The Pattern-Pulse Multifocal Visual Evoked Potential

Abstract

purpose. To define the pattern-pulse multifocal visual evoked potential (PPMVEP) and determine its characteristics in a sample of normal subjects in terms of amplitude of response attainable, the variation in waveform across visual field, and distribution of potential over the scalp and to compare pattern-pulse with contrast-reversal multifocal stimuli.

methods. VEPs were obtained by concurrently stimulating 60 regions of a cortically scaled dartboard with pulses of pattern contrast. Responses were recorded from normal subjects, by using a 32-channel electroencephalogram recording system, and elementary responses to each region were estimated by multiple regression of each of the response channel signals on stimulus signals. Left-eye, right-eye, and binocular viewing conditions were concurrently tested by dichoptic stimulation. A direct comparison was then made with contrast-reversal stimulation.

results. Response waveform sets for 12 subjects varied in maximum amplitude from 1.8 to 6.8 μV. A stereotypical distribution of waveforms held in most subjects, depending primarily on the polar angle location of the stimulus within the visual field. In a direct comparison with a contrast-reversal multifocal analysis, the pattern-pulse responses had similar waveforms and scalp topography, but were 15 times larger in amplitude. Root mean square (RMS) signal-to-noise ratio (SNR) was 1.9 times higher with pattern-pulse stimulation, corresponding to a reduction of 73% in recording time to achieve the same SNR.

conclusions. The PPMVEP can simultaneously characterize 60 regions of the visual field for both eyes in less than 7 minutes. A general methodology is illustrated that allows multifocal analysis with flexible choice of stimulus conditions.

Wide-field visual stimulation generates a complex superposition of evoked potentials due to the varying orientation of generators within the retinotopically organized early visual areas. The morphology of early cortical visual areas varies significantly between individuals ^{1 2} ; hence, the resultant superposition leads to significant interindividual variation in evoked potential waveforms. The use of focal stimuli, restricted to smaller regions of the visual field, activates smaller regions of cortex, but substantial recording times are necessary if many locations are to be studied. Multifocal visual evoked potential (MVEP) analysis refers to the simultaneous characterization of response properties for multiple visual field locations, by concurrently applying separate test stimulus waveforms to each location, and decomposing the overall response into components due to each location. ^{3 4} Such fine-grained retinotopic analysis of cortical evoked potentials is of interest both for basic research in the processing of visual information in early visual areas and for clinical application. ^{5 6 7 8 9}  

Multifocal analysis has been applied in many studies of the electroretinogram, using the m-sequences methodology developed by Sutter ^{10 11} and implemented in an analysis system (VERIS; Electro-Diagnostic Imaging, San Mateo, CA), which provides a powerful and rapid mapping of responses at a large number of retinal locations. This method was adapted ^{3 4} for the VEP by using a stimulus layout with regions increasing in size toward the periphery, to attempt to activate similar-sized patches within cortical area V1. Within each region, a checkerboard reverses in contrast according to a binary sequence termed an m-sequence. The response extracted for each region is essentially the response to contrast-reversal at a high average rate, typically 37.5 times per second. Published responses have indicated amplitudes up to a maximum of 400 nV. ^{3 4 7}  

The use of contrast-reversal stimuli is an established standard for clinical evaluation of the integrity of the visual pathways. ^{12 13} Alternative temporal modes of stimulation of contrast-detecting mechanisms include onset and offset of contrast or the presentation of brief pulses of pattern contrast, on a uniform field, with no change in mean luminance. The latter was used notably in studies by Jeffreys and Axford, ^{14 15} who suggested ¹⁵ that repetitive stimuli consisting of brief pulses of pattern contrast had an advantage over stimuli with more extended duration of contrast, because adaptive processes would not diminish response amplitude. Using an eight-region multifocal stimulus James and Maddess ^{16 17} compared reversal of stimuli contrast at pseudorandom times on an average of 25 frames per second with stimuli in which the pattern pulsed on at pseudorandom times on average 6.25 times per second and found larger and more reliable responses to the latter. 

This article presents results of an MVEP analysis using pattern-pulse presentation in each of 60 regions of a cortically scaled stimulus layout, from a group of 12 normal subjects. We sought to find the range of response amplitudes and signal-to-noise ratios (SNRs) obtainable and to find patterns of waveform distribution across visual field in this sample of normal subjects. In a further experiment, a direct comparison was made between pattern-pulse and contrast-reversal stimulation, and response strength topography in the two cases was studied by means of a dense 30-channel electrode array. 

The use of interocular comparisons has been explored to detect visual abnormalities, ^{6 7} with the two eyes being measured in succession, which introduces a source of variance between the runs. This study, following procedures used in previous work, ^{17 18 19} used a dichoptic system to stimulate each eye independently and simultaneously obtained the responses in the right and left eyes and also in the binocular viewing condition. 

Beyond the presentation of results from the pattern-pulse MVEP (PPMVEP), we sought to show how MVEP analyses can be defined with great generality and with the flexibility to present multiple stimulus conditions per region, chosen freely to probe the questions of interest. 

Methods

Stimuli

Spatial.

