Evidence for nonlinear binocular interactions in human visual cortex

~2~~9/88 S3.00+ 0.00 Copyright &$1988Pergamon Press plc

VirionRes. Vol. 28, No. IO, pp. 1139-I 143, 1988 Printed in Great Britain. All rights reserved

EVIDENCE FOR NONLINEAR BINOCULAR INTERACTIONS IN HUMAN VISUAL CORTEX LAWRENCEW. BAITCH* and DENNIS

M. LEVI

University of Houston College of Optometry, 4800 Calhoun Blvd, Houston, TX 77004, U.S.A. (&veined 11 ~~e~~

1987; in ~~~edf#r~

29 February 1988)

Abstract-Dichoptically presented uniform fields were sinusoidally modulated in luminance, with differing temporal frequencies between the eyes. This stimulus evokes a unique el~t~ph~iolo~~l response termed “beats”; visual evoked potential (VEP) components reflecting nonlinear neural behavior and which could only arise from integrative binocular units. Individuals with strabismus or amblyopia, which accompany disrupted binocular function in the visual cortex manifest a severe reduction of this nonlinea~ty, suggesting an abnormality in the binocuiar cortical processes underlying this response. Human visual cortex Binocular interaction Beats Nonlinear mechanisms

Visual evoked potential

~RODU~ON

Since the classical work of Sherrington (1904), flickering stimuli have been used to study the binocular confluence of monocular signals in the human brain. As investigators have employed more refined systems analysis ap proaches toward understanding the nature of binocular function, the use of sinusoidal temporal modulation has emerged as an important means for exploring the input/output relationships between the monocular and binocular visual pathways. If two different frequencies of sinusoidal modulation stimulate a common neuron, the neuronal output may contain Iinear component products from the stimulus frequencies f, and& as well as nonlinear products which include difference or beat (Ifi -fzl) and sum (fi +f2) frequencies (Regan, 1976; Shapley and Victor, 1978; Fricker and Kuperwaser, 1982; Baitch et al., 1987). Thus if the right and left eyes are stimulated with temporal frequencies fR and fL, the visual evoked potential (VEP) measured at the scalp should contain the Fourier components fR and fL as well as the nonlinear beat and sum frequency response components and their harmonic combinations (see Fig. 1). Since the beat and sum frequencies are not present in the stimulus, they provide unambi~o~ evidence for binocular neural interactions. They *Present address: University of Texas ~uthw~tem Me& cal Center at Dallas, Department of Ophthalmology, 5323 Harry Hines Blvd, Dallas, TX 75235-9057, U.S.A.

Amblyopia

Uniform field

are, in a sense, a si~at~e for binocular neurons, and provide a direct test for the nonlinear neural processes involved in binocularity. They ~sting~sh a “true binocular response” (Wolfe and Held, 1981; Bodis-Wollner, 1982) from the linear electrical superposition of monocular responses at the VEP scalp electrode locus (Fig. lc). A diminution of the binocular nonlinearities would suggest a depleted or abnormal binocular neural integration of the two monocular pathways. Although binocular summation in individual cortical neurons has been described as essentially linear (Ohzawa and Freeman, 1986), to our knowledge nonlinear dichoptic interactions have not been systematically explored. MJZTHODS

Dichoptic uniform field stimuli were generated using a pair of LED goggles whose light was transmitted and diffused through closed eyelids. The advantage of this type of stimulus is that it is not influenced by inaccurate accommodation, fixation, vergence or by poor spatial resolution. Luminance was modulated sinusoidally in each goggle about an identical midphotopic baseline (32 cd/m*). Modulation and temporal parameters of the stimulus, were controlled by a microcomputer which also triggered the VEP data acquisition computer. Stimulus conditions were interleaved. A multiel~trode cap was used to maintain accurate and repeatable placement of recording electrodes on the

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LAWRENCE W. BAITCHand DENNISM. LEVI

