Contrast response of temporally sparse dichoptic multifocal visual evoked potentials

Visual Neuroscience ~2005!, 22, 153–162. Printed in the USA. Copyright © 2005 Cambridge University Press 0952-5238005 $16.00 DOI: 10.10170S0952523805222046

Contrast response of temporally sparse dichoptic multifocal visual evoked potentials

TED MADDESS,1 ANDREW CHARLES JAMES,1 and ELIZABETH ANNE BOWMAN 1,2 1 2

Centre for Visual Sciences, Research School of Biological Sciences, Australian National University, Canberra, Australia Centre for Visual Sciences, John Curtin School of Medical Research, Australian National University, Canberra, Australia

(Received October 7, 2004; Accepted December 21, 2004!

Abstract Temporally sparse stimuli have been found to produce larger multifocal visual evoked potentials than rapid contrast-reversal stimuli. We compared the contrast-response functions of conventional contrast-reversing ~CR! stimuli and three grades of temporally sparse stimuli, examining both the changes in response amplitude and signal-to-noise ratio ~SNR!. All stimuli were presented dichoptically to normal adult human subjects. One stimulus variant, the slowest pattern pulse, had interleaved monocular and binocular stimuli. Response amplitudes and SNRs were similar for all stimuli at contrast 0.4 but grew faster with increasing contrast for the sparser stimuli. The best sparse stimulus provided an SNR improvement that corresponded to a recording time improvement of 2.6 times relative to that required for contrast reversing stimuli. Multiple regression of log-transformed response metrics characterized the contrast-response functions by fitting power-law relationships. The exponents for the two sparsest stimuli were significantly larger ~P ⬍ 0.001! than for the CR stimuli, as were the mean response amplitudes and signal-to-noise ratios for these stimuli. The contrast-dependent response enhancement is discussed with respect to the possible influences of rapid retinal contrast gain control, or intracortical and cortico-geniculate feedback. Keywords: Multifocal, VEP, Contrast response, Contrast gain control, Sparse stimuli

between responses to upper and lower visual field stimulation, which is characteristic of responses from the striate cortex ~e.g. Jeffreys, 1971; Baseler et al., 1994; Di Russo et al., 2002!. James ~2003! recently demonstrated that the distribution and sign of responses recorded at many locations on the scalp is the same for sparse pattern pulse and for rapid CR stimuli, even though the responses to the particular sparse stimuli used were 15 times larger than are typical for CR stimuli. A hierarchical decomposition analysis ~Repucci et al., 2001! of responses from 92 eyes ~Maddess et al., 2003! suggests that mfVEP responses to sparser stimuli are even more influenced by afferent input to the cortex than are responses to CR stimuli. This may be valuable for characterizing eye diseases by means of mfVEPs. For concurrent stimulation of the two eyes sparse stimuli can be arranged to minimize binocular suppression, further reducing recording time ~James, 2003; James et al., 2005!. Concurrent measurement of the two eyes also provides a proper statistical basis for between eye comparisons ~Atkin et al., 1980; Maddess & James, 1998; Maddess & Severt, 1999; Hood et al., 2000b!. The source of the enhancement of responses by sparse stimuli is topical. One possibility is the rapid contrast gain control mechanism found in the magnocellular pathway of primates ~Benardete et al., 1992; Benardete & Kaplan, 1999! that is similar to that reported in cat X and Y cells ~Victor et al., 1977; Victor & Shapley, 1979a,b! and human psychophysics ~Snippe et al., 2004!. This gain control mechanism produces large responses to transiently

Introduction Baseler et al. ~1994! introduced the use of a cortically scaled dartboard pattern for multifocal visual evoked potentials ~mfVEPs!. In that study, the contrast of the checkerboard patterns was modulated by pseudorandom contrast reversals ~CR! presented at a high mean reversal rate. That basic method has been shown to be valuable in tracking diseases such as multiple sclerosis ~e.g. Hood et al., 2000a; Ruseckaite et al., 2004! and Glaucoma ~e.g. Goldberg et al., 2002!. We have recently demonstrated that temporally sparse stimuli produce much larger mfVEP responses, and higher signal-to-noise ratios ~SNRs!, than conventional rapidly contrast-reversing mfVEP stimuli ~James & Maddess, 2000; James, 2003; James et al., 2005!. In temporally sparse stimuli, the contrast of each region of the stimulus ensemble is modulated by a signal in which many frames of the sequence display a null stimulus, a contrast of 0, while non-null stimuli, such as checkerboard stimuli, are presented relatively infrequently and transiently. Slowly contrast-reversed stimuli also provide larger responses but these do not display ~Fortune & Hood, 2003! the well-known effect of waveform inversion

Address correspondence and reprint requests to: Ted Maddess, Centre for Visual Sciences, Research School of Biological Sciences, Australian National University, PO Box 475, Canberra, ACT 2601, Australia. E-mail: [email protected]