Stimuli were displayed on a monitor (Clinton Monoray CRT; Clinton Electronics Corporation, Loves Park, IL), driven by a dichoptic system consisting of a VSG2/5 graphics board and ferro-electric (FE-1) shutter goggles (Cambridge Research Systems, Rochester, UK). The monitor’s framerate was 150 Hz, toggled by the shutter goggles to produce 75 Hz stimulation at each eye. The shutter goggles allowed approximately 25% transmission in the open-shutter phase and almost no transmission in the closed-shutter phase; hence, allowing on average only one eighth of the monitor luminance to be used. The mean level of luminance measured with a radiometer (CS-100; Minolta, Osaka, Japan) through the goggles while toggling was 10 cd/m², a low level, but still within the photopic range. Against this baseline, checkerboards pulsed on, with light and dark luminances of 20 and 0.1 cd/m², equivalent to a Michaelson contrast of 98%. Subjects sat in a curtained space having low-background illumination, at a viewing distance of 40 cm, fixating a small cross at the screen’s center. 

The stimulus consisted of 60 regions in a dartboard layout, scaled according to the cortical magnification factor (Fig. 1A) . The layout corresponded to the 60 region cortically scaled dartboard with pattern (VERIS; Electro-Diagnostic Imaging), which has been used in previous studies. ^{3 4 5 7 9} Total diameter was 32°, with eccentricity at the regions’ centers being 0.4°, 1.4°, 2.9°, 4.9°, 8.2°, and 13.1° in the six rings. Increasing stimulus region size with eccentricity enabled approximately similar areas of cortical area V1 to be stimulated by each region, to give results of a similar magnitude across eccentricities. ³ Check sizes at these eccentricities were 10, 17, 23, 39, 64, and 103 minutes, respectively; however, the monitor resolution at this high framerate was only 640 × 480, and the innermost ring of regions had relatively little pattern structure, which may account for small responses in these four regions in some subjects. 

Temporal.

The temporal stimulus delivered in each of the 60 regions was a sequence of pattern pulses, consisting of the presentation for one frame of a full contrast 4 × 4 checkerboard within the region. The ferro-electric shutter goggle system delivers left-right–frame pairs at a rate of 75 Hz, comprising first a frame to the left eye, then an interleaved frame to the right eye, \({1}/{150}\) second later. Recording run duration, unless otherwise stated, was 109 seconds, equal to 8192 frame pairs at 75 Hz. Within each frame pair, one or more regions could be active, the inactive regions remaining at the mean luminance. An active region could receive one of three stimulus conditions: a pattern pulse to the left eye, to the right eye, or to both eyes (denoted OD, OS, BIN, respectively). For an active region, the pattern is present for a single frame, and hence can be considered an impulse of contrast, against a zero-contrast baseline. This distinguishes the methodology from contrast- or pattern-reversal stimulation, in which a pattern is always present, but reverses in contrast at certain times. The stimulus can also be distinguished from a pattern-onset stimulus, in which a pattern appears and stays on for a longer period, equivalent to the contrast being a step function in time. 

For the 109-second runs, a stimulus sequence consisted of 73 repetitions of the three stimulus conditions, randomly shuffled in order, separated by stimulus onset intervals distributed between 0.4 and 0.6 seconds, according to a pseudorandom uniform distribution. For a recording run, this sequence was concurrently sent to the 60 regions, but with a different cyclical shift for each region, each shift being a particular multiple of 1.8 seconds. In this way, regions appeared to pulse, independently, at approximately two pulses per second, with at least a 0.4-second stimulus onset interval. Note that the binocular stimuli were included here to examine binocular summation. In a clinical application these would not be required and therefore the trial time could be reduced from the 109 seconds used in the experiments. 

In general, four runs of 109 seconds of responses were recorded from each subject, making a total of 436 seconds of recording, containing 292 presentations of each of the three conditions OS, OD, and BIN. In the initial sessions, the four runs consisted of the same randomization. The design was then changed to use different randomizations for each run. One subject was recorded with four identical runs and four different runs. Three sets of response waveform sets (described later) were calculated for same stimuli, different stimuli, and for all runs. When superimposed, all three waveform sets were similar, but with the different and all-run sets apparently smoother. To quantify this, assuming the response waveform set derived from all runs was the most accurate, the root mean square (RMS) difference over all response waveform points was calculated for same minus all-run and for different minus all-run. Expressed as a percentage of the all-run peak waveform amplitude, these RMS deviations were 9.2% for same stimuli and 5.3% for different stimuli, indicating the advantage of using different stimuli. 

Subjects

Fourteen subjects with normal or corrected-to-normal vision were recruited for the study. The age range was 22 to 55 years (median 35). The research complied with the tenets of the Declaration of Helsinki and was approved by the ethics committee of the National Center of Scientific Research. All subjects gave informed consent. 

Recordings

Recordings were made on 32 channels with a computer-based acquisition system (Synamps, with Scan 4.11 software; Neuroscan Laboratories, Sterling, VA), with electrode caps with Ag/AgCl sintered electrodes (Easycap; Falk Minow Services, Munich, Germany). For the 12 data sets in the main study, 30 electrodes were evenly distributed on a subset of the 10-10 layout, and referenced to Cz. For the topographic maps, a new cap was used that sampled 29 channels of the 10-10 layout on the posterior scalp. In all cases, two channels recorded horizontal and vertical EOG. Total amplifier gain was 75,000 times, the analog filtering bandpass was 0.1 to 100 Hz, and digitization was at 500 Hz. Stimulus markers output by the stimulus computer parallel port were recorded in the response file. 

