Brain, Vol. 124, No. 11, 2310-2318,
November 2001
© 2001 Oxford University Press
Increased visual after-effects following pattern adaptation in migraine: a lack of intracortical excitation?
School of Psychology, Birkbeck College, London, UK
Correspondence to:
Dr A. J. Shepherd, School of Psychology, Birkbeck College, University of London, Malet Street, London WC1E 7HX, UKE-mail: a.shepherd{at}psychology.bbk.ac.uk
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Abstract |
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Much research on visual function in migraine has examined early aspects of visual processing, often using detection or discrimination measures and stimuli reported to trigger an attack, e.g. striped patterns or flickering lights. Differences between people with and without migraine have been attributed to abnormal cortical processing in migraine, variously described by interictal hyperexcitability, heightened responsiveness, a lack of habituation and/or a lack of intra-cortical inhibition. Here, two experiments are presented that explore a uniquely cortical phenomenon, pattern or contrast adaptation, one using the motion after-effect, one the tilt after-effect. Pattern adaptation reflects specific interactions between groups of neurones and is therefore ideally suited to address proposed models of cortical function in migraine. These models lead to specific predictions in an adaptation study: there should be smaller effects in people with migraine than in people without. The results from both adaptation experiments, however, revealed larger effects in migraine sufferers than in headache-free control subjects. There were no differences between migraine subgroups classified according to the presence or absence of aura. These results are discussed in terms of models of cortical function in migraine.
migraine; visual adaptation; cortical hyperexcitability; inhibition; excitation
MAE = motion after-effect; MO = migraine without aura; NVA = migraine with non-visual aura; TAE = tilt after-effect; VA = migraine with visual aura
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Introduction |
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Various aspects of visual processing have been investigated in migraine due in part to the distinctive visual disturbances that may precede or accompany the headache, and in part to reports that visual stimuli can trigger an attack. One objective has been to determine the origin of any differences and their relevance to the pathophysiology of the condition, or to develop tests that have clinical use. Previous research has predominantly examined early aspects of visual processing, often using threshold detection or discrimination measures and the very stimuli reported to trigger an attack. For example, differences between people with and without migraine have been reported using tasks that assess sensitivity to temporal contrast (flickering light), spatial contrast (striped patterns), colour and orientation (Khalil, 1991
; Coleston et al., 1994; Coleston and Kennard, 1995; Wray et al., 1995; Shepherd, 1999, 2000; McKendrick et al., 2000; Palmer et al., 2000; but see also Wilkinson and Crotogino, 2000). Differences have equally been reported with suprathreshold measures such as increased visual discomfort when viewing striped patterns and altered perceived suprathreshold contrast (Wilkins et al., 1984; Marcus and Soso, 1989; Khalil, 1991; Shepherd, 2000). In general, these results have been attributed to abnormal cortical processing in migraine, although there is also some evidence for pre-cortical involvement (e.g. Coleston et al., 1994; Oelkers et al., 1999; McKendrick et al., 2000). The abnormality has been described as interictal hyperexcitability, heightened responsiveness, a lack of habituation and/or a lack of intra-cortical inhibition. Here, two experiments are presented that explore a different aspect of visual processing: pattern or contrast adaptation. Pattern adaptation is a cortical phenomenon that reflects specific interactions between groups of neurones (described further below) and is therefore well suited to assessing proposed models of cortical function in migraine.
Two existing strands of research also suggested adaptation studies may be informative in migraine. The first was the reported lack of habituation in auditory or visual evoked potentials in migraine, which likewise has been attributed to an underlying cortical abnormality (e.g. Schoenen, 1992, 1996a; Kropp and Gerber, 1993; Wang et al., 1996, 1999; Proietti-Cecchini et al., 1997). Habituation is a decline in some measurable response to repetitive stimuli, originally demonstrated using simple reflexes in animals (reviewed in Kandel et al., 1995), but also demonstrable in human electrophysiology in the typical decline in amplitude of potentials evoked by repetitive stimuli. Habituation of simple reflexes involves changes in the effectiveness of excitatory synaptic connections between specific sensory and motor neurones (Kandel and Schwartz, 1982; Levitan and Kaczmarek, 1991; Kandel et al., 1995). In contrast, the habituation demonstrable in the electrophysiological recordings reflects synaptic changes in large networks of neurones. There are conspicuous similarities between habituation and other adaptive processes in the nervous system. Pattern adaptation, for example, is a more basic and pervasive mechanism than habituation, it is a decline in response to continuous stimuli. Like habituation, it reduces redundancy, protects against response saturation (Carpenter, 1996) and involves changes in the effectiveness of specific (possibly only excitatory) synaptic connections (McLean and Palmer, 1996; Carandini and Ferster, 1997; Carandini et al., 1998).
