Lowell D. Jacobson

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 cells 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.

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.

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 cells 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 cells spatial receptive field and frequency passband.

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.

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 (Fig. 1a). 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.

Cross-correlation analyses of nonlinear systems with spatiotemporal inputs (visual neurons)

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 given, 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.<<ETX>>

Structural classification of multi-input biological nonlinear systems

Structural classification and parameter estimation results that are applicable to multi-input nonlinear biological systems are presented. To use these methods properly, it is necessary first to establish that the structure of the system under study belongs to one of the broad structural classes examined; such a priori constraints would generally be inferred from the known anatomical and physiochemical properties of the system. Using the methods presented, input-output measurements are used to restrict the structural classification of the system further and to estimate the parameters of the classified model. Ongoing efforts to identify the spatiotemporal nonlinear networks that underlie the extracellularly recorded (spike) responses of visual cortical neurons to photic stimulation are discussed.<<ETX>>