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Daily modulation of the speed–accuracy trade-off
Accepted Manuscript Daily modulation of the speed accuracy trade-off Nicolas Gueugneau, Thierry Pozzo, Christian Darlot, Charalambos Papaxanthis PII: DOI: Reference:
S0306-4522(17)30301-9 http://dx.doi.org/10.1016/j.neuroscience.2017.04.043 NSC 17751
To appear in:
Neuroscience
Received Date: Accepted Date:
15 December 2016 27 April 2017
Please cite this article as: N. Gueugneau, T. Pozzo, C. Darlot, C. Papaxanthis, Daily modulation of the speed accuracy trade-off, Neuroscience (2017), doi: http://dx.doi.org/10.1016/j.neuroscience.2017.04.043
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Daily modulation of the speed accuracy trade-off
Nicolas Gueugneau, Thierry Pozzo, Christian Darlot and Charalambos Papaxanthis
Cognition, Action et Plasticité Sensorimotrice (CAPS), INSERM UMR1093, Université de Bourgogne Franche-Comté, F-21000 Dijon, France.
() Nicolas Gueugneau UFR STAPS, INSERM U 1093, Campus Universitaire, Université de Bourgogne, B.P. 27877, 21078 Dijon, France. e-mail: [email protected]. Tel.: +33 3 80396754
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Abstract Goal-oriented arm movements are characterized by a balance between speed and accuracy. The relation between speed and accuracy has been formalized by Fitts’ law and predicts a linear increase of movement duration with task constraints. Up to now this relation has been investigated on a short-time scale only, that is during a single experimental session, although chronobiological studies report that the motor system is shaped by circadian rhythms. Here, we examine whether the speed-accuracy trade-off could vary during the day. Healthy adults carried out arm pointing movements as accurately and fast as possible towards targets of different sizes at various hours of the day, and variations in Fitt’s law parameters were scrutinized. To investigate whether the potential modulation of the speed-accuracy trade-off has peripheral and/or central origins, a motor imagery paradigm was used as well. Results indicated a daily (circadian-like) variation for the durations of both executed and mentally simulated movements, in strictly controlled accuracy conditions. While Fitts’ law held for the whole sessions of the day, the slope of the relation between movement duration and task difficulty expressed a clear modulation, with the lowest values in the afternoon. This variation of the speed-accuracy trade-off in executed and mental movements suggests that, beyond execution parameters, motor planning mechanisms are modulated during the day. Daily update of forward models is discussed as a potential mechanism.
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High-lights
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Fitts’ law hold throughout the day for both executed and imagined movements
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The speed-accuracy trade-off expresses a circadian variation
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Motor planning mechanisms appear to be optimized during the afternoon.
Key words: speed-accuracy trade-off, time-of-day modulation, arm pointing, motor imagery.
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Introduction Two basic and closely related kinematic parameters characterize most of ballistic goaloriented movements: speed and accuracy. The balance between them allows to proficiently play tennis or piano, as well as to pass a thread through the eye of a needle. Their tight correlation was initially formalized by the psychologist Fitts and since it is known as Fitts’s law (Fitts, 1954). According to this law, movement duration equals to a + b log2(2D/W), where a and b are empirical constants and log2(2D/W) is the index of task difficulty (ID). ID increases when the target width (W) decreases and/or the target distance (D) increases (Fitts, 1954, Fitts and Peterson, 1964). Consequently, Fitts’s law predicts that movement duration linearly increases with ID. The investigation of Fitts’s law under various task or environnemental constraints provides an opportunity to study the motor control process. Computational studies have shown that movement time and variability are taken into account during the planning process (Harris and Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008). As motor noise is signaldependent (Jones et al., 2002; Hamilton et al., 2004), large motor commands produce rapid but inaccurate movements, and small motor commands produce accurate but slow movements. The concomitant modulation of movement speed and precision indicates a high functional plasticity that allows the motor system to efficiently achieve the goal of the task. Up to now, the relationship between speed and accuracy has been investigated on a short-time scale only; such as, through a single experimental session, during which movement kinematics and dynamics have been experimentally controlled, as it is the case during complex motor skills learning (Shmuelof et al., 2012) or through a simple visuomotor pointing task (Mazzoni et al., 2007). Whether Fitts’s law varies on an intermediate time-scale, for example throughout the day, remains still unknown. This question is not trivial because many chronobiological studies have reported that the motor system is robustly shaped by circadian rhythms. Precisely, when humans adhere to a normal sleep-wake cycle (a diurnal activity and a nocturnal sleep) movement features, such as force (Reinberg et al., 1994, Souissi et al., 2004, Guette et al., 2005) or kinematics (Moussay et al., 2002, 2003; Edwards et al., 2007, 2008, Gueugneau et al., 2008; 2015; Gueugneau and Papaxanthis, 2010; Jasper et al., 2009), display a 24h-period cosine-like modulation with optimum values during the afternoon (Atkinson and Reilly, 1996). Here, we examine whether the relation between speed and accuracy, expressed by Fitts’s law, varies in a daily basis. We asked healthy adults to make arm pointing movements as accurately and fast as possible towards targets of different sizes at various hours of the day, 4
and looked for variations in the coefficient of correlation and slope of Fitt’s law equation. We hypothesized that modulations at the level of motor execution would lead to circadian variations in movement duration without affecting the speed-accuracy-tradeoff. Conversely, changes at a higher level of motor control would lead to a significant modulation of Fitt’s law. To further investigate whether a possible daily modulation of the relation between speed and accuracy is due to variations in peripheral (i.e., execution stage) or central (i.e., planning stage) signal processing, we used the motor imagery paradigm. During imagined movements, subjects mentally simulate movements without actually executing them (Papaxanthis et al., 2012; Michel et al., 2013; Rozand et al., 2016). Mental and actual movements share common neural and cognitive processes (Jeannerod, 2001; Moran et al., 2012) and forward models are believed to be involved in mental movement simulation as well (Wolpert & Flanagan, 2001; Gentili et al., 2015). A key point here is that the temporal features of mental movements emerge from sensorimotor predictions of forward models (Sirigu et al., 1996; Wolpert & Flanagan, 2001; Demougeot et al. 2011; Michel et al. 2013). Specifically, during motor imagery, motor commands are prepared, but are blocked before reaching the muscle level; i.e., no movement occurs that could influence the next movement, as it is the case in actual movement production. However, a copy of these motor commands, the efference copy, is still available to the forward model, which predicts the future sensorimotor states of the arm.
Methods Participants Ten right-handed healthy male adults (mean age = 24.2 ± 2.4 years), with no drug intake (including alcohol, coffee, and tobacco) that could have altered their mental or motor performance and their normal circadian rhythm (Reinberg, 1975), were involved in the study after providing their written consent. The regional ethics committee of Université de Bourgogne approved the experimental protocol, which was carried out in agreement with legal requirements and international norms (Declaration of Helsinki, 1964). Handedness (mean score 0.87 ± 0.07; a score > 0.5 indicates right hand dominance) was determined by means of the Edinburgh Handedness inventory (Oldfield, 1971). Motor imagery ability (mean score = 42.1 ± 3.1; maximum score = 56) was evaluated by the French version of the Revised Movement Imagery Questionnaire MIQ-R (Hall and Martin, 1997). The chronotypes of the participants (Morningness-Eveningness Questionnaire; Horne and Östberg, 1976) was moderate morning type (n = 3) or neither type (n = 7). All participants were synchronized with a normal diurnal activity (~7:00 to 0:00 h) alternating with night. 5
Their average body temperature, recorded 6 times per day during the test-sessions (see below), showed a regular circadian variation reaching its maximum value at ~16:00 h (see Fig. 1). One day before and the day of the experiments, participants were instructed not to engage in any physical activity in order to prevent fatigue and alter their circadian rhythmicity.
General experimental design The participants carried out actual and mental arm pointing movements 6 times during a single day (6 test-sessions: 8 a.m., 11 a.m., 2 p.m., 5 p.m., 8 p.m., and 11 p.m.). Note that we previously showed that whether the motor task is repeated during the same day or during randomized sessions over many days does not give different results in terms of circadian rhythm (Gueugneau et al., 2015). Four different pairs of square targets were used for the actual and mental arm-pointing tasks. The targets’ width (W) was 0.5 x 0.5, 1 x 1, 1.5 x 1.5, 2 x 2 cm and the inter-target distance (D) was 20 cm. Each test-session lasted ~ 30 min. Between the test-sessions, participants were distracted in a separated room by discussing, reading, or watching movies.
