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1Unité de Réadaptation et de médecine physique and 2Laboratory of Neurophysiology, Université catholique de Louvain, Brussels; 3Centre for Systems Engineering and Applied Mechanics, Université catholique de Louvain, Louvain-la-Neuve; 4Department of Electrical Engineering and Computer Science, Montefiore Institute, Université de Liège, Liège, Belgium; and 5Centre de Recherche en Sciences Neurologiques, Département de Physiologie, Université de Montréal, Montreal, Quebec, Canada
Submitted 4 April 2008; accepted in final form 18 July 2008
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ABSTRACT |
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INTRODUCTION |
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). These inhibitory connections generate antiphase oscillations in the activity of the two groups of neurons that alternately drive a pair of antagonist muscular groups (e.g., flexors–extensors) to induce periodic motion. There is growing evidence for the involvement of CPGs during walking or arm swinging in mammals (Burke 2001), including humans (Marder 2000; Miall 2007), although rhythmic movements in humans involve higher brain centers (Iwasaki and Zheng 2006; Marder 2000). Recent insights suggest that the concept of the CPG, as established for human locomotion, applies to the arm as well (Dietz 2002; Zehr et al. 2004).
Some rhythmic activities, like locomotion, are energy greedy and are sensitive to dynamic constraints induced by the environment. If walking is viewed as a force-driven harmonic oscillator, it requires a periodic forcing actuation to sustain its oscillations against damping forces, which tend to diminish the oscillations. In such systems, a particular frequency—the resonant frequency—is critical: it requires the minimum force to maintain the oscillations and therefore the minimum muscle activity. When interacting with the environment, the preferred oscillatory movements are not simply dictated by the CNS, but are constrained by the dynamics of the system as well (Hatsopoulos 1996; Kugler and Turvey 1987). For instance, a giraffe moves with a much slower pace than small mammals because giraffes have very long legs. In another context, Neil Armstrong walked on the Moon in 1969 at a much slower velocity than on Earth because gravitational attraction on the Moon is decreased by a factor of six. From the neuronal control perspective, one functional benefit of modulating the CPG frequency with sensory feedback is that it enables a system to exploit the resonant properties of musculoskeletal dynamics (Hatsopoulos 1996; Hatsopoulos and Warren Jr 1996; Iwasaki and Zheng 2006; Williams and DeWeerth 2007).
Activities are calibrated to take into account the existence of gravitational attraction, based on a lifetime of experience in a normal 1-g environment (Papaxanthis et al. 1998). For instance, our motor control anticipates the fact that more effort is required to move an outstretched limb upward than downward, due to increased gravitational torque. The changes of motor performance in altered gravity (Bock 1998) must somehow be compensated through adaptive control, which is either more or less time-consuming depending on the context (Lackner and DiZio 1996).
In this study, we investigate humans’ ability to sustain rhythmic movements in different gravitational environments. By analogy with a simple pendulum system, the self-generated pace should grow as a function of gravity. However, because the natural period is infinite in 0 g, this simplistic model fails in microgravity. Therefore we hypothesize that the movements are partly driven by a CPG in a closed loop with the arm. Since neuronal control systems cooperate with the physical constraints imposed by the dynamics of the body and the environment, we expect that a change of gravity would induce a change of frequency to perform efficient rhythmic movements that have adapted to the resonant frequency as a result of gravitational changes. Since there is no resonant frequency in 0 g, however, we predict that the pace adopted by the participants will rely mainly on the intrinsic frequency of the neural oscillator.
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METHODS |
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PARTICIPANTS. Twelve right-handed volunteers participated in the study. Their health was assessed by their individual National Centres for Aerospace Medicine as meeting the requirement ("Jar Class II") for parabolic flight. No participant reported sensory or motor deficits and they all had normal or corrected-to-normal vision. All participants gave their informed consent to participate in this study and the procedures were approved by the European Space Agency (ESA) Safety Committee and by the local ethics committee.
TASK. Subjects were successively confronted with periods of normal gravity (1 g), hypergravity (1.8 g), and microgravity (0 g) during parabolic flights (Fig. 1A). They were instructed to perform rhythmic arm movements with a handheld object (mass, 212 g; diameter, 82 mm; width, 30 mm) around two virtual obstacles situated 3 m in front of them, following an "infinity-shaped" trajectory (Fig. 1B). The first group of six participants (self-paced) were instructed to perform the movement at a self-generated pace. The second group of six volunteers (metronome-paced) followed the rhythm dictated by a metronome (one cycle every 1.5 s).
