From the spatial-frequency and orientation tuning curves, we computed peaks and bandwidths, and an index for directional selectivity. We found that the predictions derived from second-order kernels provide an accurate description of the change in the average spike rate of complex cells to single drifting sine-wave gratings. These findings are consistent with a model for complex cells that has a quadratic spectral energy operator at its core but are inconsistent with a spectral amplitude model.

Cross-correlation analyses of nonlinear systems with spatiotemporal inputs.

Methods are presented for analyzing the low-order stimulus-response cross-correlation functions (or kernels) of visual neurons studied with spatiotemporal white noise. In particular, formulas are derived that relate the low-order kernels of a cell to its responses to single-drifting, double-drifting, and counterphase gratings. The harmonic response terms contributed by the low-order kernels include a mean response term, first- and second-harmonic terms, and sum- and difference-harmonic terms. Using the formulas in this paper, one can obtain kernel-based predictions for the spatiotemporal-frequency tuning of each harmonic. These kernel-based predictions can then be compared with harmonic tuning data obtained in experiments with real grating stimuli. The methods are illustrated using data recorded from one simple and one complex cell from the primary visual cortex of the monkey. The approach of transforming low-order kernels into predicted harmonic tuning functions provides a useful data reduction technique as well as providing insight into the interpretation of kernels.

Structural testing of multi-input linear-nonlinear cascade models for cells in macaque striate cortex.

Structural testing methods based on experimental white noise stimulus-response data were used to evaluate multi-input linear-nonlinear (LN) cascade models for simple and complex cells in macaque striate cortex. An LN structural test index, based on white noise stimulation, was developed and found to be suitable for classifying cells as simple vs complex. In particular, classification results based on the LN structural test index were similar to classification results based on a traditional modulation index derived from cell responses to drifting sinewave gratings. Judging from their structural test indices, complex cells deviated more strongly from LN behavior than did simple cells. Yet, even with simple cells, on average, only about 60% of the first- and second-order white noise stimulus-response relation was consistent with LN behavior. Just two of thirteen simple cells studied had an LN consistency level that exceeded 80%. Similar results were found in tests for consistency with an LNL model which includes an additional linear post-filter. We conclude that a conventional multi-input LN network model may be a useful approximation to the response behavior of some simple cells. However, even during steady state stimulus conditions, subcortical and/or cortical nonlinearities other than a static output nonlinearity play a very significant role in shaping the responses of most simple cells in the macaque striate cortex.

Interneuronal interaction between members of quadrature phase and anti-phase pairs in the cat's visual cortex.

Interactions between adjacent simple cells recorded simultaneously from the same microelectrode placement were studied by correlational analysis. The receptive fields of pairs of such cells exhibit either 90 degrees (quadrature phase) or 180 degrees (anti-phase) phase relationships. We now show that the majority of quadrature phase pair members do not receive common input from the immediately precedent stage along the visual pathway, nor do these cells interact with each other. The anti-phase pairs show relatively strong mutual inhibition. These results suggest that each of the physically adjacent phase-related simple cells receives excitatory input from a distinct group of pre-cortical cells, and that mutual inhibitions between members of anti-phase pairs are used to construct the inhibitory subzones of these cells. We propose a model which incorporates these new results and provides a parsimonious explanation for the construction of both quadrature phase and anti-phase pairs.

Structural classification of multi-input nonlinear systems.

We present new structural classification and parameter estimation results that are applicable to multi-input nonlinear systems. The mathematical relationships between the self- and cross-(Volterra and Wiener) kernels are derived for a basic two-input nonlinear structure. These results are then used to develop classification methods for more complicated two-input structures. Algorithms for estimating the parameters (linear and nonlinear subsystems) of these structures are also presented.

Spatial and temporal frequency selectivity of neurons in visual cortical area V3A of the macaque monkey.

Response properties of neurons in V3A were studied at a retinal eccentricity of 2-4 deg. The distributions of spatial frequency bandwidths and orientation bandwidths were similar to those of neurons in V1. Peaks of spatial frequency tuning curves ranged from 0.35 to 8.0 c/deg with a mean of 1.75 c/deg. Most V3A cells showed lowpass or, less often, broad bandpass temporal frequency selectivity. The mean direction selectivity index was 0.41. The response properties of cells in V3A differed most from those in V1 with respect to the larger receptive field widths in V3A averaging about 4 deg, the consequent larger number of cycles of the preferred grating that fall within the receptive field, and the previously reported profound response suppression incurred when patches of the preferred grating are extended both within and beyond the classical receptive field. The response properties of cells in V3A differed most from those in V3 in that V3A neurons are much less selective to the speed and direction of stimulus motion than are neurons in V3. The overall response properties of cells in V3A are consistent with anatomical evidence that places this cortical area in the visual pathway from V3A to V4 and then to IT.

Responses of simple and complex cells to compound sine-wave gratings.