A second indication that adaptation studies may be useful in migraine came from research that has been conducted with other clinical groups. Various adaptation experiments have been conducted in epilepsy, schizophrenia and Parkinson's disease research to show either differences between patient and control groups or to explore the effects of centrally acting medications (Calvert et al., 1991, 1992; Blyth et al., 1992; Harris, 1994; Steinhoff et al., 1997a, 1997b).
Here, two adaptation studies are presented using two visual illusions, the tilt after-effect (TAE) and the motion after-effect (MAE). To experience the TAE, see Fig. 1. To experience the MAE, observers typically view a moving display for some time, such as random black and white dots moving coherently together, or a grating that glides in one direction within a stationary window. When a stationary pattern is then displayed, observers have the impression that it is drifting in the direction opposite to that of the original motion. It has been called the waterfall effect as it can be elicited by gazing at a waterfall and subsequently viewing rocks beside the fall (see Wade, 1994).
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The textbook explanation for the TAE relies on orientation-selective cells in the visual cortex, with large numbers of cells tuned to different orientations, and where our perception parallels some weighted combination of the firing rates of cells tuned to all orientations. With prolonged viewing of a grating, the response of cells tuned to that orientation declines and, when the pattern is removed, the cells appear unresponsive for a period of time (Maffei et al., 1973
). When the second test pattern is presented, the overall pattern of response is consequently biased away from the orientation of the adapting pattern. Similarly, the MAE can be attributed to a suppression of the activity of cells selective for a particular motion speed and direction rather than orientation (see Sutherland, 1961; Barlow and Hill, 1963; Sekuler and Blake, 1994; for a recent review, see Anstis et al., 1998).
Initially the suppression was attributed to cellular fatigue, but recent physiological research has indicated that it reflects two distinct mechanisms. One is a hyperpolarization of cells' membranes, which, in its effects, is akin to a fatigue model as it makes cells less likely to fire again (Carandini et al., 1998). The second is a dynamic alteration in the synaptic efficacy between cells that respond to the adapting display, originally modelled by an increase in inhibition, although recent evidence indicates the synaptic changes involve instead a decrease in excitation (McLean and Palmer, 1996; Carandini and Ferster, 1997; Carandini et al., 1998).
Current models of cortical function in migraine lead to specific predictions in an adaptation study: there should be smaller after-effects in people with migraine than in people without. Heightened responsiveness, as one example, may be thought to lead to larger after-effects in migraine, perhaps comparable with someone without migraine viewing a higher contrast pattern. The strength of either the MAE or TAE, however, depends on both the adapting display and the test display and is maximal for low contrast test patterns (Parker, 1972; Tolhurst and Thompson, 1975; Keck et al., 1976; Nishida et al., 1997; Ishihara, 1999; Smith and Wenderoth, 1999). If migraineurs have a heightened response to the adapting display, they should equally have a heightened response to the subsequent test display, resulting in smaller after-effects. Alternatively, heightened responsiveness may result in a broader range of cells responding to the adapting display. Since the perceptual after-effect depends on the selective suppression of cells that respond to the adapting pattern, this account again predicts smaller after-effects in migraine. Taking another example, if a component of the after-effect is due to a decrease in excitatory connections causing inhibitory connections to dominate, and if there is a lack of intra-cortical inhibition in migraine, there should again be smaller after-effects in migraine. Finally, a simple extension of a lack of habituation to a lack of adaptation also implies smaller after-effects in people with migraine than in people without.
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Methods |
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Display
For both experiments stimuli were presented on a 16 inch colour monitor connected to a Macintosh PowerBook G3 laptop computer. A separate keyboard was used to record responses. Participants were seated 60 cm from the monitor in an otherwise dark room.