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presented, spatially coarse, stimuli. Other possibilities exist including intracortical processes or event efferent modulation of lateral geniculate nucleus ~LGN! responses. Given the possible influence of a contrast-dependent mechanism, however, we have investigated the contrast-response functions of mfVEP responses to three grades of sparse stimuli and CR stimuli. Materials and methods Subjects Visual evoked potentials ~VEPs! were recorded from 14 normal subjects ~9 men and 5 women, aged 33.1 years ~615.2 SD!, range 19– 62 years! with visual acuity corrected to 609 or better. A Frequency Doubling Technology ~FDT! perimeter ~Humphrey, San Leandro, CA! was used to certify the subjects’ visual fields as normal. Each subject was tested with the Full Threshold C-20 program of the FDT. The research followed the tenets of the Declaration of Helsinki, as approved by the Australian National University’s Human Experimentation Ethics Committee under protocol M9901. Informed written consent was obtained from the subjects after the nature and possible consequences of the study were explained to them. Recording VEPs were recorded using a pair of gold-cup electrodes ~8-mm diameter!, between a point 3 cm above referenced to 4 cm below the inion ~Klistorner et al., 1998!. The earth electrode was attached to the right ear lobe. Signals were amplified 50,000 times, bandpass filtered between 1.6 and 90 Hz ~single pole RC filters!, and digitized at 203 Hz in synchrony with the visual stimulus. Signals were then digitally filtered with a zero-phase shift filter ~Chebyshev type 2! attenuating signals below 1 Hz ~4th-order filter! and above 20 Hz ~16th-order filter!.

Fig. 1. The spatial layout of the stimulus seen by one eye. A possible frame of a temporally sparse stimulus is presented in which some of the eight regions display a contrast of 0 ~see Fig. 2!. Note that each eye saw independent stimuli and so there were 16 stimulus channels in all.

The contrast of the checkerboards in each of the 16 regions was independently modulated in time by a function C~t !. The four modulation sequence types used are illustrated in Fig. 2. The possible contrast values of these temporal modulation functions were 0, 1, or ⫺1, producing respectively a uniform blank field at the mean luminance, a checkerboard, or the checkerboard reversed in contrast polarity. The sequences could also be multiplied by an unchanging scalar contrast, Cs , which could take one of the values:

Stimuli Dichoptic visual stimuli were presented at a frame rate of 101.5 Hz on a 19-inch Barco monitor ~CCID 7551, Kortrjk, Belgium! controlled by an AT Vista graphics board ~Truevision, Shadeland Station, IN!. Data analysis and display routines were written in Matlab ~The MathWorks, Natick, MA!. The viewing distance was 30 cm. The spatial layout of the stimulus is shown in Fig. 1. A red 0.75-deg square fixation spot was presented at the monitor’s center. The checks within each of each region were scaled to stimulate an approximately equal area of the striate visual cortex ~Baseler et al., 1994!: the radius of the peripheral boundary of the inner regions was set to 8 deg to render the response of the inner and peripheral regions approximately equal in amplitude. Note that due to the aspect ratio of the peripheral regions there was a small luminance artifact associated with pattern reversal. This produced a luminance change of 1.9% for peripheral stimuli presented at contrast 1. Dichoptic stimuli were produced by interleaving the images for the left and right eyes by means of a liquid crystal ~LC! stereoscopic modulator ~or shutter! ~Tektronix, Inc., Beaverton, OR! providing a total of 16 independently modulated stimulus regions, eight per eye. The noninterlaced frame rate of the monitor ~101.5 images0s! produced 50.75 images0s0eye following the LC shutter. The LC shutter and spectacles reduced the mean luminance of the monitor to 7.6 cd0m 2. Each stimulus contained 2048 frames producing a total duration of 40.4 s.

Fig. 2. Illustrations of the four types of temporal contrast modulation sequences, C~t !, applied to the 16 stimulus channels. The small inserts at right illustrate the appearance of a stimulus region that could be produced by the two or three contrast levels that could occur in the C~t ! functions. ~A! The rapidly contrast-reversing stimulus ~CR250s!, ~B! the rapid pattern pulse stimulus ~PP250s!, ~C! the slower pattern pulse stimulus ~PP60s!, and ~D! the slowest pattern pulse stimulus ~PP1.30s!. The actual length of the stimulus trains was 40.4 s. The 20 test conditions were obtained by multiplying these sequences by the scalar contrast factors, Cs ⫽ 0.2, 0.4, 0.6, 0.8, 1.0.

