Luminance-contrast mechanisms in humans: Visual evoked potentials and a nonlinear model

Vision Research 46 (2006) 4163–4180 www.elsevier.com/locate/visres

Luminance-contrast mechanisms in humans: Visual evoked potentials and a nonlinear model Vance Zemon a

a,b,c,*

, James Gordon

b,d

Ferkauf Graduate School of Psychology, Yeshiva University, Albert Einstein College of Medicine, 1300 Morris Park Avenue, Bronx, NY 10461, USA b Laboratory of Biophysics, The Rockefeller University, USA c Nathan S. Kline Institute for Psychiatric Research, USA d Department of Psychology, Hunter College of the City University of New York, USA Received 14 March 2006; received in revised form 9 July 2006

Abstract Isolated-checks were luminance-modulated temporally to elicit VEPs. Bright or dark checks were used to drive ON or OFF pathways, and low or high-contrast conditions were used to emphasize activity from magnocellular or parvocellular pathways. Manipulation of stimulus parameters and frequency analysis of the VEP were performed to obtain spatial and contrast–response functions. A biophysical explanation is offered for why the opposite polarity stimuli drive selectively ON and OFF pathways in primary visual cortex, and a lumped biophysical model is proposed to quantify the data and characterize changes in the dynamics of the system with contrast given a limited number of parameters. Response functions were found to match the characteristics of the targeted pathways.  2006 Elsevier Ltd. All rights reserved. Keywords: Visual evoked potential; Magnocellular; Parvocellular; ON pathway; OFF pathway; Contrast gain control; Shunting inhibition; Nonlinear model

1. Introduction Luminance-contrast1 information is critical for perception of form, motion, and depth (Livingstone & Hubel, 1987, 1988; Ratliff, 1965; Shapley, 1990). Differences have been observed psychophysically in brightness and darkness perception (Fiorentini, Baumgartner, Magnussen, Schiller, & Thomas, 1990), and also in low and high-contrast perception (Bowker, 1983; Georgeson & Sullivan, 1975; Zemon, Conte, & Camisa, 1993). One aim of this study is to measure electrophysiological responses to stimuli that elicit each of these perceptual responses. Parallel neural pathways appear to govern these different aspects of contrast perception. Thus, a second aim is to determine the *

Corresponding author. Fax: +1 845 215 5100. E-mail address: [email protected] (V. Zemon). 1 Throughout the remainder of this report, luminance-contrast will be referred to simply as contrast. 0042-6989/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.visres.2006.07.007

properties of these pathways with stimuli designed to emphasize contributions from select pathways. We attempt to explain in biophysical terms how positive- and negativecontrast information is processed separately in primary visual cortex, and we introduce a lumped biophysical model with a few free parameters to quantify the observed changes in dynamics of the system with contrast, referred to phenomenologically as contrast gain control (CGC). Early neurophysiological studies demonstrated a functional dichotomy in the processing of positive- and negative-contrast (Hartline, 1938a, 1938b; Kuffler, 1953). On-center (ON) and off-center (OFF) cells form this pair of parallel pathways, which remain independent up to primary visual cortex (Schiller, 1982) and which appear to mediate the separate perceptions of brightness and darkness (Fiorentini et al., 1990; Hartline, 1938b; Jung, 1973). In previous studies, we used bright or dark check stimuli to emphasize contributions to the VEP from either ON or OFF subsystems (Zemon, Gordon, & Welch, 1988;

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Zemon et al., 1995a). This work yielded physiological evidence for differences in the processing of positive- and negative-contrast information. Another important functional dichotomy exists within the primate visual system: the M-magnocellular (M) pathway exhibits high-contrast sensitivity and the P-parvocellular (P) pathway exhibits low contrast sensitivity (Kaplan & Shapley, 1986). The M and P streams, each of which is subdivided into ON and OFF subsystems, remain segregated at the initial cortical level (Hendrickson, Wilson, & Ogren, 1978; Hubel & Wiesel, 1972), beyond which interactions occur (Merigan & Maunsell, 1993; Nealey & Maunsell, 1994). Cortical neurons are known to exhibit essential nonlinearities such as rectification (De Valois, Albrecht, & Thorell, 1982; Movshon, Thompson, & Tolhurst, 1978; Spitzer & Hochstein, 1985) and contrast gain control (Carandini & Heeger, 1994; Ohzawa, Sclar, & Freeman, 1982, 1985). This latter nonlinearity was shown to be present in M but not P neurons (Benardete, Kaplan, & Knight, 1992). Here, we used stimuli of low or high and positive- or negative-contrast to explore the characteristics of these pathways in humans. Differences in the responses were found to be consistent with differences in anatomical and physiological properties of neurons in the retino-geniculocortical pathway, and the lumped biophysical model provided good fits to all of the contrast functions. A preliminary description of this work was presented elsewhere (Zemon & Gordon, 1988, 2002). 2. Materials and methods 2.1. Rationale for the separation of activity from parallel pathways To emphasize contributions from ON or OFF subsystems to the VEP, arrays of bright or dark isolated-checks (Fig. 1) were used (Zemon et al., 1988). Similar kinds of opposite polarity, positive- and negative-contrast stimuli, have been shown to be processed predominantly by respective ON and OFF pathways in monkeys (Schiller, 1982; Schiller, Sandell, & Maunsell, 1986). To separate the contributions to the VEP from M and P streams with the use of luminance-contrast, we applied the knowledge, obtained from the work of Kaplan & Shapley (1982, 1986), that: (1) the contrast sensitivity (or contrast gain as defined by the slope of the linear segment of the contrast–response function) of M cells is nearly 10 times greater than that of P cells; and (2) the response magnitudes of M cells nearly saturate at moderate contrasts (above 16%), whereas the responses of P cells increase approximately linearly with increases in contrast throughout the entire contrast range. We used isolated-check stimuli that varied from zero contrast to a maximum positive- or negative-contrast (appearance–disappearance) within the low contrast region to emphasize contributions from the M pathway to the VEP (Fig. 2). To emphasize P contributions, a high static contrast (pedestal) was used along with a temporal contrast component to modulate isolated-checks such that their minimum absolute value was equal to or greater than 16%. This type of stimulation avoids the low contrast region where the magnitudes of M-cell responses rise steeply with increases in contrast. Under this stimulus condition, M cells are expected to respond steadily with little modulated discharge. This high standing contrast is expected to generate strong shunting inhibition, which should limit responses from the M pathway (see nonlinear model below). Thus, its contribution to the VEP should be small or negligible. The more numerous P cells, however, are expected to produce a sizable modulated (summed)

Fig. 1. Examples of the bright and dark isolated-check patterns used in this study. Check size was manipulated, and the intercheck spacing was always equal to the width of a check. The luminance of the checks was sinusoidally modulated in time at 6 Hz while the uniform background field remained stationary. response under this condition, and therefore yield a dominant contribution to the VEP. (Unfortunately, there are no comparable, published single-unit data obtained under similar high-contrast pedestal conditions.) Psychophysical responses to low and high luminance-contrast stimuli are known to differ and recent work has attempted to explain these differences in terms of the physiological distinctions between M and P pathways (e.g., Pokorny & Smith, 1997).

