On the role of the cerebellum in exploiting temporal contingencies:

Neuropsychologia 42 (2004) 754–763

On the role of the cerebellum in exploiting temporal contingencies: evidence from response times and preparatory EEG potentials in patients with cerebellar atrophy Peter Trillenberg, Rolf Verleger∗ , Arjen Teetzmann, Edmund Wascher1 , Karl Wessel2 Department of Neurology, Medical University of Lübeck, D 23538 Lübeck, Germany Received 13 June 2003; received in revised form 17 November 2003; accepted 19 November 2003

Abstract Patients with degenerative cerebellar disease were compared to healthy controls in their ability to adapt behaviour to temporal contingencies, both according to instructions and according to acquired experience. Participants had to press the cued key whenever the inside of a clock face changed its colour, which could occur when the pointer, rotating once every 4 s, was at “10 h” or at “12 h” or at “2 h”. Probabilities varied between blocks at which of these three time points the colour change occurred, with participants being instructed accordingly. Response times correlated intraindividually with these instructed “a priori” probabilities in control participants only. Subjectively, at any moment, probabilities of occurrence depend on whether the imperative colour change had occurred before, thus may be better described by conditional (“a posteriori”) probabilities. Indeed, when response times were correlated to a posteriori rather than a priori probabilities, correlations increased in both groups equally from their different a priori levels. The amplitudes of preparatory EEG negativity before responding tended to obey to the same relationships, suggesting that the difference between groups was not due to pure motor impairment. Thus, these data suggest that patients with cerebellar atrophy are more impaired in implementing and using task-relevant information in a top–down manner than in learning to modify task-relevant contingencies. © 2003 Elsevier Ltd. All rights reserved. Keywords: Cerebellum; Time; Learning; EEG potentials

1. Introduction A major function of the cerebellum is its contribution to precise control of movements. This is evident by the problems in goal-directed movements, fine movements, and balance which occur due to cerebellar lesions, e.g. by chronic degeneration of cerebellar structures or by infarction of cerebellar tissue. Yet not only the motor cortex is supported by the cerebellum but also other parts of cerebral cortex. Evidence for this assumption was provided by anatomical tracer studies in monkeys (Clower, West, Lynch, & Strick, 2001; Kelly & Strick, 2000; Middleton & Strick, 2001) as well as by evidence in humans: patients with infarctions of cerebellar tissue in their acute phase suffer from cognitive impair∗ Corresponding author. Tel.: +49-451-500-2916; fax: +49-451-500-2489. E-mail address: [email protected] (R. Verleger). URL: http://www.neuro.mu-luebeck.de. 1 Present address: Max Planck Institute for Psychological Research, Munich, Germany. 2 Present address: Clinic for Neurology and Psychiatry, Braunschweig, Germany.

0028-3932/$ – see front matter © 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.neuropsychologia.2003.11.005

ments similar to those found after damage of the parietal or frontal cortex (Schmahmann & Sherman, 1998) and patients with cerebellar atrophy chronically suffer from deficits in associatively combining pairs of stimuli (Drepper, Timmann, Kolb, & Diener, 1999) and in planning solutions of problems (Grafman et al., 1992) which functions are probably accomplished by prefrontal cortex. Several suggestions have been made about what the function of the cerebellum might be in its interplay with the cerebrum: The cerebellum might serve as a store for automated procedures (Gilbert, 2001), in particular it might acquire and store feedback-free models of acting (Doyon, Penhune, & Ungerleider, 2003; Imamizu et al., 2000). It might serve as a central timing mechanism, in particular by its lateral portions (Ivry, Keele, & Diener, 1988; Ja´skowski & Verleger, 2000; Nichelli, Alway, & Grafman, 1996). It might be specialised in processing and generating sequences of excitation (Braitenberg, Heck, & Sultan, 1997). It might be specialised in predicting events in time, by this also in preparing movements (Courchesne & Allen, 1997; Nixon & Passingham, 2001). Last but not least, it might have a special role in learning, in particular in learning conditioned responses (Bracha,

