N70 and P100 can be independently affected in multiple sclerosis

N70 and P100 can be independently affected in multiple sclerosis

Electroencephalograph)' and Clinical Neurophysiology, 1991, 8 0 : 1 - 7 © 1991 Elsevier Scientific Publishers Ireland, Ltd. 0168-5597/91/$03.50 ADONIS...

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Electroencephalograph)' and Clinical Neurophysiology, 1991, 8 0 : 1 - 7 © 1991 Elsevier Scientific Publishers Ireland, Ltd. 0168-5597/91/$03.50 ADONIS 016855979100051U

EVOPOT 89195

N70 and P100 can be independently affected in multiple sclerosis M. Felice Ghilardi a, F e r d i n a n d o Sartucci b Julie R. B r a n n a n a,c, M a r c o C. Onofrj d Ivan Bodis-Wollner a, L e l a n d M y l i n a a n d R. Stroch a 9

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Departments of a Neurology and c Neurobiology, Mount Sinai School of Medicine, New York, N Y (U.S.A.), b Department of Neurology, Unioersit~ di Pisa, Pisa (Italy), and d Department of Neurology, Universit& di Chieti, Chieti (Italy) (Accepted for publication: 10 May 1990)

Summary

We have studied the relationship between N70 and P100 of the pattern visual evoked potential in 98 patients with multiple sclerosis and in 59 controls. In patients with multiple sclerosis, P100 was either absent or had prolonged latency in 121 eyes (61.7%), while N70 was absent or prolonged in 97 eyes (49.5%). The total number of eyes with either N70 a n d / o r P100 abnormalities was 137 (69.9%). Eighty eyes (40.8%) had abnormal latency of both P100 and N70, while 41 eyes showed P100 delays without corresponding N70 changes. Seventeen eyes had abnormal N70, but normal P100 latency. N70 and P100 appear to be more often absent in the definite rather than in the possible multiple sclerosis group. These data show that N70 and P100 can be independently affected in patients with MS. Key words: Visual evoked potential; Multiple sclerosis; N70; P100; Parallel pathways

Halliday et al. (1972, 1973) were the first to demonstrate that the major positive component (P100) of the pattern visual evoked potential (PVEP) can be delayed or is even absent in patients with optic neuritis or multiple sclerosis (MS). Since then, P100 delay has been considered a hallmark of visual system impairment not only for MS, but also for many other neurological and ophthalmological diseases. The preceding negative component (commonly called N70), although described, has been measured and considered a marker of visual pathway dysfunction only in a few MS studies (Collins et al. 1978; Kaufman and Celesia 1985), since it is considered an 'unreliable' peak. However, when proper stimulus conditions are used, N70 is stable and reliable. This early negative peak of the PVEP, which occurs around 70-80 msec, is a postsynaptic cortical component of the PVEP and reflects visual processes that are different from those shown by P100. In fact, N70 shows clear spatial tuning, while P100 does not (Parker et al. 1982; Plant et al. 1983; May and Lovegrove 1987; Previc 1988; Onofrj 1990); furthermore, contrast (Kulikowski 1977; Previc 1988), field size and retinal location of the stimulus (Les~vre and Joseph 1979; Les~vre 1982; Onofrj 1990) differently affect the two components. Because of the characteristic 'disseminating' pattern of MS, visual processes may be dissociated at any point along their Correspondence to: Dr. M. Felice Ghilardi, College of Physicians and Surgeons of Columbia University, Center for Neurobiology and Behavior, 722 W 168th Street, Research Annex, Room 819, New York, NY 10032 (U.S.A.).

pathways. Thus, MS can provide a model to evaluate if N70 and P100 reflect sequential or parallel processing. The aim of this retrospective study was to investigate the relationship of N70 and P100 components of the PVEP to vertical sinusoidal gratings (2.3 cpd) in 98 MS patients and 59 matched controls. Our results show that P100 latency can vary independently from N70 latency in patients with MS.

