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Dynamic stability of locomotor respiratory coupling during cycling in humans
Neuroscience Letters 383 (2005) 333–338
Dynamic stability of locomotor respiratory coupling during cycling in humans S´ebastien Villard, Jean-Franc¸ois Casties, Denis Mottet ∗ Universit´e Montpellier 1, 700, av. du Pic St Loup, 34090 Montpellier, France Received 19 January 2005; received in revised form 5 April 2005; accepted 6 April 2005
Abstract We explored the locomotor respiratory coupling (LRC) during a 50-min constant-load submaximal cycling exercise. A 4-week recombinant human erythropoietin (r-HuEPO) treatment improved participants’ aerobic capabilities, but did not elicit significant changes in LRC. The distributions of the respiratory frequency over pedalling frequency ratios were systematically bimodal, with a preferred use of 1/3 and 1/2, and a progressive shift of the higher mode from 1/3 towards 1/2 with exercise duration. These results are interpreted in the framework of the sine circle map as the result of coordination dynamics between the physiological subsystems involved in the breathing pedalling cooperation. © 2005 Elsevier Ireland Ltd. All rights reserved. Keywords: Locomotor respiratory coupling; Sine circle map; Farey tree; Exercise duration; Dynamical systems; r-HuEPO
In mammals, the capacity to sustain endurance exercises is related to their ability to efficiently integrate respiration and locomotion. Generally, this cooperation is presented as the complete entrainment of breathing cycles by the locomotion rhythm. This is especially true in quadrupeds, where galloping speed performance leads to a 1/1 ratio between stride frequency and respiratory frequency [4,5,12]. However, in less constrained locomotion tasks, like in bipedal locomotion, the analysis of locomotor respiratory coupling (LRC) showed that the two rhythmic processes of locomotion and respiration are generally frequency locked at low integer ratios (such as 1/2, 1/3 or 1/4) [5]. LRC is a generic mechanism that involves mechanical and neural interactions between the two subsystems. From the point of view of mechanics, breathing entrainment can be the results of passive interactions such as impact loading of the thorax, “visceral piston” and flexion/extension movements of the axial skeleton that tend to enhance expiration [4]. Active breathing entrainment can also be the consequence of muscles simultaneously involved in both locomotion and respi∗ Corresponding author at: EA 2991 Efficience & D´ eficience Motrice, Facult´e des Sciences du Sport, Universit´e Montpellier 1, 700, av. du Pic St Loup, 34090 Montpellier, France. Fax: +33 467415750. E-mail address: [email protected] (D. Mottet).
0304-3940/$ – see front matter © 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2005.04.047
ration, especially in tetrapods [4] and in human arm propulsion (e.g., in rowing or wheelchair locomotion) where strong couplings are reported [2,20]. As a consequence, mechanical couplings are stronger in quadrupeds than in humans, for which the upright position generates less constrains and allows larger ventilatory adaptations [5]. The observed diversity in the ratios between stride frequency and respiratory frequency in humans suggests that LRC is not simply due to a passive and active mechanical interactions between locomotor and respiratory systems. Moreover, Temprado et al. [21] recently showed that breathing was coordinated with simple repetitive wrist movements, a task where almost no mechanical coupling exists. The second mechanism that plays an important role in LRC is neurological coupling at different levels of the neural system. A common neural drive from the subthalamic and mesencephalic locomotor regions triggers an immediate increase in respiratory and cardiovascular rhythms at the onset of locomotor exercise [9]. Such a central control seems to require the activation of spinal locomotion generators [13,23], and Viala [23] proposed a model integrating several pattern generators to explain the coupling relationships between locomotion and respiration in rabbits. More recently, Morin and Viala [14] showed that proprioceptive peripheral feedback from locomotor limbs plays an important role in the modulation of LRC. All these neural
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Fig. 1. The first five levels of the Farey tree representing the hierarchy in the sine circle map. The most stable coupling occurs at level −1, when the frequency ratios are 0/1 (i.e., only one oscillator moves) or 1/1 (i.e., both oscillators move together at the same frequency).