Data Analysis

The continuous record data file was transferred to a data analysis environment (Matlab; Mathworks, Natick, MA). Data runs were extracted from the continuous file according to the stimulus markers and reviewed for artifacts, which were excluded from analysis. Signals were digitally filtered with a bandpass of 1 to 45 Hz, using a third-order Butterworth filter, forward and backward to cancel phase shifts. Signals were then resampled in synchrony with the stimulus frames, to give an integral number of samples per frame. The set of 30 scalp electrodes was augmented with a zero signal for the reference channel Cz, and the average signal over the resultant set was subtracted from each signal, to give the average-referenced response signal set. 

The mapping from visual stimulus to recorded responses was modeled as a multiple-input, -output system with finite memory. For each channel of response, a multiple-input, finite-impulse response model was fitted. The multiple inputs are the signals representing the presentation of each of the three stimulus conditions in each of the 60 regions: 3 × 60 = 180 channels. The finite memory was assumed to extend from 50 to 300 ms. Longer system memories were also used for comparison, but made little difference in the results. The model was fitted to minimize the sum of squares of residuals between predicted and observed response by the least-squares regression method, described in the ^Appendix. The resultant estimates are a set of response waveforms, one for each stimulus condition, for each region. 

This analysis technique can be contrasted with the cross-correlation technique, which calculates the signal-averaged response to each stimulus type, ignoring all other stimulus types, on the assumption that the effect from other stimulus types will converge to zero with increasing length of the run. The least-squares method used in this study produces the estimated response waveform of each stimulus condition and region, corrected for the overlapping responses to the other stimulus conditions and regions. 

Standard errors were calculated by the method given in the ^Appendix. As noted therein, a single value can be taken as applying to all response points for a given electrode channel. 

Wherever the measure of RMS signal strength presented, it is calculated as the square root of the mean of the squares of waveform values within the time window 50 to 120 ms, expressed in microvolts. RMS SNRs of a waveform or waveform set are calculated by dividing RMS signal strength by the estimated standard error. 

Pearson correlation coefficients between two waveform sets were calculated by the sum of products of the corresponding waveforms, each within the time window 50 to 120 ms, divided by the square root of the product of the sum of squares of waveforms of the two waveform sets, again within the time windows of 50 to 120 ms. 

To establish precise timing correspondence between stimulus pulses and response waveforms, recordings were made with a photodiode placed in turn against stimulus regions at the top, middle, and bottom of the screen, to derive adjustments for the time taken during vertical traces on the monitor. The diode signal was recorded by the data acquisition system (Synamps; Neuroscan Laboratories), with reduced gain, and the data processed through the entire analysis sequence and then measured for latency. This gave latency corrections for each region. Response waveforms were interpolated and resampled at poststimulus times corrected to ±0.4-ms accuracy. Responses for right-eye condition were also advanced by one frame time, or \({1}/{150}\) second = 6.67 ms, to compensate for the lag in right-eye stimulation caused by the shutter goggles (described earlier). 

Latency corrections led to advance of the waveforms by up to 11 ms, which with the right-eye correction led to an advance of up to 17.7 ms. The filtering inherent in resampling of the waveforms for correction produced some spread of the signal even beyond this. Together, these effects produced waveforms that began before 50 ms, which was the minimum latency estimated in the regression procedure. 

Presentation of Response Waveforms

Presentation of sets of response waveforms across the visual field was made with a rectilinear layout (Fig. 1C) derived from the rings and sectors of the dartboard geometry. This presentation uses space efficiently and facilitates comparison of waveforms around isoeccentric rings (columns in Fig. 1C ). The layout is indexed vertically (rows) by the polar angle above the horizon of the region’s center, from −75° to 75°. It is indexed horizontally (columns) by the eccentricity in the visual fields to the left or right of the region’s center. This layout can also be considered an idealization of the approximately log-polar mapping from the visual hemifields to the primary visual cortex in right and left hemispheres. ²⁰ Note, as an exception, that the four innermost regions (Fig. 1B , box) are inserted into the center of the columns marked as 1.4° eccentricity (Fig. 1C , box). The eight second-ring regions are then displaced to the top and bottom two rows. 

Results

The data set for the standard experiment recorded from the 12 normal subjects consisted of a five-dimensional array of microvolt responses, the dimensions being time, electrode channel, stimulus condition (OS, OD, BIN), stimulus region in visual field, and the subject number. From this array can be extracted various slices, averages, contrasts and derived parameter values. 

We first consider an example extracted from this data set. Over the set of 12 subjects, the electrode channel with the largest overall RMS strength was at location POz, on the midline 7.4 cm above the inion. Figures 1B and 1C show response waveforms over the set of visual field regions in subject 1 for electrode POz. Waveforms for the two monocular stimulus conditions OS and OD are superimposed. 

Figure 1B shows responses in a layout corresponding to visual field location, but linearized in eccentricity, for comparison with Figure 1C , which uses the rectilinear layout that will be used henceforth. Each waveform is the estimated response to a pattern-pulse presentation for the given eye and region. The I-shaped indicators at time 0 on each subplot indicate plus and minus one SE, plotted about zero. Close agreement was found between the OS and OD responses. The Pearson correlation coefficient between the OS and OD waveform sets is 0.96. 