Materials and methods

Subjects Controls were 59 subjects (13 males and 46 females) without any signs or symptoms of visual system dysfunction. Visual acuity was 20/25 or better in both eyes with or without correction. The age range of this group was 17-73, with mean (+ standard deviation) equal to 36 (+13.6) years. The clinical notes of 158 patients referred for PVEP testing to our lab over 2 years with clinical suspicion a n d / o r diagnosis of MS were reviewed and 98 patients were selected according to the diagnostic criteria of McAlpine (1972). The age of the MS population was not significantly different from that of control subjects. Following the same criteria, they were further divided into 2 groups: 46 patients classified as having clinically definite MS; and 52 as having clinically probable or possible MS. During the testing session, the patients wore their best correction for visual acuity, which ranged from 20/200 to 20/15:163 eyes had visual acuity better than

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M.F. GH1LARDIET AL

or equal to 20/30 (83.16%); in 24 eyes (12.34%) acuity was in the 2 0 / 3 5 - 2 0 / 7 0 range, and in 9 eyes (4.59%) it was equal to 20/200.

Procedure The stimuli were vertical gratings with a sinusoidal luminance profile, generated on a Joyce Electronics display unit with a mean luminance of 100 c d / m 2. The contrast, defined as the difference of maximum and minimum luminance over their sum, was 45%. The spatial frequency tested was 2.3 cpd, which was counterphase modulated at 1.5 Hz. The entire stimulating field subtended 9 o of visual angle. Patients and control subjects sat 1.44 m from the screen. Each eye was tested separately, while a patch occluded the fellow eye; fixation was facilitated by a black dot on the center of the screen. PVEPs were recorded using golden cup electrodes placed at z5 (active site) and z63 (reference), 'z' referring to the midline and the following numbers to the percentage of the inion-nasion distance from the inion. A ground electrode was placed on the midforehead. Electrode impedance was always below 5 k~2. Although at least 2 or 3 additional recording sites were used, here we shall consider only the responses recorded from z5 referred to z63. Signals were filtered between 0.3 and 100 Hz, amplified 50,000 times, and averaged on-line with Nicolet 1170 or NeuroScope Siegen averagers. At least 200 responses per trial were collected, stored on floppy disks and plotted. To insure reliability, all responses were replicated at least twice. The latencies of the major negative (N70) and positive (P100) peaks were measured; their amplitude was measured from their peak to baseline. Baseline was computed from 50 msec of signal preceding the onset of the response. When a reliable peak could not be identified or replicated in at least two traces, it was considered absent.

Statistical analysis All data for each subject were entered and analyzed by a C L I N F O PLUS statistical package. Since the

distribution of the measurements was not gaussian, the data were transformed by using either the normal logarithm or the square root of the values. Means and standard deviations of N70 and P100 latencies were calculated for the 3 groups (controls, patients with definite MS, and patients with possible MS). Limits of normal values were set at 99% confidence limits. Analysis of variance and univariate regression were performed on all data.

Results

(A) Controls Means and standard deviations of P100 and N70 latencies and amplitudes are reported in Table I. The normal range (99% confidence limits) for P100 and N70 latencies was from 90.8 to 116.4 msec and from 63.4 to 82.2 msec, respectively. In our controls, the maximum interoCular latency difference found for P100 was 8 msec (mean 2.4 msec) and for N70 it was 6 msec (mean 1.88 msec). Interocular amplitude variation was up to 40% for P100 and up to 60% for N70. P 1 0 0 / N 7 0 ratio was never less than 1 and more than 12 (Fig. 1). In our control population, the regression line of P100 versus N70 latency had an r value of 0 . 5 5 : N 7 0 latency accounted for about 30% of the variance associated with P100 latency ( r 2 = 0 . 3 0 6 7 ) , This suggests that approximately 70% of P100 latency variance is independent of N70 latency. The dependence of P100 amplitude on N70 amplitude was estimated t o b e even lower (r 2 = 0.20762). Visual acuity had no significant effects on either P100 or N70 latencies and amplitudes.

( B) Multiple sclerosis The means, standard deviations and standard errors of the measured parameters for the control and the 2 MS groups are reported in Table I. Of all the 196 eyes tested, P100 was absent in 12 (6.12%). P100 latency was prolonged in 109 (55.6I%), and normal in 75 eyes

DEFINITE MS (@7 EYES)

CONTROLS (118 EYES)

I0

PO88ilN.E M8 (94 EYE8)

I01

PIOO/N70 amplitude ratio Fig. l. The frequency distribution of P100/N70 amplitude ratio for the controls, the patients with definite and possible MS are expressed in percentages.

N70 AND P100 IN MULTIPLE SCLEROSIS TABLE I Mean

S.D.