mechanisms contribute to enhance the coupling between respiration and locomotion. From a dynamical systems point of view, coupling is a fundamental natural phenomenon commonly met in chemical reactions, convective fluids or electrical circuits. In biological systems, couplings have been detected from the microscopic level of synchronous firing of neurons to the macroscopic level of cooperative behaviour of animals and humans [17]. To address this issue of coupling between subsystems, the sine circle map provides a general mathematical framework for understanding the frequency-locking behaviour of two oscillators with different natural frequencies. Depending on the strength of the coupling, multiple stable r´egimes occur, where low order frequency ratios are more stable and have a wider basin of attraction (Arnold tongues) than high order ones. Moreover, the difference in stability of frequency ratios p/q and m/n that follow the unimodular rule |p × n − q × m| = 1 corresponds to the branches in the Farey tree (Fig. 1), a number theoretic organisation of the rational numbers in the unit interval that captures the hierarchical stability of the frequency ratios in the sine circle map. This approach leads to two predictions that are easy to check experimentally. The first prediction is that the most stable frequency-locking ratios should appear in the most constrained cases, when only extremely simple ratio can be performed [16]. This prediction was experimentally confirmed for LRC in galloping quadrupeds, where the 1/1 frequency locking is the rule [12], or in running humans where respiration and locomotion are frequency locked at simple ratios such as 1/2 or 1/3 [5]. The second prediction is that the switch from one ratio to another should follow the sine circle map dynamics. Unimodular transitions that characterise switches in the vicinity of the starting ratio, represent the optimal path from one frequency-locking ratio to another during efficient adaptation to task constraints. This point was well demonstrated with the paradigm of multi-frequency bimanual coordination [15,16,22]: increasing movement frequency (i.e., decreasing coupling strength for a given frequency ratio) induced unimodular switches from less stable ratios towards
more stable ones. As far as LRC is concerned, this prediction has never been explicitly tested, but indirect evidence exists. For example, Amazeen et al. [2] showed that the sine circle map hierarchy adequately characterises stable coordination patterns between locomotor and respiratory subsystems. Moreover, Bramble and Carrier [5] showed that experienced runners switch from “1/4” coordination (one respiratory cycle to four strides) to “1/2” via “1/3” coordination, which suggests that changes in LRC occurred from less to more stable ratios during exercise, and that these changes followed the unimodular rule. Finally, the general idea that simple and stable frequency ratios are associated with maximum adaptive efficiency seems easy to extend from multi-frequency bimanual coordination to LRC in humans. During high intensity running exercise, coordinating stride rate and respiratory rhythm seems related to energetic benefit [18] and endurancetrained athletes exhibit high levels of coupling at low integer ratios [3]. In cycling, the relative part of mechanical constraints is minimised, and this should enlarge the relative part of neurological mechanisms and reveal more flexible adaptations. Therefore, in the present study, we address the issue of the relations between respiratory frequency (Rf ) and pedalling frequency (Pf ) in cycling, and use the sine circle map as tool to reveal the logic of the observed changes in their ratio (Rf /Pf ). We expect switches in LRC from less stable frequency relations to more stable ones when task difficulty increases, and unimodular transitions between frequency ratios. We experimentally manipulated task difficulty in two different ways while keeping workload constant relative to participants’ capability. First, we recorded LRC at different periods of time during long duration exercise to examine fine tuned adaptations to exercise duration. Second, we artificially increased participants’ aerobic capabilities by means of recombinant human Erythropoietin (r-HuEPO) treatment. It has been shown that r-HuEPO treatment improves maximal oxygen consumption (V˙ O2 