Contrast-response of sparse mfVEPs 0.2, 0.4, 0.6, 0.8, and 1. Thus, the four temporal modulation types, and five scalar contrasts, collectively determined 20 possible stimulus conditions. Four subjects were tested with all 20 conditions, while the remaining ten subjects were tested with six conditions comprising the three modulation sequences of Figs. 2 ~A, C, & D! tested at contrasts 0.4 and 1.0. The subjects completing trials for all conditions completed six repeats of each condition, while the other ten subjects completed four repeats. The resulting total recording durations were thus 4.04 or 2.69 min0condition. Blocks of trials of each stimulus condition were presented in a randomized order. Four types of temporal modulation sequence were studied: 1. Rapid contrast reversing, similar to that used in most multifocal VEP studies to date. The stimulus regions could display one of the two polarities of checkerboard, as illustrated by the inserts at right of Fig. 2A, and the polarity was chosen randomly with equal probability on each frame. This produces a mean rate of 25.4 reversals0s0region0eye, denoted CR25/s. 2. Rapid pattern pulse. The two polarities of checkerboard are pulsed on with probability 104 each, on each video frame, otherwise the region is left uniform at the mean luminance. This produces a mean rate of 25.4 presentations0s0region0 eye, denoted PP25/s. 3. Slower pattern pulse. The two polarities of checkerboard are pulsed on with probability 1016 each, on each video frame, otherwise the region is left uniform at the mean luminance. This produces a mean rate of 6.3 presentations0s0region0 eye, denoted PP6/s. 4. Slowest pattern pulse. Stimulus events occur at randomized intervals uniformly distributed between 400 and 600 ms. Each event is the pulse presentation for one video frame of a checkerboard to either left eye, right eye, or both eyes, each with probability 103. Each eye thus receives presentation on two of the three conditions, producing 403 presentations0s0 region in each eye, denoted PP1.3/s. In some cases the binocular condition of this stimulus is treated separately, denoted PPbin. The first three stimulus types have been previously studied at full contrast in normal subjects ~James et al., 2005!, and the fourth has the temporal characteristics used in a 60-region multielectrode study ~James, 2003!. Sequences for the 16 regions0eyes were produced by rotating a single-base sequence in a circular buffer with lags of 2.6 s between each sequence. Elementary response waveforms for each region and eye were estimated from the observed compound response signal by multiple regression of the response signal on regressors derived from the stimulus sequences, see James ~2003! and James et al. ~2005! for details. This method produces least-squares estimates of the elementary component waveforms, correcting for the overlap in responses due to the concurrent stimulation of multiple regions. It is superior to the cross-correlation technique which has often been used in white-noise type analyses ~Lee & Schetzen, 1965!, which does not correct for the cross-contamination of responses present in a finite record length. An alternate approach is the use of nearly exactly orthogonal sequences ~Baseler et al., 1994!, such as m-sequences; however, we use the multiple regression technique as it allows efficient waveform estimates to be obtained with more flexibility in the design of the stimulus.

155 Responses were estimated for a period of 30 sampled points, that is, from 0 ms to 285.7 ms poststimulus inclusive. Waveforms generally had the initial peak between 55 and 95 ms, referred to as C1, and a second peak in the period 105–175 ms, referred to as C2 ~Fig. 3!. As reported by others, responses from the upper and lower hemifields had initial peaks of opposite ~e.g. Jeffreys, 1971; Baseler et al., 1994; Di Russo et al., 2002!. Results Fig. 3 illustrates the individual responses across the visual field, for the four temporal stimulus types, and contrast levels 1.0 and 0.4. The waveforms shown are averages across the 14 subjects ~or 4 subjects for Fig. 3B!. Responses from the lower–inner regions ~2 and 4 in Fig. 1! have a more triphasic appearance, with other responses being biphasic. Although this has been reported before ~Jeffreys & Axford, 1972; James, 2003!, the figure illustrates that the effect persists across a substantial range of contrasts and temporal densities of stimuli. Fig. 4 shows the mean contrast-response functions for the peak C1 response, taken as the maximum absolute value in the time window 55–95 ms. There is one curve for each stimulus region, each point representing an average across the four subjects and their two eyes. Standard errors ~error bars at right of each panel of Fig. 4! are shown for stimulus region 3 ~see Fig. 1!, which had representative SE values. Fig. 4 also illustrates that response size greatly increases ~n.b. ordinate values! with increasing sparseness of the transiently presented stimuli ~see also Fig. 3!. Responses from the lower right quadrant ~open hexagrams! were dominant in most subjects. The C1 and C2 response peaks for all 14 subjects were fitted by multiple linear regression to quantify the effects of the factors age, sex, visual field location, and temporal sparseness. These factors tend to have multiplicative effects, hence the data are logarithmically transformed to allow additive models to be fitted. Examination of the residuals indicates that log-transformation also stabilizes the variance across the response range. The transformation used was to decibels power ~dB!: for a peak value C1, the dB value is C1dB⫽20 log 10 ~C1!. Decibels were used rather than a straight log-transform due to the common usage of decibels in the perimetry and contrast threshold literature. Subject was also fitted as a nuisance variable capturing the variation in response amplitude between individuals ~not shown!. The models for dB peak value also contained a linear term in 20 * log 10 ~contrast!, corresponding to a power-law model for response on contrast. Thus, for each temporal stimulus condition a power-law model of the form R ⫽ kC z,