Mental arm movements Participants were comfortably seated on an adjustable chair in front of a table. For each mental trial, one pair of targets was drawn on a paper sheet that was firmly fixed on the table. The perpendicular distance of the targets from the participant’s chest was 20 cm, 10 cm below the xyphoid process. The participants’ right arm was relaxed on the table and their right index finger was placed either on the left or the right target (the starting position was counterbalanced). From this position, they were requested to mentally simulate pointing between the two targets as accurately and as fast as possible as they would actually do (see next subsection). We instructed participants to feel themselves performing the motor task in a first person perspective (motor or kinaesthetic imagery). Imagining a movement in the first person is a necessary condition to engage the motor system (Gueugneau et al. 2013; Avanzino et al. 2015). None of the participants reported difficulties to mentally simulate arm-pointing movements. Because of the short duration of a single movement and the coarse resolution of mental movement time, measurements of several movements are necessary to obtain valid and reliable measurements in motor imagery protocols (Sirigu et al., 1996, Gueugneau et al., 2008). Therefore, each mental trial consisted of 10 alternated mental movements. For each
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pair of targets, participants carried out 10 mental trials (i.e., a total of 40 trials per testsession).
Actual arm movements Participants adopted the same body posture as for the mental movements, holding a pencil in their right hand. They were asked to point between the two targets as accurately and as fast as possible. One trial consisted of 10 alternated actual movements between the two targets and started either from the left or the right target. For each pair of targets, participants carried out 10 trials (i.e., a total of 40 trials per test-session). When a participant missed more than two targets during a trial, this one was cancelled (invalid trial) and retaken at the end of the session. Spatial accuracy of valid trials was measured by counting the total number of errors; i.e., the number of times that participants did not point inside the target. The experimenter could easily count the missed targets in each trial, as the pencil left visible traces and allowed to clearly identify in and out target pointing.
Movement duration recording For each test-session, the 80 trials (40 actual and 40 mental) were randomized. Actual and mental movement durations (MD) were recorded by means of an electronic stopwatch (temporal resolution 1 ms) that participants hold in their left hand. They started the stopwatch when they actually or mentally initiated the movement and they stopped it when they had actually or mentally accomplished it. This method of self-chronometry provides reliable results (see Sirigu et al. 1996; Gueugneau et al., 2008; Rozand et al., 2015).
Statistical analysis For each participant, we computed the average actual and mental movement durations, as well as their standard deviations (SD), and verified that they were all normally distributed (Kolmogorov–Smirnoff test, p>0.05) and that sphericity was not violated (Mauchly's test, p>0.05). Then, we processed as follows: We calculated the 4 IDs (6.3, 5.3, 4.7 and 4.3 bits) from the width of the targets (W: 0.5, 1, 1.5 and 2 cm) and fixed inter-target distance (A: 20 cm). Fitts’s law predicts a linear relationship between MD and ID. Thus, the reliability of Fitts’ law was assessed from the equation MD = a + b x ID, by computing the slope (b parameter) and the determination coefficient (r²) for both groups and individual data. An ANOVA was then performed, with Time of day as the within-subject factor upon b and r for both actual and mental movements 7
(in case of a non-normal distribution, an ANOVA of Friedman was used). The Tukey’s test was used for Post-Hoc comparisons when necessary. When a modulation was observed, the circadian variation was assessed by a population mean Cosinor analysis. The population mean cosinor analysis (Gouthiere et al., 2005; Nelson et al., 1979) combines the results from single cosinor analyses of each participant to produce an average curve describing the considered variable. The best-fit 24h period cosine curve for each condition was evaluated by using the formula: y(ti) = M + A(ωti + Ø), where M is the Mesor (i.e., the mean theoretical value around which the cosine model fluctuates), A is the Amplitude of the fluctuation, and Ø is the Acrophase (i.e., the time of the maximal theoretical value reached by the cosine curve). A circadian modulation was validated when the cosine model fits well to the experimental values (coefficient of determination) and when significant amplitude was detected. This latter is determined by the amplitude-test (Ftest) that compares the variance accounted for a cosine model versus a straight-line fit to the time series data. Rhythmicity is validated when the null hypothesis (i.e., amplitude equals zero in the model) is rejected. The population mean Cosinor analysis was also used to examine circadian modulations upon actual and mental movement durations for the different target sizes. Finally, to further examine the relation between actual and mental movements, mean values of the slope (b parameter) and of the determination coefficient (r²) of Fitts’ law for both actual and mental movements were entered in a two-way ANOVA with Movement (Actual vs Mental) and Time of day as within-subject factors.
EMG recording and EOG analysis during mental trials We verified that the participants’ arm muscles were silent at rest, before the movement starts, and that their eyes remained motionless during the mental trials. We recorded the electromyographic (EMG) signals from the biceps brachii (elbow flexor) and triceps brachii (elbow extensor) during both actual and mental arm movements. EMG signals were recorded by means of two silver-chloride surface electrodes of 10-mm diameter placed on the belly muscle with an inter-electrode distance (centre to centre) of 2 cm. EMG signals were also recorded at rest (5 trials of 6s) before each test-session, by asking the participants to totally relax their muscles (rest condition). The reference electrode was placed on the ventral side of 8
the left wrist. EMG signals were recorded at a frequency of 1000 Hz, band pass filtered (10600 Hz) and stored for off-line analysis using BIOPAC software acquisition. Muscle activation during mental trial and rest was quantified by computing RMS (Root Mean Square) using the following formula: RMS =
1 MD
MD
∫ ( EMG)²dt , 0
where MD is the movement duration. During mental trials, the muscles normally involved in movement execution were silent. Quantitatively, the RMS EMG activity was very low (mean individual values ranged between 4 µV and 10 µV) and similar to those obtained when the same muscles were totally relaxed (mean individual values ranged between 4 µV and 9 µV). A two-way repeated measurements ANOVA (6 times-of-day: 8 a.m., 11 a.m., 2 p.m., 5 p.m., 8 p.m., 11 p.m.) × 2 conditions: rest, mental) performed for each muscle separately did not reveal any main or interaction effects (for all comparisons, p > 0.05). We also controlled that participants did not move their eyes during the mental trials by recording EOG signals during mental arm movements. EOG activity was checked online, and if the experimenter observed any EOG activity above the baseline level, the trial was discarded from further analysis. According to this, 37 trials (1.5 %) were invalid and performed again.
Results
Accuracy during actual movements The participants missed the targets 297 times (1.3 %) in a total of 24000 movements (10 participants x 6 test-sessions x 4 pairs of targets x 10 trials x 10 arm pointing movements per trial). Importantly, the number of errors remained stable all along the day whatever the size of the targets; neither the Time of day (F5,45 = 2.08; p = 0.09) nor the Target size (F3,27 = 2.08; p = 0.14), or their interaction (F15,135 = 0.49; p = 0.93), had a significant effect on the number of errors as revealed by a two way repeated-measures ANOVA. The total number of errors is reported in Table 1. Moreover, the number of invalid trials was 101 out of a total of 2400 trials (4.2%). We did not find any main or interaction effect of time-of day and target width on the number of invalid trials (p > 0.05 for all analyses). None of the participants missed more than 3 targets during a single trial. These findings suggest that any change in movement 9
duration during the day could not be attributed to a motor strategy that privileged speed rather than accuracy.
Actual pointing movements Figure 2A shows the relationship between actual movement durations and ID for the 6 test-sessions. It can be observed that actual movements fitted Fitts’ law, as indicated by the strong linear correlation of MD and ID for each experimental session (r² ranged= 0.94 - 0.99; p < 0.01 for each experimental session). Indeed, for each test-session, actual movement durations significantly increased as ID increased (main effect of Target size: F3,27 = 181.5; p < 0.001; on average 5.47 ± 0.11, 4.48 ± 0.09, 3.93 ± 0.10 and 3.63 ± 0.14 s; from the largest to the smallest ID, respectively). Note also that individual data were analysed and actual durations were highly correlated with ID in every experimental session for each participant (for all individual values, r² range = 0.77 – 0.99). Interestingly, while r² values were stable among the 6 test-sessions (p > 0.1 for all comparisons), the slope of the linear correlation (b parameter) was significantly modulated (see the biphasic pattern of variation with a trough in the afternoon, Fig. 2B). The population mean cosinor analysis revealed a circadian rhythm for the b parameter (data strongly fitted with a 24h period cosine curve, r² > 0.95; p < 0.01). ANOVA analysis also indicated a significant effect of Time of day (F5,45 = 6.05; p < 0.001). Post-hoc comparisons revealed that: (i) the slope at 8 a.m., 8 p.m. and 11 p.m. were not significantly different (p > 0.05), but were higher than those observed at 11 a.m., 2 p.m., and 5 p.m. (p < 0.05), (ii) the slopes at 2 p.m. and 5 p.m. were not significantly different (p > 0.05), but were lower than those observed at 8 a.m., 8 p.m. and 11 p.m. (p < 0.05). The variation of the slope during the day was due to the circadian modulation of actual movement durations for all target widths (population mean cosinor analysis, r² > 0.98 and p < 0.01 for each target, see Fig. 2C). In general, actual movement durations progressively decreased from the morning (grand average: 4.93 ± 0.10 s at 8 a.m.) to the afternoon (grand average: 4.14 ± 0.08 s at 2 p.m.), and then increased until the evening (grand average: 4.40 ± 0.09 s at 11 p.m.). The best fitted 24h period cosine curves are also depicted in the Fig. 2C. The time at which the 24h period cosine models reached their lowest values (batyphase) were not significantly different between the 4 target widths (paired t-tests, p > 0.1).