Waveform Types and Distribution

The amplitude of responses in Figure 1C ranged up to 4.5 μV, with 42 regions having both monocular waveforms higher than 1 μV. Waveform shapes varied across the visual field, as expected for responses generated by regions on the convoluted folds of the retinotopically mapped early visual areas. Nevertheless, a pattern emerged comprising four typical waveform types, with incidence largely corresponding to the polar angle of the stimulus location, corresponding to rows in Figure 1C . Considering polar angles running from lower vertical meridian to upper vertical meridian—that is, from the bottom row to the top row of Figure 1C —the four types are (1) triphasic positive-negative-positive (PNP), with the negative middle peak largest and with peaks at approximately 70, 100, and 150 to 180 ms, respectively; (2) biphasic positive negative (PN), with the positive initial peak largest and with peaks at approximately 70 and 120 ms, respectively. Nine regions have this form, all in the lower visual field; (3) biphasic negative-positive (NP), with peaks at approximately 80 and 140 ms, respectively, mainly in the upper visual field; and (4) a single positive peak (P) at approximately 100 ms, in the 10 regions adjacent or near the upper vertical meridian. 

Figure 2 shows response sets for 12 normal subjects in the binocular viewing condition for electrode POz. Response sets were independently scaled, with 2 μV, as indicated. The distribution of waveforms varied between individuals. Nine of the 12 had distributions of the four waveform types that are similar to those of subject 1, with the distributions in subjects 11 (small responses) and 12 (large responses) being unusual. 

For these 12 waveform sets, columns 2 to 5 of Table 1 give summary statistics of signal strength and SNR. Considering the 720 separate waveforms from 12 subjects and 60 regions, 68% of them had RMS SNRs greater than 2, and 48% had SNRs greater than 3. 

Figure 3 shows a grand mean-response set, averaging all 12 subjects without normalization. Response sets are for electrode channel POz, and the two monocular conditions are superimposed as solid lines (denotation of the thick gray line is described below below). The waveform types and their distributions reemphasize the pattern of peaks and troughs described previously, with the addition of clearer triphasic PNP waveforms for the inner regions of the lower visual field. Inspection of Figure 2 reveals that most individuals have significant asymmetry in their responses to stimulation of the left and right visual fields. This is not unexpected, given the frequently large degree of asymmetry of the left and right occipital cortex. ¹ However, the grand mean has much greater symmetry. There is thus no evidence for a consistent bias in VEP asymmetry in the left and right visual fields. 

Interocular Comparison

As has been found, ^{6 7} responses received by the left and right eyes correspond closely, reflecting the binocular convergence of the human visual system. In Figures 1C and 3 OS and OD waveform sets, plotted on electrode POz, are superimposed, showing close correspondence. RMS difference over the time window of 50 to 120 ms and over all regions was 0.019 μV for the grand mean data in Figure 3 , which is only 0.86% of the peak amplitude. The Pearson correlation coefficient between OS and OD data in each individual are given in Table 1 . 

Binocular Summation

We concurrently measured a third condition, that of binocular stimulation, in which the shutter system delivered a pattern pulse to the left eye, and 1/150 second later a pulse with the same pattern to right eye. Figure 3 displays the binocular response waveforms in thick gray lines, superimposed on the OS and OD responses. Waveform shape and timing were generally similar to the monocular cases, but amplitude was larger. 

To study the response strength produced with binocular summation, the RMS response strength in the window of 50 to 120 ms was calculated in each region in each subject for the binocular responses. The same was calculated for the average monocular response, taken as the average of the OS and OD responses. In each subject, a least-squares regression line, with constant, was fitted for the binocular RMS response strengths for each region against the monocular RMS response strengths. The slope of the fitted line for each subject is given in Table 1 . The slope for the grand mean was 1.30, and all slopes were well below the factor of 2 that would be produced if linear summation had been performed. 

Number of Waveform Components

The singular value decomposition (SVD) can be used to express each waveform in a set of waveforms as a sum of terms, each term consisting of a waveform common across the set multiplied by a coefficient particular for each spatial location. ^{21 22} The first component of the SVD expansion produces the least-squares fit of the waveform set to a single common waveform shape, scaled by a coefficient for each location. The SVD was calculated for each data set of Figure 2 (electrode POz, binocular viewing) for the time window 50 to 120 ms. Each subsequent component (e.g., SVD2, SVD3) produces the least-squares fit to the residual signal from the previous fit. Table 1 gives the percentage of variance accounted for by each component. As expected from the diversity of waveforms across the visual field, the one-component fit leaves a large percentage of variance unaccounted for. The SVD2 components were large; however, there was an abrupt decrease in power in the SVD3 components. For each subject, the waveform set can thus be approximated by mixtures, varying across space, of two common waveforms. 

Response Topography and Comparison with Contrast-Reversal Stimulation

To gain a direct comparison with the type of contrast-reversal stimuli that have been used in previous multifocal studies, a further subject’s responses were recorded on each of 2 days to pattern-pulse and then contrast-reversal stimulation. Recordings were obtained with a 29-electrode array across the posterior scalp to allow comparison of waveforms and precise response topography. 

The pattern-pulse design contained only the binocular condition, and 16 runs of 55 seconds were recorded on each day. Other stimulation parameters were identical with those for the previous 12 subjects. A set of response waveforms from subject 13 for the 29 scalp electrodes used is shown in Figure 4 . The waveforms are extracted from one region, at 13.1° in the left visual field and polar angle 45° below the horizon. Data from the 2 days are superimposed, showing excellent replicability (RMS differences provided later). The layout of the waveforms follows a mapping obtained by flattening the curve of the scalp, centering on the electrode POz. Electrode names according to the 10-10 system are indicated. Iz is at the inion, and spacing along the midline was 3.7 cm. 