Experiment 1: motion
A 14° square background window displayed random black and white pixels (average luminance 30 cd/m2) moving coherently in one of four directions (up, down, left and right). Two speeds of motion were used, one that has been reported to produce the maximum MAE for static test displays (3°/s) and a faster speed (9°/s) that has been reported to produce the maximum MAE for dynamic test displays (Verstraten et al., 1998). (Static and dynamic test displays have been employed to separate two subpopulations of motion sensitive neurones, possibly reflecting the parvocellular and magnocellular pathways, respectively. Only results for static test conditions are reported here since several people did not complete the dynamic tests. In an attempt not to induce migraine, the trials were terminated if anyone found the display aversive). A central stationary black fixation square (sides subtended 0.5°) displayed a sequence of white letters and numbers at a rate of 4 Hz. The rest of the screen was covered with opaque black card. To compare the effects of an attention task on the MAE, in one condition participants fixated on the black square and passively viewed the display, whereas in the second condition they actively attended to the letter and number sequence and responded every time there was a number rather than a letter (after Chaudhuri, 1990).
On each trial the motion stopped after 60 s and the background window displayed stationary black and white pixels that, however, appeared to drift in the opposite direction (the MAE). Since the after-effect can be revived or suppressed with eye movements, participants were instructed to fixate on the central square, but nonetheless to pay attention to the whole display. They indicated when the illusory motion stopped by pressing the `Q' key.
Three practice trials were followed by 16 experimental trials with the background moving at the slow speed (eight with passive viewing, eight with active) and eight with the background moving at the faster speed (passive viewing only). The order of the three blocks of eight trials was randomized and, within each block, the particular direction of motion was selected randomly with the constraint that each was presented on two non-consecutive occasions.
Experiment 2: orientation
Low contrast 3 cpd (cycles/degree) Gaussian blurred gratings (Michelson contrast 14.5%) were presented in a circular patch (diameter 15°) on a uniform grey background. The average luminance of the gratings and background was 30 cd/m2.
Thirty discrimination trials were presented first to ensure the participants could distinguish gratings tilted ±2, ±4, ±6, ±8 and ±15° from vertical. Each pattern was displayed for 400 ms, then replaced by a uniform grey screen until a response was made. Participants were instructed to keep their heads upright and to look at the centre of the display. They signalled whether the lines appeared tilted up and to the right or left, by pressing the `7' or `6' keys, respectively. Auditory feedback was given if a mistake was made. Participants were then presented with the adaptation display, a grating oriented ±15° from vertical. To prevent the grating from fading away during adaptation or generating after-images, participants moved their eyes slowly along a thin grey central horizontal bar (length 2.6°). After 60 s the test phase started, consisting of a uniform grey screen for 200 ms, a test grating for 400 ms, then the uniform grey screen until a response was made. No feedback was given as, following adaptation, there were no longer correct or incorrect responses. The adaptation pattern was then presented for a top-up period of 15 s, followed by a further test phase. This cycle of top-up adaptation and test phase was repeated until 30 test patterns had been presented. Participants then completed the entire sequence again for the second adaptation pattern (±15°).
There were six test gratings for each adaptation pattern: vertical, +2, +4, +6, –2 and –4° where `+' and `–' indicate gratings oriented in the same or opposite direction from vertical as the adaptation pattern, respectively. The test orientation for each trial was selected randomly, with the constraint that each was presented five times. The –2 and –4° patterns were included as a check on accuracy as their perceived orientation should not be affected by the adaptation (the degree of perceived tilt may be affected, but the direction of tilt should not be).
Participants
Thirty migraine sufferers completed the motion experiment, 25 completed the orientation experiment. All fulfilled the Headache Classification Committee of The International Headache Society (1988) criteria for migraine. Migraine sufferers are traditionally classified according to the presence (MA) or absence (MO) of aura. Since these studies employed visual tests, here the MA group was divided into two: those with exclusively non-visual (NVA) and those with visual (VA) aura (Table 1).
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Thirteen headache-free control subjects completed both experiments (10 females, three males, aged between 23 and 62 years, average age 42 years), none of whom had headaches that fulfilled the International Headache Society criteria for migraine. Informed written consent was obtained in accordance with the declaration of Helsinki (1991) and ethical approval was obtained from Birkbeck College's School of Psychology Ethical Committee.