2.2. A biophysical model A biophysical model is proposed to demonstrate how, through the process of rectification, the arrays of bright or dark isolated-checks might be processed separately by cortical neurons with low maintained discharge rates that receive input directly from ON or OFF cells, respectively

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Fig. 2. Illustration of the temporal presentation of bright or dark checks under appearance–disappearance and pedestal contrast conditions. At time zero, sinusoidal modulation (6 Hz) of check luminance begins, while background luminance (LB) remains stationary. A positive sinewave is used in the case of bright checks, and a negative sine-wave is used for dark checks. Mean contrast (Cmean) and depth of modulation (DOM) are always equal for the appearance–disappearance condition; whereas, Cmean is much greater than DOM for the pedestal condition (see text for details).

(Fig. 3). Also, this model incorporates another nonlinearity, based on shunting inhibition, to characterize the contrast-dependent changes in system dynamics referred to as contrast gain control (CGC). Visual input signals have been shown to increase the conductance of cortical neurons, specifically by increases in GABAA-mediated shunting inhibition (BorgGraham, Monier, & Fre´gnac, 1998), which results in a decrease in cellular temporal integration. In this manner, increases in stimulus contrast produce decreases in the recipient cell’s time constant. This type of nonlinearity is incorporated here in a lumped biophysical model merely to quantify the VEP contrast–response functions plotted in Section 3 using a small number of parameters. This lumped model will be described here in detail. It should be emphasized, however, that the veracity of the temporal transfer function implied in this formulation is not tested here given the single temporal condition used in this investigation. In this model, parallel ON and OFF streams enter V1 and remain segregated at their initial cortical projection sites, which are on spiny stellate neurons in layer IVc (Gilbert & Wiesel, 1979, 1985). This morphological type of cortical cell is the most likely candidate for the establishment of the functional class of simple cells discovered by

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Hubel & Wiesel (1962, 1968). The rectification point for simple cells that receive direct input from either ON or OFF cells is set by inhibition exerted by interneurons (presumably GABAergic ones) in the cortex. The amount of this inhibition is determined by the average firing rates of ON and OFF afferent fibers entering the cortex. These inhibitory interneurons serve to hyperpolarize and lower to near zero spikes/s the maintained discharge rates of these simple cells, which cause them to behave like half-wave rectifiers (De Valois et al., 1982; Movshon et al., 1978; Spitzer & Hochstein, 1985). Somogyi (1989) demonstrated that there is a wide variety of GABAergic interneurons present in the visual cortex. Some of these cells form synapses distally on dendrites and might provide the basis for the subtractive (hyperpolarizing) inhibition that lowers the maintained discharge rate. It is assumed that the level of intracortical inhibition generated in this manner is sufficient to prevent OFF cells that receive increased activation from positive-contrast elements in their surround regions from contributing to cortical responses. Only ON cells that receive direct input from positive-contrast elements in their center regions are expected to drive recipient cortical neurons. An analogous situation would exist for OFF cells and arrays of negative-contrast elements (not depicted in Fig. 3). The model assumes greater strength for center than surround mechanisms for both ON and OFF cells, which is supported by physiological work (Croner & Kaplan, 1995). It also assumes higher mean firing rates for the population of ON than OFF cells when bright checks are presented, and the reverse situation when dark checks are presented, which also has support in the literature (Victor, 1987). Also, a threshold-like mechanism is posited to account for some of the VEP results. Contrast gain control was first described for retinal ganglion cells in cats (Shapley & Victor, 1978, 1979a, 1979b, 1981) and it has since been demonstrated in the M pathway of primates (Benardete et al., 1992; Kaplan & Shapley, 1986). In previous work, a mathematical model of single-cell behavior in the cochlea was based upon a shunting mechanism (Furman & Frishkopf, 1964). This nonlinear (divisive) mechanism has been incorporated into models to account for CGC as reflected in both VEP data (Zemon & Gordon, 2002; Zemon et al., 2003) and cortical simple cell data (Carandini & Heeger, 1994; Carandini, Heeger, & Movshon, 1997). An equivalent circuit for the lumped cellular model incorporates shunting inhibition and it is depicted in Fig. 4. A conductance change across the cellular membrane associated with shunting results in a change in the transfer characteristics and time constant of the system. Borg-Graham et al. (1998) have shown that in response to visual stimulation neurons of cat primary visual cortex exhibit strong, transient shunting inhibition that increases somatic membrane conductance by more than threefold relative to the resting state. The time course of this conductance change and its apparent reversal potential indicate the principal involvement of c–aminobutyric acid (GABAA) receptor-mediated synapses. The other membrane channels illustrated here (associated with excitatory, inhibitory, and leakage currents) are not thought to contribute much to the stimulus-driven change in membrane conductance (e.g., Carandini & Heeger, 1994). Although it is not intended to imply that the observed effects occur in single cortical neurons, there is VEP evidence to suggest that the bulk of CGC effects in humans is cortical in origin (Zemon, Conte, & Camisa, 1987). In the model, we assume that a change in specific shunting conductance (gs) associated with stimulus modulation contributes to the VEP and that this change is proportional to the weighted sum of stimulusdriven inhibitory signals (Vj with weighting coefficient mj) impinging ion channels on the model cell via GABAA-mediated P (gs ¼ nj¼1 mj V j Þ. These inhibitory signals are linearly related to contrast, or depth of modulation (D), such that gs can be expressed as follows: gs = m(D  d0), where m is a coefficient of proportionality and it is used as a parametric measure of the strength of this stimulus-driven shunting inhibition, d0 is threshold depth of modulation and it is incorporated as a second parameter in the model because some data sets exhibit a clear threshold effect. If D is less than d0, then the level of excitation needed to exceed the level of intracortical inhibition present