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Zhao, Wunderlich, Morrissy, & Bloedel, 1997; Daum et al., 1993; Thompson & Kim, 1996; Woodruff-Pak, Goldenberg, Downey-Lamb, Boyko, & Lemieux, 2000). No single study can definitely decide between these different and overlapping hypotheses. But any study may help in exploring boundary conditions for selected hypotheses. Here we wanted to investigate the role of the cerebellum for implementing and modifying response preparation according to temporal contingencies. To this end, the temporal interval between a warning stimulus (“S1”) and the imperative stimulus (“S2”) was varied over trials. Several sources of evidence suggest that performance in such conditions of temporal variation requires the cerebellum: In a recent study in monkeys (Nixon & Passingham, 2001) responses of animals with cerebellar lesions were overly delayed when the timing of S2 was variable rather than fixed. In fMRI studies in healthy humans, the posterior cerebellar lobe was activated in blocks in which the S1–S2 interval was variable, as compared to blocks in which this interval was fixed (Dreher & Grafman, 2002; Sakai et al., 2000; see also Ramnani & Passingham, 2001; Schubotz, Friederici, & von Cramon, 2000). What might be the role of the cerebellum in dealing with temporal uncertainty? Two related activities might be of importance: an overall model of the relevant temporal relations has to be created and implemented, and furthermore the model has to be refined by practice. For example, two persons who are to play a rhythmically difficult syncopated piece of music might differ either in their basic rhythmical abilities and/or in their abilities to modify their performance by feedback and practice. Correspondingly, patients with cerebellar disease might either be basically impaired in performing according to temporal relations, and/or might be impaired in refining this temporal model by practice. These two alternatives may be distinguished to some degree by comparing the effects of instructions to the effects of modifying this instructed set by experience. This was done in the present study in the following way: the imperative stimulus S2 could appear at three time points after the warning stimulus, on-line illustrated as 10, 12, 2 h on a clock-face by

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a continuously rotating pointer. Occurrence of S2 was most probable at the earliest time point in one block, at the middle time point in the other, and equally probable at all time points in the third. Participants were instructed accordingly. Implementation of this basic information in behaviour was measured by correlating the probabilities of these time points to each participants’ mean response times (RT), individually across the 9 measured values (3 time points in 3 blocks). The modifying effect of experience was measured by correlating behaviour across these nine values to conditional, “a posteriori” probabilities and comparing these correlations to the mentioned “a priori” probabilities. A posteriori probabilities are defined as P(ti | not (t1 or . . . or ti−1 )), i.e. the probability that S2 will be presented at some time point ti depends on its a priori probability P(ti ) but also on the prerequisite that S2 was not presented before, P(not (t1 or . . . or ti−1 )). This holds for probability variations across time because the passing of time is unidirectional. Therefore, this feature of increasing probability of the terminal event has been called “ageing”. A priori and a posteriori probabilities differed drastically in at least two out of the three blocks (cf. Fig. 1, and Section 2 for details): when all three time points were a priori equally probable, a posteriori probabilities continuously increased (“ageing distribution”). Further, when a priori probabilities steadily decreased from the first to the last time point, these time points were a posteriori equally probable (“non-ageing distribution”). In normal participants, response times correlate better with a posteriori than with a priori probabilities (Elithorn & Lawrence, 1955; Niemi & Näätänen, 1981; Trillenberg, Verleger, Wascher, Wauschkuhn, & Wessel, 2000). In the present context, correlations to a priori probabilities reflect the extent participants modify their behaviour according to instructions, and correlations to a posteriori probabilities reflect how participants adapt their behaviour over and above the information given by instructions. It has been argued that different patterns of responses between healthy participants and cerebellar patients may reflect the patients’ motor impairment above all rather than some

Fig. 1. Design of the probability distributions. The left-side panel shows the probabilities of trials having one of the three possible SOAs (stimulus-onset asynchronies between the cueing stimulus S1 and the imperative stimulus S2) or being no-go trials, for each of the three probability distributions that were used in different blocks. The right-side panel shows the probabilities as experienced by the subjects (a posteriori probabilities). For explanation of the terms Age, Gauss, and N-age see text.