The response at and around electrode POz had the PN waveform typical of sectors at −45° polar angle, then inverting between electrodes Oz and Iz, with the inverted response sharper on the contralateral (right) side. The waveforms cannot, however, be fitted by a single profile. An SVD ^{21 22} had the first component accounting for 85% of the power, with the first two components accounting for 99%, indicating the likely presence of more than one generating site. 

Figure 5A shows topographic maps of RMS signal strength for each of the 60 regions of stimulation. The average of the two replicates was used, and the RMS over the interval of 50 to 120 ms was calculated. Electrode locations are indicated in the map at top left, and correspond to the locations in Figure 4 . In other maps, the location POz is marked, as well as the location with the largest RMS strength. Contour lines represent steps of 0.3 μV. Note that all responses are taken against average reference (see the Methods section). 

The response waveforms at the electrodes having the largest RMS for each region are plotted in Figure 6A , with the replicates from the 2 days in solid lines (thick gray lines explained later). For the characteristic biphasic PN waveforms of the peripheral regions at −45° polar angle, the peak strength was at location POz; however, in many other regions, the peaks were displaced to electrode locations on the contralateral side (Fig. 5) . The four regions at 1.4° eccentricity in lower visual field in particular had strong peaks on the occipital line—in three cases, displaced contralaterally and with triphasic waveforms. 

The overall largest peak had an amplitude of 3.64 μV, and overall RMS signal strength for the selected channels over the 60 regions was 0.84 μV. The replicates for the 2 days were in many cases indistinguishable, with the overall RMS difference between the plotted waveform sets equal to 0.17 μV. Table 1 , row 13-PP indicates statistics for the overall strongest channel POz, with an RMS SNR of 4.82. 

During each of these two sessions, 16 runs of 55 seconds were also recorded with contrast-reversal stimuli. The checkerboards were present at full contrast (98%) on all frames, but in a random selection of exactly half the frames, light and dark checks were swapped. The viewing condition was binocular, at 75 Hz per eye. The contrast of the stimulus was thus reversed at random times, on average 37.5 times per second. This is statistically equivalent to the m-sequence stimulus used in other studies. ^{3 4 5 7 9} Response waveforms were taken as the estimates of the first slice of the second-order kernel, as in those studies (see ^Appendix). 

Figure 5B shows response topography for the contrast-reversal responses, plotted as for Figure 5A , with the exception that the contour step size was 0.02 μV—that is, 15 times smaller than for the pattern-pulse stimulation. Topography showed close similarity at corresponding receptive field locations. The Pearson correlation coefficient between the RMSs of pattern-pulse and contrast-reversal responses, over all regions and electrode channels, is 0.84. For comparison, correlation between replicates on the 2 days was 0.93 for the pattern-pulse and 0.78 for the contrast-reversal stimuli. 

As for the pattern-pulse data, the waveforms for the electrode channel with the largest RMS strength for each region were selected. Figure 6B shows the two response set replicates superimposed as solid traces. As with the pattern-pulse replicates, they are very close, with RMS difference of 0.022 μV; however, the overall largest peak had amplitude of only 0.27 μV, and overall RMS strength for the selected channels over the 60 regions was 0.057 μV. For channel POz, the RMS SNR was 2.49, or 1.94 times less than the pattern-pulse RMS SNR. 

For comparison, the average of the two pattern-pulse response sets is also superimposed in Figure 6B , shown as a thick gray trace, scaled down by 15 times. Likewise, the average contrast-reversal waveforms for the channels presented in Figure 6B are superimposed in Figure 6A as thick gray traces, after they were scaled up by 15 times. In many regions, the initial peaks matched closely, whereas there was greater variation in the later phases of the responses. 

Correlation coefficients were calculated between the waveforms. When the optimal electrodes were selected, as in Figure 6 , correlation between average pattern-pulse and average contrast-reversal cases was 0.76. For comparison, correlation between the two replicates was 0.98 for the pattern-pulse and 0.94 for the contrast-reversal. When calculated over all electrodes and all regions, correlation between average pattern-pulse and average contrast-reversal was 0.66, whereas correlation between the replicates was 0.90 for pattern-pulse and 0.73 for contrast-reversal. 

Discussion

Amplitudes and SNR Compared with Contrast-Reversal Stimulation

A striking finding was the large amplitudes obtained in response to pattern-pulse stimulation, particularly when compared with the amplitudes of the responses to contrast-reversal stimulation. The 13 subjects studied had pattern-pulse responses in the range of 1.8 to 6.8 μV. For the subject studied with contrast-reversal stimulation, peak amplitude was 0.27 μV, which is in line with the amplitudes of 100 to 300 nanovolts of previously published contrast-reversal multifocal responses. ^{3 4 5 7 9}  

Adaptation of the response to contrast as a function of the preceding stimulation has been observed in a number of neuronal classes and visual response signals, recorded by a variety of techniques. Extracellular recordings from the retina indicate a rapid-gain control mechanism, acting within approximately 100 ms, in the retinal ganglion cells of the cat ^{23 24 25} and the M retinal ganglion cells of the primate. ^{26 27} Slower contrast adaptation effects acting over the time scale of seconds have also been observed in retinal ganglion cells, ^{28 29} and contrast adaptation effects have been described at a variety of time scales in recordings from cortical neurons. ^{30 31 32 33}  

Adaptation of the contrast-response function of the VEP has been described in several studies. ^{34 35 36 37} Victor et al. ³ in particular focused on the dynamics of adaptation immediately after step changes in the contrast of a contrast-reversal checkerboard. That study found that after a low to high transition in contrast modulation depth, response amplitude decayed to approximately one fourth within 700 ms. After high- to low-contrast transitions, response amplitude recovered within a similar time. Beyond this time interval, a less than 10% change in amplitude was observed. 