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Fig. 3. A nonlinear model, based on cortical rectification, that may explain how bright (positive-contrast) and dark (negative-contrast) signals are processed separately through the ON and OFF pathways, respectively. In this example, bright checks centered on either ON or OFF cells are sinusoidally modulated in time above the background (B) luminance level. Linear filtering (L) of signals predominates in precortical ON and OFF pathways. A sufficiently high maintained discharge (MD) rate in retinal ganglion and LGN neurons enables sinusoidal modulation of the discharge rate above and below this level of spontaneous activity. Upon entering the primary visual cortex (dashed vertical line), signals from ON and OFF pathways project separately to spiny stellate/simple (S) neurons and convergently to inhibitory (I) interneurons. The I interneurons average the excitatory signals received from ON and OFF cells, and their (approximately constant) output is responsible for the low spontaneous discharge rate in the recipient cortical cells. S neurons are hypothesized to consist of both linear component (L) and nonlinear components (Ns, shunting inhibition, and Nr, half-wave rectification associated with the low MD rate). The modulated excitatory input to S cells that receive ON-cell signals will exceed the averaged inhibitory input, but the lower excitatory input to S cells that receive OFF-cell signals will be below the inhibitory level (rectification point), and therefore, will not be reflected in that S cell output. S afferent fibers may project separately or convergently onto pyramidal/complex (C) neurons, which are thought to be the principal generators of the VEP. is not attained and a cortical response does not occur. If the value of d0 is negative, it implies that there is sizeable spontaneous EEG activity at the stimulus frequency even when D is zero. The following system differential equation results: ia ¼ i0 þ

n C di0 i0 X þ mj Vj : g0 dt g0 j¼1

ð1Þ

Where: ia  source current, i0  generator current, g0  specific generator conductance (initial system conductance without stimulus-driven shunting inhibition, and a third parameter in the model), C  membrane capacitance, Vj  stimulus-driven inhibitory signal of jth shunting channel (assumed to be constant in the steady-state condition), mj  constant coefficient of Vj. Although not tested in this study, we expect the free parameters in this model to depend on temporal frequency. Preliminary data that support this expectation were presented recently at the Annual Meeting of the Association for Research in Vision and Ophthalmology (Zemon et al., 2006). The system frequency response and its associated gain and phase characteristics are as follows: g =C ; System frequency response F ðjxÞ ¼ K 0 jx þ p

ð2Þ

g0 =C ffi; Gain jF ðjxÞj ¼ K pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi p2 þ x2

ð3Þ

  x ; Phase / ¼ arg ½F ðjxÞ ¼  tan1 p

ð4Þ

where p ¼

g0 þ gs 1 ¼ ; s C

For each contrast–response function, an algorithm based on the Generalized Reduced Gradient (GRG2) nonlinear optimisation code (developed by Leon Lasdon and Allan Waren) and incorporated in Microsoft Excel Solver is used with a least-squares criterion to fit the model to the data and yield best estimates for response amplitude and phase: ! g0 =C ffi ; Response amplitude AR ¼ ðD  d 0 Þ K pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð6Þ p2 þ x2 Response phase /R ¼ / þ /0 ;

ð7Þ

where /0 is initial phase of the fundamental frequency response (i.e., the response phase minus any contrast-dependent phase shift, /), and this fourth and final free parameter in the model reflects largely the phase associated with transmission delay in the system. The total time constant for the system (s) is given by: s¼

C C : ¼ g0 þ gs g0 þ mðD  d 0 Þ

ð8Þ

An increase in shunting conductance shortens the time constant of this system. The end result, in phenomenological terms, is contrast gain control: response compression (decreased gain) and phase advance with increases in contrast.

2.3. Stimuli

ð5Þ

s  time constant of system, x is the angular temporal frequency of the stimulus and of the relevant response component, Kffi is a gain setting which pffiffiffiffiffiffi is fixed at a value of 10 for all fits, and j ¼ 1. (The gain setting, K, influences the initial specific conductance of the system and a value of 10 was found empirically to yield good fits across all observers and conditions. Thus, it is a constant and not a free parameter.)

In early experiments, stimuli were presented on a Tektronix 608 electrostatic display (P31 phosphor), by means of a microcomputer-based visual stimulator (Milkman et al., 1980; Ratliff & Zemon, 1982), with a field size of 8.8 deg square (viewing distance = 57 cm) and a background luminance of 150 cd/m2. In later experiments, stimuli were presented on a Princeton Graphics RGB display, by means of a VENUS system (Neuroscientific Corp.), with a field size of 8 deg (viewing distance = 114 cm) and a background luminance of 100 cd/m2. The frame rates for the Tektronix and Princeton Graphics displays were 270 and 119 Hz, respectively.

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were presented successively in 1-s steps (duration of 120 frames on the Princeton display). The isolated-check patterns (2 · 2 to 128 · 128) were presented in decreasing order of check size (increasing number of checks/row) from 240 to 1.875 minarc. Spatial tuning functions were obtained under two contrast conditions: Appearance–disappearance, low contrast: Cmean = 8%, DOM = 8% (to emphasize M contribution). Pedestal, high contrast: Cmean = 48%, DOM = 16% (to emphasize P contribution). 2.3.2. Contrast–response functions Contrast–response functions were also obtained under two types of stimulus conditions: appearance–disappearance and pedestal. These conditions were presented in both 1-min and swept-parameter runs. In most conditions, a 32 · 32 isolated-check pattern was employed because it yielded strong responses and sizeable asymmetries between responses to bright and dark stimuli. For 1-min and swept-parameter runs under the appearance–disappearance condition, the same contrast levels were presented in ascending order with one exception—in the sweep runs, a uniform field equal in luminance to that of the background field of the isolated-check stimuli was presented initially for 1 s. This served to eliminate a large transient response at the start of a run. Previous work has demonstrated that a 1-s period is adequate to control for this effect in the VEP (Victor, Conte, & Purpura, 1997). 2.3.2.1. Appearance–disappearance. Cmean = DOM = 1, 2, 4, 8, 16, 32% (to emphasize M contribution).

Fig. 4. Equivalent circuit for the lumped cellular model. Each type of ion channel (depolarizing, e, hyperpolarizing, i, leakage, l, and shunting, s) is represented by a battery and a resister (or conductance, g). These channels are connected in parallel with each other and with the membrane’s capacitance. The potential across the plasma membrane is given as Vm.