max ) by increasing haemoglobin concentration and oxygen transport to the working muscles [7,19]. As the main limiting factor in endurance exercise is the physiological coupling between respiration and locomotion (i.e., oxygen transport by the cardiovascular system [11]), an increase in oxygen transport is expected to allow a greater independence between respiration and locomotion. Twelve male national level cyclists participated in this study. They gave informed written consent after approval of the study by the legal ethics committee (Comit´e Consultatif de Protection des Personnes en Recherche Biom´edicale, Hˆopital Saint Eloi, Montpellier, France). Detailed description of the experimental protocol can be found in [7], but we summarise below the relevant aspects. The experiment started with the measurement of the reference behaviour for each participant during the first two sessions (i.e., before treatment). During session ref (day 0), participants performed an incremental exercise test to exhaustion to assess their maximal oxygen uptake (ref V˙ O2 max )
S. Villard et al. / Neuroscience Letters 383 (2005) 333–338
and power output (refPOWmax ). The measured ref V˙ O2 max of each participant was used to adapt the load during session REF (day 2), where participants performed for 50 min at a constant load corresponding to 65% of their ref V˙ O2 max . Then, following a double-blind procedure, participants received either 50 U/kg r-HuEPO (EPO group) or 1 ml NaCl 0.9% (PLA group) subcutaneously three times a week for 4 weeks. After the treatment, during session trt (day 25), participants performed a second incremental exercise test to exhaustion to assess their new maximal oxygen uptake (trt V˙ O2 max ) and power output (trtPOWmax ). Next, participants performed two 50-min constant-load exercises (ABS and REL). During session ABS (same absolute power as before treatment), participants performed for 50 min at a constant load corresponding to 65% of ref V˙ O2 max . During session REL (same relative power as before treatment), participants performed for 50 min at a constant load corresponding to 65% of trt V˙ O2 max (i.e., their new V˙ O2 max after treatment). To minimise sequencing effects, the order of the ABS and REL sessions was randomly chosen for each participant (day 27 or 29). Each exercise was performed on cycle ergometer (Ergoline 800S, Hoechberg, Germany) at preferred pedalling frequency. Breathing and pedalling were continuously sampled breath by breath and analyzed by an automated system (Jaeger Oxycon Alpha, Hoechberg, Germany). Incremental exercises consisted of a 3-min warm-up at 60 W, followed by an increase in load by steps of 30 W every minute until exhaustion. Constant-load exercises consisted of a 4-min resting baseline, followed by a 50-min plateau at the experimentally chosen load. During constant-load exercises, participants were allowed to take off the mouthpiece of the recording system for about 5–7 min in the first and second part of the exercise. As a consequence, constant-load exercises were divided in three parts for data analysis: from minutes 10 to 15 (Begin), from minutes 25 to 30 (Middle) and from minutes 45 to 50 (End). For the Begin, Middle and End parts, Rf /Pf was computed for each individual breathing cycle and mapped in a level 3 Farey tree1 : each observed Rf /Pf ratio was assigned to a Farey interval bounded by the corresponding ratios at level 4. This mapping in the Farey tree (Fig. 1) allowed calculation of (i) the percentage of each Farey ratio; (ii) the percentage of unimodular transitions among all observed transitions; and (iii) the average number of consecutive cycles that stay within each Farey interval. The latter variable is a local measure of stability which is an indication of the effective attractiveness of the Farey interval of interest: even if perturbed by random fluctuations always present in biological systems, the system 1 As the number of Farey ratios depends on the size of the tree (Fig. 1), we first needed to select the size of the Farey tree. Here, we used a brute force strategy to determine the size of Farey tree that best fitted the distribution of the observed ratios: we systematically tested all the Farey trees from level −1 to level 13 for each trial. As no significant differences were found, the average value (i.e., level 3 tree) was used in all analyses.