Mental pointing movements
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Figure 3A shows the relationship between mental movement durations and ID for the 6 test-sessions. Mental movements fitted Fitts’ law whatever the time of day (strong linear relation between MD and ID with r² ranging from 0.90 - 0.97; p < 0.01 for all the experimental sessions). For each test-session, mental movement durations significantly increased as ID increased (main effect of Target size: F3,27 = 76.55; p < 0.001; on average 4.05 ± 0.08, 4.44 ± 0.10, 4.96 ± 0.09, and 5.84 ± 0.11 s; from the largest to the smallest ID, respectively). Individual data were also analysed and mental durations were highly correlated with ID in every experimental session for each participant (for all individual values: r² range = 0.66 – 0.99). As for actual movements, while r² values were stable among the test-sessions (p > 0.1 for all comparisons), the b parameter was significantly modulated (see the biphasic pattern of variation with a trough in the afternoon, Fig. 3B) and the population mean cosinor analysis revealed a circadian rhythm for this parameter as the data strongly fitted a 24h period cosine curve (r² > 0.90; p < 0.01). ANOVA analysis also indicated a significant effect of Time of day (F5,45 = 9.83; p < 0.001). Post-hoc comparisons revealed that: (i) the slope at 8 a.m., 8 p.m. and 11 p.m. were not significantly different (p > 0.05), but were higher than those observed at 11 a.m., 2 p.m., and 5 p.m. (p < 0.05), (ii) the slopes at 2 p.m. and 5 p.m. were not significantly different (p > 0.05), but were lower than those observed at 8 a.m. and 11 p.m. (p < 0.05). The variation of the slope during the day was due to the circadian modulation of mental movement durations for all target widths (population mean cosinor analysis, r² > 0.98 and p < 0.01 for each target, see Fig. 3C). In general, actual movement durations progressively decreased from the morning (grand average: 5.55 ± 0.28 s at 8 a.m.) to the afternoon (grand average: 4.48 ± 0.2 s at 2 p.m.), and then increased until the evening (grand average: 4.87 ± 0.25 s at 11 p.m.). The best fitted 24 h period cosine curves are depicted in Fig. 2C. The time at which the 24 h period cosine models reached their lowest values (batyphase) were not significantly different between the 4 target widths (paired t-tests, p > 0.1).
Relationship between actual and mental movements We compared the modulations of the b parameter (slope values in Fitts’ law) for actual and mental movements (see Fig. 2B and 3B). A two-way ANOVA (Movement [Actual vs Mental] x Time of day) only detected a main effect of Time of day (F5,45=25.33; p < 0.001), but neither a main effect of Movement nor an interaction effect (F1,9=0.11; p = 0.74 and 11
F5,45=0.91; p =0.48 respectively). Post-hoc comparisons revealed that: (i) the slope at 8 a.m., 8 p.m. and 11 p.m. were not significantly different (p > 0.05), but were higher than those observed at 2 p.m., and 5 p.m. (p < 0.05), (ii) the slopes at 2 p.m. and 5 p.m. were not significantly different (p > 0.05). Moreover, no modulation was detected for the whole r² values, combining both actual and mental movements (ANOVA of Friedman χ2 = 1.93; p > 0.05).
Discussion
The aim of this study was to identify potential daily modulations of the speed– accuracy trade-off in arm pointing movements and to test whether this modulation originated from peripheral (i.e., execution stage) or central (i.e., planning stage) motor processing. We thus assessed the durations of actual and mental movements at different times of the day by means of an experimental set up allowing to check Fitts’ law, that is a well-established relationship between speed and accuracy. Our main findings point out that the relation between speed and accuracy is modulated during the day. Precisely, while Fitts’ law, expressed by the linear relation between movement time (MD) and index of task difficulty (ID), held for both actual and mental movements during the day, the slope of the MD/ID relation showed a clear circadian variation with the lowest values in the afternoon. The daily modulation of movement parameters is well documented from chronobiological studies, showing that movement control is, at least partly, driven by the circadian master clock of our organism (i.e., the supra-chiasmatic nuclei; Moore, 1997). For instance, maximal force (Gauthier et al., 2001; Guette et al., 2005), performance in anaerobic exercises (Souissi et al., 2004), as well as the kinematics of simple motor tasks (Moussay et al., 2002, 2003) or fine skilled movements (Gueugneau et al., 2008, 2010, 2015; Jasper et al., 2009), clearly exhibit circadian variations, with the best performances in the afternoon. Here, we show that motor rules, like Fitts’ law, describing movement control at an abstract level, are also modulated during the day. The cosine-like variation of the MD/ID relation is instructive in a strict chronobiological perspective, as it was in antiphase with body temperature (compare Fig. 1 with Fig. 2B and Fig. 3B). This suggests that the basic circadian rhythms of our organism shape the speed-accuracy tradeoff in arm movement control. The slope of the MD/ID relation reflects the motor system sensitivity to changes in task difficulty, i.e., the steeper the slope is, and the more the motor system is affected by task constraints. Consequently, the daily modulation of MD/ID slope may indicate modifications 12
at the level of motor planning and control. Note that spatial precision in actual movements did not vary during the day, thus changes in movement time could not be attributed to a strategy privileging speed in the detriment of accuracy at some hours of the day. Initially, Fitt’s theory (1954) proposes that the motor system behaves like a stochastic communication channel with a transmission capacity limited by a signal-dependent noise. The slope of the relation indicates the information capacity of the motor system; i.e., the central processing rate (Schmidt & Lee, 1999). Since, computational neurosciences confirmed that Fitts’ law emerges from noise within the neural motor commands (Harris and Wolpert, 1998). Motor commands are corrupted by a signal-dependant noise, which could be observed in the variability of electromyographic signals and force output (Jones et al., 2002; Hamilton et al., 2004). Large motor commands produce rapid but inaccurate and variable movements, and small motor commands produce accurate but slow movements (Harris and Wolpert, 1998). Note that the size of the motor command refers to the force output for a given muscle group, which depends on both the number of motor units recruited and their firing rate, see Jones et al., 2002. In this framework, Fitts’s law thus emerges as the consequence of an optimal control strategy in the presence of an intrinsic variability in motor command. Movements appear to be planned according to their upcoming variability by minimizing the effects of noise in motor commands (Harris and Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008). In this vein, it has been shown that the slope of the MD/ID relation is increased in stroke patients, compared to healthy subjects, performing pointing tasks related to a Fitts’ paradigm (McCrea and Eng, 2005). This finding has been interpreted as a consequence of an increased neuromotor noise within movement planning process. Interestingly, at the cortical level, neural modulations within primary motor and sensorimotor areas during a Fitts’ task could not be only explained by changes in motor aspects of the behaviour, but are highly related to the target size. Moreover, neural modulations are prominent in the phase preceding movement initiation (Ifft et al., 2011), further highlighting the fact that the link between movement speed and accuracy seems to be handled by predictive mechanisms. Hence, which mechanisms may subserve the modulation of the speed-accuracy tradeoff, in such a way that subjects regulate differentially movement duration across the day according to task constraints? We propose two hypotheses that are not mutually exclusive: one at the functional level and the other at the neurobiological level. First, the circadian modulation of the basic natural physical activity (Brown et al., 1990; Natale, 2002), i.e., the activity needed to achieve most of our daily professional and social obligations (walking, writing, tapping, etc.,) may explain at the functional level the 13