We have studied the responses of simple and complex cells in the primary visual cortex of the cat to rigidly drifting compound sine-wave gratings as a function of the phase offset between fundamental and harmonic frequencies that both fell within the passband of the cell. Simple cells show phase-dependent increases and decreases in peak and mean response which are predictable on the basis of a cell's line weighting function. However, the amplitudes and phases of the base and harmonic frequencies in the response are, in general, not well predicted by the relationships of these same components in the compound grating stimuli. These distortions are shown to be largely a consequence of the rectification that follows linear summation at the simple cell stage. Such distortions are, in principle, correctable when the responses of a second simple cell, as part of a 180 deg phase pair, are taken into account. Complex cells typically showed a strong nonlinear response component at the difference frequency of drifting compound gratings. This was sometimes accompanied by a linear response component at one, or both, of the separate stimulus frequencies. Information about the absolute phases of the frequency components of a compound grating is not preserved in the nonlinear response of complex cells; however, information about the local phase difference between the gratings is preserved. In effect, the nonlinear component of the complex cell response is proportional to the time-varying signal envelope that results from the mutual interference of stimulus frequencies that fall in the cell's spatial receptive field and frequency passband.

Diversity of complex cell responses to even- and odd-symmetric luminance profiles in the visual cortex of the cat.

We have tested the hypothesis that complex cell receptive fields are made up of subfields which, for a given cell, have either exclusively even or exclusively odd symmetry. To do this we have measured the response of complex cells in the visual cortex of the cat to members of pairs of spatially limited even-symmetric stimuli (single light and dark bars) and pairs of odd-symmetric stimuli ("light-dark" and "dark-light" double bars) successively drifting across their receptive fields. The strength of a cell's response was estimated by measuring the sum of all spikes produced by a stimulus. Some complex cells respond about equally to single light and dark bars; others respond appreciably more to either the light or dark bar. The central tendency of average response histograms was estimated by measuring the mean with respect to position across the width of the receptive field. Many complex cells show distinct spatial offsets between the mean for narrow single light and that for dark bars as well as between means to double bars of opposite phase. Combined offset plots were constructed with the spatial offsets between means for single light bars and single dark bars along the x axis and the offsets between means to double bars of opposite phase along the y axis. There is significant scatter in the combined offset points; some falling at the origin, some at significant distances from the origin along the axes, and others well within each of the four quadrants. These diverse localizations in the offset plots rule out the simple models of complex cell spatial substructure described above and, therefore, imply considerable heterogeneity within the population of complex cells.

Response suppression by extending sine-wave gratings within the receptive fields of neurons in visual cortical area V3A of the macaque monkey.

Even though there are many more cycles of the "optimal" grating extending across the receptive fields of cells in V3A than of cells in V1 and V2, the spatial frequency bandwidths in V3A are no narrower than in V1 or V2. Thus, the inputs to V3A cells are not combined in a phase coherent manner across the entire receptive field. Moreover, the defined receptive fields of cells in V3A are generally surrounded by suppressive regions which are, on average, much stronger than those found for neurons in V1 and V2. Even within the classical receptive field, most neurons in V3A respond far more vigorously to a limited patch of a few cycles of a grating at the preferred spatial frequency than to wider grating stimuli. This intra-receptive field suppression demonstrates a new level of response complexity, and suggests that V3A cells may antagonistically combine nonlinear mechanisms that themselves encode stimulus energy over a restricted region of space and spatial-frequency.

Spatial and temporal frequency selectivity of neurones in visual cortical areas V1 and V2 of the macaque monkey.

The spatial and temporal frequency selectivity of 148 neurones in the striate cortex, V1, and of 122 neurones in the second visual cortical area, V2, of the macaque monkey were studied using sine-wave gratings of suprathreshold contrast drifting over the receptive field at the preferred orientation and direction. Neurones in V1 and V2 were selective for different but partially overlapping ranges of the spatial frequency spectrum. At retinal eccentricities of 2-5 deg from the fovea, the spatial frequency preferences for neurones ranged from 0.5 to 8.0 cycles/deg in V1 and from 0.2 to 2.1 cycles/deg in V2 and were on average almost 2 octaves lower in V2 than in V1. Spatial frequency full band widths in the two cortical areas were in the range 0.8-3.0 octaves, with a mean value of 1.8 octaves, in the parafoveal representation of both V1 and V2, and 1.4 and 1.6 octaves respectively in the foveal representation of V1 and V2. Most neurones in V1 and some in V2 responded well at temporal frequencies up to 5.6-8.0 Hz before their responses dropped off at still higher frequencies. In V1, 68% of the neurones exhibited low-pass temporal tuning characteristics and 32% were very broadly tuned, with a mean temporal frequency full band width of 2.9 octaves. However, in V2 only 30% of the neurones showed low-pass temporal selectivity and 70% of the cells had bandpass temporal characteristics, with a mean full band width of 2.1 octaves. In V2 the minimal overlap of bandpass tuning curves across the temporal frequency spectrum suggests that there are at least two distinct bandpass temporal frequency mechanisms as well as neurones with low-pass temporal frequency tuning at each spatial frequency. A matrix of spatial and temporal frequency combinations was employed as stimuli for neurones with bandpass temporal frequency selectivity in both V1 and V2. The resultant spatio-temporal surfaces provided evidence that a neurone's preference for spatial frequency is essentially independent of the test temporal frequency; however, in V2 there was some tendency for temporal frequency peaks to shift slightly towards lower frequencies when non-optimum values of spatial frequency either above or below the preferred value were tested. Neurones with pronounced directional selectivity were encountered over a wide range of spatial frequencies, although in both cortical areas there was a tendency for an increased incidence of directional selectivity among neurones which were selective for lower spatial frequencies and higher temporal frequencies.