Arrays of isolated-checks (Fig. 1), embedded in a static background, were modulated sinusoidally at 6 Hz such that the spatial pattern attained peak contrast at one point in the cycle and minimal contrast a half cycle later (Fig. 2). The luminance of the checks was modulated either above (sine-wave phase) or below (negative sine-wave phase) that of the background. In the stimulus condition that is designed to emphasize M function, this resulted in appearance and disappearance of bright or dark checks. In the pedestal stimulus condition, the checks never disappeared, but were modulated about a mean contrast level and remained either bright or dark throughout the experimental run. Two contrast parameters were specified (refer to Fig. 2): mean contrast (Cmean) and depth of modulation (DOM). C mean ¼

LC  LB LB

and DOM ¼

LM  LC LB

where LC is the mean luminance of the checks, LM is the maximum luminance (bright check case) or minimum luminance (dark check case), and LB is the static background luminance. Check size and contrast were parametrically varied in both 1-min-run and swept-parameter experiments. 2.3.1. Spatial tuning functions For the 1-min-run experiments, five isolated-check patterns (4 · 4 to 64 · 64) were used with check sizes that ranged in octave steps from 4.125 to 66 minarc (Tektronix display) or 3.75 to 60 minarc (Princeton display). For the swept-parameter-run experiments, seven spatial conditions

2.3.2.2. Pedestal. Cmean = 32% or 48%, DOM = 1, 2, 4, 8, 16, 32% (to emphasize P contribution). For 1-min and swept-parameter runs under the pedestal condition, the same depth of modulations were presented in ascending order as under the appearance–disappearance condition. Mean contrast was fixed at 32% for all 1-min stimuli and at 48% for all sweep stimuli. The last pedestal condition in 1-min runs, DOM = Cmean = 32%, is identical to the last appearance–disappearance condition, and these two stimuli are expected to yield essentially identical responses that combine sizable activity from both M and P pathways. (Percent in the case of each contrast parameter is with respect to the background luminance, LB.) 2.3.2.3. Low-contrast pedestal. Note that in the appearance–disappearance condition both contrast parameters, Cmean and DOM, are varied, whereas in the pedestal condition only DOM is varied. The change in Cmean in only the appearance–disappearance condition raises the possibility that a nonlinear mechanism dependent upon mean contrast might effect differences in the data apart from any distinctions between M and P streams. We conducted an additional experiment to investigate the possible role that this contrast parameter might play in the generation of differential results in contrast functions under appearance–disappearance and pedestal conditions. In this research, contrast–response functions were measured with only DOM varied (1, 2, 4, and 8%) and a fixed low mean contrast (Cmean = 8%). This low contrast, pedestal condition is expected to drive the M pathway predominantly and eliminate any differential role of mean contrast in data generation.

2.4. VEP recording Gold-cup electrodes were placed along the midline of the scalp according to the 10–20 system (Jasper, 1958): active electrode at Oz (near the occipital pole), reference electrode at Cz (vertex of the head), and ground electrode at Pz (midway between Oz and Cz). The electroencephalogram (EEG), recorded in synchrony with the stimulus, was amplified, filtered (bandpass of either 0.03–100 Hz or 0.1–100 Hz), digitized at a rate of either 270 Hz (one sample per frame of the Tektronix display) or 238 Hz (two samples per frame of the Princeton Graphics display), and stored in the computer.

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2.5. Analysis The fundamental frequency component was the dominant component in the responses to the stimuli used here and its amplitude and phase values, the response measures of interest, were derived from cosine and sine coefficients extracted from the EEG by means of a discrete Fourier transform. Phase was measured relative to stimulus (sine) phase. Amplitude and phase measures were plotted as a function of check number (checks/deg) and depth of modulation (in percent of background luminance). For the contrast (depth of modulation) functions, the nonlinear model (described above) was used to fit smooth curves through the amplitude and phase data. The best fitting estimates of parameter values for the model are given for each data set. The quality of each fit is assessed by computation of R2, which indicates the proportion of variability in the given data set explained by the model. Variability in repeat 1-min-run response functions was assessed by computation of the x2 statistic (Keppel, 1991). Variability in swept-parameter response functions was assessed through the use of a multivariate statistic, referred to as T 2circ , introduced by Victor & Mast (1991). For each mean fundamental response, a circular 95% confidence region was established, and its confidence limits are plotted for both amplitude and phase values (Zemon, Hartmann, Gordon, & Pru¨nte-Glowazski, 1997). A signalto-noise ratio could be derived for each response by dividing the mean amplitude of the fundamental component by the radius of the confidence circle. A significant response is defined by a signal-to-noise ratio of greater than one, which is indicated by the lower confidence limit for mean amplitude exceeding zero microvolts (for additional information refer to Zemon et al., 1997).

2.6. Participants Five adult female observers (age range: 20–54 years) participated in the study. One participant was tested under all experimental conditions. Participants had normal (20/20) or corrected-to-normal visual acuity. All participants gave informed consent to participate in this study, and the experiments were conducted in accordance with the principles embodied in the Declaration of Helsinki (Code of Ethics of the World Medical Association).

2.7. Procedure The sebum was abraided at each electrode site with a mildly abrasive (Redux) electrode paste prior to attaching electrodes to the scalp with Elefix paste and a patch of gauze. The experiments were conducted in a dimly lit room. Observers were seated in a comfortable chair at the appropriate viewing distance and instructed to fixate a small dark dot in the center of the display. All participants were tested monocularly. For 1-min-run experiments, left and right eye stimulation was used to obtain repeated measures for each experimental condition. Each type of swept-parameter stimulus was presented 10 times.

3. Results Response functions obtained under 1-min-run conditions are illustrated for three participants and those obtained under swept-parameter conditions are illustrated for the one participant who was tested under all experimental conditions. 3.1. Spatial tuning functions Spatial tuning functions for the amplitude and phase of the fundamental frequency component, obtained with bright and dark isolated-check patterns under appear-

ance–disappearance (low contrast) and pedestal (high contrast) conditions, are depicted for three participants in Figs. 5 and 6. Although there are clearly individual differences in the functions, similarities are present as well. The appearance–disappearance amplitude functions exhibit a bandpass characteristic. Typically, dark checks elicited larger responses than did bright checks. It is apparent that, under appearance–disappearance conditions, responses elicited by dark checks are larger in amplitude under small check conditions than are responses elicited by bright checks. These findings are consistent with VEP data published previously (Zemon et al., 1988). Data collected under the high contrast, pedestal conditions exhibit broader tuning functions than do those collected under the appearance–disappearance conditions. In fact, the pedestal functions are rather flat and exhibit little or no fall-off at the smallest checks used. The corresponding phase data show that responses to bright and dark checks are similar in phase even though their luminance signals are 180 deg out-of-phase, which also is consistent with previous work (Zemon et al., 1988) and supports the claim that these VEPs are contrast-dependent (not local luminance-dependent) responses. Note that even for the largest check condition used (check size = 64 0 ), the phases are similar for responses to bright and dark stimuli. For all three participants, there is a phase lead in the pedestal contrast functions relative to the appearance–disappearance contrast functions. In the appearance–disappearance plots, there are no consistent phase shifts with changes in check size. In the pedestal plots, however, phase decreases in general with increases in check number (decreases in check size). Thus, the phase differences between corresponding data in the two contrast conditions vary with check size: these differences are greatest for the largest check size and negligible for the smallest check size. Strength of effect of the parametric manipulation was assessed for each set of repeated-measure data through the application of the fixed-effect analysis of variance model and the x2 statistic (Keppel, 1991). For the appearance–disappearance conditions (bright and dark), the effects of varying check size for all three observers are significant at the 0.0005 level. Corresponding x2 values indicate that 85–94% of the variability in the functions is associated with the parametric manipulation of the stimuli. For the pedestal conditions (bright and dark), the effects of varying check size are significant for two of the three observers. Under the dark condition, significance level for observers EP and MC is 0.0005, with respective x2 values of 0.86 and 0.95. For the bright condition, the p value for observer EP is 0.016, and for observer MC, it is 0.001, with respective values of 0.60 and 0.81. For the third observer, YH, p values obtained with bright and dark pedestal conditions are 0.102 and 0.140, respectively. The lower x2 values found for this observer under bright (0.38) and dark (0.32) conditions reflect the rather flat spatial functions.