The consequence of contrast gain control effects for the pattern-pulse experimental stimulus is that the interval of zero contrast (approximately 0.5 seconds) between pulses allows the system to recover most of its maximum contrast sensitivity. Longer average interstimulus intervals were also tried, but amplitude did not increase significantly beyond 500 ms. This asymptotic effect is also in line with recent results obtained with magnetoencephalography, ³⁸ in which the cortical response to periodically presented stimuli increases in strength almost linearly with interstimulus interval up to approximately 500 ms and then approaches an asymptote. 

By comparison, a contrast-reversal stimulus has spatial contrast present at all times, and also a high rate of temporal contrast change, in the form generally used in multifocal analysis reversals occur on average 37.5 times per second. Both these properties are likely to keep the system in a low-gain state, producing the small responses observed. Similar results directly comparing binary and pattern-pulse stimuli have now been obtained in a larger study. ³⁹  

Also of note is the similarity in topography (Fig. 5) and waveforms (Fig. 6) between the responses to pattern-pulse and contrast-reversal stimulation. Although large-field pattern onset and contrast-reversal stimuli are often considered to have different properties, the evidence in the current study is that, at least in the case of the rapidly reversing stimuli that have been used in multifocal analysis heretofore, responses are similar but smaller compared with pattern-pulse stimulation. Waveform shapes are most similar in the first phase of response and more varied in later phases. Recent equivalent-current–dipole analysis of the magnetic fields evoked by m-sequence stimulation suggests that for this rapid contrast reversal stimulation the generators lie within the striate cortex (V1). ⁴⁰ It is thus possible that the early phase of the pattern-pulse response also originates in V1, whereas the generators of the later phases vary more between the two stimulation conditions. 

Whereas amplitude increased by 15 times, the measure of RMS SNR, for identical durations of recording, only increased from 2.49 to 4.82—that is, 1.94 times. Similar results have been obtained in an earlier study. ³⁹ The ratio is caused by the fact that the standard error of the responses in the contrast-reversal case was lower, by a factor of 7.73. This itself was expected, because a greater number of stimuli were presented in the same recording time, reducing variance of the estimated response per stimulus. There was thus a tradeoff between stimulating at a high rate, to reduce parameter variance, and stimulating more slowly, to prevent gain control mechanisms from reducing response amplitude. If the amplitude were to increase linearly with interstimulus interval (ISI), but the standard error were to increase by the square-root of ISI, because of fewer presentations in a given recording time, then the RMS SNR increases by the square-root of the average ISI. This advantage continues up to the point where the amplitude flattens off, which for pattern-pulse appears to be approximately 0.5 to 1 second. 

The improvement that occurred in going from contrast-reversal to pattern-pulse stimuli translates into an important practical advantage in recording time. The RMS SNR can be expected to increase only as the square root of recording time, even if recording quality is maintained at a constant level. Hence, an improvement of 1.94 times in RMS SNR is equivalent to a reduction of 3.7 times in the duration of recording—that is, by 73%. Reducing recording time by 73% has clear benefits from the perspective of subject fatigue. Also subjects report that the pattern-pulse stimulus is easier to tolerate than binary contrast-reversal stimuli. 

Clinical Potential

The results shown in Figure 2 indicate that good-quality data sets can be obtained in 7.3 minutes of recording time, in the three conditions OS, OD, and BIN. If the binocular condition is dropped, then similar quality results should be obtainable for the two monocular conditions OS and OD in less than 5 minutes recording time. 

Interocular comparison ^{6 7 18 19} can be used by which a patient’s other eye serves as their own control when abnormality is not symmetrically distributed. This analysis gains power when the two eyes have been tested simultaneously, as a source of variance between recording runs is eliminated, and binocular stimulus conditions can also be added that could be of value in some contexts. ^{18 19}  

The potential clinical applications are significant, for the diagnosis and monitoring of disorders both of the retina and of the visual pathways and cortex. In the case of retinal disorders, the VEP provides an amplified and less invasively recorded access to the retina’s output, compared with the electroretinogram, and can be quicker and more precise than visual field perimetry. ⁴¹ For disorders of the nervous system such as multiple sclerosis, deficits that are localized within the optic nerve may be masked by undamaged fibers when a wide-field stimulus is used, as in the established routine VEP analysis. ^{18 19} There is hope of developing a method with sensitivity and specificity rivaling that of imaging techniques, but with a lower cost, such that routine longitudinal monitoring of patients would be feasible. 