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should remain longer within a deeply attractive Farey interval than within a less attractive one. Analysis of variance (ANOVA) was used to test the effects of the experimental factors on pedalling related dependent variables (frequency, Pf ; power output, POW), respiratory related dependent variables (frequency, Rf ; oxygen uptake, V˙ O2 ; tidal volume, VT ; ventilatory flow, V˙ E ), and LRC related dependent variables (frequency ratio, Rf /Pf , percentage and local stability of each Farey ratio and percentage of unimodular transitions). For maximal tests, the experimental factors were between group treatment (EPO versus PLA) and repeated measures before and after (ref versus trt). For long duration exercises, the experimental factors were between group treatment (EPO versus PLA) and repeated measures during sessions (REF, ABS and REL) and during parts (Begin, Middle, End). Experimental effects were considered significant when the α risk probability was lower than 0.05 after Greenhouse–Geisser correction. To assess the amount of variance attributed to each significant effect, effect size (ES) was also determined [1]. A first expected result was that r-HuEPO administration resulted in a significant increase in V˙ O2 max (+8.5%) and POWmax (+9.1%) in the EPO group (group × before/after interaction: respectively, F(1, 10) = 13.36, p = 0.0044, ES = 48.50%, and F(1, 10) = 12.79, p = 0.005, ES = 68.97%). However, as far as the relations between respiration and locomotion are concerned, in constant-load exercises, no significant effects of the r-HuEPO treatment were found: Pf , Rf and Rf /Pf did not change significantly (respectively: F(2, 20) = 0.42, p = 0.659; F(2, 20) = 2.80, p = 0.085 and F(2, 20) = 2.64, p = 0.096). These results confirms that the rHuEPO treatment improves aerobic capacity in maximal tests [7], but the present contribution revealed that these changes did not elicit significant changes in LRC during submaximal long duration exercises. A second and more important part of the present results concerns the effects of exercise duration. Oxygen consumption (V˙ O2 ) was found to decrease as exercise progressed (F(2,
Fig. 2. Average oxygen gain (i.e., ratio of consumed oxygen over produced power) as a function of exercise duration. The linear decrease in oxygen gain with exercise duration reveals an increased energetic efficiency with exercise duration.
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Fig. 3. Effects of exercise duration on respiratory frequency Rf (top left panel), pedalling frequency Pf (bottom left panel) and their ratio Rf /Pf (right panel). Respiratory frequency increased with exercise duration while pedalling frequency decreased, which resulted in a progressive change in LRC towards 1/2.
20) = 6.84, p = 0.0187, ES = 18.91%). As the power output was constant during the whole exercise, this lower oxygen uptake for a given power output (Fig. 2) indicates a better energetic efficiency at the end of the exercise. As shown in Fig. 3, average respiratory frequency Rf increased with exercise duration (F(2, 20) = 42.51, p = 0.0001, ES = 57.12%) while average pedalling frequency Pf decreased (F(2, 20) = 8.38, p = 0.0097, ES = 41.54%). This combined change in the numerator and denominator resulted in an increase in the average Rf /Pf ratio (F(2, 20) = 41.6, p = 0.0001, ES = 73.89%), which evolved from about 3/8 to about 1/2 during exercise (Fig. 3, right panel) while its standard deviation was getting larger (F(2, 20) = 14.27, p = 0.0026, ES = 83.28%). We also noted that, due to a decrease in VT (F(2, 20) = 31.53, p = 0.0026, ES = 80.19%), V˙ E did not change significantly (F(2, 20) = 0.99, p = 0.387) when respiratory frequency increased with exercise duration. A detailed analysis of the mapping of the Rf /Pf ratios in the Farey tree (Fig. 4) revealed a bimodal distribution, where 1/2 and 1/3 systematically occurred more frequently than any other ratios. This result is important because it clearly indicates that the distribution of the Rf /Pf ratios is not the result of fluctuations around the mean value, and that the mean is actually a poor indicator of the effective distribution. Indeed, the bimodal distributions in Fig. 4 suggest that the observed Rf /Pf ratios result from a delicate balance between 1/2, 1/3 and the other ratios. Moreover, exercise duration changed this balance. This qualitative result was confirmed with the analysis of the occurrence of the distribution modes, showing a raising use of 1/2 from Begin to End (F(2, 20) = 7.65, p = 0.0097, ES = 34.50%) and the opposite phenomenon for the less stable 1/3, which was more frequent at the beginning than at the end of exercise (F(2, 20) = 8.28, p = 0.0087, ES = 45.05%). Hence, exercise duration induced a shift in the distribution of LRC ratios, where the mode progressively varied from 1/3 to 1/2. This change towards a ratio located higher in the Farey tree hierarchy should be accompanied