S.E.

P100 latency (in msec) Normals 103.6 Possible MS 122.0 Definite MS 132.1

4.9 18.2 22.4

0.45 1.78 2.50

N70 latency (in msec) Normals Possible MS Definite MS

72.8 80.7 84.6

3.5 10.0 10.8

0.33 1.01 1.30

P100 amplitude (in/~V) Normals Possible MS Definite MS

6.1 3.2 2.9

2.6 1.9 1.6

0.24 0.19 0.18

N70 amplitude (in/~V) Normals Possible MS Definite MS

2.2 1.0 0.9

1.5 0.9 0.8

0.14 0.09 0.09

P100-N70 interpeak latency (in msec) Normal 30.8 Possible MS 40.7 Definite MS 44.1

4.1 16.7 18.0

0.38 1.67 2.18

P100/N70 amplitude ratio Normal 2.78 Possible MS 8.85 Definite MS 11.53

1.97 14.02 43.57

0.25 1.41 5.24

(38.26%). Significant interocular differences for P100 latency (more than 9 msec) were found in 49 patients. On the other hand, N70 was absent in 29 eyes (14.80%), had prolonged latency in 68 eyes (34.7%), and was normal in 99 (51.3%). Twenty-four patients showed significant interocular differences for N70 latency (more than 8 msec). A delayed N70-P100 peak interval was found in 58 out of 167 eyes, which had also a delayed P100 and in 2 eyes with normal P100 and N70 latencies. P 1 0 0 / N 7 0 amplitude ratio was less than 1 in 11 eyes and more than 12 in 22 eyes (Fig. 1). Moreover, a chi-square analysis comparing N70 versus P100 showed that the 2 peaks had a different diagnostic yield ( X 2 = 34.88; df= 1; P < 0 . 0 0 1 ) . These results hold for the whole group: however, differences emerged when we separated definite from possible MS patients. (1) Definite MS. In this group (n = 46), 37 patients (81%) had absent P100 (9) or abnormal P100 latency, and the same number of patients had either absent N70 (16) or abnormal N70 latency (21). P100 was normal in 28 eyes (30.4%), absent in 12 eyes (13%), and had prolonged latency in 52 (56.6%); while N70 was normal in 34 eyes (36.95%), absent in 24 eyes (26.1%), and had prolonged latency in 34 (36.95%). The total number of eyes with abnormal P100 was 64 (69.6%), while N70 was abnormal in 58 eyes (63.04%). The combined diagnostic yield of N70 and P100 was 78.2%, that is, 72 out of 92

tested eyes had abnormal latency of at least 1 of the 2 PVEP components. In 50 eyes both P100 and N70 presented some abnormalities. Both PVEP components were absent in 12 of them, while they were both delayed in 26 eyes. In the rest of them (12 eyes), N70 was absent and P100 delayed. In the 8 eyes, which showed abnormal N70 latency but normal P100 latency, P100 latency was always within the 95 and 99% confidence limits. (2) Possible MS. In this group (n = 52), 40 patients (76.9%) had abnormal P100 latency, while 22 (42.3%) had abnormal N70 latency. P100 was normal in 47 eyes (45.2%) and had prolonged latency in 57 (54.8%). In this group, P100 was present for all eyes. N70 was normal in 65 eyes (62.5%), absent in 5 eyes (4.8%), and had prolonged latency in 34 (32.7%). In summary, 66 out of 104 examined eyes (63.5%) showed abnormalities in at least 1 of the 2 PVEP components. Twenty-seven eyes had normal N70 latency and abnormal P100 latency; of the 9 eyes with abnormal N70 and normal P100, 5 showed also a borderline P100 latency. A 1-way A N O V A was performed on latency and amplitude data. The independent variable consisted of these 3 groups: (1) patients with definite MS (92 eyes); (2) patients with possible MS (104 eyes); (3) age-matched normal observers (122 eyes). Statistically significant differences were found between P100 latency for these 3 groups ( P < 0.0001; F (2, 299) = 81.85). Subsequent to ANOVA, Newman-Keuls test adapted for unequal samples was used to determine whether or not significantly differences occurred between all pairs of means. Statistically significant differences were found between the distributions of all the 3 groups ( P < 0.01). The same statistical procedure was followed for the analysis of N70 latency data: statistically significant differences were again found between N70 latency for these 3 groups ( P < 0.0001; F (2, 2 8 2 ) = 50.87) and between the means of the control group versus groups 2 ( P < 0.01) and 3 ( P < 0.01), and between groups 2 and 3 ( P < 0.05). Significant differences were also found for the amplitudes of both N70 ( P < 0.0001; F (2, 282) = 35.39) and P100 ( P < 0.0001; F (2, 2 9 9 ) = 66.75) for the 3 groups. However, amplitude differences were significant only for group 1 versus groups 2 and 3, but not for group 2 versus group 3. Similar results were obtained when we analyzed the P100-N70 interpeak latency for the 3 groups ( P < 0.0001; F (2, 282) = 25.74); significant differences were found for group 1 versus groups 2 and 3, but not between groups 2 and 3. Statistically significant differences were found for P 1 0 0 / N 7 0 amplitude ratio only for the control group versus group 3 ( P < 0.05). At a closer inspection of the data, both N70 and P100 components were more often absent in the group of definite MS than in the possible MS group: N70 was absent in 26% and 5% of the eyes of definite and