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cognitive problem (e.g. Ravizza & Ivry, 2001). Therefore, it was of considerable interest to track the state of preparation immediately before each of the three time points. This may be achieved by recording EEG potentials. When participants prepare for the imperative stimulus, a slow negative potential called contingent negative variation (CNV, Walter, Cooper, Aldridge, McCallum, & Winter, 1964) is developing during the S1–S2 interval. Though reflecting motor preparation above all, CNV reaches its maximum at the expected time point of S2, not at the time of the response following S2 (Verleger, Wauschkuhn, van der Lubbe, Ja´skowski, & Trillenberg, 2000). Therefore, CNV in particular its centro-parietal component, probably indicates the assembling and maintaining of stimulus-response links appropriate to the expected S2 alternatives (Ulrich, Leuthold, & Sommer, 1998; Verleger et al., 2000) with the presentation of S2 then serving as a trigger for executing this assembled chain of processing, like a pulse that releases a tensed spring. CNV might well be seen as reflecting the tensing of the spring, binding together the expected stimulus patterns and the appropriate responses (Verleger et al., 2000). Our preceding study on healthy participants (Trillenberg et al., 2000) showed that CNV indeed reached its maximum during the variable S1–S2 interval before those time points that were most probable in a given block. So it was expected that this pre-S2 CNV would indeed be a measure of the level of preparation, uncontaminated by impairments of motor execution, and the question could be asked whether CNV amplitudes would correlate to a priori and a posteriori probabilities, and whether these correlations would be different between patients and control group.

2. Methods 2.1. Subjects Twelve patients with cerebellar atrophy and twelve right-handed control subjects participated in this study after their informed consent had been obtained according to the declaration of Helsinki. The control subjects (five men and seven women), aged 23–31 years (average 26), had no history of neurological or psychiatric disease. The patient group (six men and six women) consisted of six younger patients, with their age comparable to the control group (range 24–44 years, mean 33 years) and six patients in their mid-fifties (range 53–59 years, mean 55 years). Median duration of the disease was 7 years (range 3–21 years). Diagnostic workup included medical history, routine physical examination, laboratory tests, electrophysiological testing (visual, auditory and somatosensory evoked potentials) and CT or MRI. In addition, genetic testing for SCA1, 2, 3, and 6 (Klockgether, Wullner, Spauschus, & Evert, 2000) and SCA4 (Hellenbroich et al., 2003) was performed in all patients, and SCA2 was diagnosed in two patients, SCA4 in four. Autosomal-dominant genetic transmission was as-

sumed in three other patients, but no gene locus could be ascertained. Workup served to identify and exclude patients with Friedreich’s ataxia and those with metabolic, toxic, infectious, immunological, vascular, or paraneoplastic cerebellar disease. Clinically, 7 of 12 patients had one or several extracerebellar signs: proprioception was impaired in 5 patients. In four patients, abnormal eye movements (slow horizontal saccades in three patients and internuclear ophthalmoplegia in one patient) reflected pontine dysfunction. Atrophy of the optic nerve was noted in one patient. If latencies of somatosensory evoked potentials were used to identify subclinical involvement of proprioception, only two patients had purely cerebellar disease. No patient had pyramidal signs. The severity of ataxia was rated in 10 of 12 patients on an ataxia scale (Trouillas et al., 1997) ranging from 0 to 100. On this scale, these patients reached 31 on average (range 23–42), which corresponds to moderate ataxia. Two patients received Oxitriptan for symptomatic therapy of ataxia, one patient was treated with Tiaprid. In addition, two patients were treated with drugs not acting on the nervous system. 2.2. Stimuli and procedure A dark-grey ring (outer diameter 5.6 cm, 2.9◦ of visual angle) representing the face of a clock was displayed in the centre of the light-grey screen. A black radial line, representing the pointer, moved continuously on the ring in clock-wise direction, needing 3.9 s for one revolution. Each trial started when this pointer was at the ‘6 h’ position, by onset of the cueing stimulus (S1) which was a yellow triangle appearing in the centre of the “clock”, symbolising an arrow-head pointing left or right (0.5◦ maximum width; 0.3◦ maximum height). Subjects were instructed to press a key with the left or right hand as indicated by the arrow as soon as its colour changed from yellow to red (imperative stimulus S2). The arrow disappeared after a correct response or else when the pointer was at ‘4 h’ (3250 ms after S1 onset, in no-go trials and with incorrect responses) and the next trial started when the pointer reached the 6 h position. The imperative colour change could occur at “10 h”, “12 h”, “2 h”, or not at all (“no-go”). These clock positions will here be defined more technically in ms as stimulus onset asynchronies (SOA) between S1 and S2, 1300 ms (SOA1), 1950 ms (SOA2), 2600 ms (SOA3). Which of the four alternatives (three SOAs and no-go) occurred was chosen randomly according to a given probability distribution. Three different probability distributions were used in different blocks (left panel of Fig. 1): (1) An ‘ageing’ distribution (‘Age’), with equal probabilities of 0.25 for each SOA and no-go. (2) A ‘Gauss’ distribution with a clear maximum at the central SOA2 (0.625) and equal probabilities of 0.125 for SOA1, SOA3 and no-go.