Source Localization

Dipole modeling of responses for each region separately was tried using the brain electrical source analysis (BESA) program (Megis Software, Munich, Germany). Sources for the initial peak were located in the contralateral hemispheres; however, dipole location could not be found to vary coherently with stimulus location within a hemifield. It was confirmed that two dipoles would be required to model waveforms in the window 50 to 150 ms, with largely overlapping activation waveforms, as has been suggested by previous studies. ^{42 43 44} Source modeling based on multifocal response sets has achieved some success by using the constraint of common temporal waveforms for regions, ⁴⁵ but was limited to the assumption of a single dipole source for each region. 

Application for Preliminary Screening in VEP Studies

A large class of experimental designs in the area of VEP and more cognitively oriented event-related potential (ERP) research consists of the presentation of various stimulus conditions to a subject in the central visual field. The problems of cancellation of signal between visual field locations and the intersubject variability mean that great variability is injected into these data sets, reducing the statistical power with which to see effects. A more rational way to proceed would be to place visual stimuli in visual field locations known generally to have strong and homogeneous VEP properties, or better, first to map the visual field of each subject, and then to place stimuli on the basis of this map. ⁴⁶  

Generality of Design

This study demonstrated how a broader class of multifocal experimental designs can be implemented than has been possible with contrast-reversal stimuli. The set of stimulus conditions to be presented at each location can be chosen without constraint, as can the temporal properties of the presentations, to most efficiently test the system and questions under consideration. Each condition gives rise to a component block in the design matrix (see ^Appendix), and the regression procedure decomposes the overall response into components assigned to each condition and location. Standard errors of response components can also be estimated, and the techniques of statistical inference applied to draw conclusions. It is hoped that this study illustrates a general framework that may enable a significant expansion of the range of application of multifocal techniques. 

Appendix 1

Estimation of Response Waveforms

The mapping from visual stimulus to each response channel is modeled to the first approximation as a linear superposition of components due to each of the three stimulus conditions (OS, OD, and BIN) in each of the 60 regions of the dartboard (Fig. 1A) . This can be expressed in the multiple regression framework by the equation  

\[y{=}X\mathbf{{\beta}}{+}\mathbf{{\epsilon}}\]

The vector y contains the response values for one channel; the matrix X is the design matrix, which consists of a horizontal concatenation of blocks, one block per condition–region pair. Each block consists of columns, being delayed versions of the appropriate stimulus signal, for the range of delays to be modeled, generally covering the window 50 to 300 ms. The columns consist mainly of zeros, with ones being placed at the times corresponding to stimulus presentation. The vector β contains the regression coefficients, covering all combinations of delay, condition, and region (i.e., the response waveforms to be estimated). The vector ε is the residual between predicted and recorded responses. 

The estimated regression coefficient vector b that minimizes the sum of squares of residuals \({\parallel}\mathbf{{\epsilon}}{\parallel}^{2}\) is given by solving the normal equation  

\[(X{^\prime}X)\mathbf{b}{=}X{^\prime}\mathbf{y}\]

This is calculated for each response channel, and the results are then reshaped into a multidimensional array containing estimated waveforms for each channel–condition–region combination. 

The array X and the vector b are constructed on a time base at the stimulus frame pair rate 75 Hz. The response at 150 Hz is deinterleaved to give two vectors y on time-base 75 Hz. These are processed separately, and the results reinterleaved to give waveforms at 150 Hz. The number of elements in β is given by the number of regions times the number of conditions times the number of stimulus steps in the time window of interest. In this study that gives p = 60 × 3 × 20 = 3600, where p is parameters. The length of y is the number of stimulus steps (n = 8192) for a single run and correspondingly longer for multiple runs. The size of X would be n × p; however, in practice it is never explicitly constructed, only the expressions X′X and X′ y are constructed. 

To validate the experimental design and estimation procedure, an artificial response waveform set was constructed, having 40 delta function impulses 1 μV in amplitude distributed at various latencies over 40 of the regions and being otherwise zero in the remaining regions. The response signal that would be expected from such a response set was simulated, in response to one repetition of the first stimulus sequence used in this study. From this noise-free simulated response signal, the estimation procedure was applied to recover estimated response waveforms. The estimated waveforms were identical with the original waveform set, to within machine accuracy—that is, the largest error was 4.8 × 10⁻¹⁵. 

For the contrast-reversal multifocal stimulus in Figures 5B and 6B the estimation procedure is similar, with the regression vectors consisting of ±1, derived from the transitions of state of the contrast. As has been explained in relation to the m-sequence MVEP analysis, ³ the first slice of the second-order kernel contains most of the response power. It is obtained by regression on a regression vector derived by taking the pointwise product of the contrast signal with a delayed version of itself. 

Standard Errors, RMS Signal Strength, and SNRs

Standard errors have seldom been presented in published multifocal results, and so care was taken in this study to estimate reliable values. Three different approaches were performed, to check for consistency. First, the classic method from regression analysis is to calculate an estimate s ² of the noise variance ς², from the regression residuals  

\[s^{2}{=}\ \frac{1}{(n-p)}\ {\parallel}\mathbf{y}{-}X\mathbf{b}{\parallel}^{2}\]

where n is the number of data points and p is the number of parameters estimated. The estimated variance matrix of the parameter estimates is  

\[{\hat{V}}(\mathbf{{\hat{{\beta}}}}){=}s^{2}(X{^\prime}X)^{-1}\]

The square roots of the diagonal elements of this matrix give the standard errors of the corresponding parameter estimates. The designs in this study are balanced, with the same number of stimuli of each class presented, and it was found that the values along the diagonal X′X varied by less than 2%. This justifies the use of a single standard error value for all parameters. 