M.F. G H I L A R I ) I ET AL.

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TABLE 11 The numbers in parentheses represent the expected frequency, Absent

Delayed

Normal

Total

Eyes definite MS

24 (13.6)

34 (24.9)

34 (53.5)

92

Eyes possible MS

5 (15.4)

34 (28.1)

65 (60.5)

104

NTO latency *

Total

29

68

99

196

P I O 0 latency * *

Eyes definite MS

l2 (5.6)

52 (51.2)

28 (35.2)

92

Eyes possible MS

0 (6.40)

57 (57.8)

47 (39.8)

104

Total

12

109

* d f 2; X2 = 23.65475; * * d f 2; X2 = 5.3727843,

75

196

P < 0.01. P < 0.02.

possible MS patients, respectively, while P100 was absent in 13% of the eyes of definite MS patients and always present in the eyes of possible MS subjects (Table II). (3) The effect of visual acuity. Of the 9 eyes with visual acuity equal to 20/200 (which were all in the definite MS group), 5 had absent N70 and P100, 2 had absent N70 and delayed P100, and 2 had normal latencies. N70 and P100 were contemporaneously absent in 4 eyes with visual acuity ranging from 20/35 to 20/70, and in 3 eyes with visual acuity better than or equal to 20/30. In the latter group, N70 alone was absent in 15 eyes. Regression lines performed on the remaining data showed that the visual acuity accounted for 1% ( r = 0.12; r 2 = 0.01) and 0.02% ( r = 0.016; r 2 = 0.0002) of P100 and N70 latency variation, respectively. To analyze the relationship between visual acuity and amplitude of N70 and P100 in the MS patients, we arbitrarily assigned a value of 0:001 #V to the 'absent peaks.' This value was chosen since the minimum accurate resolution of the machine is approximately 0,05 /~V. In this way, for PI00 amplitude and visual acuity we obtained an r value equal to - 0 . 2 4 (r 2 = 0.06; F (1,194) = 12.1; P < 0.001) and for N70 amplitude and visual acuity r was equal to - 0 . 2 1 (r2 =0.05; F (1, 194)= 9.16; P = 0.0028).

Discussion Our study shows that N70 and P100 can be independently affected in patients with MS. In 17 eyes, N70 was abnormal while P100 was still within normal limits.