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Fig. 5. Amplitude and phase of the fundamental frequency component plotted as a function of check size for three participants. Circles and triangles represent repeated measures for the same condition. Responses to bright checks are depicted by open symbols, and responses to dark checks by filled symbols. Appearance–disappearance stimuli: low contrast (Cmean = DOM = 8%).

For one representative participant, amplitude and phase measures of the fundamental component obtained with swept-parameter stimulation are plotted versus check number for appearance–disappearance and pedestal conditions in Fig. 7. Here, each data point represents a total of 10 s of data, and error bars depict 95% confidence limits based on the multivariate statistic of Victor & Mast (1991). Phase data points are omitted when the respective responses are in the noise (lower confidence limit for mean amplitude drops below zero microvolts). It is apparent that the characteristics of these functions are similar to those obtained with 1-min runs. 3.2. Contrast functions For three observers, amplitude and phase measures of the fundamental frequency component along with estimates of the corresponding time constants are plotted versus depth of modulation for both appearance–disappearance (Cmean = DOM) and pedestal (Cmean = 32%) conditions (check size = 9 0 ; 3.75 checks/deg) in Figs. 8 and 9. The smooth curves through the sets of data illustrate the

fits of the nonlinear model. Considering the amplitude data, it is clear that the functions associated with dark checks exhibit a steeper initial slope (contrast gain) than do the functions associated with bright checks. Again, this finding is consistent with previous results (Zemon et al., 1988). The appearance–disappearance contrast conditions yielded compressive functions for both bright and dark check stimuli, and the corresponding phase data exhibit a relative lead with increasing DOM. These nonlinear features of the response functions are characteristic of contrast gain control. Time constant values decrease monotonically over a wide range with increases in DOM: 119–398 ms at 1% to 6–18 ms at 32%. The pedestal conditions yielded less compressive amplitude functions (almost perfectly linear in the case of observer AO). As with the appearance–disappearance data, dark check stimuli yielded greater contrast gain than did bright check stimuli. The phase plots for AO were nearly horizontal, which is also indicative of linear responses. The remaining observers, however, exhibit a relative phase lag with increases in DOM, and based on the model the negative slopes in these plots are indicative of decreases

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Fig. 6. Amplitude and phase of the fundamental frequency component plotted as a function of check size for three participants. Symbol representation is the same as that used in Fig. 6. Pedestal stimuli: high contrast (Cmean = 48%, DOM = 16%).

in shunting conductance with increases in DOM. The corresponding time constant plots demonstrate negative values that decrease with increases in DOM for these two observers. Negative time constant values reflect negative conductances in the model system. The extreme positive and negative deflections in the time constant plot for AO under the dark condition reflect positive total conductance in the system initially that switchs to negative total conductance at about 4% DOM (associated with a slight negative slope in the phase plot). Recall that total conductance is the sum of initial and shunting conductances, and therefore, these two components of conductance are about equal when total conductance is near zero. Under both appearance–disappearance and pedestal conditions, the phase functions collected with bright and dark check stimuli are quite similar. As observed in the spatial tuning functions, phases in the appearance–disappearance conditions lag corresponding phases in the pedestal conditions. This lag is greatest at low DOM conditions.

Note that the stimuli at the highest DOM used are identical for appearance–disappearance and pedestal conditions, and so, the phase results obtained with these two conditions do not differ appreciably. In this limiting case, the pedestal stimulus is an appearance–disappearance stimulus. Again, strength of effect of the parametric manipulation was assessed for each set of repeated-measure data through the application of the fixed-effect analysis of variance model and the x2 statistic (Keppel, 1991). For both appearance–disappearance and pedestal (bright and dark) conditions, the effects of varying depth of modulation for all three observers are significant at the 0.0005 level. Corresponding x2 values range from 0.93 to 0.98. Parameter estimates from the model fits, along with computed time constant and R2 values, are given for all the data displayed in Figs. 8 and 9 in Table 1. For the appearance–disappearance (A–D) paradigm, initial phase (/0) values are similar within an observer across bright

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Fig. 7. Swept-parameter check-size functions (amplitude and phase) for one observer obtained under appearance–disappearance (Cmean = DOM = 8%) and pedestal (Cmean = 48%, DOM = 16%) conditions. Each symbol represents the vector-mean of ten measurements and the error bars represent 95% confidence limits established with a multivariate statistic. Responses to bright checks are depicted by open symbols, and responses to dark checks by filled symbols.

and dark conditions, and the values are close to –200 deg for all observers. Initial specific conductance (g0) values are somewhat lower under bright than dark conditions for all observers and range from 0.63 to 2.44 lS/cm2 overall. Threshold estimates (d0) are slightly lower under dark than bright conditions for these observers and range from 0.67 to 2.36% overall. Coefficient m, which is the model’s parameter for setting the strength of stimulus-driven shunting inhibition and conductance, is similar across bright and dark conditions for two observers, but it is considerably different for the third observer, MC (bright: 1.38, dark: 4.28 lS/cm2/%). All values of m are positive, which indicate increases in shunting conductance with increases in DOM, and a greater value indicates a greater degree of shunting inhibition. Proportion of variability in the data explained by the model, as expressed by R2, is in general high: with the exception of the bright condition for AO (0.79), values range from 0.94 to 0.98. For the pedestal (Ped) paradigm, the initial phase parameter has values about 90 deg for the three observers, and therefore, there are phase leads relative to corresponding appearance–disappearance data. Initial specific conductance (g0) values are lower than corresponding values obtained under appearance–disappearance conditions and they are slightly lower under bright than dark conditions for all observers with a range from 0.28 to 0.72 lS/cm2. Threshold estimates (d0) are also lower under

dark than bright conditions and for one observer under the dark condition it is considerably negative. This negativity appears to represent prominent activity in the EEG at the stimulus frequency even without modulation. Coefficient m is approximately zero for observer AO, which reflects the lack of a stimulus-driven change in conductance. For the remaining observers, m is negative under both bright and dark conditions, which reflects increases in negative conductance (decreases in negative time constant) with increases in DOM. R2 values for the model’s fits range from 0.91 to 0.99. For one observer (MC), amplitude and phase measures of the fundamental component obtained with swept-parameter stimulation are plotted versus depth of modulation for appearance–disappearance and pedestal conditions in Fig. 10. Here, each data point represents a total of 10 s of data, and error bars depict 95% confidence limits based on the multivariate statistic of Victor & Mast (1991). Phase data points are omitted when the respective responses are in the noise (lower confidence limit for mean amplitude drops below zero). Again, it is apparent that the characteristics of these functions are similar to those obtained with 1-min runs. In the appearance–disappearance amplitude functions, the responses to dark checks are above the noise level for DOMs of 2% and greater, whereas responses to bright checks do not exceed the noise level until the DOM is 8% or greater. Both amplitude functions are