by an increase in stability and we tested this prediction by focusing on the transitions between ratios. The analysis revealed that 48% of the breathing cycles resulted in a transition to a higher or lower level in the tree and that 80% of these transitions followed the unimodular rule, yet without significant changes with exercise duration (respectively, F(2, 20) = 2.77, p = 0.7154 and F(2, 20) = 3.27, p = 0.4424). When focusing on effective local stability after a transition, a four ways ANOVA2 (i.e., treatment × session × part × mode: 1/2, 1/3) revealed that 1/3 became less attractive with exercise duration while the inverse was true for 1/2 (part × mode interaction: F(2, 18) = 9.18, p = 0.0018, ES = 23.42% as illustrated in Fig. 5). Hence, exercise duration induced a shift from a 1/3 LRC at the beginning of the exercise towards a 1/2 LRC at the end, and this shift was accompanied with an exchange in local dynamic stability (i.e., deepness of the basin of attraction), the most frequent LRC being the most stable after a transition. The aim of this study was to address LRC from a phenomenological point of view, where a collective variable such as the Rf /Pf ratio is supposed to summarise the numerous interactions among the multiple neural, muscular and physiological mechanisms involved in the regulation of locomotion and respiration. According to the hierarchy in the sine circle map, we expected higher order LRC under r-HuEPO treatment and a shift toward lower order ratios with exercise duration. A first result of the present study is the lack of change in LRC regulation after r-HuEPO treatment. The greater aerobic performance after r-HuEPO treatment did not result in significant changes in the coordination between respiration and locomotion during long duration exercise at 65% of V˙ O2 max . One possible explanation is that exercise intensity was not high enough to trigger visible adaptations. Indeed, 2 One participant (for whom transitions occurred in only 6% of the cycles) was excluded from this analysis.
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Fig. 4. Typical distributions of the LRC frequency ratios mapped in a level 3 Farey tree, for the part Begin, Middle and End of the 50-min constant-load exercises. Distributions are bimodal and progressively shift towards 1/2 (i.e., a more stable level 0 ratio) with exercise duration.
Fig. 5. Local stability index for the two modes of the Rf /Pf distribution (1/2 and 1/3) and for the part Begin, Middle and End of the 50-min exercise. An exchange of stability occurred between 1/2 and 1/3 with exercise duration: 1/3 is locally more stable at the beginning of the exercise and 1/2 is locally more stable at the end.
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oxygen deficit due to high exercise intensity seems to play a key role in fatigue resistance [8], but faster V˙ O2 kinetics after r-HuEPO supplementation tends to minimise this oxygen deficit [7]. Hence, increasing oxygen deficit with higher workload might be necessary to reveal adaptations in LRC after r-HuEPO treatment, but would make a 50-min exercise extremely difficult to sustain. A second and more important result is the significant changes in LRC that exercise duration brought out. Simultaneously with an increased energetic efficiency (Fig. 2), we observed a shift in Rf /Pf that was the consequence of a change in both Rf and Pf (Fig. 3). The increase in Rf was combined with a decrease in VT , with the result that V˙ E did not change with exercise duration. This lack of change in the global ventilatory response during exercise indicates that the reasons for the changes in Rf should be looked for elsewhere. Indeed, the starting point of the observed LRC regulations seems to be the necessary optimisation of energetic efficiency to postpone fatigue. Slowing down Pf is known to minimise the wasted internal energy due to tissues viscosity and co-contractions [10]. Hence, the better energetic efficiency gained by decreasing pedalling rate accounts for the observed changes in Pf which, in