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MANIPULATION OF THE GRAVITATIONAL CONTEXT. The experiments took place in the Airbus A300 zerog aircraft on six flights out of Bordeaux (France) spread out over two ESA campaigns. A total of 180 parabolas were performed (2 campaigns x 3 flight days x 30 parabolas per flight).
Figure 1A illustrates one parabola. From a steady horizontal flight (1 g), the aircraft gradually pulled up its nose and started climbing at an angle of approximately 45° for about 20 s, during which the aircraft experienced an acceleration of around 1.8 x g, the gravity level at the surface of the Earth (g = 9.81 m·s–2). The engine thrust was then reduced to the minimum required to compensate for air drag and the aircraft then followed a free-fall ballistic trajectory (a parabola) lasting an additional 20 s, during which weightlessness was achieved. At the end of this period, the aircraft pulled out of the parabolic arc, a maneuver that gave rise to another 20-s period of 1.8 g, after which it returned to normal flight attitude (1 g) before the next parabola. During the parabolas, the resultant g vector was always directed to the floor of the aircraft. Lateral and forward/backward components were in the range 10–3 g and were negligible.
Two participants were tested on each flight during the first and the second blocks of 15 parabolas. The task was carried out continuously across the different gravitational fields, including the 2- to 5-s transition phases separating the stable gravitational phases (Fig. 1A).
DATA ANALYSIS. We calculated the period of the rhythmic movement as the time elapsed between two successive crossings of the center of the path, as defined by the average horizontal and vertical positions (see red dot on Fig. 1B). Since data were not normally distributed, a nonparametric Kruskal–Wallis ANOVA on ranks was used to test the effect of gravity and repetition of parabolas within each group. Significance across gravity conditions was assessed with Dunn's post hoc comparisons (alpha level was P < 0.05). Since no effect was found across repetition of parabolas, we pooled data together in each condition of gravity (0 g [–0.05 g; 0.05 g], 0.5 g [0.05 g; 0.9 g], 1 g [0.9 g; 1.1 g], 1.4 g [1.1 g; 1.65 g], 1.8 g [>1.65 g]).
Computational models
CPG.
The CPG consists of two neurons that are connected with mutually inhibitory synapses, in a configuration of half-center oscillator. The dynamics of the CPG were first derived by Matsuoka (1985). This model describes the firing rate of a real biological neuron with self-inhibition. The CPG model is presented in Fig. 2. The firing rates x1(t) and x2(t) are governed by the following system of equations
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 | (1) |
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. The outputs of each neuron y1(t) and y2(t) are taken as the positive part of x1(t) and x2(t), respectively
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 | (2) |
 | (3) |
We considered only one proprioceptive input 
(t) to the CPG. However, any number of inputs can be applied to the oscillator, which can either be proprioceptive signals or signals from other neurons. The input is arranged to excite one neuron and inhibit the other, by applying the positive part ([(t)]+) to N1 and the negative part ([(t)]–) to N2. The inputs are scaled by the gain h. The tonic excitation c is self-sufficient to generate the oscillation (i.e., a proprioceptive input is not necessary). The two time constants 
1 and 2 determine the speed and shape of the oscillator output. For stable oscillations, 1/2 
[0.1; 0.5] describes when the endogenous—or natural—frequency of the oscillator is proportional to 0.112/1 (Williamson 1998).
PENDULUM SUBSYSTEM.
The proprioceptive feedback signals [h()]+ and [h()]– are equivalent to the angular displacement of a damped pendulum under the influence of gravity (Fig. 2). This simplistic model has previously been used to describe a variety of biological movements and has been shown to sufficiently represent the dynamics of a one-degree-of-freedom system (Obusek et al. 1995). As such, the motion of the mechanical subsystem is governed by
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(t) of a mass m attached to a fixed point by a string (length l). The parameter 
is a constant for the torsional viscous dissipation and g is gravity. In addition, this pendulum system is driven by a forcing torque Tout(t), which depends on the CPG output following
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The closed-loop system is then described by three sets of parameters. The first set describes the CPG (1, 2, β, , c), the second set parameterizes the pendulum subsystem (m, l, g, ), and the last parameters adjust the coupling between the two systems (h, K).
NUMERICAL SIMULATIONS.