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scalp. The active electrodes were located at Or, 0, , Oz and P, and were referenced to Fp (1 O-20 International Electrode Placement System). The right ear served as ground. VEP’s were amplified and filtered within a 0.3-100 Hz bandpass; 100 averages composed each waveform of 2000 msec duration. Two waveforms recorded from identical stimulus conditions were averaged together; this average was then subjected to Fourier analysis. There is considerable between-subject variation in VEP amplitude. Thus, in order to facilitate comparisons between normal and stereoblind observers, we computed the signal-noise ratio (S/N) of the beat. Noise was detined as the mean amplitude of the Fourier component frequencies in the response excluding: the stimulus frequencies fR and fL, the difference (beat) ( lfR -.fLl) frequencies, and the first, second and third harmonics of those frequencies (up to 54 Hz) Other definitions of S/N ratio, e.g. computing the S/N ratio using only frequencies centered about 2 Hz did not alter the results. However, the present definition of noise also applies to the sum frequency, and to other components of the waveform. Five subjects with normal acuity, eye movements and strabismic stereopsis, and five stereoblind and/or amblyopic subjects were studied. Observers were classified as stereoblind based upon stereoacuity of ~2000 set arc on the Randot test, the Wirt test, the Titmus Stereofly and the A0 Vectograph. RESULTS

AND DISCUSSION

Fourier analysis of VEP’s recorded from normal subjects (Fig. 2a) indicates the presence of a number of nonlinear response components which include a strong component at the beat frequency, at the stimulus frequencies, as well as components at their harmonic combinations. A complete description of the binocular responses must take into account the neural mechanism or mechanisms underlying each of the various nonlinearities. However, due to the robust nature of the beat frequency responses and the low signalto-noise ratio of the sums and other components, we confine our analysis to the beats in this report. We examined the temporal tuning (Fig. 3) of a 2 Hz beat response by maintaining the beat frequency as the carrier frequencies were both incremented together (e.g. 6&L, 1&/14~., l&/20& The 2 Hz beat was chosen due to its strong perceptual salience, and its electro-

la.

right monocular

lb.

left monocular

lc.

linear summation model

Id.

nonlinear summation mode1

Fig. 1. ~h~rnati~lly illustrates two models for the manner in which a sinusoidally-modulated dichoptic uniform field stimulus of two differing monocular frequencies can manifest a visual evoked potential recorded at the scalp: the linear summation model (lc) assumes that there is no binocular integration of the two monocular signals and that the VEP is purely the arithmetic sum of the right monocular IS Hz (la) and the left monocular 20 Hz (1b) signals summating electrically at the scalp electrode locus. The nonlinear summation model (Id) includes linear as well as nonlinear products (difference and sum frequencies) that would result from integration of the two monocular signals in binocular cortical units.

physiological potency, This function peaks at roughly 18 Hz with a S/N ratio as high as 50: 1 in some normal subjects. In order to confirm that the beat responses are not monocular nonlinearities nor harmonic artifacts, VEP’s from mon~ularly-presented single temporal frequency stimulation (e.g. 5R/OLor 10,/O,) were recorded. No significant responses were obtained at 2 Hz resulting in signal to noise ratios near 1.0 (Fig. 3). To further substantiate the binocular origin of the nonlinear cortical responses, results from normal subjects were compared to a population of subjects with known, quantified losses of binocular function stereoblind individuals. Stereoblind observers are considered to have broadly-based deficits in binocular function (Hohmann and Creutzfeldt, 1975; Lema and Blake, 1977; Levi et al., 1979; Crawford et al., 1983; Lennerstrand, 1978). A similarity can be seen between the linear addition model and the waveforms obtained from stereoblind subjects (Fig. 2~). Fourier analysis confirmed that compared to normals,

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Evidence for nonlinear binocular interactions

normal

A

FREQUENCY

(Hz)

FREQUENCY

(Hz)

D ‘#8000 1 C

stereoblind

Fig. 2. VEP waveforms (2000 msec epoch) recorded in response to dichoptically presented uniform-fields, sin~idally rn~~at~ at 18 Hz, right eye, and 20 Hz, left eye, 80% m~uiation. Note similarity of these VEP’s recorded from normal (2A) and stereoblind (2C) human subjects to the nonlinear summation models respectively. Fourier analysis (2B and 2D) confirms the strong presence of a 2 Hz beat component and other no~inea~ti~ in the normal VEP, and the severe reduction of those nonlinearities in the stereoblind VEP. The reduction of the beat amplitude in the presence of intact 18 and 20 Hz components punctuates the specific loss of binocular output from the visual cortices of the stereoblind subjects.