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Fig. 8. Amplitude and phase of the fundamental frequency component plotted as a function of depth of modulation (DOM) for three participants, along with corresponding time constant plots, under appearance–disappearance (Cmean = DOM) conditions with 9 0 bright or dark checks (3.75 checks/deg). Symbol representation is the same as that used in Fig. 5.

compressive with larger amplitudes obtained under the dark check condition. As with the 1-min-run data from this observer, dark stimuli yield shorter time constant values than do bright stimuli. Similarly, in the pedestal amplitude functions, responses to dark checks exceed the noise level at lower DOMs than do responses to bright checks. These data are lower in amplitude, however, than corresponding 1-min-run data. This is likely the result of the higher pedestal (mean) contrast used in the swept-parameter (48%) as compared to the 1-min (32%) conditions. With these appearance–disappearance functions, as with the corresponding 1-min data, the model yielded lower initial specific conductance under the bright than dark condition (1.14 vs. 2.19 lS/cm2). Initial phase values (bright: 236; dark: 249 deg) differ slightly from corresponding 1-min functions. Threshold values are higher under bright than dark conditions (2.49 vs. 1.07%), as with the corresponding 1-min data, and swept-parameter values are higher than corresponding 1-min values. This latter difference may be attributed to the greater amount of EEG data that contributes to a single data point in the 1-min functions than in the swept-parameter functions (60 s vs. 10 s). As is the case for this observer in the 1-min-run experiment, coefficient m is considerably higher under dark than bright

conditions (3.56 vs. 1.83 lS/cm2/%). Both plots of time constant values vs. DOM exhibit a 20-fold decrease in temporal integration over the range of 1–32% (bright: 270 to 14; dark: 139 to 7 ms). The R2 values for both functions are extremely high (bright: 0.97; dark: 0.99). Again, the pedestal conditions yielded lower initial specific conductances than did corresponding appearance–disappearance conditions and the bright condition yielded a slightly lower value than did the dark condition (0.27 vs. 0.47 lS/cm2). As with the 1-min data, relative to corresponding appearance–disappearance values, initial phase values are advanced (bright: 128; dark: 89 deg) and threshold values are lower (bright: 0.35; dark: 0.93%). Also, again associated with negative slopes in the phase plots, coefficient m values are similarly negative (bright: 0.48; dark: 1.53 lS/cm2/%), and time constant values are negative and decrease in negativity with increases in DOM (bright: 3714 to 53; dark: 756 to 16 ms). R2 values are similar (bright: 0.89; dark: 0.90). The same types of contrast functions obtained from 1-min runs are plotted for the same observer under the 1.875 checks/deg condition (check size = 18 0 ) in Fig. 11. In this case, the amplitudes obtained under bright and dark check conditions are similar. Thus, unlike the case of small (9’) check stimuli, no bright/dark asymmetry is present in

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Fig. 9. Amplitude and phase of the fundamental frequency component plotted as a function of depth of modulation (DOM) for three participants, along with corresponding time constant plots, under pedestal conditions (Cmean = 32%) with 9 0 bright or dark checks (3.75 checks/deg). Symbol representation is the same as that used in Fig. 5.

Table 1 K = 10

/0 (deg) g0 (lS/cm2) d0 (%) m(lS/cm2/%) R2

Bright

Dark

AO

MC

IG

AO

MC

IG

220.6 138.7 0.79 0.28 2.36 0.56 2.57 0.14 0.79 0.97

192.6 100.9 0.63 0.43 1.16 0.30 1.38 0.97 0.97 0.95

213.2 57.9 1.48 0.41 1.31 1.46 4.41 1.55 0.96 0.91

208.6 118.6 1.52 0.42 1.91 0.20 2.49 0.09 0.94 0.99

197.7 94.0 2.44 0.72 0.67 1.67 4.28 0.81 0.98 0.99

219.5 84.3 1.80 0.50 1.22 1.12 3.62 1.30 0.94 0.94

A–D Ped A–D Ped A–D Ped A–D Ped A–D Ped

Freq = 6 Hz, C = 0.8 lF/cm2.

these data. These results are consistent with our previous work (Zemon et al., 1988). As was the case in Figs. 8 and 9, compressive functions were obtained using the appearance–disappearance condition, and approximately linear functions were obtained using the pedestal condition. Here again, the appearance–disappearance condition yields a phase advance with increasing DOM and the pedestal condition yields a relative phase lag with increasing DOM. Also similar to Figs. 8 and 9, responses exhibit a phase lag (60 deg) under appearance–disappearance as com-

pared to pedestal conditions at a low DOM (8%), and no relative lag at the highest DOM (32%) where the two types of conditions are identical. Under appearance–disappearance conditions, initial specific conductance values are similar for the two functions (bright: 1.53; dark: 1.27 lS/cm2), as are values for coefficient m (bright: 2.62; dark: 2.33 lS/cm2/%). Initial phase values differ slightly (bright: 186; dark: 163 deg), and as with the previous data sets the dark check condition yielded a lower threshold value than did the bright

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Fig. 10. Swept-parameter contrast–response functions: Amplitude and phase of the fundamental frequency component plotted as a function of depth of modulation (DOM) for one observer, along with corresponding time constant plots, under appearance–disappearance (Cmean = DOM) and pedestal (Cmean = 48%) conditions with 9 0 bright or dark checks (3.75 checks/deg). Responses to bright checks are depicted by open symbols, and responses to dark checks by filled symbols.

check condition by a factor of two (bright: 1.77; dark: 0.80%). The time constant plots again illustrate a 20-fold drop in temporal integration over a DOM range of 1–32% (bright: 193 to 9; dark: 222 to 11 ms). The R2 values are extremely high (bright: 0.97; dark: 0.99). Under pedestal conditions, initial specific conductance values are negative but also similar for the two functions (bright: 0.58; dark: 0.69 lS/cm2). Coefficient m values (bright: 0.71; dark: 1.23 lS/cm2/%) and threshold values (bright: 0.32; dark: 2.11%) are negative as well. As with the smaller check condition, initial phase values are around 90 deg (bright: 103; dark: 77 deg). The

time constant plots again illustrate negative values for both functions and decreases in negativity with increases in DOM with an approximate 20-fold change in values over the range of 1–32% (bright: 622 to 35; dark: 416 to 20 ms). The R2 values demonstrate excellent fits of the model to the data (bright: 0.97; dark: 0.96). In the appearance–disappearance condition, both Cmean and DOM are varied, whereas in the pedestal condition, only DOM is changed in an experimental session. In order to control for the effect of parametric changes in Cmean on low contrast responses, an additional experiment was conducted using a constant (but low) Cmean of

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Fig. 11. Amplitude and phase of the fundamental frequency component plotted as a function of depth of modulation (DOM) for one observer, along with corresponding time constant plots, under appearance–disappearance (Cmean = DOM) and pedestal (Cmean = 32%) conditions with 18 0 bright or dark checks (1.875 checks/deg). Symbol representation is the same as that used in Fig. 5.

