Objective evidence for phase-independent spatial frequency analysis in the human visual pathway

Vision Res. VoL 28, No. 1, pp. 18%191, 1988 Printed in Great Britain. All fights reserved

0042-6989/88 $3.00+0.00 Copyright © 1988 Pergamon Journals Ltd

RESEARCH

NOTE

OBJECTIVE EVIDENCE FOR PHASE-INDEPENDENT SPATIAL FREQUENCY ANALYSIS IN THE HUMAN VISUAL PATHWAY D. REGAN1"* and MARIAN P. REGAN2 Departments of 1Ophthalmology and 2Mathematics, Dalhousie University, Halifax, Nova Scotia, Canada (Received 5 January 1987; in revised form 29 May 1987)

Abstract--Electrophysiological responses in human index an interaction between responses to two gratings that is relatively independent of the distribution of light in the retinal image. Two 5 cycle/deg sinewave gratings were superimposed, one counterphase-modulated at Fl Hz and the other at F2 Hz. Nonlinear interaction terms of frequency (nFI +_mF2)were recorded that could not be produced by superimposing the FI Hz grating on blank-field 7 Hz flicker. A local luminance origin could be excluded for the (2F1 + 2F2) term and for the suppression of 2F 1 and 4F1, but not for the (F1+ F2), (FI + 3F2) and (5F2- FI) terms. The relative spatial phase of the two gratings was varied, thus altering the light distribution in the retinal image without changing its spatial power spectrum. The (2F 1+ 2F2) Hz contrast-specific grating-grating interaction term was almost unaffected by these substantial changes in retinal image light distribution providing that the spatial frequency power spectrum of the retinal image was held constant. The (2FI + 2F2) term and the suppression of 2F1 were both tuned to spatial frequency. Spatial vision

Contrast sensitivity

Evoked potentials

INTRODUCTION

This note addresses the question whether the human visual pathway contains supr~tthreshold mechanisms that are sensitive to the spatial frequency power spectrum of the retinal image independently of the distribution of light in the retinal image. METHODS

We superimposed two vertical sinewave gratings, each of 5 c/deg spatial frequency on the face of a Joyce CRT of mean luminance 264 cd/m 2 with a white P4 phosphor. The fixed grating's contrast was 20%, and it was counterphase-modulated by an F~ Hz sinewave (nominally 8 Hz). The variable grating's contrast was 40%, and it was counterphasemodulated by an F2 Hz sinewave (nominally

*Please address reprint requests to: D. Regan, Psychology Department, B.S.B., York University, 4700 Keele Street, North York, Ontario, Canada M3J 1P3. t A complete account of the mathematics is in the progress of publication (Regan, 1987).

Spatial frequency

7 Hz). The CRT's static calibration characteristic was linear to within 2% up to 85% contrast. Evoked potentials were analyzed in the frequency domain by a Bruel & Kjaer analyzer model 2032 using a nondestructive zoom-FFT technique (Regan, 1987) that provided a resolution of 0.0078 Hz over a d.c.-100 Hz bandwidth for a 320 sec recording period (i.e. 12,800 real frequency bins) with frequency-domain averaging also. This technique allows very small evoked potential components to be recorded at excellent signal-to-noise ratios. Up to 20 discrete frequency components were recorded simultaneously. Their frequencies were equal to (nF~ + mF2) to an accuracy of at least 0.03%, where n and m are integers or zero.t In the context of spatial vision two of the second order nonlinear (nFt + mF2) terms in the human evoked potential (namely F~ + F2 and F~ - F2) have previously been used to study interactions between adjacent edges (Ratliff and Zemon, 1982; Zemon and Ratliff, 1982, 1984). Second order cross-modulation terms have also been described in cat retinal ganglion cell firing (Victor, 1977; Victor and Shapley, 1980) and, 187

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Fig. 1. Discrete frequency components of the steady-state evoked potential. Two sections of the d.c.-100 power spectrum are shown at ultra-narrowband 0.0078 Hz resolution. (A) The stimulus was a single grating that was counterphase-modulated at a nominal 8 Hz (actually 7.938 Hz). For comparison purposes the alpha region near I0 Hz is included in the spectrum. (B) The grating in (A) was exactly superimposed on a second grating that was counterphase-modulated at a nominal 7 Hz (actually 7.080 Hz). (C) The grating in (A) was superimposed on an unpatterned field flickering at 7.080 Hz. For any small retinal area the superimposed F 2 Hz grating in (B) was identical to the superimposed flicker in (C). Thus, the terms boxed in (B) index nonlinear grating-grating interactions and are not explicable in terms of flicker processing or grating-flicker interactions. Ordinates are the dimensions of volts2. Recording was between the inion and an electrode midway between inion and vertex with vertex grounded. Viewing was binocular.

although higher-order terms were not resolved, their presence could be inferred (Victor and Shapley, 1980, p. 475). In human there is some psychophysical evidence for nonlinear interactions between simultaneously-presented gratings (Sagi and Hochstein, 1983, 1985). RESULTS AND DISCUSSION