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(3) A ‘non-ageing’ distribution (‘N-age’), with probabilities decreasing from 0.5 at SOA1 to 0.25 at SOA2 and further down to 0.125 for both SOA3 and no-go. A posteriori probabilities, as defined in Section 1, are displayed in the right panel of Fig. 1. These probabilities increase across SOAs for the ‘Age’ distribution, stay constantly at 0.5 for the ‘N-age’ distribution, and also differ somewhat from a priori probabilities for the ‘Gauss’ distribution. Furthermore, the a posteriori probability for SOA3 is 0.5 in all three probability distributions. The three probability distributions were realised in blocks of 400 trials each (with short breaks after every 40 trials) each block lasting for 31 min. The order of blocks was balanced across participants according to a Latin square. The probability distributions were described to participants by informing them about the SOA that was most likely a priori (Gauss: SOA2; N-age: SOA1; Age: all equal). That is, instructions did not mention the a posteriori probabilities which, according to our expectation, would be decisive in affecting response times and CNV. 2.3. Data recording EEG was recorded from 19 positions according to the 10/20 system (F3, Fz, F4, T7, C3 , C1, Cz, C2, C4 , T8, P7, P3, Pz, P4, P8, PO7, PO8, O1, O2; C3 and C4 were 1 cm in front of C3 and C4) using Ag/AgCl electrodes (Picker-Schwarzer) with mastoids linked via a 5 k resistor as reference. EEG and EOG were amplified in the frequency band 0.03–35 Hz by a Nihon-Kohden 4421 amplifier. To control for transmission of ocular artefacts to the EEG, the electrooculogram (EOG) was recorded both horizontally, bipolarly from electrodes at the outer canthi, and vertically, from electrodes above versus below the right eye. Manual responses were recorded with two force-sensitive isometric keys, one for the right hand and one for the left hand, affixed at the front edge of the armrests of the experimental chair. Electronic force sensors were built in either key, whose voltage output increased proportionally to the exerted pressure. Data (EOG, EEG and response force) were digitised at 100 Hz from 100 ms before S1 to 3200 ms after S1 (600 ms after SOA3). 2.4. Data analysis Response times were measured in each trial relative to S2, defined as the moment when response force exceeded 2 Newton (N) (Newton is the unit of force, kg m/s2 . 2 N is the force exerted by a mass of 204 g on its base, under standard gravitation). This criterion is well in the range used with usual all-or-none response keys. Trials with premature (<150 ms), wrong or missing responses were excluded from further response-time and EEG analysis, and mean response times were computed for each of the three SOAs under the three probability distributions separately.