The coupled CPG–pendulum model was implemented in MATLAB (The MathWorks, Natick, MA). For all simulations, we used the Runge–Kutta integration method with a time step of 1 ms, with the initial condition
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RESULTS |
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Figure 3 illustrates the average of the period measured in the two groups of volunteers as a function of gravity level. In the self-paced group (light gray disks), we observed a significant decrease between 1 and 1.8 g (P < 0.001). Gravity during the transition phases (0.5 and 1.4 g) also noticeably scaled the average period. Our data strongly suggest an influence of gravity on the rhythm naturally adopted by the subjects. When compared with the self-paced group, the period of movement was longer in all gravity fields in the metronome-paced group (dark gray disks), as dictated by the metronome (P < 0.001). Despite the fact that the rhythm was imposed in this condition, the period was surprisingly still modulated by the gravitational context (P < 0.001) and performance degraded from the instructed 1.5-s pace with increased gravity. However, subjects did not slow down their movement further from 0.5 to 0 g. Indeed, the periods were similar in the self-paced group (P > 0.05) and slightly smaller in 0 g in the metronome-paced group (P < 0.001).
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Considering first the self-paced group, we ran an iterative procedure to find the best parameters that fit the observed period as a function of gravity (see legend of Fig. 3 for details). We found that participants were mainly influenced by the pendulum subsystem in nonzero-gravity fields. Indeed, the natural period of a pendulum is inversely related to gravity following
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The strength of this model resides in its ability to approach the data of the metronome-paced group by adjusting only a few parameters. First, the endogenous period of the CPG was set to the instructed period (1.5 s) by tuning 1. Second, the coupling factor h that links the pendulum output to the CPG dramatically decreased from 20 to 1, which emphasizes the fact that the entrainment becomes much less influenced by the resonant properties of the coupled system. Third, the length of the pendulum increased by 5 cm. Remarkably, we also found biomechanical evidence that subjects of this group performed the movements further from their body by 5 ± 0.1 cm (mean ± SE, P < 0.001). This adaptation allowed participants to follow the imposed rhythm while performing the movement at a pace closer to the resonant frequency of their upper limb.
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DISCUSSION |
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), but also in leg and arm swinging in humans (Abe and Yamada 2003; Holt 1990). Moving at the resonant frequency offers several advantages, including maximization of the movement amplitude and predictability as well as minimization of the degrees of freedom, of the endpoint variability, and of the energy associated with the movement (Goodman et al. 2000; Holt et al. 1995). Our data strongly suggest a functional and flexible role of the CPG in driving rhythmic arm movements in all gravitational fields, regardless of the instructions to follow. Since human beings live in a normal Earth environment, the endogenous period of the CPG in the self-paced group was set to the natural frequency adopted by the participants in 1 g (1.25 s). Although the effect of gravity on the period of the upper limb in nonzero-gravity phases rests on simple mechanics, the same strategy would not have been applied to 0 g. Indeed, in microgravity, the motor system can no longer take advantage of gravity to drive the arm at the resonant frequency. Observations in microgravity suggest a strategy relying more on the intrinsic properties of the CPG. Furthermore, the tight coupling of the oscillator with the actuated system results in quick entrainment and stability to perturbations, despite the fact that subjects were dramatically placed into new environmental conditions such as microgravity. Indeed, participants were stable from the first two cycles of periodic movements. This behavior is a direct theoretical consequence of the model and is illustrated in Fig. 4. The phase plot (Fig. 4, right panel) shows the fast convergence of the motion to a limit cycle, which emphasizes the robustness of the entrainment mechanism. The left panel (Fig. 4) shows the output of the CPG (solid line) and the input of the pendulum (dotted line) as a function of time. One can observe that after a few cycles, the CPG and the pendulum are locked to a common period, despite the fact that the pendulum could not oscillate in microgravity. The structure of the mechanical subsystem (pendulum) is not identified, per se, by the CPG, leading to a computationally efficient collaborative mechanism.