~1!

was simultaneously estimated by fitting equations of the form: log~R! ⫽ log~k! ⫹ z ⫻ log~C!. Providing the model is a good fit, we are therefore able to simultaneously characterize multiplicative gain factors, k, between responses obtained to different temporal stimulus conditions, and also the form of the contrast-response functions characterized by z and k. The particular model summarized in Tables 1 ~A, B! contained the effects ~1! a reference mean condition, ~2! a factor for Superior Visual Field ~Sup VF!, ~3! a factor for the temporal stimulus types, ~4! decibel contrast ~with which to estimate the exponent z for the Reference condition!, and ~5! a factor representing the interactions between decibel contrast and temporally sparse conditions ~with

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Fig. 3. Elementary response waveforms, averaged over subjects. Panels A–D are for the four temporal stimulus types, as indicated. The responses for the eight spatial regions are laid out topographically corresponding to the stimulus layout ~Fig. 1!. The averaged waveforms of left and right eye are plotted, averaged across 14 subjects ~Panels A, C, D! or four subjects ~Panel B!. Superimposed are responses for contrast 1.0 ~solid line! and contrast 0.4 ~dashed line!. Estimates of the standard errors for each waveform are indicated by error bars at time ⫽ 0. Triphasic responses tend to be obtained from inferior central visual field ~regions 2 and 4 of Fig. 1!, with biphasic responses elsewhere. Note that the ordinate scales vary over a factor of 10 across the different temporal stimulus types.

which to estimate the differences of exponents for the sparse conditions compared to z for the Reference condition!. Although these factors were fitted simultaneously, the results are present in Tables 1A and 1B for clarity. A factor for subject was also fitted. The subject factor is a nuisance variable that quantified the variation in overall VEP amplitude between subjects and is not shown. Table 1 shows the outcome of modelling the simultaneous effects that collectively determine the C1 responses ~see the table legend for row and column definitions!. The overall model was highly significant with an r 2 value of 0.767. In this parameterization the reference condition ~row 1! is the Contrast-Reversing stimulus @Table 1, Ref~CR250s!# at a contrast of 1.0, and the value of k is the amplitude of the average response to CR250s stimuli, 0.292 µV. The significance of the difference of that value from 0 is given in the P column. The fitted coefficients for the gains ~k! for the other temporal stimuli ~PP250s, PP60s, PP1.30s, PPbin! are the difference in decibels compared to the reference condition, Ref~CR250s!. Therefore the P values give the significance of the differences from the reference condition. Thus, the increment of 21.59 dB for the slow pattern pulse ~PP1.30s! means responses to that stimulus are 12.0 times larger ~P ⬍ 0.001! than the reference CR250s condition of 0.292 µV ~cf. Figs. 3A & 3D!. The condition

PPbin refers to the binocular responses that were simultaneously estimated with the monocular PP1.30s responses ~Methods!. The other significant multiplicative effect was superior visual field region ~Sup!, which had responses depressed by ⫺2.78 dB ~60.173 SE! on average across all conditions. The coefficients z CR to z PPbin provide the differences from the reference exponent, zRef~CR250s!, for the power-law fits for each sparse stimulus condition @eqn. ~1!#. Hence the total exponent for the PP60s case was 0.090 ⫹ 0.467 ⫽ 0.557. Like the gains for each stimulus type in Table 1A, the P values of 1B give the significance of the differences from zRef~CR250s! for the exponents for each sparse condition. There were no significant effects of age, sex, or visual field factors such as left versus right hemifields, temporal versus nasal, or inner versus peripheral. A four-quadrant model was also fitted, but when compared with the simpler model containing the superior visual field factor was not significantly different on an F-change statistic. When included in the multiple regression, none of these other factors affected the basic outcomes for the effects of sparse versus CR250s stimuli, suggesting that the fitted values in Table 1 were not affected by spurious correlations. It is worth repeating ~Methods! that the data for contrast 0.2, 0.6, and 0.8 were obtained

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Fig. 4. Contrast-response functions for the four temporal variants of the mfVEP stimuli. The points are averages across subjects and eyes ~N ⫽ 8!. There is thus one curve per stimulus region. The region numbers of the legend correspond to those of Fig. 1. Filled symbols are for inner regions ~1– 4!, open for the peripheral regions ~5–8!. This means symbol type corresponds to the quadrant. The number of sides on the polygonal symbols ascends with region number. Solid lines are for regions presented to the superior visual field, dashed inferior. Representative standard errors are shown at right in each panel. The ordinate scales rise in octaves with increasing sparseness ~A–D!. The panel titles give the temporal stimulus condition. Although the PP1.30s stimulus produces the largest responses they are somewhat noisier than the PP60s responses.