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Trials containing artefacts (out-of-scale-values, zero lines, slow drifts larger than 60 ␮V from the beginning to the end of the trial, fast drifts larger than 100 ␮V/500 ms) were excluded from further EEG analysis. In order not to lose trials in which participants blinked or moved their eyes, transmissions of vertical and horizontal EOG into the EEG as ocular artefacts were estimated separately in areas of maximum EOG variance by linear regression, and were then subtracted throughout from the EEG data. Since we wanted to correlate the level of pre-S2 CNV and response time, it was necessary to measure the unaltered level of CNV, not diminished by the high-pass filter of the amplifier (5 s time constant). Analytical correction (Elbert & Rockstroh, 1980) was used to remove the effects of the high-pass filter. This method iteratively calculates the unwanted decrease at a given time based on the already corrected output at the preceding time point, and then corrects this decrease (see Joyce, Gorodnitsky, Teder-Sälejärvi, King, & Kutas, 2002, for critical evaluation of this method). EEG was averaged across all artefact-free and correctly responded trials time-locked to S1 separately for ‘Age’, ‘N-age’ and ‘Gauss’ blocks, from 100 ms before S1 until occurrence of S2, i.e. until 1.3, 1.95, 2.6, 3.25 s after S1 for trials with SOA1, SOA2, SOA3, and no-go respectively. By this, the averages were not confounded by potentials evoked by S2. CNV was measured in the intervals 100 ms prior to the 3 SOA time points, relative to a 100 ms baseline preceding S1. Maps of potentials were obtained with a self-written program based on a spherical spline algorithm (Perrin, Pernier, Bertrand, & Echallier, 1989). 2.5. Statistical analysis As the most comprehensive measure of participants’ adaptation to probabilities, correlations were computed within each participant between probabilities (a priori as well as a posteriori) and individual performance (mean RT as well as mean CNV amplitudes measured at Cz and PO8) across the 9 measured values (3 distributions × 3 SOAs). These individual correlation coefficients were Fisher-z-transformed for t-tests between groups. The mean correlation coefficients across subjects to be reported were obtained as inverse z transforms of the averaged individual z-transformed coefficients. The control group’s values were compared to the entire group of patients as well as separately to the six younger patients (similar age as the control group) and to the six older ones.

3. Results 3.1. Response times Response times are shown in Fig. 2 for both groups, as a function either of a posteriori probability of the SOA,or of a priori probability of the SOA, or of SOA. Evidently, a

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Fig. 2. Reaction times (RT), average over the 12 healthy participants (left) and the 12 patients (right). These values are displayed as a function either of a posteriori probability of the SOA (upper panel) or of a priori probability of the SOA (middle panel) or of SOA (lower panel). Squares denote values from the Age block, triangles from the Gauss block, circles from the N-age block. Note that, though patients have absolutely larger values, scale range is identical in all panels (100 ms).

posteriori probabilities determined RTs in the most straightforward way, at least in the control group, which had adapted better to the a posteriori probabilities than the patients (r = −0.79 versus −0.55 on average over participants, t(22) = 4.16, P < 0.001). This difference was independent of age, holding also true for separate comparisons of the control group to either the younger or the older patients (Table 1). In both groups the correlations between RT and a priori probabilities (middle panels of Fig. 2) were smaller than the a posteriori correlations, −0.43 in the control group, −0.09 in the patients. Again, this group difference was significant (measured likewise in the z-transformed correlations, like all other tests of correlations in this Section 3). This also held true when comparing the control group to the younger subgroup of patients, whereas there was only a tendency (P = 0.11) when comparing the control group to the elderly patients (Table 1).

To clarify whether the group difference in the effect of a posteriori probabilities could be accounted for by the difference in the effect of a priori probabilities, the correlation of RT and a priori probabilities was subtracted from the correlation of RT and a posteriori probabilities (not indicated in Table 1). This difference reflects the increased influence of a posteriori probabilities over and above the influence of a priori probabilities. This increase was significant in both groups (t(11) = 7.40, P < 0.001 in the patients, t(11) = 5.40, P < 0.001 in the control group) with no difference between groups (t(22) = 0.66, n.s.). Thus, it appears that both groups used the information given by a posteriori probabilities to the same extent, thus that their difference in correlations to a posteriori probabilities was actually due to their difference in correlations to a priori probabilities. An obvious question is to what extent RTs simply got faster with the passing of time during a trial, i.e. to what

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Table 1 Product-moment correlations of averaged response times (RTs) with a posteriori probabilities, a priori probabilities, and SOA across the 9 instances (3 SOA distributions × 3 SOAs) a posteriori

a priori

SOA

a posteriori (SOA partialled out)

a priori (SOA partialled out)