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Results |
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Experiment 1: MAE
The MAE duration depends on factors such as the duration and speed of the adapting display, and the use of static or dynamic test patterns. For the present conditions the MAE should be longer for the 3°/s conditions than for the 9°/s (Verstraten et al., 1998
). Since the MAE duration did not differ for the four motion directions (up, down, left and right), the data from each direction were combined, and overall averages are plotted in Fig. 2. Three trends are immediately clear. (i) The MAE for both groups is longer for the slow adaptation speed than for the fast, as expected. In the control group, the MAE duration at each speed is comparable with values reported previously for similar adaptation conditions (e.g. Chaudhuri, 1990; Verstraten et al., 1998). (ii) The MAE at each speed is markedly longer in the migraine group than in the control group. (iii) The attention task had no effect on the MAE for either group. The first two trends were confirmed by a one between (group), one within (speed) ANOVA (analysis of variance): there was a significant effect of group [F(1,37) = 8.61, P = 0.006], indicating that the MAE for the migraine group was significantly longer than that for the control group. There was also the predictable significant effect of speed [F(1,37) =47.54, P = 0.0001]. Furthermore, there was a significant interaction between group and speed [F(1,37) = 5.90, P =0.02] that may indicate greater differences between the groups at the slow adaptation speed than at the fast, possibly reflecting differences in parvocellular and magnocellular function. These implications could be examined using static and dynamic test displays, as described in the Introduction (for example, see Verstraten et al., 1998).
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Classifying the migraine sub-groups according to the presence or absence of visual aura revealed no significant differences whether the sub-groups were classified as VA, NVA and MO [F(2,23) < 1], or using the more traditional classification of VA versus MO [F(1,17) < 1, see Table 2
]. Finally, there were no significant associations between the MAE at either speed and the participants' age, duration of migraine, frequency of attacks or the time elapsed since the last attack.
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Experiment 2: TAE
There were no differences between the groups when judging the orientation of the gratings prior to adaptation (average errors 1.5 out of 30 for each group, Table 3A
). As the error rates are low, both groups evidently could judge the orientation of the gratings reliably, before adaptation.
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The orientation judgements following adaptation are presented in Table 3B
. As there were no significant differences following adaptation to the pattern oriented to the right or left, the data from the two adaptation orientations have been combined. Column headers in Table 3B therefore denote the orientation of the test pattern when oriented at vertical, or tilted in the same direction as the adapting pattern. The table entries denote the proportion of times the test pattern was judged oriented opposite to the orientation of the adapting pattern. For other than the vertical test pattern, Table 3B therefore shows the proportion of times that adaptation biased the perceived orientation of the test pattern away from its veridical orientation.
It was expected that vertical patterns would be perceived to be tilted in a direction opposite to the adapting pattern in both groups. Of interest was whether the +2, +4 and +6° test patterns were perceived tilted in the opposite (i.e. non-veridical) direction. Consider first the control group's data. On average, on 94% of the trials the vertical grating was indeed judged to be oriented in a direction opposite to that of the adapting pattern, a rate that differs significantly from chance performance [t(12) = 15.14, P < 0.0001]. On 49% of the trials a grating oriented 2° in the same direction from vertical as the adapting pattern was judged oriented in the opposite direction, a rate that differs significantly from the judged orientation of the same grating prior to adaptation [t(12) = 6.28, P < 0.0005]. Even a grating oriented at 4° in the same direction as the adapting orientation was, on occasion, judged to be oriented in the opposite direction, but not at a rate that differed significantly from the judged orientation prior to adaptation [t(12) = 1.27, n.s.]. These effects in the control group's data are comparable in size with values reported previously for similar adaptation conditions (e.g. Smith and Wenderoth, 1999).
The data from the migraine group show larger effects: on 95% of the trials the vertical grating was judged to be oriented away from that of the adapting grating, a rate that also differs significantly from chance performance [t(24) =29.34, P < 0.0001]. On 64% of the trials a grating oriented 2° in the same direction as the adapting pattern was judged to be oriented in the opposite direction, a rate that differs significantly from the judged orientation of the same grating prior to adaptation [t(24) = 10.64, P < 0.0001] and from the judgements of the control group [t(36) = 2.1, P < 0.05]. Similarly, the grating oriented at 4° was judged to be oriented in the opposite direction at a significantly higher rate following adaptation [t(24) = 3.24, P < 0.005] and more often than in the control group, although the group difference failed to reach significance [t(36) = 1.5, two-tailed P = 0.1]. A grating oriented at 6° was, on occasion, judged to be oriented in the opposite direction, but not at a rate that differed significantly from the judged orientation prior to adaptation, or from the control group [t(24) = 0.9, n.s.; t(36) = 1.2, n.s.].