On the other hand, P100 was abnormal in 41 eyes which had normal N70. These results have important clinical and theoretical implications. From a clinical point of view, the combined use of N70 and P100 latencies increased the diagnostic yield by 9%. A few papers have described the results of the combined use of N70 and PI00 peak latencies in MS studies performed with pattern reversal mode. Kaufman and Celesia (1985) measured both N70 and P100 latencies in a small group of MS patients. Using 15' of arc checks (fundamental spatial frequency of 2.8 cpd), PVEPs were abnormal in 13 out of 18 eyes: with 31' check size (fundamental spatial frequency equal to 1.3 cpd) they found ' P V E P abnormalities" in 23 out of 28 tested eyes. Unfortunately, more details are not available for comparison with our data. Results somewhat similar to ours were obtained by Collins et al. (1978) in 98 MS patients and 50 controls. Direct comparison between N70 and P100 diagnostic yields was not discussed in this paper, although the authors stated that some aspect of the negative components paralleled P I00 latency, and N70 could be abnormal in the presence of normal P100. These findings agree with the results of our study. In both studies: (1) P100 had the highest diagnostic yield: (2) N70 was present in all the controls: (3) N70 was absent in almost the same number of eyes (Collins et al.: 13%: ours: 14%1, while P100 was absent in 8~ and 6% of the two populations, res pectivel 3 . Furthermore. in our study, the use of non-parametric tests reveals that N70 was more often absent than P100: in fact. N70 was not measurable in 26% and 5~ of the eyes of definite and possible MS patients, respectively, while Pt00 was absent in 13% of the definite MS eyes and always present in the possible MS eyes. These findings raise a question: is the absence or. better, the non-detectability of N70 a hallmark of visual pathway dysfunction? N70 is very sensitive to vartation of stimulus parametersL such as spatial frequency and contrast level. The amplitude of N70 is highest for medium-high spatial frequencies (Parker el al. 1982: Plant et al. 1983: May and Lovegrove 1987: Previc 1988: Onofrj 1990), that is, 4.6--6.9 cpd. near the peak of foveal contrast sensitivity (Campbell and Green 1965~. Onofrj (1990) found that N70 was absent (or not detectable) in 40% of 30 normal subjects, using counterphase modulated full-field stimuli of 1 cpd. while N70 was present in all the 30 subjects when spatial frequencies of 2 and 4 cpd were used. In agreement with this finding, all our controls had reliable N70 for 2.3 cpd gratings. Thus, the absence of N70 in our MS patients should be considered a pathological sign. What is the meaning of an N70 delay or absence'? One of the possible variables to be taken into account is vtsual acuity. We found abnormal P100 in 7 out of 9 patients with visual acutty equal to 20/200: in these same patients N70 was absent, while in the other 2

N70 A N D P100 IN M U L T I P L E SCLEROSIS

patients with visual acuity of 20/200 N70 and P100 latencies were within normal limits. A practical advantage of using sinusoidal gratings is that one can obtain reliable PVEP even with blur due to non-optimal correction. Bobak et al. (1987) have demonstrated that the effect of up to 2 diopters blur is negligible on the P100 latency of the PVEP obtained with 2.3 cpd sinusoidal gratings in normal observers. In a noncycloplegic eye with 20/15 visual acuity, + 2 diopters blur corresponds to a visual acuity of approximately 20/200. Thus, it is unlikely that low visual acuity accounts for the P100 abnormalities in this group of patients. The role of visual blur on N70 latency and N70 and P100 amplitudes obtained with sinusoidal gratings has not yet been established. Different authors have found that a small amount of blur attenuates the amplitude of P100 obtained with checks (Regan and Richards 1971; Spekreijse et al. 1973). Traces obtained using 3 diopters blur and different check sizes (Sokol and Moskowitz 1981; Fig. 1) seem to indicate that amplitudes are more affected than latencies. This could partly explain the significant correlation that we obtained between visual acuity and amplitudes in the MS population. On the other hand, the absence of N70 cannot be explained in terms of low visual acuity only: in fact, this potential was absent also in 18 subjects with visual acuity better than or equal to 20/30. There are different hypotheses to explain the relatively higher undetectability of N70 compared to P100 in our MS population. We can easily exclude that in our patients with MS P100, but not N70, had higher amplitude than in normals, thus 'hiding' or annulling the preceding negative deflection. In fact, our data show a significant amplitude decrease for both N70 and P100 peaks. Another possibility is that in MS patients, both P100 and N70 have similar amplitude decrements, but, since N70 has a lower signal-to-noise ratio than P100, the final effect is a disappearance of N70 with a relative preservation of P100. Although in 11 eyes, P100/N70 ratio was less than 1, in our MS population with detectable N70 and P100 peaks, the P100/N70 amplitude ratio tended to increase compared to normals (9.96 versus 2.78). This increase was more evident for the definite MS group versus the controls (11.53 versus 2.78; P < 0.05). The different results obtained for N70 and P100 could be theoretically explained by a differential effect of demyelination on variability and conduction velocity. For instance, if variability was markedly increased without change in mean conduction velocity, then N70 could become undetectable, while P100 was still within normal limits. Regardless of the exact explanation, our results show that N70 can be absent in the presence of normal P100, which suggests that N70 undetectability in MS patients does reflect visual system dysfunction. In addition to the clinical diagnostic relevance of our