Control group All patients Test t(22)

−0.79 −0.55 4.16, <0.001

−0.43 −0.09 3.21, 0.004

−0.49 −0.56 0.60

−0.76 −0.42 4.57, <0.001

−0.71 −0.37 3.45, 0.003

Young patients Test vs. control group t(16)

−0.52 3.37, 0.004

0.05 3.93, 0.001

−0.7 −1.67

−0.35 4.16, 0.001

−0.35 2.81, 0.01

Old patients Test vs. control group t(16)

−0.57 3.88, 0.001

−0.37 0.95

−0.49 4.28, 0.001

−0.39 3.18, 0.006

Test of young vs. old pats t(10)

0.39

−0.23 1.68

−2.4, 0.04

1.74

0.72

0.18

Correlations were computed individually, then z-transformed for all computations, and the average was back-transformed to enter the table. t-values that indicate differences between groups (P < 0.05) are printed in bold. Three left-side rows: normal correlations. Right-side rows: correlations between RT and the two probabilities with the correlation between RT and SOA partialled out.

extent they correlated with SOA (lower panels of Fig. 2). Mean correlation reached −0.56 in the patients and −0.49 in the control group, not reliably different from each other. As indicated by Table 1, the young and older subgroup of patients differed significantly from each other in this respect, but neither subgroup differed from the control group. Further, the correlation with SOA did not affect the other correlations, as could be ascertained by computing partial correlations, with the effect of SOA removed (right columns of Table 2). It might be argued that the patients’ problems in adapting to temporal probabilities above all was due to their lack of adaptation to the early time point in N-age (cf. Fig. 2): This frequent fast occurrence might have been simply too fast for the patients. Therefore, correlations were again computed for each participant, but including eight values rather than nine, leaving out the early N-age SOA. The differences between groups in correlations to a priori and a posteriori probabilities were only slightly reduced by this manipulation and still remained significant. Therefore, the patients’ problem cannot be reduced to general slowness (correlation of RT and a priori probabilities: −0.44 in the control group, −0.19 in the patients, t(22) = 2.05, P = 0.053; RT and a posteriori probabilities: −0.81 in the control group, −0.61 in the patients, t(22) = 3.23, P = 0.004; RT and

SOA: −0.60 in the control group, −0.56 in the patients, t(22) = 0.70, n.s.). Taken together, the pattern of correlations suggests that patients were well able to adapt their responses to temporal probabilities of occurrence, not worse than the control group (same increase in correlations from a priori to a posteriori probabilities) but that patients were less able to adjust their temporal expectations beforehand in order to adopt a general set (lower correlations to a priori probabilities). 3.2. CNV Grand means of the Cz recordings are displayed in Fig. 3. The figure suggests that CNV amplitudes were much smaller in the patients than in the control group, and that the patients’ time course of CNV lacked modulation according to the different probability distributions. Furthermore, the topographic distribution of CNV amplitudes, displayed in Fig. 4, seems to indicate that the patients did not have a Cz maximum of CNV amplitudes. This topographic difference was corroborated by an overall analysis of all 19 recording sites (recording sites × group: F(18, 360) = 7.7, P < 0.001; data were not normalised, Urbach & Kutas, 2002). Therefore, analyses were not only performed of the data recorded from Cz, where the control group had their largest amplitudes,

Table 2 Product-moment correlations of averaged CNV amplitudes recorded from Cz with a posteriori probabilities, a priori probabilities, and SOA across the nine instances (3 SOA distributions × 3 SOAs)

Control group All patients Test t(22)

a posteriori

a priori

SOA

a posteriori (SOA partialled out)

a priori (SOA partialled out)

−0.53 0.12 4.21, <0.001

−0.27 −0.27 0.03

−0.29 0.42 4.35, <0.001

−0.52 −0.10 2.71, 0.01

−0.38 −0.15 1.12

0.35 9.61, <0.001

−0.13 0.80

0.57 4.89, <0.001

−0.39 −0.61

0.24 2.50, 0.02

Young patients Test vs. control group t(16) Old patients Test vs. Control group t(16)

−0.12 2.21, 0.04

Test of young vs. old pats t(10) See legend of Table 1 for further details.