8% (dark checks only, check size = 18 0 ). The results obtained with this pedestal condition in 1-min runs for observer MC are illustrated in Fig. 12. The amplitude and phase data shown here are quite similar to those obtained using the appearance–disappearance condition. Note that the amplitude function is relatively steep (high-contrast gain) over the range of depth of modulations used here. Also, note that a phase advance occurs with increases in DOM. Although, the low pedestal contrast limits the DOM to a maximum of 8%, the curves from the model’s fit are extended as if 32% DOM was achieved. The initial specific

conductance value of 1.69 lS/cm2 and the initial phase value of 177 deg are about the same as the values obtained with this check size under both bright and dark appearance–disappearance conditions. The value of 3.43 lS/ cm2/% for coefficient m is somewhat greater than the corresponding values obtained with this check size under appearance–disappearance conditions. A lower threshold value (0.05%) resulted than that obtained with appearance–disappearance stimuli. The extended time constant plot again illustrates a 20-fold drop in temporal integration over a theoretical DOM range of 1–32% (156–7 ms). The R2 value is 0.90.

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brightness and darkness are segregated at the level of the retina or LGN. At these stages, both ON and OFF cells respond (because of their sizable maintained discharge rates) with a change in firing rate to increments and decrements in light that fall within the center region of their receptive fields. Based on the nonlinear model, we suggest how through cortical rectification, brightness and darkness perception may be established by activity in ON and OFF pathways. This suggestion is supported by the work of Schiller and coworkers who used 2-amino-4-phosphonobutyric acid (APB) to block selectively the ON pathway in monkeys and found disruption in the responses to bright checks but not to dark checks, as measured electrophysiologically (Schiller, 1982) and psychophysically (Schiller et al., 1986). For both spatial tuning and contrast–response functions, the results obtained under appearance–disappearance and pedestal conditions parallel respective M and P responses to luminance-contrast (Kaplan, 2003). Similar results were obtained with conventional and swept-parameter techniques. 4.1. Spatial tuning functions

Fig. 12. Amplitude and phase of the fundamental frequency component plotted as a function of depth of modulation (DOM) for one observer, along with the corresponding time constant plot, under a low contrast (Cmean = 8%) pedestal condition with 18’ dark checks (1.875 checks/deg). Symbol representation is the same as that used in Fig. 5.

4. Discussion VEPs to bright and dark checks demonstrate differences in ON and OFF-cell activity and support previous VEP findings (Zemon et al., 1988) as well as anatomical work in humans (Dacey & Petersen, 1992) and physiological work in monkeys (Chichilniskey & Kalmar, 2002). Also, a psychophysical study of the contributions of ON and OFF pathways to apparent motion perception obtained findings consistent with our VEP data (Shechter & Hochstein, 1990). It is unlikely that the perceptual functions of

The broader VEP spatial-tuning functions obtained under the high-contrast, pedestal condition as compared to the low-contrast, appearance–disappearance condition are consistent with differences observed in spatial tuning between P and M cells, where the higher spatial frequency cut-off in P cells is attributed to smaller receptive field center mechanisms (Derrington & Lennie, 1984). Thus, these VEP results suggest that in humans, too, receptive field center sizes are smaller for P than for M cells. The relatively flat spatial functions found under pedestal conditions might be an electrophysiological correlate of the perceptual phenomenon referred to as ‘‘contrast constancy’’ (Georgeson & Sullivan, 1975). Phase data obtained under appearance–disappearance and pedestal conditions differ dramatically for large check conditions but are nearly identical for small check conditions. Perhaps this is attributable to contrast gain control, which may be greater under low spatial frequency conditions. Alternatively, small checks may tap primarily one pathway (presumably P) under appearance–disappearance and pedestal conditions. The finding that fundamental phases obtained under the appearance–disappearance condition lag the corresponding data collected under the pedestal condition appears to conflict with the knowledge that the M pathway transmits information faster than does the P pathway. Response phase, however, reflects processes other than simple delays. In fact, published data from monkeys indicate that responses from M and P cells to luminance-contrast shift their phase relations depending on stimulus conditions such as retinal illuminance and temporal frequency (Benardete et al., 1992; Lee, Pokorny, Smith, Martin, & Valberg, 1990). Lee and colleagues showed that phases of M cells

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lead those of P cells under low temporal and high retinal illuminance conditions, but lag corresponding P cell responses under high temporal and low retinal illuminance conditions. Furthermore, VEPs necessarily reflect an additional (cortical) level of processing which might introduce an alteration in phase relations from those seen at the level of the LGN. 4.2. Contrast–response functions The amplitude compression and phase advance observed in contrast–response functions obtained under the appearance–disappearance conditions are similar to those obtained from M-type cells in the retina and LGN of monkeys (Benardete et al., 1992; Derrington & Lennie, 1984; Kaplan & Shapley, 1986), and these nonlinear effects have been referred to as contrast gain control. Some GABAergic interneurons form synapses proximally (i.e., near the cell body), which may provide the basis for shunting inhibition, a possible mechanism for the phenomena of CGC in cortical neurons described by Ohzawa et al. (1982, 1985). Shunting inhibition is thought to depend on the geometry of excitatory and inhibitory synapses that impinge on a neuron (Lettvin, 1962). If a neighboring inhibitory synapse is activated when an excitatory current is entering a cell, a portion of this current will be shunted out of the cell before it can act on the trigger zone for generation of action potentials. This results in a divisive effect. This type of effect was first noted for the crustacean nervemuscle synapse by Fatt & Katz (1953). The mechanism of shunting inhibition, apparently associated with GABAA-receptor-mediated synapses, serves to increase the conductance of cells in response to visual stimulation (Anderson, Carandini, & Ferster, 2000; Borg-Graham et al., 1998; Hirsch, Alonso, Reid, & Martinez, 1998) and thus shortens the system’s integrative time constant. Here, model fits indicate a 20-fold drop in time constant values over the range of depth of modulations used. At the lowest DOM, the time constant values were between 119 and 398 ms, and at the highest DOM, the values were between 6 and 18 ms. These estimates are consistent with psychophysical estimates of temporal integration: 70– 200 ms for threshold performance (Bloch, 1885; Breitmeyer & Ganz, 1977) and 10 ms for suprathreshold performance (Bernstein & Futch, 1973; Kietzman & Gillam, 1972; Mansfield, 1973). The 20-fold decrease in time constant is also consistent with results obtained from cortical neurons by Carandini et al. (1997) under conditions most similar to normal viewing. The larger time constant values are greater than those typically observed in retinal ganglion cells (Benardete and Kaplan, 1992, 1999), and therefore, probably reflect temporal integration in cortical neurons. The large decrease in time constant values with increases in depth of modulation is also consistent with strong CGC effects observed previously in VEPs and attributed to cortical processes (Zemon et al., 1987). In fact, Reid, Victor, and Shapley (1992), in a study of neurons in cat