from four subjects, while the data for contrast 0.4 and 0.8 were obtained for 14 subjects. The data for the PP250s condition was only obtained from four subjects and so outcomes for that condition should be treated with some caution. Fig. 5 summarizes the fitted contrast-response model parameters for the C1 responses. Notice that the model presented in Table 1 has been reparameterized here so that instead of the mean differences from the CR250s condition being computed, the mean values for each temporal condition are given. Also, for ease of understanding the actual mean C1 values, rather than decibel values, are presented in Fig. 5A. So, while the model was fit in the log domain, the resulting fitted values, and their SE, have been transformed back to the linear domain. As was clear from the contrast-response curves of Fig. 4, the exponents governing the contrast-response tend to grow with increasing temporal sparseness. Of practical importance for the design of a visual field mapping technique, a significant parameter is the signal-to-noise ratio ~SNR!. This arises because a potential problem with sparser stimuli is that fewer stimulus events are presented within a given stimulus period than in the CR250s case. Thus, one would expect the variance in the estimated responses to grow with increasing sparseness. For the sparser stimuli to be of any benefit from the clinical perspec-

tive, they would have to generate large enough responses to overcome the increase in variance and provide a genuine improvement in SNR. The regression method used to estimate the elementary response waveforms produces a standard error ~SE! value for every point in every response waveform, including for the C1 peak value ~James, 2003!. By taking the ratio of the C1 value on its SE we obtain an amplitude SNR, equivalent to a t-statistic. Fig. 6 summarizes these SNR values at contrast 0.4 and 1.0, for the 28 eyes of the 14 subjects in the study. The figure shows the number of C1 values, from all stimulus regions, eyes and subjects, that exceed a given SNR ~t-value!. At the lower contrast ~0.4!, the performance of the four temporal modulation conditions is similar, with about 50% of responses exceeding 2.5 SE. At contrast 1.0, the performance for CR250s stimuli is much the same as at contrast 0.4, while the SNRs for the sparser stimuli perform much better, with about 50% of the responses to the PP60s stimulus reaching 4.8 SE. Note that where the curves of Fig. 6B cut the 50% level ~dotted horizontal line! that these points correspond closely to the median SNR values. Thus, the values in the rows marked PP250s to PPbin of Table 2A indicate that the curves for sparse stimuli of Fig. 6B are significantly different from the CR250s condition at the 50% level.

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T. Maddess, A.C. James, and E.A. Bowman Table 1. Summary of a multiple-regression model giving the main effects determining the C1 peaks ~see Fig. 3!, r 2 ⫽ 0.767 a A Parameter Ref (CR25/s) Sup VF PP250s PP60s PP1.30s PPbin

20log 10 ~k!

SE

P

k

⫺95% CL

95% CL

⫺10.70 ⫺2.778 6.51 15.29 21.59 20.15

0.492 0.173 0.488 0.377 0.377 0.377

⬍0.001 ⬍0.001 ⬍0.001 ⬍0.001 ⬍0.001 ⬍0.001

0.292 0.726 2.12 5.81 12.0 10.2

0.262 0.699 1.89 5.34 11.0 9.34

0.326 0.755 2.36 6.33 13.1 11.1

B Parameter

z

zRef (CR25/s) zPP250s zPP60s zPP1.30s zPPbin

0.090 0.106 0.467 0.381 0.450

SE

P

⫺95% CL

95% CL

0.040 0.066 0.057 0.057 0.057

0.027 0.115 ⬍0.001 ⬍0.001 ⬍0.001

0.011 ⫺0.024 0.355 0.270 0.339

0.169 0.236 0.578 0.493 0.561

a ~A! From left to right the columns represent: ~1! the fitted parameter name; ~2! the fitted decibel @20log 10 ~k!# value of that parameter; ~3! the SE in the decibel values; ~4! the significance P, the multiplicative gain @k, see eqn. ~1!# corresponding to the decibel values; and ~5&6! the 95% confidence limits in k. Note that the 695% confidence limits on the multipliers are asymmetric due to the initial log-transformation. ~B! The layout is very similar to A but given eqn. ~1!, the exponents, z, are not in decibels, and so there is no value k for them, thus the listed 95% CL are for z. In this parameterization, the first row ~italics! of each table represents fits to a reference condition. For A and B, the reference condition is contrast reversing ~CR250s!. Thus, in the first row of A the column labelled 20log 10 ~k! and SE give the Mean 6 SE C1 response amplitude obtained to CR250s stimuli ~⫺10.70 6 0.492 dB!. The k value in that row gives the equivalent mean C1 real world amplitude of 0.292 µV. Similarly, the row marked zRef~CR250s! is the exponent for the reference condition @see eqn. ~1!#. The other rows give the fitted differences from their respective reference conditions @Ref ~CR250s! or zRef~CR250s!#, and the P values give the significance of those differences.