daily calibration of the motor output (Gueugneau et al., 2015). Indeed, we have recently showed that the higher basic physical activity in the afternoon, compared to the morning or the evening, improves sensorimotor predictions (Gueugneau et al., 2015), probably via a mechanism of self-supervised learning that update the internal models of movement on a daily basis (Wolpert et al., 2001). During voluntary movements, the controller, integrating the kinematic and dynamic constraints of the task, generates the appropriate neural commands, whereas the forward model, by relating the sensory signals of the state of the effector (e.g. position, velocity) to the motor commands, predicts the future states of the effector. Thus, the reinforcement of both the forward model and the controller by daily physical activity would be necessary to optimize motor performance (Wolpert et al., 2001). In the afternoon, the higher sensorimotor activity (Natale et al., 2002; Gueugneau et al., 2015) may reinforce the functional linkage between the controller and the forward model, and thus lead to an enhancement of the upcoming motor performance. This could in fine result in optimized movement durations for specific accuracy demands (i.e., a weaker slope in Fitts’ law). During a complex motor learning task, many days of motor training are necessary to optimize motor performance, estimated by changes of the speed-accuracy trade-off (Shmuelof et al., 2012). Repeating a ballistic wrist-pointing task, in a range of imposed movement durations, led to a shift of the speed-accuracy trade-off, with a reduction in trial-to-trial variability and an increase in movement smoothness (i.e., improved trajectory accuracy) (Shmuelof et al., 2012). In this context, forward model-based learning could account for the shift of the speedaccuracy trade-off that subserves the improvement of motor performance (Shadmehr et al., 2010). In our experiment, the modulation of the speed-accuracy trade-off (a modulation of the slope of the MD/ID relation) may be driven by similar mechanisms at the time-scale of the day. However, arm movements are regulated by both feedforward (motor planning and prediction) and feedback (sensorimotor correction) processes (Desmurget & Grafton, 2000). Our results on executed movements are thus not sufficient to conclude about the potential mechanisms implicated in the daily modulation of Fitts’s law. Although we cannot exclude potential peripheral mechanisms, such as execution noise, our findings regarding imagined movements reinforce the premise of a motor planning/feedforward mechanism involved in the daily regulation of the motor output. A key point here is the fact that the temporal features of mental movements emerge from sensorimotor predictions (Sirigu et al., 1996; Wolpert et al., 1998; Wolpert & Flanagan, 2001). During motor imagery, motor commands are prepared, but are blocked before reaching the muscle level. However, a copy of these motor commands, the 14
efference copy, is still available to the forward model, which predicts the future sensorimotor states of the arm and provides temporal information that is very similar to that resulting from actual movements. The fact that we observed a clear circadian modulation in the slope of the MD/ID relation during mental movements, i.e., in the absence of any motor output and afferent feedback, is thus a good indicator of optimized sensorimotor predictions at the motor planning level. Second, at the neurobiological level, the circadian modulation of brain neurotransmitters such as dopamine (Huang et al., 2015) might also have a potential role in the daily modulation of the speed-accuracy trade-off. Dopamine is a key determinant in motor control (Mazzoni et al., 2007). For example, a fundamental feature of Parkinson’s disease characterised by a dysfunction of the dopaminergic system - is generalized movement slowing (bradykinesia), which cannot be explained by an intrinsic limitation in execution (England and Schwab, 1961), but rather is a problem of scaling speed to movement distance (Berardelli et al., 2001). An explanation for this scaling deficit is that bradykinesia is a compensatory response: patients slow down because of a loss of accuracy at normal speeds (Montgomery and Nuessen, 1990; Sheridan and Flowers, 1990; Phillips et al., 1994). More interestingly, by comparing patients with Parkinson’s disease with healthy controls, Mazzoni and colleagues 2007 have shown that movement speed selection may emerge as a result of an implicit value assignment of movement energy cost for a specific task constraint. As indicated by the authors “patients show a reluctance to make fast movements because of the energy expenditure required, although they are capable of executing them as well as control subjects and without expending more energy”. Putting the speed-accuracy trade-off within the framework of cost and reward may thus offer a complementary mechanism to support our data. Indeed, the circadian fluctuation of biological markers - including brain dopamine (Huang et al., 2015) may lead to time-of-day changes in the subjective cost of movement speed for a given task constraint. So, the daily modulation of the slope of the MD/ID relation that we observed in healthy subjects might be partly subserved by biological rhythm in the brain dopaminergic system, which in turn modulates the implicit value assigned to movement energy cost. Further studies are nevertheless necessary to give strength to this hypothesis. To conclude, the speed-accuracy trade-off is modulated during the day, with an increased sensitivity of the motor system to task constraint in the morning and evening. This leads to an optimized motor performance during the afternoon, as revealed by the modulation of the steepness of the slope for both actual and imagined movements. This circadian-like fluctuation was in antiphase with body temperature, suggesting an effect of circadian rhythms 15
upon motor planning processes. The underlying mechanisms may be an update of sensorimotor predictions through the higher basic physical activity in the afternoon (selfsupervised learning) (Gueugneau et al., 2015), or a daily shift of the implicit value assignment of movement energy for movement speed selection.
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Table Number of errors Target
8 a.m.
11 a.m. 14 p.m. 17 p.m. 20 p.m. 23 p.m.
5mm
12
11
8
13
11
11
10mm
11
13
12
12
11
11
15mm
14
14
12
14
12
14
20mm
13
15
13
14
12
13
50
53
45
53
46
49
Total by target
Grand Total
Table 1. Total number of errors, i.e., pointing movements outside the target, for each target
size and for each test-session.
21
Figure legends Figure 1. Daily variation of body temperature.
Average values (± SD) of participants’ body temperature as a function of the time of day. The best-fitted cosine function is also depicted (grey curve). The cosinor analysis gave a significant circadian rhythm (population-mean-cosinor analysis; p < 0.01) which peak at ~ 16:00h. The dashed line shows the average value (i.e., the Mesor) of the temperature rhythm. Figure 2. (A) MD/ID relations for executed movements are shown for all the experimental
sessions. Mean values are presented with their best fitted line. (B) We reported from (A) the value of the b parameter in the Fitts equation for each experimental session. Data are shown with their best fit 24h period cosine curve. (C) Mean (±SD) movement durations recorded for the executed motor tasks during the six experimental sessions and the four target sizes. Data are shown with their best fit 24h period cosine curve. Figure 3. (A) MD/ID relations for imagined movements are shown for all the experimental
sessions. Mean values are presented with their best fitted line. (B) We reported from (A) the value of the b parameter in the Fitts equation for each experimental session. Data are shown with their best fit 24h period cosine curve. (C) Mean (±SD) movement durations recorded for the imagined motor tasks during the six experimental sessions and the four target sizes. Data are shown with their best fit 24h period cosine curve.
22
Temperature (°C)
36.8
36.3
35.8 0
4
8
12 16 20 24
Time of day (h)
23
Actual Pointing Movement A
8 a.m.
Movement Duration (s)
7
11 a.m.
7
5
5
5 r2 = 0.94
3 3
5
5 p.m.
7
r2 = 0.97
3 3
7
5
r2 = 0.99
3
5
5
7
11 p.m.
5 r2 = 0.98
3
7
3
7
5
3
r2 = 0.98
3
7
8 p.m.
7
5
2 p.m.
7
3
5
r2 = 0.98
3
7
3
5
7
20
24
Index of Difficulty
B b parameter (slope)
1.1
1.0
0.9
0.8 0
4
8
16
Time of day (h)
C Movement Duration (s)
12
5
5 5 mm
3 0
8
16
24
15 mm
5
10 mm
3 0
16
24
16
24
20 mm
5
3
8
3 0
8
16
24
0
8
Time of day (h)
24
Mental Pointing Movement A
8 a.m.
Movement Duration (s)
7 5
r2 = 0.94 3
5
5 p.m.
7
5 r2 = 0.97
3
7
3
5
5
3
3
5
7
11 p.m.
7 5
r2 = 0.99 3 5 7 3
3
r2 = 0.98
3
7
8 p.m.
7
5
2 p.m.
7
5
3
r2 = 0.98 3 5 7 3
r2 = 0.98 5
7
Index of Difficulty
B b parameter (slope)
11 a.m.
7
1.1 1.0 0.9 0.8 0.7 0
4
8
12
16
20
24
Time of day (h)
Movement Duration (s)
C
7
7
5
5 5mm
10mm
3
3 0
8
16
24
7
0
8
16
24
16
24
7 15mm
20mm
5
5
3
3 0
8
16
24
0
8
Time of day (h)
25
Numbers of errors Total by target
Target
8 a.m.
11 a.m. 14 p.m. 17 p.m. 20 p.m. 23 p.m.
5mm
12
11
8
13
11
11
10mm
11
13
12
12
11
11
15mm
14
14
12
14
12
14
20mm
13
15
13
14
12
13
50
53
45
53
46
49
Grand Total
Table 1. Total number of errors, i.e., pointing movements outside the target, for each target
size and for each test-session.
26
High-lights
•
Fitts’ law hold throughout the day for both executed and imagined movements
•
The speed-accuracy trade-off expresses a circadian variation
•
Motor planning mechanisms appear to be optimized during the afternoon.