First it was necessary to identify frequency components that were specific to spatial contrast rather than being explicable in terms of

local flicker. Figure 1 illustrates the crucial control experiment. Figure I(A) shows two sections of the EEG power spectrum recorded during stimulation with a single grating that was counterphasemodulated at (nominally) F = 8 Hz. The response consisted of sharply-defined spikes at 2FI = 16 Hz, 4F~ -- 32 Hz and (not shown) other even harmonics of 8 Hz. Even at this ultra-high frequency resolution, VEP frequency components were often concentrated into a single 0.0078 Hz bin, implying, as noted previously

Research Note (Regan, 1966, 1972), an amplitude and frequency stability that is quite remarkable for a physiological system. Figure l(B) shows two sections of the spectrum recorded when a second grating, counterphase-modulated at 7 Hz, was exactly superimposed on the Fig. I(A) grating with a relative spatial phase of zero. The 2FI and 4F~ spikes were abolished, and several new terms appeared of frequency (nFl +_mF2). One of these cross-modulation terms, the (F~ + F2) Hz component, was larger than any other frequency component of the response. The terms that index a nonlinear interaction between responses to the two gratings are shown in boxes. Four control experiments were then carried out. First, an instrumental control: a linear photocell was placed in front of the CRT and its output subjected to the same spectral analysis as that used in Fig. 1. Nonlinear cross-modulation products were essentially zero, the largest having 0.02% of the power of the linear F~ and F2 signals. Then' the EEG amplifier's linearity was tested: when fed with two equal-amplitude sinewaves, the largest cross-modulation term was 0.04% of the power of t~aetwo fundamental sinewave components at full drive. Next the sum of 7 and 8 Hz sinusoids was fed directly into the spectral analyzer. Cross-modulation terms were essentially zero (below 0.01% of the amplitude of the sinewave inputs). We conclude that the nonlinear terms, boxed in Fig. I(B), were not due to nonlinearity of the CRT, the EEG amplifier or the spectral analyzer. The fourth control experiment was physiological. A uniform (unpatterned) field flickering sinusoidally at 7 H z was superimposed on the Fig. I(A) grating. The flickering field had the same mean luminance as the F2 Hz grating and the modulation depth was 40%. The rationale of this experiment was that if we consider any given small retinal area there is no difference whatsoever between the superimposed 7 H z grating in Fig. I(B) and the superimposed homogeneous 7 Hz flicker in Fig. I(C). Yet Fig. I(C) shows that this superimposed blank-field 7 Hz flicker produced a dramatically different effect to a superimposed 7 Hz counterphase-modulated grating. The nonlinear interaction terms boxed in Fig. I(B) were absent in Fig. 1(C), the Fig. I(A) 2F~ and 4F~ terms that were abolished in Fig. I(B) are not abolished in Fig. I(C). These findings do not reject the possibility that the (F~ + F2), (F~ + 3F2) and (5F~ - F~)

189

terms in Fig. I(B) were due to local luminance processing. In Fig. 1(C), the Fl Hz local flicker in adjacent bars was in antiphase, while the F2 Hz flicker was in the same phase over the entire stimulus field. Therefore, any (Fi + F2) component due to local luminance processing would be in antiphase in adjacent bars (Bennet, 1933), and would cancel over the whole stimulus field. Therefore, the absence of an (F~ +F2) component in Fig. 1(C) does not allow us to exclude a local luminance origin for the (Fi +F2) component in Fig. I(B). The same argument holds for the (F~+3F2) and (5F2-F~) terms (Bennet, 1933). But, if the (2F~ + 2F2) term in Fig. I(B) were due to local luminance processing it should also be present in Fig. I(C), because the (2F~ + 2 F : ) terms generated by adjacent bars would have a relative phase of 360 deg. Because the (2FI + 2F2) term is not present in Fig. I(C) we can conclude that local luminance processing does not generate the (2F~ + 2F2) term in Fig. l(C), and this implies that the (2F~ + 2F2) term in Fig. l(B) is not due to local luminance processing. In addition, the failure of homogeneous-field flicker to abolish the 2F1 and 4F1 terms in Fig. I(C) indicates that their abolition in Fig. l(B) is not due to the processing of local luminance but rather to the processing of spatial pattern. Having established that the (2F1 + 2F2) terl~. specifically indexes the visual processing of pattern rather than local flicker we then asked whether it was determined by the spatial frequency power content of the stimulus independently of the particualr pattern of light distribution in the retinal image. Our rationale was as follows. We varied the relative phase of the two superimposed gratings. This manoeuvre dramatically changed the luminance distribution in the retinal image while leaving the spatial frequency power content unaffected. Figure 2 shows the results of this manipulation for two subjects. The observation that the (F1 + F2), (FI + 3F2) and (5F2- F~) terms fall to zero at 90 deg spatial phase is again consistent with a local luminance origin. At 90 deg spatial phase, half of each F1 Hz bar is covered by an F2 Hz bar while the other half is covered by a second F2 Hz bar with 180 deg temporal phase. Following the previous argument, (F~ +F2), (F~ + 3F2) and ( 5 F 2 - F 0 terms of local luminance origin will cancel at 90 deg spatial phase. On the other hand, Fig. 2(B) and (D) show that the (2F~ + 2F2) term is tolerably independent of the particular light distribution in the retinal