Figs. 7–9 and Table 2 summarize the output of regression models similar to those of Fig. 6 and Table 1, but where the dependent variable is now the median SNR across visual field regions for each eye. As for C1 amplitude decibel SNR dB ⫽ 20log 10 ~SNR! was fitted but the fitted values have been transformed back to SNR for ease of understanding in Figs. 7–9. As with the model for C1 values ~Table 1!, a nuisance factor for subjects was also fitted. Table 2 shows results for a model parameterization like that for Table 1 where the significance of the differences for the different stimulus conditions can be seen in the rows without italics. The PP60s stimulus generates large SNRs, that were significantly higher than those obtained for the CR250s condition ~Table 2!, by 4.18 6 0.554 dB or 1.62 times ~95% confidence limits of 1.43 and 1.83!. As might be expected, the larger responses obtained to the pattern-pulse stimulus ~Fig. 5, Table 1! do not make up for the large increase in SE due to the low number of stimulus presentations and so do not perform as well as PP60s. The PP250s stimulus also seems to be inefficient as its responses remain small while error variance increases, thus the SNR for PP250s is actually worse than that of the CR250s stimulus. Although only data from four subjects was available for PP250s in this study, another study of 13 subjects comparing SNRs obtained to CR250s, PP250s, and PP60s agrees with the findings here ~James et al., 2005!. The SNR versus contrast functions resulting from the fitted gains and exponents are shown in Fig. 8. Notice that the basic form of the fitted SNR functions tends to follow that of the contrastresponse functions shown in Fig. 4. Fig. 9 summarizes the regression results for the SNR of the C2 peak ~Methods! ~r 2 ⫽ 0.745!.

Overall the results are similar except for the fact that the SNRs are overall lower than for C1. The result is not unexpected because response waveforms tend to differ most at these longer latencies at all contrasts and temporal conditions. Discussion The increase in response amplitudes and signal-to-noise ratios reported here for stimuli presented at contrast 1.0 are consistent with our previous results ~James, 2003; James et al., 2005!. The best signal-to-noise ratio improvements were found for the PP60s stimulus ~4.18 dB!. This corresponds to an improvement in recording time required to achieve a criterion SNR of 2.62 times. In a companion study on 13 different subjects ~James et al., 2004!, the predicted improvement in recording time for the same stimuli was 2.46 times. The typical recording duration here was 2.67 min, so a CR250s stimulus would require about 6.67 min to achieve the same SNR. More recent experiments indicate what could be guessed for the data presented here, that the best SNRs are achieved for stimuli whose temporal sparseness is intermediate between the PP60s and PP1.30s stimuli used here. Perhaps the most interesting result was that at contrast 0.4 the benefits of sparse stimuli over CR250s stimuli seem to disappear. This is best seen in Fig. 6 and in the exponents describing the increase in response with contrast ~Tables 1 & 2, Figs. 5 & 7!. Thus, unlike responses to CR250s stimuli, responses to sparse stimuli drop dramatically with reducing contrast. Since the number of presentations in the stimulus remains constant, this translates into rapidly declining SNRs for the estimated responses to the

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Fig. 5. Summaries of a multiple-regression model related to that of Table 1 giving ~A! the C1 peak responses to contrast 1.0, and ~B! the exponents of power-law functions describing the contrast response @eqn. ~1!#. The abscissa labels represent: Rapid contrast reversal ~CR250s!, rapid pattern pulse ~PP250s!, slower pattern pulse ~PP60s!, slowest pattern pulse ~PP1.30 s!, pattern pulse binocular condition ~PPbin! extracted from the slowest pattern pulse case. The figures are related to Table 1. In Table 1, the fitted coefficients represent differences from the CR250s condition. Here the coefficients are the means for each condition. Although the model was fitted using log-transformed data ~dB!, the C1 results have been transformed back to µV to aid understanding. The error bars are SE, some are occluded by the symbols.

sparse stimuli. The SNRs for the PP250s case were worse than the CR250s case. This agrees with the relatively poor SNRs obtained in a companion study for a PP250s stimulus ~James et al., 2004! and also with results for a temporally very similar stimulus from another group ~Hoffmann et al., 2003!. It is important to note that the same number of slices and response coefficients were estimated for all stimuli so there is no bias in the standard errors observed for the different temporal conditions presented here due to different complexities of the regression model. We have only presented results for the C1 and C2 peak response amplitudes and SNRs. Part of the reason for this is that the regression method used to estimate the kernels ~James, 2003; James et al., 2005! provides estimates of the SNR for the peaks, and all other points in each kernel waveform. In fact, we also examined the mean amplitudes and SNRs within windows encompassing the C1 and C2 peaks. The conclusions reached regarding the effects of contrast are essentially the same as when considering the peak values. The two quicker stimuli, PP60s and PP250s, had the possibility of contrast reversal, while for the slower PP1.30s stimulus checkerboards were only ever presented with one polarity. In subsequent experiments using a 60-regions stimulus, we have found that at the higher presentation rates contrast reversal does improve SNRs somewhat, given that light adaptation will come into play. For presentation rates around 1 or 20s the effect is small to nonexistent. SNRs were lower for C2 than for C1 ~cf. Figs. 8 & 9!. This may mean that it is unwise to take the peak-to-peak measure of the response since it would add variance to the response estimates. Some of this variability is probably due to the more triphasic