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findings, the different results obtained for N70 and P100 are not inconsistent with the hypothesis that the two peaks represent different signal processes of the visual system a n d / o r they have different origins (Halliday and Michael 1970; Jeffreys 1977; Darcey et al. 1980; Lesrvre 1982; Maier et al. 1986). Although there is general agreement about the cortical origin of N70, the precise source of the two peaks is still a matter of debate. It is possible that the conflicting conclusions reached by these different studies are related to important differences in stimulus and analysis selection, and in electrode montage. It is now well established that N70 responds differently than P100 to certain stimulus characteristics. As previously discussed, N70 reaches its maximum amplitude for spatial frequencies in the mid to high range of the contrast sensitivity curve, while P100 does not show the same dependence on spatial frequency. Onofrj (1990) has shown that this is also true using left and right hemifield stimulation, which produces a paradoxical lateralization of both N70 and P100 (Barrett et al. 1976). N70 is recorded only on the derivations ipsilateral to the stimulated field, and its amplitude increases with increasing spatial frequency from 1 to 2-4 cpd. On the other hand, P100 spreads over ipsi- and contralateral derivations, and its amplitude does not increase with increasing spatial frequency. Lesrvre (1982) pointed out that N70 amplitude does not change with increasing field size from 2 ° to 20 ° (as P100 does), but N70 disappears when the central 5 o of visual field are occluded. These data support the hypothesis that N70 is mostly a foveal contrast-dependent component, while P100 probably also represents luminance parafoveal processing. Lastly, upper and lower field stimulation performed in normal subjects with checkerboards (Michael and Halliday 1971; Lesrvre and Joseph 1979; Kriss and Halliday 1980; Lesrvre 1982) and gratings (Skrandies 1984; Previc 1988) seem to draw a further important distinction between N70 and P100: it is possible that P100 is mostly generated by lower field stimulation, while major contributions to N70 come from upper hemifield stimulation. N70 abnormalities of PVEP recorded from the midline electrode in an MS patient could be related to the presence of visual upper field defects. Conversely, absence or attenuation of P100 could be related to visual lower field defects. An interesting interpretation of this phenomenon is given by Previc (1988), who attributes a magnocellular origin to the lower hemifield-dominated P100 and a parvocellular origin to the upper hemifield-dominated N70. Demyelinative diseases seem to be mostly associated with magnocellular dysfunction, since contrast sensitivity studies have shown that low spatial and high temporal frequencies (which are tied to the magnocellular pathway; Derrington and Lennie 1984) were primarily im-

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paired in MS patients (Medjbeur and Tulunay-Keesey 1986; Regan and Maxner 1986). Previc (1988) suggests that if P100 and N70 represent mostly magnocellular and parvocellular processes, respectively, in MS patients one should find a greater degree of abnormality for PIO0 than for N70. Although a certain degree of caution should be exerted in fully accepting this hypothesis, our data, in agreement with the study by Collins et al. (1978), show that in MS patients P100 is more often abnormal than N70. Furthermore, although there was no difference in the distributions of N70 latency between definite and possible MS eyes, it appears that this peak was more often absent in the definite rather than possible MS eyes. If N70 reflects mostly foveal processes and PI00 is mostly a parafoveally generated peak as discussed earlier, it is possible that, in general, parafoveal pathways are more affected in MS, while in definite MS an additional involvement of foveal processes occurs. However, 2 lines of evidence would seem to contradict this hypothesis. First, the fact that color desaturation is a prominent feature early in the disease (Fallowfield and Krauskopf 1984) suggests that parvo and not the magno pathways may be involved. Secondly, Hess and Plant (1983) report a relative sparing of the high temporal and low spatial frequency mechanism in resolved optic neuritis, a result that would suggest a relative sparing of magno pathways. In conclusion, our data suggest that N70 and P100 can be independently affected by MS. It is clear that more studies are necessary to determine the physiological underpinning of this separation. Additionally, the use of N70 with P100 increased the diagnostic yield, which implies a need for more widespread clinical use of both components. We thank Dr. A. Glover for helpful suggestions in a previous version of the paper, and Dr. C. Camras for discussing with us several aspects of the paper.

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