27
S0306-4522(17)30301-9 http://dx.doi.org/10.1016/j.neuroscience.2017.04.043 NSC 17751
To appear in:
Neuroscience
Received Date: Accepted Date:
15 December 2016 27 April 2017
Please cite this article as: N. Gueugneau, T. Pozzo, C. Darlot, C. Papaxanthis, Daily modulation of the speed accuracy trade-off, Neuroscience (2017), doi: http://dx.doi.org/10.1016/j.neuroscience.2017.04.043
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Daily modulation of the speed accuracy trade-off
Nicolas Gueugneau, Thierry Pozzo, Christian Darlot and Charalambos Papaxanthis
Cognition, Action et Plasticité Sensorimotrice (CAPS), INSERM UMR1093, Université de Bourgogne Franche-Comté, F-21000 Dijon, France.
() Nicolas Gueugneau UFR STAPS, INSERM U 1093, Campus Universitaire, Université de Bourgogne, B.P. 27877, 21078 Dijon, France. e-mail: [email protected]. Tel.: +33 3 80396754
1
Abstract Goal-oriented arm movements are characterized by a balance between speed and accuracy. The relation between speed and accuracy has been formalized by Fitts’ law and predicts a linear increase of movement duration with task constraints. Up to now this relation has been investigated on a short-time scale only, that is during a single experimental session, although chronobiological studies report that the motor system is shaped by circadian rhythms. Here, we examine whether the speed-accuracy trade-off could vary during the day. Healthy adults carried out arm pointing movements as accurately and fast as possible towards targets of different sizes at various hours of the day, and variations in Fitt’s law parameters were scrutinized. To investigate whether the potential modulation of the speed-accuracy trade-off has peripheral and/or central origins, a motor imagery paradigm was used as well. Results indicated a daily (circadian-like) variation for the durations of both executed and mentally simulated movements, in strictly controlled accuracy conditions. While Fitts’ law held for the whole sessions of the day, the slope of the relation between movement duration and task difficulty expressed a clear modulation, with the lowest values in the afternoon. This variation of the speed-accuracy trade-off in executed and mental movements suggests that, beyond execution parameters, motor planning mechanisms are modulated during the day. Daily update of forward models is discussed as a potential mechanism.
2
High-lights
•
Fitts’ law hold throughout the day for both executed and imagined movements
•
The speed-accuracy trade-off expresses a circadian variation
•
Motor planning mechanisms appear to be optimized during the afternoon.
Key words: speed-accuracy trade-off, time-of-day modulation, arm pointing, motor imagery.
3
Introduction Two basic and closely related kinematic parameters characterize most of ballistic goaloriented movements: speed and accuracy. The balance between them allows to proficiently play tennis or piano, as well as to pass a thread through the eye of a needle. Their tight correlation was initially formalized by the psychologist Fitts and since it is known as Fitts’s law (Fitts, 1954). According to this law, movement duration equals to a + b log2(2D/W), where a and b are empirical constants and log2(2D/W) is the index of task difficulty (ID). ID increases when the target width (W) decreases and/or the target distance (D) increases (Fitts, 1954, Fitts and Peterson, 1964). Consequently, Fitts’s law predicts that movement duration linearly increases with ID. The investigation of Fitts’s law under various task or environnemental constraints provides an opportunity to study the motor control process. Computational studies have shown that movement time and variability are taken into account during the planning process (Harris and Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008). As motor noise is signaldependent (Jones et al., 2002; Hamilton et al., 2004), large motor commands produce rapid but inaccurate movements, and small motor commands produce accurate but slow movements. The concomitant modulation of movement speed and precision indicates a high functional plasticity that allows the motor system to efficiently achieve the goal of the task. Up to now, the relationship between speed and accuracy has been investigated on a short-time scale only; such as, through a single experimental session, during which movement kinematics and dynamics have been experimentally controlled, as it is the case during complex motor skills learning (Shmuelof et al., 2012) or through a simple visuomotor pointing task (Mazzoni et al., 2007). Whether Fitts’s law varies on an intermediate time-scale, for example throughout the day, remains still unknown. This question is not trivial because many chronobiological studies have reported that the motor system is robustly shaped by circadian rhythms. Precisely, when humans adhere to a normal sleep-wake cycle (a diurnal activity and a nocturnal sleep) movement features, such as force (Reinberg et al., 1994, Souissi et al., 2004, Guette et al., 2005) or kinematics (Moussay et al., 2002, 2003; Edwards et al., 2007, 2008, Gueugneau et al., 2008; 2015; Gueugneau and Papaxanthis, 2010; Jasper et al., 2009), display a 24h-period cosine-like modulation with optimum values during the afternoon (Atkinson and Reilly, 1996). Here, we examine whether the relation between speed and accuracy, expressed by Fitts’s law, varies in a daily basis. We asked healthy adults to make arm pointing movements as accurately and fast as possible towards targets of different sizes at various hours of the day, 4
and looked for variations in the coefficient of correlation and slope of Fitt’s law equation. We hypothesized that modulations at the level of motor execution would lead to circadian variations in movement duration without affecting the speed-accuracy-tradeoff. Conversely, changes at a higher level of motor control would lead to a significant modulation of Fitt’s law. To further investigate whether a possible daily modulation of the relation between speed and accuracy is due to variations in peripheral (i.e., execution stage) or central (i.e., planning stage) signal processing, we used the motor imagery paradigm. During imagined movements, subjects mentally simulate movements without actually executing them (Papaxanthis et al., 2012; Michel et al., 2013; Rozand et al., 2016). Mental and actual movements share common neural and cognitive processes (Jeannerod, 2001; Moran et al., 2012) and forward models are believed to be involved in mental movement simulation as well (Wolpert & Flanagan, 2001; Gentili et al., 2015). A key point here is that the temporal features of mental movements emerge from sensorimotor predictions of forward models (Sirigu et al., 1996; Wolpert & Flanagan, 2001; Demougeot et al. 2011; Michel et al. 2013). Specifically, during motor imagery, motor commands are prepared, but are blocked before reaching the muscle level; i.e., no movement occurs that could influence the next movement, as it is the case in actual movement production. However, a copy of these motor commands, the efference copy, is still available to the forward model, which predicts the future sensorimotor states of the arm.
Methods Participants Ten right-handed healthy male adults (mean age = 24.2 ± 2.4 years), with no drug intake (including alcohol, coffee, and tobacco) that could have altered their mental or motor performance and their normal circadian rhythm (Reinberg, 1975), were involved in the study after providing their written consent. The regional ethics committee of Université de Bourgogne approved the experimental protocol, which was carried out in agreement with legal requirements and international norms (Declaration of Helsinki, 1964). Handedness (mean score 0.87 ± 0.07; a score > 0.5 indicates right hand dominance) was determined by means of the Edinburgh Handedness inventory (Oldfield, 1971). Motor imagery ability (mean score = 42.1 ± 3.1; maximum score = 56) was evaluated by the French version of the Revised Movement Imagery Questionnaire MIQ-R (Hall and Martin, 1997). The chronotypes of the participants (Morningness-Eveningness Questionnaire; Horne and Östberg, 1976) was moderate morning type (n = 3) or neither type (n = 7). All participants were synchronized with a normal diurnal activity (~7:00 to 0:00 h) alternating with night. 5
Their average body temperature, recorded 6 times per day during the test-sessions (see below), showed a regular circadian variation reaching its maximum value at ~16:00 h (see Fig. 1). One day before and the day of the experiments, participants were instructed not to engage in any physical activity in order to prevent fatigue and alter their circadian rhythmicity.
General experimental design The participants carried out actual and mental arm pointing movements 6 times during a single day (6 test-sessions: 8 a.m., 11 a.m., 2 p.m., 5 p.m., 8 p.m., and 11 p.m.). Note that we previously showed that whether the motor task is repeated during the same day or during randomized sessions over many days does not give different results in terms of circadian rhythm (Gueugneau et al., 2015). Four different pairs of square targets were used for the actual and mental arm-pointing tasks. The targets’ width (W) was 0.5 x 0.5, 1 x 1, 1.5 x 1.5, 2 x 2 cm and the inter-target distance (D) was 20 cm. Each test-session lasted ~ 30 min. Between the test-sessions, participants were distracted in a separated room by discussing, reading, or watching movies.