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Fig. 2. The effect of relative spatial phase on the amplitudes o( nonlinear interactions between two superimposed gratings. As phase was changed from 0 to 180 deg, the light distribution across the retinal image changed considerably, but the spatial frequency power content remained constant. The interaction terms in (A) were strongly affected, l~ut the (2Ft + 2F2) term in (B) was comparatively independent of relative phase. Panels (C) and (D)] show similar results for a second subject. Amplitudes are in microvolts pk-pk. Other technical details as for Fig. I(B).

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Research Note

the phase-independence that is shown by some complex cells in monkey visual cortex (De Valois et al., 1982). Furthermore, the nonlinear VEP properties of frequency doubling [Fig. I(A)] and the VEP interaction components boxed in Fig. I(B) can be modelled in terms of a compressive rectifier (Regan, 1987), thus providing a second parallel with the complex cell: De Valois et al. (1982) state that many complex cells in macaque give a frequencydoubled response to a counterphase-modulated grating [see Fig. 1(A)] that is "virtually the same at every spatial phase," implying that, as for retinal Y cells (Victor and Shapley, 1979), the number of rectifying subunits distributed throughout the visual field is large. (Though other authors found that the nonlinear response varied with spatial phase in the complex cortical cells that they studied, implying that those cells contained rather few subunits in the receptive fields [Spitzer and Hochstein, 1985].) The fact that the (2F1Jr 2F2) term contains only even multiples of F1 and F2 is consistent with the tentative suggestion that the term could reflect an interaction between 2FI and 2F2 signals that are themselves produced at an earlier stage of contrast-specific processing [cf. Fig. 1(A)]. The orientation tuning of this phase-independent term is described elsewhere (Regan, 1987). Acknowledgements--Our thanks to Janet Lord for assistance in preparing this manuscript. We thank the two anonymous reviewers for their valuable comments. Parts of this research was supported by the Natural Sciences and Engineering Research Council, the Medical Research Council of Canada, and the National Eye Institute, and sponsored by the U.S. Air Force Office of Scientific Research.

REFERENCES Bennet W. R. (1933) New results in the calculation of modulation products. Bell Syst. Tech. J., pp. 228-243.

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De Valois R. L., Albrecht D. G. and Thorell L. G. (1982) Spatial frequency selectivity of cells in macaque visual cortex. Vision Res. 22, 545-559. Fiorentini A., Pirchio M. and Spinelli D. (1983) Electrophysiological evidence for spatial frequency selective mechanisms in adults and infants. Vision Res. 23, 119-127. Julesz B. (1980) Spatial nonlinearities in the instantaneous perception of textures with identical power spectra. Phil. Trans. R. Soc. B 290, 83-94. Ratliff F. and Zemon V. (1982) Some new methods for the analysis of lateral interactions that influence the visual evoked potential. Ann. N.Y. Acad. Sci. 388, 113-124. Regan D. (1966) Some characteristics of average steadystate and transient responses evoked by modulated light. Electroenceph. clin. Neurophysiol. 20, 238-248. Regan D. (1972) Evoked Potentials in Sensory Psychology and Clinical Medicine. Chapman & Hall, London; Wiley, New York. Regan D. (1983) Spatial frequency mechanisms in human vision investigated by evoked potential recording. Vision Res. 23, 1401-1408. Regan D. (1987) Human Brain Electrophysiology: Evoked Potentials in Science and Medicine. Chapman & Hall, London; Oxford Univ. Press, New York. Sagi D. and ~Hochstein S. (1983) Discriminability of suprathreshold compound spatial frequency gratings. Vision Res. 23, 1595-1606. Sagi D. and Hochstein S. (1985) Lateral inhibition between spatially adjacent spatial-frequency channels. Percept. Psychophys. 37, 315-322. Spitzer H. and Hochstein S. (1985) A complex-cell receptive field model. J. NeurophysioL 53, 1266-1286. Victor J. D. and Shapley R. M. (1979) The nonlinear pathway of Y ganglion cells in cat retina. J. gen. Physiol. 74, 671~589. Victor J. D. and Shapley R. M. (1980) A method of nonlinear analysis in the frequency domain. Biophys. J. 29, 459-483. Victor J. D., Shapley R. M. and Knight B. W. (1977) Nonlinear analysis of cat retinal ganglion cells in the frequency domain. Proc. natn. Acad. Sci. U.S.A. 74, 3068-3072. Zemon V. and Ratliff F. (1982) Visual evoked potentials: Evidence for lateral interactions. Proc. natn. Acad. Sci. U.S.A. 79, 5723-5726. Zemon V. and Ratliff F. (1984) Intermodulation components of the visual evoked potentials: responses to lateral and superimposed stimuli. Biol. Cybernet. 50, 401-408.