turn, result in changes in Rf , probably due to an entrainment of locomotion on respiration. The final result of this increase in energetic efficiency by decreasing Pf along with exercise duration resulted in parallel changes towards simpler LRC ratios. A third important point concerns the dynamic stability of the observed LRC ratios during exercise. About one half of the breathing cycles were followed by a transition towards a different Rf /Pf ratio, which is rather surprising for a submaximal constant-load exercise where the physiological constraints on the respiratory system remain globally invariant (i.e., steady state for ventilation [7]). The bimodal distribution of the Rf /Pf ratios indicates that the global physiological demand on the cooperation between the respiratory and locomotor systems is reached by a more subtle distribution than Gaussian variations around the mean. This observation suggests that the effective distribution of the Rf /Pf ratios is the result of a combined process, where the physiological demand acts as a global guide for the LRC in the landscape provided by the sine circle map. In other words, it seems that the observed distribution of the Rf /Pf ratios emerges from the dynamic stability principles defined by the sine circle map, which accounts locally for the multimodal distributions favouring simple ratios, and the physiological demand that globally drives the average LRC value. Based on the coupled dynamical systems perspective, the observed changes in the distribution of LRC ratios with exercise duration (Fig. 4) can be explained by the loss of stability of the higher order frequency-locking r´egimes due to raising the task difficulty [16,22]. Such a loss of stability induces transitions to wider Arnold tongues, which accounts rather well for the preferential use of the 1/2 coordination with exercise duration (Fig. 4). The present results suggest that the same dynamical principles are at work in bimanual coordination and in
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LRC, two systems with different structural properties, but where the sine circle map captures the dynamics of coupling at a macroscopic level. Although the precise nature of the coupling cannot be determined on the basis of the present contribution, the use of a pedalling task minimises the role of mechanical constraints and puts to the fore neurophysiologic reasons for LRC. As the role of spinal control, via central pattern generators and reflex loops, is essential in the generation and coordination of rhythmical behaviours in vertebrates [13], we suggest that the observed shift towards a simpler frequency locking with exercise duration might be due to a progressively rising influence of the spinal circuitry in the control of LRC. Spinal influences tend to synchronise rhythmical behaviours in a very stable 1/1 frequency locking [14,23] or in-phase coordination [6]. In this contribution, the qualitative changes in LRC observed during a 50-min cycling exercise were interpreted as the use of more stable coordination patterns according to the dynamics of the sine circle map. As in many systems of coupled nonlinear oscillators, such changes in coupling relations also characterise a more efficient response to task constrains: our results are qualitatively similar to [18] showing that runners with more stable LRC (1/1 frequency ratio) were also more efficient. In this way, more stable coordination patterns might improve efficiency to postpone fatigue in long duration exercise. Acknowledgements We wish to thank the participants in the present study and the whole staff from the “Service de Physiologie Clinique” (Prof. C. Pr´efaut) at the Hˆopital Arnaud de Villeneuve (Montpellier, France). Special thanks go to P. Connes and C. Caillaud for their support and experienced consulting. References [1] H. Abdi, Introduction au traitement statistique des donn´ees exp´erimentales, Presses Universitaires de Grenoble, 1987. [2] P.G. Amazeen, E.L. Amazeen, P.J. Beek, Coupling of breathing and movement during manual wheelchair propulsion, J. Exp. Psychol. Hum. Percept. Perform. 27 (2001) 1243–1259. [3] P. Bernasconi, P. Burki, A. Buhrer, E.A. Koller, J. Kohl, Running training and co-ordination between breathing and running rhythms during aerobic and anaerobic conditions in humans, Eur. J. Appl. Physiol. Occup. Physiol. 70 (1995) 387–393. [4] D. Boggs, Interactions between locomotion and ventilation in tetrapods, Comp. Biochem. Physiol. A: Mol. Integr. Physiol. 133 (2002) 269.