The second method used the bootstrap principle. ⁴⁷ The raw response signal was partitioned into eight segments. From these, 100 random selections with replacement of eight segments were made and the regression procedure repeated. The standard deviation of parameter estimates across these simulated data sets estimates the standard error of the estimated parameters. 

The third method partitions the data into two halves, from which two sets of parameters are estimated—say, b ₁ and b ₂. Assuming that these two parameter sets have the same expected value, β, and additive noise with the same variance at each point, say δ², then the difference, b ₂ − b ₁, will have an expected value of zero and noise variance 2δ². This variance can be estimated by the mean-square value of the difference, b ₂ − b ₁. The average of the two parameter sets, ( b ₂ + b ₁ )/2, has a noise variance of δ²/2. We thus estimate the noise variance of the averaged parameter set by the mean-square of the difference, divided by four. 

These three methods gave consistent results, for example, for the response waveform set of Figure 1C , the estimates of standard error of each point were 0.26, 0.24, and 0.23 μV, for the three methods, respectively. 

The third method was also used to estimate standard error when pooling two separate response sets, such as between recording days, as in Figure 6 . 

 Supported by the Department of Life Sciences, National Center of Scientific Research (CNRS), France.

 Submitted for publication June 19, 2002; revised September 11, 2002; accepted September 25, 2002.

 Disclosure: A.C. James (P)

 The publication costs of this article were defrayed in part by page charge payment. This article must therefore be marked “advertisement” in accordance with 18 U.S.C. §1734 solely to indicate this fact.

 

Figure 1.

 

(A) The 60-region cortically scaled dartboard stimulus, with four sample regions (checkered), showing a pattern pulse. Lines: stimulus region size and layout; these do not appear on the actual stimulus. (B) Response set with OS and OD viewing conditions superimposed in subject 1, electrode at POz, and (C) the response set on rectilinear layout, by eccentricity (ring eccentricity, cf. abscissa of A) and polar angle above horizon. The small error bar preceding each trace indicates ±1 SE from the regression (see ^Appendix).

Figure 2.

 

Response sets for the binocular viewing condition, for electrode POz, for 12 normal subjects. The scale bar for each set indicates 300 ms (x-axis) and 2 μV (y-axis). ±1 SE is indicated at time 0 on each waveform.

Table 1.

 

Response Summary Statistics

Subject	Signal	Noise	SNR	Amp	OS.ODρ	BINβ	SVD1	SVD2	SVD3
1	1.66	0.34	4.90	5.82	0.96	1.28	48	48	3
2	0.76	0.25	3.02	3.18	0.89	1.36	69	27	3
3	1.26	0.44	2.85	4.74	0.87	1.23	59	35	3
4	0.99	0.30	3.26	5.21	0.79	1.39	70	24	4
5	0.94	0.30	3.12	3.76	0.86	1.28	68	27	3
6	1.57	0.52	3.02	5.89	0.77	1.11	71	23	4
7	1.05	0.38	2.79	4.81	0.89	1.44	56	41	2
8	0.47	0.26	1.80	1.79	0.56	1.56	81	15	2
9	0.87	0.47	1.87	4.12	0.79	1.50	61	34	3
10	0.90	0.29	3.13	3.05	0.86	1.35	66	30	2
11	0.61	0.23	2.71	4.03	0.71	1.40	71	19	3
12	2.07	0.55	3.75	6.85	0.89	1.22	68	26	4
GM	0.79	0.24	3.31	2.84	0.95	1.30	61	37	2
13-PP	0.71	0.15	4.82	3.04	n/a	n/a	84	12	3
13-CR	0.04	0.02	2.49	0.20	n/a	n/a	65	23	7

Figure 3.

 

Response set calculated as the grand mean of the 12 subjects of Figure 2 , for electrode POz, viewing conditions OS and OD superimposed as solid lines, binocular viewing superimposed as thick gray lines.

Figure 4.

 

Waveforms on all electrode channels in subject 13, for the region at 13.1° left, polar angle 45° below horizon. Replicates from two different days are superimposed. Scalp position is mapped flattened about the electrode at POz, with 10-10 electrode positions indicated.

Figure 5.

 

Topographic maps of RMS response strength for subject 13 for each stimulus region. The flattening and electrode locations and names for each map are as for Figure 4 . All electrode locations are indicated in upper left map. Location POz and the electrode with largest RMS are indicated on other maps. (A) For pattern-pulse stimulation, contour step size was 0.3 μV. (B) For contrast-reversal stimulation, contour step size was 15 times smaller (i.e., 0.02 μV).

Figure 6.

 

Response waveform sets in subject 14. (A) For the pattern-pulse stimulation, the waveform for the channel with the largest RMS from Figure 5A was plotted for each region. Two replicates from different days are superimposed as solid lines. Thick gray line: averaged contrast-reversal response, for the corresponding electrode in each location, scaled up in magnitude 15-fold. (B) For the contrast-reversal stimulation, the waveform for the channel with the largest RMS from Figure 5B was plotted for each region, with two replicates superimposed as solid black lines. Thick gray line: the averaged pattern-pulse response, for the corresponding electrode in each location, scaled down in magnitude 15-fold.

The author thanks Jean Bullier, Ted Maddess, and Simo Vanni for helpful comments on the manuscript.