Mental arm movements Participants were comfortably seated on an adjustable chair in front of a table. For each mental trial, one pair of targets was drawn on a paper sheet that was firmly fixed on the table. The perpendicular distance of the targets from the participant’s chest was 20 cm, 10 cm below the xyphoid process. The participants’ right arm was relaxed on the table and their right index finger was placed either on the left or the right target (the starting position was counterbalanced). From this position, they were requested to mentally simulate pointing between the two targets as accurately and as fast as possible as they would actually do (see next subsection). We instructed participants to feel themselves performing the motor task in a first person perspective (motor or kinaesthetic imagery). Imagining a movement in the first person is a necessary condition to engage the motor system (Gueugneau et al. 2013; Avanzino et al. 2015). None of the participants reported difficulties to mentally simulate arm-pointing movements. Because of the short duration of a single movement and the coarse resolution of mental movement time, measurements of several movements are necessary to obtain valid and reliable measurements in motor imagery protocols (Sirigu et al., 1996, Gueugneau et al., 2008). Therefore, each mental trial consisted of 10 alternated mental movements. For each
6
pair of targets, participants carried out 10 mental trials (i.e., a total of 40 trials per testsession).
Actual arm movements Participants adopted the same body posture as for the mental movements, holding a pencil in their right hand. They were asked to point between the two targets as accurately and as fast as possible. One trial consisted of 10 alternated actual movements between the two targets and started either from the left or the right target. For each pair of targets, participants carried out 10 trials (i.e., a total of 40 trials per test-session). When a participant missed more than two targets during a trial, this one was cancelled (invalid trial) and retaken at the end of the session. Spatial accuracy of valid trials was measured by counting the total number of errors; i.e., the number of times that participants did not point inside the target. The experimenter could easily count the missed targets in each trial, as the pencil left visible traces and allowed to clearly identify in and out target pointing.
Movement duration recording For each test-session, the 80 trials (40 actual and 40 mental) were randomized. Actual and mental movement durations (MD) were recorded by means of an electronic stopwatch (temporal resolution 1 ms) that participants hold in their left hand. They started the stopwatch when they actually or mentally initiated the movement and they stopped it when they had actually or mentally accomplished it. This method of self-chronometry provides reliable results (see Sirigu et al. 1996; Gueugneau et al., 2008; Rozand et al., 2015).
Statistical analysis For each participant, we computed the average actual and mental movement durations, as well as their standard deviations (SD), and verified that they were all normally distributed (Kolmogorov–Smirnoff test, p>0.05) and that sphericity was not violated (Mauchly's test, p>0.05). Then, we processed as follows: We calculated the 4 IDs (6.3, 5.3, 4.7 and 4.3 bits) from the width of the targets (W: 0.5, 1, 1.5 and 2 cm) and fixed inter-target distance (A: 20 cm). Fitts’s law predicts a linear relationship between MD and ID. Thus, the reliability of Fitts’ law was assessed from the equation MD = a + b x ID, by computing the slope (b parameter) and the determination coefficient (r²) for both groups and individual data. An ANOVA was then performed, with Time of day as the within-subject factor upon b and r for both actual and mental movements 7
(in case of a non-normal distribution, an ANOVA of Friedman was used). The Tukey’s test was used for Post-Hoc comparisons when necessary. When a modulation was observed, the circadian variation was assessed by a population mean Cosinor analysis. The population mean cosinor analysis (Gouthiere et al., 2005; Nelson et al., 1979) combines the results from single cosinor analyses of each participant to produce an average curve describing the considered variable. The best-fit 24h period cosine curve for each condition was evaluated by using the formula: y(ti) = M + A(ωti + Ø), where M is the Mesor (i.e., the mean theoretical value around which the cosine model fluctuates), A is the Amplitude of the fluctuation, and Ø is the Acrophase (i.e., the time of the maximal theoretical value reached by the cosine curve). A circadian modulation was validated when the cosine model fits well to the experimental values (coefficient of determination) and when significant amplitude was detected. This latter is determined by the amplitude-test (Ftest) that compares the variance accounted for a cosine model versus a straight-line fit to the time series data. Rhythmicity is validated when the null hypothesis (i.e., amplitude equals zero in the model) is rejected. The population mean Cosinor analysis was also used to examine circadian modulations upon actual and mental movement durations for the different target sizes. Finally, to further examine the relation between actual and mental movements, mean values of the slope (b parameter) and of the determination coefficient (r²) of Fitts’ law for both actual and mental movements were entered in a two-way ANOVA with Movement (Actual vs Mental) and Time of day as within-subject factors.
EMG recording and EOG analysis during mental trials We verified that the participants’ arm muscles were silent at rest, before the movement starts, and that their eyes remained motionless during the mental trials. We recorded the electromyographic (EMG) signals from the biceps brachii (elbow flexor) and triceps brachii (elbow extensor) during both actual and mental arm movements. EMG signals were recorded by means of two silver-chloride surface electrodes of 10-mm diameter placed on the belly muscle with an inter-electrode distance (centre to centre) of 2 cm. EMG signals were also recorded at rest (5 trials of 6s) before each test-session, by asking the participants to totally relax their muscles (rest condition). The reference electrode was placed on the ventral side of 8
the left wrist. EMG signals were recorded at a frequency of 1000 Hz, band pass filtered (10600 Hz) and stored for off-line analysis using BIOPAC software acquisition. Muscle activation during mental trial and rest was quantified by computing RMS (Root Mean Square) using the following formula: RMS =
1 MD
MD
∫ ( EMG)²dt , 0
where MD is the movement duration. During mental trials, the muscles normally involved in movement execution were silent. Quantitatively, the RMS EMG activity was very low (mean individual values ranged between 4 µV and 10 µV) and similar to those obtained when the same muscles were totally relaxed (mean individual values ranged between 4 µV and 9 µV). A two-way repeated measurements ANOVA (6 times-of-day: 8 a.m., 11 a.m., 2 p.m., 5 p.m., 8 p.m., 11 p.m.) × 2 conditions: rest, mental) performed for each muscle separately did not reveal any main or interaction effects (for all comparisons, p > 0.05). We also controlled that participants did not move their eyes during the mental trials by recording EOG signals during mental arm movements. EOG activity was checked online, and if the experimenter observed any EOG activity above the baseline level, the trial was discarded from further analysis. According to this, 37 trials (1.5 %) were invalid and performed again.
Results
Accuracy during actual movements The participants missed the targets 297 times (1.3 %) in a total of 24000 movements (10 participants x 6 test-sessions x 4 pairs of targets x 10 trials x 10 arm pointing movements per trial). Importantly, the number of errors remained stable all along the day whatever the size of the targets; neither the Time of day (F5,45 = 2.08; p = 0.09) nor the Target size (F3,27 = 2.08; p = 0.14), or their interaction (F15,135 = 0.49; p = 0.93), had a significant effect on the number of errors as revealed by a two way repeated-measures ANOVA. The total number of errors is reported in Table 1. Moreover, the number of invalid trials was 101 out of a total of 2400 trials (4.2%). We did not find any main or interaction effect of time-of day and target width on the number of invalid trials (p > 0.05 for all analyses). None of the participants missed more than 3 targets during a single trial. These findings suggest that any change in movement 9
duration during the day could not be attributed to a motor strategy that privileged speed rather than accuracy.
Actual pointing movements Figure 2A shows the relationship between actual movement durations and ID for the 6 test-sessions. It can be observed that actual movements fitted Fitts’ law, as indicated by the strong linear correlation of MD and ID for each experimental session (r² ranged= 0.94 - 0.99; p < 0.01 for each experimental session). Indeed, for each test-session, actual movement durations significantly increased as ID increased (main effect of Target size: F3,27 = 181.5; p < 0.001; on average 5.47 ± 0.11, 4.48 ± 0.09, 3.93 ± 0.10 and 3.63 ± 0.14 s; from the largest to the smallest ID, respectively). Note also that individual data were analysed and actual durations were highly correlated with ID in every experimental session for each participant (for all individual values, r² range = 0.77 – 0.99). Interestingly, while r² values were stable among the 6 test-sessions (p > 0.1 for all comparisons), the slope of the linear correlation (b parameter) was significantly modulated (see the biphasic pattern of variation with a trough in the afternoon, Fig. 2B). The population mean cosinor analysis revealed a circadian rhythm for the b parameter (data strongly fitted with a 24h period cosine curve, r² > 0.95; p < 0.01). ANOVA analysis also indicated a significant effect of Time of day (F5,45 = 6.05; p < 0.001). Post-hoc comparisons revealed that: (i) the slope at 8 a.m., 8 p.m. and 11 p.m. were not significantly different (p > 0.05), but were higher than those observed at 11 a.m., 2 p.m., and 5 p.m. (p < 0.05), (ii) the slopes at 2 p.m. and 5 p.m. were not significantly different (p > 0.05), but were lower than those observed at 8 a.m., 8 p.m. and 11 p.m. (p < 0.05). The variation of the slope during the day was due to the circadian modulation of actual movement durations for all target widths (population mean cosinor analysis, r² > 0.98 and p < 0.01 for each target, see Fig. 2C). In general, actual movement durations progressively decreased from the morning (grand average: 4.93 ± 0.10 s at 8 a.m.) to the afternoon (grand average: 4.14 ± 0.08 s at 2 p.m.), and then increased until the evening (grand average: 4.40 ± 0.09 s at 11 p.m.). The best fitted 24h period cosine curves are also depicted in the Fig. 2C. The time at which the 24h period cosine models reached their lowest values (batyphase) were not significantly different between the 4 target widths (paired t-tests, p > 0.1).