Fig. 6. The proportion of C1 responses exceeding a criterion signal-tonoise ratio ~SNR!. ~A! At contrast 0.4, all the functions are similar with about 50% of responses exceeding 2.5 SE. ~B! At contrast 1, about 50% of PP60s responses exceed 4.8 SE. For ~B!, the mean of the functions in ~A! is shown as a dot-dashed line ~mean C ⫽ 0.4, legend!.

character of responses obtained for the lower-central visual field ~Fig. 3!. A hierarchical decomposition analysis for data from 92 eyes used dichoptic CR250s and PP60s stimuli ~Maddess et al., 2003! indicated that the triphasic waveforms were more heavily influenced by intracortical processing with feedback delays in the order of 30 ms, possibly suggesting extrastriate influences. The fact that the triphasic nature of the responses was seemingly unaffected by contrast ~Fig. 3! might suggest that the increase in response size is generated before signals arrive at the cortex, the cortical component simply scaling with input size. The shape of the contrast-response functions seen here for CR stimuli is generally in accord with other mfVEP studies using both pattern-reversal stimuli ~Baseler & Sutter, 1997; Hasegawa & Abe, 2001! and pseudorandom flash stimuli ~Klistorner et al., 1997!. Klistorner et al. ~1997! used the idea that the first and second off-diagonal of the second-order response kernel ~K2,1 and K2,2 , sometimes referred to as the first and second slices of the secondorder kernel!, for their frame time of 15 ms, should be more related to the responses of the M and P systems, respectively. K2,1 and K2,2 characterize the quadratic interaction to pairs of stimuli presented

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T. Maddess, A.C. James, and E.A. Bowman Table 2. Summary of a multiple-regression model giving the main effects determining the median (for each eye) C1 SNR, r 2 ⫽ 0.745 a A Parameter Ref (CR25/s) PP250s PP60s PP1.30s PPbin

⫺95% CL

95% CL

2.10 0.700 1.43 1.20 1.08

2.91 0.964 1.83 1.54 1.46

20log 10 ~k!

SE

P

7.96 ⫺1.71 4.18 2.68 1.98

0.702 0.718 0.554 0.554 0.554

⬍0.001 0.019 ⬍0.001 ⬍0.001 0.004

z

SE

P

⫺95% CL

95% CL

0.059 0.097 0.084 0.084 0.084

0.016 0.798 ⬍0.001 ⬍0.001 ⬍0.001

0.030 ⫺0.164 0.195 0.158 0.272

0.263 0.217 0.522 0.485 0.599

k 2.48 0.821 1.62 1.36 1.26

B Parameter zRef (CR25/s) zPP250s zPP60s zPP1.30s zPPbin

0.146 0.026 0.358 0.321 0.436

a Column definitions are as in Table 1. Also as in Table 1 the rows for the reference conditions, ~A! Ref~CR250s! and ~B! zRef~CR250s!, summarize the mean values for the C1 amplitude ~7.96 dB, k ⫽ 2.48! and the contrast response exponent for the contrast-reversing stimulus. The other rows give the differences ~significant or otherwise, see column P ! from the appropriate reference parameter, Ref~CR250s! or zRef~CR250s!.

one and two frames apart, hence K2,2 is more biased to slower response interactions. Their contrast-response functions for K2,1 and K2,2 did look like the expectations for M- and P-cells ~Kaplan & Shapley, 1986!, that is, K2,1 responses saturated more rapidly with increasing contrast. Baseler and Sutter ~1997! attempted to extract components from the ~larger! K2,1 response that corresponded to the delays expected for M- and P-cells. Their fast, M-associated, component showed very early saturation similar to the CR250s contrast-responses obtained here ~Fig. 4A!.

An interesting feature of multifocal responses to stimuli containing no null stimuli is that the true diagonal of the second-order kernel, K2,0 , is inestimable ~Klein, 1992!, which is why K2,1 and K2,2 are conventionally used. Note that this is true for both pattern-reversal and pseudorandom flash stimuli. In the present study, the PP250s and PP60s are ternary and so the true diagonal of the second-order, K2,0 , can be estimated. K2,0 characterizes the quadratic response to a single presentation of a checkerboard ~or strictly quadratic responses to a presentation and itself with no

Fig. 7. Summaries of a multiple-regression models related to Table 2 providing ~A! the C1 signal-to-noise ratios at contrast 1.0, and ~B! the exponents of power-law functions describing the SNR vs. contrast response. The abscissa labels are the same as for Fig. 5. Note that SNR initially rises ~A! with increasing temporal sparseness but then falls as the increase in error variance due to the slower presentation rate overwhelms the benefit of the increasing response amplitude ~cf. Fig. 5!.