4 +

*

T

8

10

14

18

22

28

NORMAL STEREOSUND NORMAL @ON)

30

FREQUENCY (RIGHT EYE)

Fig. 3. Temporal tuning of 2Hz beat (60% mutation). For binocular functions, the right/left eye frequency pairs were incremented in tandem (e.g. 6,/f!,, lOa.12, Hz) so that the difference between them (the beat frequency) remained a constant 2 Hz. For the monocular single-frequency function (the lowest on the graph), only the right eye stimulus luminance was modulated (e.g. 6,/O,, 10,/O, Hz); the left eye was held at baseline luminance. Note significant difference between binocular functions of normal and stereoblind subjects, and the similarity of the stereoblind to the normal monocular single-frequency function. These results give evidence for a depletion or abnormality of functioning binocular units in the visual cortices of the stereoblind subjects. Error bars indicate standard deviation.

stereoblind subjects demonstrated severe losses in the beat frequency component amplitudes throughout the frequency domain and at all modulation depths tested. As seen in Fig. 3, there is a strong similarity between the dichoptic data obtained from the amblyopic population and the function obtained from normals monocularly, using one, rather than two temporal frequencies, i.e. both are near the noise. The VEP responses of the stereoblind observers, from different electrodes for a particular condition (18,/20,; 2Hz Beat, 80% modulation) is shown in Fig. 4. Under this condition the difference between the S/N ratios of normal and stereodeficient subject responses is clearly evident. In Figs 2b and d, the asymmetry between the 18 and 20 Hz response amplitudes in the normal subject, and the greater symmetry in the stereoblind response would suggest differences in the degree of interaction between those monocular signals. However, we found no consistent trend in the ratio between the right and left eye frequency responses, except that the lower frequency usually masked the response to the

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LAWRENCE W. BAITCHand DENNISM. LEVI

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Fig. 4. Differences between single-to-noise ratios of normals and stereoblinds are most evident in response to this particular stimulus condition (i&/20, Hz, 80% modulation). insignificant differences across VEP channels reflect the diffuse, u~fo~-field nature of the stimulus. Scalp electrode loci: channel 1 = 0, - Fp; channel 2 = 0, - Fp; channel 3 = 0, - F,,; channel 4 = P, - F. (IO-20 International Electrode Pia&meni System).

or mechanisms which, like those involved in stereopsis, are sensitive to abnormal binocular experience early in life. Because the flickering, uniform field stimulus does not require accurate fixation, vergence or high visual acuity, it shows promise for studying the development of the confluence of cortical binocular signals (Fox et al.,1980;Braddick et al.. 1980; Held et al., 1980). Acknowledgements-We are grateful to Stanley Klein for his assistance with data analysis and critical reading of the manuscript,and to Richard Srebro for his valuable ideas and comments. This research was supported by a National Eye Institute NRSA Postdoctoral Award FYO5874 to L. Baitch and a National Eye Institute Grant EYOi728 to D. Levi.

REFERENCES

higher. Both normal and stereoblind observers could just as easily show symmetry as asymmetry between those responses. DISCUSSION

we have recorded unTo summarize, ambiguous nonlinear binocular signals in normal subjects, and show such signals to be absent or depleted in observers with anomalies of binocular vision. We have made some preliminary attempts to model the normal responses found in this study using electronic circuitry, and have found that in order to model the normal human VEP (e.g. Fig. Za), a central rectifying nonlinearity is required after the confluence of the two individual sinusoids. If r~tifi~tion only occurs prior to “binocular integration” of independent sinusoids, the beat component is not manifest. While previous nonlinear binocular visual system models (Spekreijse, 1966; Pinkasov, 1987) suggest a more peripheral rectification prior to summation of monocular signals, the present results suggest that additional nonlinearities occur after binocular integration. While the precise nature of the mechanisms generating the nonlinear binocular interactions which we have reported remains uncertain, they appear to be related to the processes involved in stereopsis or at least are shown to be susceptible to the same factors which preclude the development of stereopsis. The response products described here arise via a nonlinear mechanism

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Evidence for nonlinear binocular interactions Shapley R. and Victor J. (1978) The effect of contrast on the transfer properties of the cat retinal ganglion cells. J. Physiol., Lmd. 285, 2X-298. Sherrington C. (1904) On binocular tlicker and the correlation of activity of corresponding retinal points. Br. J. Psychol. 1, 26-60.

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