Mental pointing movements
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Figure 3A shows the relationship between mental movement durations and ID for the 6 test-sessions. Mental movements fitted Fitts’ law whatever the time of day (strong linear relation between MD and ID with r² ranging from 0.90 - 0.97; p < 0.01 for all the experimental sessions). For each test-session, mental movement durations significantly increased as ID increased (main effect of Target size: F3,27 = 76.55; p < 0.001; on average 4.05 ± 0.08, 4.44 ± 0.10, 4.96 ± 0.09, and 5.84 ± 0.11 s; from the largest to the smallest ID, respectively). Individual data were also analysed and mental durations were highly correlated with ID in every experimental session for each participant (for all individual values: r² range = 0.66 – 0.99). As for actual movements, while r² values were stable among the test-sessions (p > 0.1 for all comparisons), the b parameter was significantly modulated (see the biphasic pattern of variation with a trough in the afternoon, Fig. 3B) and the population mean cosinor analysis revealed a circadian rhythm for this parameter as the data strongly fitted a 24h period cosine curve (r² > 0.90; p < 0.01). ANOVA analysis also indicated a significant effect of Time of day (F5,45 = 9.83; p < 0.001). Post-hoc comparisons revealed that: (i) the slope at 8 a.m., 8 p.m. and 11 p.m. were not significantly different (p > 0.05), but were higher than those observed at 11 a.m., 2 p.m., and 5 p.m. (p < 0.05), (ii) the slopes at 2 p.m. and 5 p.m. were not significantly different (p > 0.05), but were lower than those observed at 8 a.m. and 11 p.m. (p < 0.05). The variation of the slope during the day was due to the circadian modulation of mental movement durations for all target widths (population mean cosinor analysis, r² > 0.98 and p < 0.01 for each target, see Fig. 3C). In general, actual movement durations progressively decreased from the morning (grand average: 5.55 ± 0.28 s at 8 a.m.) to the afternoon (grand average: 4.48 ± 0.2 s at 2 p.m.), and then increased until the evening (grand average: 4.87 ± 0.25 s at 11 p.m.). The best fitted 24 h period cosine curves are depicted in Fig. 2C. The time at which the 24 h period cosine models reached their lowest values (batyphase) were not significantly different between the 4 target widths (paired t-tests, p > 0.1).
Relationship between actual and mental movements We compared the modulations of the b parameter (slope values in Fitts’ law) for actual and mental movements (see Fig. 2B and 3B). A two-way ANOVA (Movement [Actual vs Mental] x Time of day) only detected a main effect of Time of day (F5,45=25.33; p < 0.001), but neither a main effect of Movement nor an interaction effect (F1,9=0.11; p = 0.74 and 11
F5,45=0.91; p =0.48 respectively). Post-hoc comparisons revealed that: (i) the slope at 8 a.m., 8 p.m. and 11 p.m. were not significantly different (p > 0.05), but were higher than those observed at 2 p.m., and 5 p.m. (p < 0.05), (ii) the slopes at 2 p.m. and 5 p.m. were not significantly different (p > 0.05). Moreover, no modulation was detected for the whole r² values, combining both actual and mental movements (ANOVA of Friedman χ2 = 1.93; p > 0.05).
Discussion
The aim of this study was to identify potential daily modulations of the speed– accuracy trade-off in arm pointing movements and to test whether this modulation originated from peripheral (i.e., execution stage) or central (i.e., planning stage) motor processing. We thus assessed the durations of actual and mental movements at different times of the day by means of an experimental set up allowing to check Fitts’ law, that is a well-established relationship between speed and accuracy. Our main findings point out that the relation between speed and accuracy is modulated during the day. Precisely, while Fitts’ law, expressed by the linear relation between movement time (MD) and index of task difficulty (ID), held for both actual and mental movements during the day, the slope of the MD/ID relation showed a clear circadian variation with the lowest values in the afternoon. The daily modulation of movement parameters is well documented from chronobiological studies, showing that movement control is, at least partly, driven by the circadian master clock of our organism (i.e., the supra-chiasmatic nuclei; Moore, 1997). For instance, maximal force (Gauthier et al., 2001; Guette et al., 2005), performance in anaerobic exercises (Souissi et al., 2004), as well as the kinematics of simple motor tasks (Moussay et al., 2002, 2003) or fine skilled movements (Gueugneau et al., 2008, 2010, 2015; Jasper et al., 2009), clearly exhibit circadian variations, with the best performances in the afternoon. Here, we show that motor rules, like Fitts’ law, describing movement control at an abstract level, are also modulated during the day. The cosine-like variation of the MD/ID relation is instructive in a strict chronobiological perspective, as it was in antiphase with body temperature (compare Fig. 1 with Fig. 2B and Fig. 3B). This suggests that the basic circadian rhythms of our organism shape the speed-accuracy tradeoff in arm movement control. The slope of the MD/ID relation reflects the motor system sensitivity to changes in task difficulty, i.e., the steeper the slope is, and the more the motor system is affected by task constraints. Consequently, the daily modulation of MD/ID slope may indicate modifications 12
at the level of motor planning and control. Note that spatial precision in actual movements did not vary during the day, thus changes in movement time could not be attributed to a strategy privileging speed in the detriment of accuracy at some hours of the day. Initially, Fitt’s theory (1954) proposes that the motor system behaves like a stochastic communication channel with a transmission capacity limited by a signal-dependent noise. The slope of the relation indicates the information capacity of the motor system; i.e., the central processing rate (Schmidt & Lee, 1999). Since, computational neurosciences confirmed that Fitts’ law emerges from noise within the neural motor commands (Harris and Wolpert, 1998). Motor commands are corrupted by a signal-dependant noise, which could be observed in the variability of electromyographic signals and force output (Jones et al., 2002; Hamilton et al., 2004). Large motor commands produce rapid but inaccurate and variable movements, and small motor commands produce accurate but slow movements (Harris and Wolpert, 1998). Note that the size of the motor command refers to the force output for a given muscle group, which depends on both the number of motor units recruited and their firing rate, see Jones et al., 2002. In this framework, Fitts’s law thus emerges as the consequence of an optimal control strategy in the presence of an intrinsic variability in motor command. Movements appear to be planned according to their upcoming variability by minimizing the effects of noise in motor commands (Harris and Wolpert, 1998; Tanaka et al., 2006; Guigon et al., 2008). In this vein, it has been shown that the slope of the MD/ID relation is increased in stroke patients, compared to healthy subjects, performing pointing tasks related to a Fitts’ paradigm (McCrea and Eng, 2005). This finding has been interpreted as a consequence of an increased neuromotor noise within movement planning process. Interestingly, at the cortical level, neural modulations within primary motor and sensorimotor areas during a Fitts’ task could not be only explained by changes in motor aspects of the behaviour, but are highly related to the target size. Moreover, neural modulations are prominent in the phase preceding movement initiation (Ifft et al., 2011), further highlighting the fact that the link between movement speed and accuracy seems to be handled by predictive mechanisms. Hence, which mechanisms may subserve the modulation of the speed-accuracy tradeoff, in such a way that subjects regulate differentially movement duration across the day according to task constraints? We propose two hypotheses that are not mutually exclusive: one at the functional level and the other at the neurobiological level. First, the circadian modulation of the basic natural physical activity (Brown et al., 1990; Natale, 2002), i.e., the activity needed to achieve most of our daily professional and social obligations (walking, writing, tapping, etc.,) may explain at the functional level the 13