1.64

1.11

1.94

0.09 4.37, <0.001

0.05 2.66, 0.02

−0.28 1.26

−0.35 0.11

1.31

1.10

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Fig. 3. Grand means of EEG potentials evoked at Cz (vertex) for the three probability distributions Age (bold black), Gauss (thin) and N-age (bold grey). The dotted vertical lines denote the three time points at which the imperative stimuli could be presented (1300, 1950, 2600 ms). At each of the two earlier time points, trials where S2 was actually presented at that time point dropped out from the average from that time point onwards, avoiding confounding of the displayed time courses by potentials evoked by S2. Upper panel: average over the 12 healthy participants. Lower panel: average over the 12 patients. Negative is plotted upwards. Horizontal lines mark baseline levels.

but also on recordings from PO8, where the patients had their largest amplitudes. Yet, results were principally the same, so the PO8 results will not be reported, for brevity. Amplitudes recorded from Cz are shown in Fig. 5 for both groups, as a function either of a posteriori probability of the SOA, or of a priori probability of the SOA, or of SOA. Correlations between a posteriori probabilities and CNV amplitudes reached −0.53 on average in control participants (more negative, i.e. larger, amplitudes for high probabilities), significantly larger than in the patients (r = +0.12; t(22) = 4.21, P < 0.001; Table 2). This difference was largely independent of age, holding also true for separate

comparisons of the control group to either the younger or the older patients (Table 2). Correlations between CNV and a priori probabilities did not differ between groups (−0.27 for either group). There was a marked difference between groups in correlations between CNV and SOA. As the grand means in Fig. 3 show, this difference reflects the slight increase of CNV during the course of any trial in the control group (r = −0.29) in contrast to the decrease in the patients (r = +0.42). This change over time during a trial might be a confounding factor in the relations to a posteriori and a priori probabilities. Therefore, like with RT, partial correlations were

Fig. 4. Maps of grand mean CNV amplitudes, weight-averaged across the three SOAs and the three probability distributions. View on the scalp from the top, with forehead above, back of the head below. The head surface is displayed in stereographic projection, resulting in stretched distances near the equator. Both maps have the same scale (0 ␮V, light, to −6.2 ␮V, dark shade).

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Fig. 5. CNV amplitudes (mean of 100 ms before each of the three SOAs) at Cz (vertex), average over the 12 healthy participants (left) and the 12 patients (right). Note that scale range is identical in all panels (6 ␮V), though patients have absolutely smaller values. See legend of Fig. 2 for further details.

computed, removing the effects of SOA (Table 2). Indeed, thereafter, the previous similarity between both groups of correlations between CNV and a priori probabilities tended to cease, although the difference became significant only in comparison of the young subgroup to the control group.

4. Discussion Patients with cerebellar atrophy were less well able than healthy participants to adapt their response times to probabilities of temporal occurrence. The design of this experiment provided the possibility to distinguish between two factors contributing to this deficit: the ability to establish a basic expectation on temporal relations on the one hand, and the ability to modify this basic model by practice on the other hand. The latter factor was measured by the increase of correlations to RT from a priori probabilities to a posteriori probabilities and was found not

to differ between control group and patients. The former factor, ability to establish a basic temporal model, was measured by correlations of RT to a priori probabilities. It was this factor in which patients and control group were found to differ. So we propose that the relevance of the cerebellum when preparatory intervals are variable, as reported in the monkey-lesion study of Nixon and Passingham (2001) and in fMRI human studies (Dreher & Grafman, 2002; Sakai et al., 2000), is due to this activity of establishing and maintaining a basic temporal model, assuming that this activity is more complex when the intervals are variable. This basic impairment in establishing a model of temporal relations may be interpreted as a “frontal” dysfunction of planning, thus adds to other evidence about deficits of cerebellar patients in this domain (Drepper et al., 1999; Grafman et al., 1992). Further, the experiment allowed for obtaining some control over a third, confounding factor, which is the passing of time per se. It might be suspected that patients perform the better the more time is available for preparation, due to their