Fig. 8. Estimated functions for the median SNR vs. contrast, for the responses of each eye based on the coefficients of Fig. 7 for the C1 peak. Unlike Fig. 4 these functions, being derived from a multiple regression, are independent of the effects of subject and superior visual field location. The legend symbols are the same as the abscissa labels of Figs. 5 and 7. SNR rises more quickly with contrast for the sparser stimuli. Table 2 shows the differences from the CR250s condition are highly significant for the PP60s and PP1.30s stimuli.

Contrast-response of sparse mfVEPs

Fig. 9. Estimated functions for the median SNR vs. contrast, based on the fitted coefficients for the C2 peak. SNRs rise more slowly for the C2 peak providing overall lower SNRs than for C1.

delay!. For sparse stimuli, K2,1 and K2,2 are not accurately estimated due to the lack of stimuli presented at delays of one or two frames. Using the logic of Klistorner et al. ~1997!, K2,0 may be even more related to M-cell responses, and even less related to P-cell responses, than K2,1 . This may explain why the contrastresponses to CR stimuli obtained here ~Fig. 4A! look similar to those for the M-associated responses of Baseler and Sutter ~1997!. The smaller responses for CR250s stimuli at all contrasts could in part be due to the fact that neighboring regions always contain a valid stimulus, compared to the case of temporally sparse stimuli, where neighbouring test regions are often blank. Thus, a contrastdependent form of lateral suppression, as occurs in LGN neurons ~Solomon et al., 2002!, and is observed psychophysically ~Andreissen & Bouma, 1976!, could be operating for CR stimuli. Such lateral suppression has been found in fMRI studies to operate at least partially in V1 ~Zenger-Landolt & Heeger, 2003!. We also cannot rule out influences such as modulation of feedback from area MT, which contains cells with more steeply rising contrastresponse functions ~Sclar et al., 1990!. Some influence of temporal sparseness upon the strength of the feedback would be required in that case. The lower exponents for the more temporally dense stimuli are reminiscent of the effect of cooling V1 upon some LGN cells ~Przybyszewski et al., 2000!. Those authors showed that cooling V1 caused reduction in the exponents of power-law fits to the contrast-response functions of some P-cells. On a related note, McClurkin et al. ~1994! showed that most macaque LGN neurons decrease their information transmission rate ~bits0s! when the cortex is cooled. Thus, one might expect an increase in LGN bit-rate when the cortex is highly activated by high contrast stimuli, with a concomitant increase in SNR as seen here. Thus, efferent modulation of LGN responses cannot be ruled out at this stage. One cortical effect, binocular suppression, was not a major determinant of exponent size because the explicitly binocular pattern pulse stimuli had similar exponents to those of the monocular responses obtained within the same trials ~Tables 1 & 2, Figs. 8 & 9!. The enhancement of responses by transient presentation of high contrast, spatially coarse, stimuli observed here is reminiscent of

161 the operation of the contrast gain control of M-cells ~Benardete et al., 1992; Benardete & Kaplan, 1999! and cat X- and Y-cells ~Victor et al., 1977; Victor & Shapley, 1979a,b!, whereby the gain of the cells can change dramatically on a time scale of tens of milliseconds. Cortical contrast adaptation seems to operate on a much slower time scale ~Maddess et al., 1988; Sclar et al., 1989!. Human sensitivity to brief pulses presented against flickering backgrounds seems to be governed by a very rapid contrast gain control ~Snippe et al., 2004!, the dynamics of which are very similar to those reported by Victor and coworkers for ganglion cells ~Victor et al., 1977; Victor & Shapley, 1979a,b!. The possibility that the K2,0 responses obtained to the PP60s stimulus are more M-related makes this a more reasonable prospect. An interesting psychophysical correlate of the response enhancement we see here is perhaps the “over-contrast” effect first described by Kulikowski ~1972! ~see also Kitterle & Corwin, 1979; Maddess & Kulikowski, 1999!, in which transiently presented, spatially coarse, stimuli have higher subjective contrast than those presented more slowly. Correlative enhancement of the VEP was also reported ~Kulikowski, 1972! In conclusion, the lack of SNR enhancement for temporally sparse stimuli at low contrasts may be informing us about contrast gain control mechanisms and0or efferent control of the LGN. Variants of temporally sparse stimuli may thus be applicable to studying these processes. Correlative human and primate experiments would be the most informative. The present demonstration that concurrent assessment of both eyes with no binocular suppression, and increased SNR compared to CR stimuli, would seem to have both scientific and clinical utility.

Acknowledgments We would like to acknowledge support from the ANU Centre for Visual Sciences, the ANU block grant, and the very astute comments of a reviewer that greatly assisted in the presentation of this manuscript.

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