daily calibration of the motor output (Gueugneau et al., 2015). Indeed, we have recently showed that the higher basic physical activity in the afternoon, compared to the morning or the evening, improves sensorimotor predictions (Gueugneau et al., 2015), probably via a mechanism of self-supervised learning that update the internal models of movement on a daily basis (Wolpert et al., 2001). During voluntary movements, the controller, integrating the kinematic and dynamic constraints of the task, generates the appropriate neural commands, whereas the forward model, by relating the sensory signals of the state of the effector (e.g. position, velocity) to the motor commands, predicts the future states of the effector. Thus, the reinforcement of both the forward model and the controller by daily physical activity would be necessary to optimize motor performance (Wolpert et al., 2001). In the afternoon, the higher sensorimotor activity (Natale et al., 2002; Gueugneau et al., 2015) may reinforce the functional linkage between the controller and the forward model, and thus lead to an enhancement of the upcoming motor performance. This could in fine result in optimized movement durations for specific accuracy demands (i.e., a weaker slope in Fitts’ law). During a complex motor learning task, many days of motor training are necessary to optimize motor performance, estimated by changes of the speed-accuracy trade-off (Shmuelof et al., 2012). Repeating a ballistic wrist-pointing task, in a range of imposed movement durations, led to a shift of the speed-accuracy trade-off, with a reduction in trial-to-trial variability and an increase in movement smoothness (i.e., improved trajectory accuracy) (Shmuelof et al., 2012). In this context, forward model-based learning could account for the shift of the speedaccuracy trade-off that subserves the improvement of motor performance (Shadmehr et al., 2010). In our experiment, the modulation of the speed-accuracy trade-off (a modulation of the slope of the MD/ID relation) may be driven by similar mechanisms at the time-scale of the day. However, arm movements are regulated by both feedforward (motor planning and prediction) and feedback (sensorimotor correction) processes (Desmurget & Grafton, 2000). Our results on executed movements are thus not sufficient to conclude about the potential mechanisms implicated in the daily modulation of Fitts’s law. Although we cannot exclude potential peripheral mechanisms, such as execution noise, our findings regarding imagined movements reinforce the premise of a motor planning/feedforward mechanism involved in the daily regulation of the motor output. A key point here is the fact that the temporal features of mental movements emerge from sensorimotor predictions (Sirigu et al., 1996; Wolpert et al., 1998; Wolpert & Flanagan, 2001). During motor imagery, motor commands are prepared, but are blocked before reaching the muscle level. However, a copy of these motor commands, the 14
efference copy, is still available to the forward model, which predicts the future sensorimotor states of the arm and provides temporal information that is very similar to that resulting from actual movements. The fact that we observed a clear circadian modulation in the slope of the MD/ID relation during mental movements, i.e., in the absence of any motor output and afferent feedback, is thus a good indicator of optimized sensorimotor predictions at the motor planning level. Second, at the neurobiological level, the circadian modulation of brain neurotransmitters such as dopamine (Huang et al., 2015) might also have a potential role in the daily modulation of the speed-accuracy trade-off. Dopamine is a key determinant in motor control (Mazzoni et al., 2007). For example, a fundamental feature of Parkinson’s disease characterised by a dysfunction of the dopaminergic system - is generalized movement slowing (bradykinesia), which cannot be explained by an intrinsic limitation in execution (England and Schwab, 1961), but rather is a problem of scaling speed to movement distance (Berardelli et al., 2001). An explanation for this scaling deficit is that bradykinesia is a compensatory response: patients slow down because of a loss of accuracy at normal speeds (Montgomery and Nuessen, 1990; Sheridan and Flowers, 1990; Phillips et al., 1994). More interestingly, by comparing patients with Parkinson’s disease with healthy controls, Mazzoni and colleagues 2007 have shown that movement speed selection may emerge as a result of an implicit value assignment of movement energy cost for a specific task constraint. As indicated by the authors “patients show a reluctance to make fast movements because of the energy expenditure required, although they are capable of executing them as well as control subjects and without expending more energy”. Putting the speed-accuracy trade-off within the framework of cost and reward may thus offer a complementary mechanism to support our data. Indeed, the circadian fluctuation of biological markers - including brain dopamine (Huang et al., 2015) may lead to time-of-day changes in the subjective cost of movement speed for a given task constraint. So, the daily modulation of the slope of the MD/ID relation that we observed in healthy subjects might be partly subserved by biological rhythm in the brain dopaminergic system, which in turn modulates the implicit value assigned to movement energy cost. Further studies are nevertheless necessary to give strength to this hypothesis. To conclude, the speed-accuracy trade-off is modulated during the day, with an increased sensitivity of the motor system to task constraint in the morning and evening. This leads to an optimized motor performance during the afternoon, as revealed by the modulation of the steepness of the slope for both actual and imagined movements. This circadian-like fluctuation was in antiphase with body temperature, suggesting an effect of circadian rhythms 15
upon motor planning processes. The underlying mechanisms may be an update of sensorimotor predictions through the higher basic physical activity in the afternoon (selfsupervised learning) (Gueugneau et al., 2015), or a daily shift of the implicit value assignment of movement energy for movement speed selection.
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Table Number of errors Target
8 a.m.
11 a.m. 14 p.m. 17 p.m. 20 p.m. 23 p.m.
5mm
12
11
8
13
11
11
10mm
11
13
12
12
11
11
15mm
14
14
12
14
12
14
20mm
13
15
13
14
12
13
50
53
45
53
46
49
Total by target
Grand Total
Table 1. Total number of errors, i.e., pointing movements outside the target, for each target
size and for each test-session.
21
Figure legends Figure 1. Daily variation of body temperature.
Average values (± SD) of participants’ body temperature as a function of the time of day. The best-fitted cosine function is also depicted (grey curve). The cosinor analysis gave a significant circadian rhythm (population-mean-cosinor analysis; p < 0.01) which peak at ~ 16:00h. The dashed line shows the average value (i.e., the Mesor) of the temperature rhythm. Figure 2. (A) MD/ID relations for executed movements are shown for all the experimental
sessions. Mean values are presented with their best fitted line. (B) We reported from (A) the value of the b parameter in the Fitts equation for each experimental session. Data are shown with their best fit 24h period cosine curve. (C) Mean (±SD) movement durations recorded for the executed motor tasks during the six experimental sessions and the four target sizes. Data are shown with their best fit 24h period cosine curve. Figure 3. (A) MD/ID relations for imagined movements are shown for all the experimental
sessions. Mean values are presented with their best fitted line. (B) We reported from (A) the value of the b parameter in the Fitts equation for each experimental session. Data are shown with their best fit 24h period cosine curve. (C) Mean (±SD) movement durations recorded for the imagined motor tasks during the six experimental sessions and the four target sizes. Data are shown with their best fit 24h period cosine curve.
22
Temperature (°C)
36.8
36.3
35.8 0
4
8
12 16 20 24
Time of day (h)
23
Actual Pointing Movement A
8 a.m.
Movement Duration (s)
7
11 a.m.
7
5
5
5 r2 = 0.94
3 3
5
5 p.m.
7
r2 = 0.97
3 3
7
5
r2 = 0.99
3
5
5
7
11 p.m.
5 r2 = 0.98
3
7
3
7
5
3
r2 = 0.98
3
7
8 p.m.
7
5
2 p.m.
7
3
5
r2 = 0.98
3
7
3
5
7
20
24
Index of Difficulty
B b parameter (slope)
1.1
1.0
0.9
0.8 0
4
8
16
Time of day (h)
C Movement Duration (s)
12
5
5 5 mm
3 0
8
16
24
15 mm
5
10 mm
3 0
16
24
16
24
20 mm
5
3
8
3 0
8
16
24
0
8
Time of day (h)
24
Mental Pointing Movement A
8 a.m.
Movement Duration (s)
7 5
r2 = 0.94 3
5
5 p.m.
7
5 r2 = 0.97
3
7
3
5
5
3
3
5
7
11 p.m.
7 5
r2 = 0.99 3 5 7 3
3
r2 = 0.98
3
7
8 p.m.
7
5
2 p.m.
7
5
3
r2 = 0.98 3 5 7 3
r2 = 0.98 5
7
Index of Difficulty
B b parameter (slope)
11 a.m.
7
1.1 1.0 0.9 0.8 0.7 0
4
8
12
16
20
24
Time of day (h)
Movement Duration (s)
C
7
7
5
5 5mm
10mm
3
3 0
8
16
24
7
0
8
16
24
16
24
7 15mm
20mm
5
5
3
3 0
8
16
24
0
8
Time of day (h)
25
Numbers of errors Total by target
Target
8 a.m.
11 a.m. 14 p.m. 17 p.m. 20 p.m. 23 p.m.
5mm
12
11
8
13
11
11
10mm
11
13
12
12
11
11
15mm
14
14
12
14
12
14
20mm
13
15
13
14
12
13
50
53
45
53
46
49
Grand Total
Table 1. Total number of errors, i.e., pointing movements outside the target, for each target
size and for each test-session.
26
High-lights
•
Fitts’ law hold throughout the day for both executed and imagined movements
•
The speed-accuracy trade-off expresses a circadian variation
•
Motor planning mechanisms appear to be optimized during the afternoon.
27