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motor impairment. In contrast to this objection, the groups did not differ in their correlations between RT and time (SOA), and when correlations with time were controlled by partial correlation, the different effects of a priori probability continued to exist. One may argue that there was a confound in our comparison between the three probability distributions: no-go trials had probabilities of 12.5% in Gauss and N-Age blocks, but of 25% in Age blocks. This might have reduced participants’ response readiness in the Age blocks, indicated by their somewhat slower responses times and by reduced CNV amplitudes in this block. Yet, this difference in a priori probabilities was a virtually unavoidable consequence of the intention to have equal (50%) a posteriori probabilities of no-go trials across distributions (Fig. 1). Since the response times in the Age block fit so well in the overall linear relationship of a posteriori probabilities and response times (Fig. 2) we believe that this latter relationship is indeed more decisive for response readiness than that possible confound. True, the control group’s CNV amplitudes were lower in the Age block than would be expected by a posteriori probabilities (Fig. 5). Yet, it is uncertain whether this is due to the higher a priori frequency of no-go trials, for example CNV amplitudes became larger, rather than smaller, in Verleger et al. (2000) when the frequency of no-go trials increased from 0% (“simple go”) to 50%. Our sample of patients comprised a younger subgroup (mean age 33 years) and an older one (mean 55 years). Differences from the young control group were found both in the younger and in the older subgroup of patients, with more marked differences in the younger subgroup. Thus, the differences between patients and control group were obviously not due to age. Since the differences from the control group were more marked in the young patients, it may be suspected that these patients were more affected by the disease than the elderly. Yet this was not the case. Young and old patients did not differ in disease duration (8 years versus 11 years in young versus elderly, t = 0.81), ataxia score (33 versus 29, t = 0.92), proportion of patients having genetic locus identified (3 versus 3), extracerebellar ocular signs (2 versus 2), pathological SEPs and VEPs (4 versus 3), receiving relevant medication (2 versus 1) or having pyramidal signs (0 versus 0). Only the proportion of patients with impaired proprioception might be seen as different (4 versus 1). Nevertheless, it seems plausible that the disease has some other dynamics in the young patients, who were affected at an age at which most old patients had still been healthy. Alternatively or additionally, old patients might have had more resources to develop compensatory mechanisms, having lead a healthy life for longer time than the young patients. We expected to get supporting evidence about a non-motor source of impairment by recording CNV amplitudes immediately preceding the imperative stimuli. Patients’ amplitudes were generally very small, in particular at Cz where CNV amplitudes use to be largest (e.g. Verleger et al.,

2000). This small size of CNV had to be expected, according to several other studies recording cerebellar patients’ movement-related negativities (review: Verleger, 2002), both when measured as CNV, like in the present study (Verleger et al., 1999; Yamaguchi, Tsuchiya, & Kobayashi, 1998) and as readiness potential, not locked to external stimuli (Gerloff, Altenmüller, & Dichgans, 1996; Shibasaki, Shima, & Kuroiwa, 1978; Wessel, Verleger, Nazarenus, Vieregge, & Kömpf, 1994). In particular, the diffuse topography, lacking a clear centro-parietal midline maximum, is a usual finding in these patients (Gerloff et al., 1996; Tarkka, Massaquoi, & Hallett, 1993; Verleger et al., 1999; Wessel et al., 1994). So it might be argued that the lack of CNV modulation according to event probabilities is entirely trivial: when there is nothing, nothing can be modulated. However, in contrast to this notion, modulation of CNV amplitude by experimental variation was found in a previous studies of ours, with some of the participating patients being identical to the present ones (Verleger et al., 1999): Though being generally smaller in the patients than in normals, CNV became larger by the same amount in patients as in healthy subjects preceding difficult bimanual movements. Thus, the lack of any modulation of the patients’ CNV amplitude as found in the present study might well be a specific phenomenon, pointing to a specific dysfunction of the cerebellum brought about by the present experimental manipulation. Thus, keeping the above reservations in mind, the lack of modulation of CNV amplitudes may be interpreted as converging evidence to the RT results, suggesting that the patients’ diminished adaptation to a priori probabilities cannot be reduced to peripheral problems in motor execution.

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