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striate cortex, also concluded that the prominent decrease in time constant values is likely cortical in origin. Additional research in which temporal frequency is parametrically manipulated is needed to provide a better measure of temporal integration in the system. The amplitude vs. contrast functions obtained under pedestal conditions increase linearly, or are slightly compressive, with a shallow slope. These functions are similar to those obtained from P-type neurons in the monkey (Kaplan & Shapley, 1986; Kaplan, Purpura, & Shapley, 1987). It is unlikely that these nearly linear VEP functions are a reflection of summation of M responses driven by nonoptimal stimuli: the compressive character of M contrast functions depends on stimulus contrast and not on response magnitude (Albrecht, Geisler, & Crane, 2003; E. Kaplan, personal communication; Lee et al., 1990). The use of a fixed low-mean contrast pedestal unconfounded the effects of depth of modulation and mean contrast and demonstrated that (M-type) high-contrast gain and phase advance (Benardete et al., 1992; Derrington & Lennie, 1984) depend primarily on DOM rather than on mean contrast. The physiological basis for the threshold effect found in some contrast–response functions might be the amount of intracortical inhibition that must be exceeded by excitation to elicit activation of first-order cortical neurons. The P pathway exhibits phase-invariance with changes in contrast. Similarly, one observer in the present study did produce approximately phase-invariant data under pedestal conditions. The remaining two observers generated low-gain amplitude data that were either nearly linear or slightly compressive with DOM, but with corresponding phase plots that demonstrated a relative lag with increases in DOM. The nonlinear model proposed here requires negative conductance in the visual system to fit these results. For these observers, the resultant time constant values are also negative with decreases in absolute magnitude with increases in DOM. Thus, in each case, the total conductance of the system was negative over the entire range of DOM used. One possible explanation for this result is that the high mean contrast pedestal produced a high maintained level of shunting inhibition in the recipient cells and modulation about this level resulted in decreases in the magnitude of shunting inhibition (i.e., a ‘‘ceiling effect’’). Alternative explanations, however, are also possible. Comparable stimuli have not been employed in singlecell studies on primates, and such studies are required to determine if a similar effect exists at the cellular level and the physiological basis of this effect. It should be noted that comparable VEP data were collected from monkeys and humans on the same apparatus and yielded similar functions (Zemon, Mehta, Schroeder, & Gordon, 1995b). The phenomenon of negative conductance has been observed in several fields of study including neuroscience. Engineers have designed CMOS circuits to produce negative conductance for the purpose of voltage gain enhancement (Yan & Geiger, 2000), and it is possible that negative conductance serves a similar role in the visual system. In

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the nervous system, it has been identified in asymmetric reciprocal inhibitory circuits (Manor et al., 1999) and associated with N-methyl-D-aspartate (NMDA)-receptor-mediated Na+ currents (Moore, Hill, & Grillner, 1993). In fact, it has been demonstrated at the level of the LGN (Kwon, Nelson, Toth, & Sur, 1992) and visual cortex (Fox, Sato, & Daw, 1990) that NMDA-receptor activation plays a critical role in contrast gain enhancement. The steeper slopes in dark as compared to bright check contrast functions under pedestal and appearance–disappearance conditions suggest that the contrast gain of OFF cells is greater than that of ON cells for the parvocellular as well as magnocellular pathway. There appear to be perceptual consequences for this physiological difference. Asymmetries have been reported in psychophysical responses to increments and decrements of light, with thresholds to decrements typically lower than those to increments (Boynton, Ikeda, & Stiles, 1964; Bowen, Pokorny, & Smith, 1989; Bowen, Pokorny, Smith, & Fowler, 1992; Cohn & Lasley, 1975; DeMarco, Smith, & Pokorny, 1994; Krauskopf, 1980). Also, flicker-induced darkness enhancement is greater than brightness enhancement (Magnussen & Glad, 1975). It should be noted, however, that this asymmetry in the VEP (present only with small check conditions) is lost or reverses at low luminance levels (Zemon, Gordon, Siegfried, & Lam, 1992). Selective deficits in ON/OFF processes have been implicated in multiple sclerosis (Regan, Milner, & Heron, 1976), cerebral palsy (May, 1978), congenital stationary night blindness (Sieving, 1993), and Duchenne muscular dystrophy (Fitzgerald, Cibis, Giambrone, & Harris, 1994a; Fitzgerald, Hartmann, & Zemon, 1994b). There is evidence to support the suggestion that deficits in M/P processes exist in disorders as diverse as glaucoma (Greenstein, Seliger, Zemon, & Ritch, 1998; Quigley, Sanchez, Dunkelberger, L’Hernault, & Baginski, 1987), Alzheimer’s disease (Sadun & Bassi, 1990; Siegfried, Coslett, & Zemon, 1995), retinitis pigmentosa (Alexander, Rajagopalan, Seiple, Zemon, & Fishman, 2005), and schizophrenia (Butler et al., 2001). Thus, there are possible clinical applications for these electrophysiological techniques. Acknowledgments We thank Norman Milkman, Michelangelo Rossetto, and Gary Schick for technical assistance, Mary Conte for valuable assistance in data collection, Yvonne Holland for aid in the preparation of this manuscript, and E. Eugenie Hartmann for a helpful review of an earlier draft of the manuscript. Also, we thank Ehud Kaplan, George Hu, Andrew Meyer, Robert Shapley, and Jonathan Victor for valuable discussions, and Bruce Knight for his support of this work, which was funded by National Institutes of Health Grants EY02439 to V. Zemon and EY01428 to B. Knight, and by PSC/CUNY Faculty Research Award to J. Gordon.

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