There were no significant differences between the migraine sub-groups whether classified as VA, NVA, MO [F(2,22) < 1, n.s.] or whether those with visual aura were compared with those without [F(1,18) < 1, n.s.; see Table 3]. There were no significant associations between the average TAE and the participants' age, duration of migraine, frequency of attacks or the time elapsed since the last attack.
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Discussion |
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Two adaptation experiments, one on motion, one on orientation, both revealed larger effects in people with migraine than in people without. This was a surprising result as smaller effects were expected based on current models of cortical function in migraine. Despite these group differences, however, there were no significant differences between the migraine sub-groups on either experiment. Interpreting this result is complicated by mixed reports from previous studies (Woestenberg et al., 1993
; cf. Afra et al., 1995; Chronicle et al., 1995; Chronicle and Mulleners, 1996; Wang et al., 1996; Shepherd, 2000). One possibility is that in those studies that have reported differences between the migraine sub-groups, other factors co-varied with migraine type. Shepherd, for example, reported differences between migraine and control groups on three visual tasks, but no differences between the migraine sub-groups (Shepherd, 2000). Classifying the participants according to a performance measure related to visual discomfort (`pattern sensitivity', whether illusions were reported when viewing small, high contrast, 3 cpd striped patterns), or according to whether or not headache could be induced by visual patterns, however, produced more intelligible results than classifying according to the presence or absence of aura.
In the present experiments there was a significant association between MAE duration following adaptation to the faster moving display (9°/s) and (i) whether visual stimuli were reported to trigger migraine attacks [point biserial correlation coefficient (rpb) = 0.42, P < 0.05] and (ii) the same measure of pattern sensitivity [rpb = 0.51, P < 0.01]. These positive correlations indicate that the MAEs experienced by those who reported visual triggers, or by those who saw illusions when viewing high contrast, mid-spatial frequency striped patterns, were longer than those who did not. Moderate positive correlations were also obtained following adaptation to the slower moving display (3°/s), but these did not approach significance with two-tailed tests [rpb = 0.27, t(28) = 1.5, P = 0.14; rpb =0.30, t(28) = 1.7, P = 0.10]. There was also a significant association between the proportion of trials on which the tilt illusion occurred and pattern sensitivity [rpb = 0.41, t(23) =2.1, P < 0.05] but not, in this smaller sample, with visual triggers [rpb = –0.13, t(23) = 0.62, n.s.]. Together with the overall similarity between the migraine sub-groups and the differences between each sub-group and the control subjects (Tables 2 and 3), these data may indicate (i) a continuum of cortical anomaly in migraine regardless of aura symptoms, rather than qualitative differences between the migraine sub-groups; and (ii) that those who report differences between people with and without aura may have recruited by chance participants in whom migraine classification is confounded with some other factor or combination of factors.
What, then, may these data reveal about cortical processing in migraine? As described in the Introduction, changes in neuronal response following adaptation result from at least two mechanisms: a hyperpolarization of cells' membranes and a change in (possibly only excitatory) synaptic connections between cells that respond to the adapting display. The hyperpolarization has been proposed to reflect both intrinsic neuronal mechanisms (Carandini et al., 1998; Sanchez-Vives et al., 2000) and modification of (again possibly only excitatory) tonic synaptic inputs (Carandini and Ferster, 1997; Carandini et al., 1998, 1999). It would appear unlikely that there could be further membrane hyperpolarization in migraine than in control subjects, although any hyperpolarization may last longer. Larger after-effects may indicate, for example, differences in intrinsic neuronal mechanisms between the two groups such as in the time course of cellular recovery or of channel activation and inactivation. Recently, impaired central metabolism and reduced mitochondrial energy reserves have been discussed in migraine (Schoenen, 1994, 1996a; Gerber and Schoenen, 1998; Wang et al., 1999). The continuous neuronal response during the adaptation phase would place substantial energy demands on cells in the visual cortex: ion levels must be restored and vesicles refilled after prolonged activity, both of which require energy. Reduced mitochondrial energy reserves could delay these restorative processes resulting in the enhanced after-effects in the migraine group. Alternatively, mutations in neuronal P/Q-type Ca2+ channels have been established in familial hemiplegic migraine, and calcium-channel blockers are used as prophylactic treatment in other forms of migraine (Kraus et al., 1998; Siniatchikin et al., 1998). Although neither the pathophysiological consequences of the channel mutations nor the mechanism of action of calcium channel blockers are well understood, reduced inactivation of calcium channels in migraine could increase intracellular calcium resulting in prolonged after-effects from sustained transmitter release, from sustained after-hyperpolarization or from other effects on calcium-dependent ion channels. Each of these could make cells less likely to respond to test patterns following adaptation.