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; Williams and DeWeerth 2007; Williamson 1998), we rested our study on the well-established mathematical formulation of the oscillator by Matsuoka (1985), which provides a simple physiologically plausible model and allows for natural feedback connections. Whereas a more complex CPG model is very likely to converge to the observed behavior (more degrees of freedom), our conclusions will remain at least qualitatively valid with other very simple oscillators, as we verified with a Van der Pol oscillator (supplementary materials).1 Furthermore, although the modeling of a biologically plausible double-arm pendulum system is out of the scope of the present study, it is worth mentioning that a mass-spring system would also predict similar results. In that simple harmonic oscillator, the resonant frequency is proportional to the square root of the stiffness of the spring. In other words, the larger the stiffness, the shorter the period. Interestingly, a study by Fisk et al. (1993) reported larger stiffness of the upper limb for increasing levels of gravity in reaching movements during parabolic flights. Thus a mass-spring model with an explicit dependence of stiffness on gravity would predict comparable results. To sum up, our conclusions will remain compatible with changes in the equations describing the CPG or the mechanical subsystem.
Finally, our results show that a given oscillator quickly converges to the most efficient driving frequency without requiring major changes in its pool of parameters. Indeed, in the metronome-paced group, the same model was able to fit the data as reliably as in the self-paced group. On the one hand, participants increased the distance from the shoulder joint to the end-effector to optimize the movement at the instructed tempo. On the other hand, despite a weak coupling between the CPG and the pendulum, the influence of gravity was still largely present (because subjects reported they could successfully follow the tempo). Consistent with the results reported here, an influence of gravity was also observed in a study investigating grip-load force coupling in parabolic flights during cyclic vertical arm movements (Augurelle et al. 2003). Participants who never experienced altered gravity failed to synchronize their simple rhythmic movements (1 Hz) with a clock signal. They adopted too fast a tempo in 1.8 g but could match the rhythm in 0 g (Augurelle et al. 2003; see Fig. 4, frequency, 1.8 g).
Altogether, behavior in microgravity is different from that in nonzero-gravity fields. Indeed, activities in hypergravity can be inferred from normal Earth gravity by applying a gain on calibrated actions in 1 g, whereas microgravity behavior follows from intrinsically very different rules, since mass and weight become structurally decoupled. However, the same model structure could explain the whole data set by altering the values of a subset of parameters. This process could be responsible for the classically observed slowing of movement in weightlessness (Berger et al. 1997; McIntyre et al. 2001; Mechtcheriakov et al. 2002).
Recently, rhythmic movements have been shown to be performed with better performance than discrete aiming tasks (Miall and Ivry 2004; Smits-Engelsman et al. 2006). Since the human body is a redundant system (Bernstein 1967), the programming of a movement as a whole (i.e., global optimum) should theoretically be more efficient than sequentially optimized submovements (i.e., sum of local optima). Furthermore, these global optima are able to adapt to different conditions. By considering together the system and its environment, the CNS can estimate another dynamic property—the resonant frequency—which is crucial in performing efficient and robust rhythmic movements (Marder and Goaillard 2006). Earlier experiments showed that the CPG frequency and, consequently, the movement frequency can be altered by sensory feedback from the musculoskeletal system (see e.g., McClellan and Sigvardt 1988), which facilitates resonance tuning. Here, resonance tuning might have been driven by an adjustment of interneuronal gains within the CPG. In contrast, the coupling parameter h did not change across gravity levels for a given condition (self-paced vs. metronome-paced), which suggests a control at a higher cortical level. Interestingly, its value decreased between the self-paced (h = 20) group and the metronome-paced group (h = 1), suggesting that the entrainment relies more on the resonant properties of the coupled system in the free condition (self-paced group). Large feedback gains (h 
20) have been shown to increase the range of resonant frequencies to which the closed-loop system can be entrained (Williams and DeWeerth 2007). These flexible mechanisms ensure stable performance despite large fluctuations in the external environment. By allowing for plasticity, the programs implemented by neural control circuits can be parameterized instead of providing single-purpose hard-wired circuits and are thus much more useful to the organism (Katz 1995).
In the context of altered gravity environment, our results provide interesting insights into the role of CPGs in regulating rhythmic arm movements. We show that gravity is an essential parameter that is profoundly integrated in our CNS and is important when tuning the frequency of periodic actions to resonance to sustain competitive movements.
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GRANTS |
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ACKNOWLEDGMENTS |
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FOOTNOTES |
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1 The online version of this article contains supplemental data. 
Address for reprint requests and other correspondence: P. Lefèvre, Centre for Systems Engineering and Applied Mechanics (CESAME), Université catholique de Louvain, Avenue Georges Lemaître 4, B-1348 Louvain-la-Neuve, Belgium (E-mail: philippe.lefevre{at}uclouvain.be)
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ABSTRACT
INTRODUCTION
g (with 
(0) = 0. The system quickly converges to a limit-cycle behavior.