In contrast to a cellular explanation, it is also possible that enhanced after-effects in migraine result from changes in the synaptic connections between cells that respond to the adapting display. As described earlier, recent research has indicated that the changes reflect decreased excitation rather than increased inhibition. This research includes physiological studies in vivo using intra- and extra-cellular recordings in cats and monkeys (Carandini and Ferster, 1997; Carandini et al., 1998; Sanchez-Vives et al., 2000) as well as a comparison of the effects of iontophoretically blocking inputs mediated by GABA (
-amino butyric acid) versus glutamate receptors in cat striate cortex (McLean and Palmer, 1996). Models of cortical function in migraine have previously emphasized a lack of inhibition. If, however, these data can be generalized, prolonged after-effects in migraine may indicate a lack, or extended suppression, of cortical excitatory connections, or increased cortical inhibition in migraine.
Enhanced after-effects may equally reflect a cellular receptor hypersensitivity. Untreated patients with Parkinson's disease (characterized by a loss of dopamine) exhibit smaller TAEs than matched controls, whereas untreated patients with schizophrenia (associated with excessive activity in dopaminergic pathways) exhibit larger TAEs with short (100 ms) test patterns (Calvert et al., 1992). Furthermore, drugs that block or potentiate dopamine receptor activity respectively decrease and increase the size of the MAE and TAE (Harris, 1994). Enhanced after-effects in the migraine group are consistent with this research, since dopamine receptor hypersensitivity has also been reported in migraine (Del Zompo, 2000; Fanciullacci et al., 2000). However, other centrally acting drugs can also decrease or increase after-effects, e.g. those that target GABAergic and cholinergic neurones (Blyth et al., 1992; Steinhoff et al., 1997a,1997b). The role of dopamine, calcium or GABA in the group differences reported here could be clarified if adaptation studies were included in future clinical trials.
Without clinical trials, aspects of the alternative cellular and synaptic explanations can nevertheless be addressed using adaptation studies. The present studies have examined the appearance of test patterns following adaptation. A second general effect is that detection thresholds for patterns with similar spatial or temporal characteristics are elevated following adaptation. However, when very brief (e.g. 30 ms) test patterns are used, there may be no threshold elevation. This is compatible with a network explanation that involves feedback between cells responsive to the adapting display, if the feedback pathways have insufficient time to operate with brief test patterns (Wilson and Humanski, 1993, p. 1133). If enhanced after-effects in migraine reflect a cellular mechanism, akin to fatigue, which makes the cells less likely to fire again whatever the visual input, there should be large differences between migraine and control groups. If, however, the enhanced after-effects reflect synaptic changes, there should be no differences between the groups using brief test patterns. The role of synaptic changes in these group differences may be clarified by comparing the brief with longer duration test patterns in either this detection threshold experiment or a TAE experiment (see Calvert et al., 1992), or by using disinhibition paradigms or adaptation to plaids rather than gratings (e.g. Tolhurst and Thompson, 1975; Carandini et al., 1998; Clifford et al., 2001). Further discussion of these issues is not warranted, however, until additional studies have been completed to examine how general these results are and whether parallel results are found for other classic visual after-effects.
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Acknowledgements |
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I would like to thank Dr Paul Whittle for providing laboratory space in the Department of Experimental Psychology, University of Cambridge, enabling testing of participants from a previous migraine subject panel. Pilot data were presented at the 10th Anglo-Dutch Migraine Association Meeting, Edinburgh, 2000. Both experiments used low-level routines written in C, some of which were based on Denis Pelli's `Video Toolbox'. This work was supported by two grants, one from the Central Research Fund of the University of London, one a Birkbeck College Research Grant.
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Received January 16, 2001. Revised May 31, 2001. Accepted July 2, 2001.
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