[5] D.M. Bramble, D.R. Carrier, Running and breathing in mammals, Science 219 (1983) 251–256. [6] R.G. Carson, S. Riek, Moving beyond phenomenology: neuromuscular–skeletal constraints upon coordination dynamics, in: J.P. Piek (Ed.), Motor Behavior and Human Skill, Human Kinetics, 1998, pp. 209–230. [7] P. Connes, S. Perrey, A. Varray, C. Prefaut, C. Caillaud, Faster oxygen uptake kinetics at the onset of submaximal cycling exercise following 4 weeks recombinant human erythropoietin (r-HuEPO) treatment, Pflugers Arch. 447 (2003) 231–238. [8] A.P. Demarle, J.J. Slawinski, L.P. Laffite, V.G. Bocquet, J.P. Koralsztein, V.L. Billat, Decrease of O(2) deficit is a potential factor in increased time to exhaustion after specific endurance training, J. Appl. Physiol. 90 (2001) 947–953. [9] F.L. Eldridge, D.E. Millhorn, T.G. Waldrop, Exercise hyperpnea and locomotion: parallel activation from the hypothalamus, Science 211 (1981) 844–846. [10] M.P. Francescato, M. Girardis, P.E. di Prampero, Oxygen cost of internal work during cycling, Eur. J. Appl. Physiol. Occup. Physiol. 72 (1995) 51–57. [11] N.L. Jones, K.J. Killian, Exercise limitation in health and disease, N. Engl. J. Med. 343 (2000) 632–641. [12] C.L. Lafortuna, E. Reinach, F. Saibene, The effects of locomotorrespiratory coupling on the pattern of breathing in horses, J. Physiol. 492 (Pt 2) (1996) 587–596. [13] E. Marder, D. Bucher, Central pattern generators and the control of rhythmic movements, Curr. Biol. 11 (2001) R986–R996. [14] D. Morin, D. Viala, Coordinations of locomotor and respiratory rhythms in vitro are critically dependent on hindlimb sensory inputs, J. Neurosci. 22 (2002) 4756–4765. [15] C.E. Peper, P.J. Beek, Are frequency-induced transitions in rhythmic coordination mediated by a drop in amplitude? Biol. Cybern. 79 (1998) 291–300. [16] C.E. Peper, P.J. Beek, P.C. van Wieringen, Frequency-induced phase transitions in bimanual tapping, Biol. Cybern. 73 (1995) 301– 309. [17] A. Pikovsky, M. Rosenblum, J. Kurths, Synchronization: A Universal Concept in Nonlibear Sciences, Cambridge University Press, 2001. [18] B. Rassler, J. Kohl, Coordination-related changes in the rhythms of breathing and walking in humans, Eur. J. Appl. Physiol. 82 (2000) 280–288. [19] G. Russell, C.J. Gore, M.J. Ashenden, R. Parisotto, A.G. Hahn, Effects of prolonged low doses of recombinant human erythropoietin during submaximal and maximal exercise, Eur. J. Appl. Physiol. 86 (2002) 442–449. [20] G.P. Siegmund, M.R. Edwards, K.S. Moore, D.A. Tiessen, D.J. Sanderson, D.C. McKenzie, Ventilation and locomotion coupling in varsity male rowers, J. Appl. Physiol. 87 (1999) 233–242. [21] J. Temprado, L. Milliex, L. Grelot, T. Coyle, S. Calvin, M. Laurent, A dynamic pattern analysis of coordination between breathing and rhythmic arm movements in humans, Neurosci. Lett. 329 (2002) 314–318. [22] P.J. Treffner, M.T. Turvey, Resonance constraints on rhythmic movement, J. Exp. Psychol. Hum. Percept. Perform. 19 (1993) 1221– 1237. [23] D. Viala, Coordination of locomotion and respiration, in: A.D. Miller, A.L. Bianchi, B.P. Bishop (Eds.), Neural Control of Respiratory Muscles, CRC Press, New York, 1997, pp. 285–296.
Dynamic stability of locomotor respiratory coupling during cycling in humans S´ebastien Villard, Jean-Franc¸ois Casties, Denis Mottet ∗ Universit´e Montpellier 1, 700, av. du Pic St Loup, 34090 Montpellier, France Received 19 January 2005; received in revised form 5 April 2005; accepted 6 April 2005
Abstract We explored the locomotor respiratory coupling (LRC) during a 50-min constant-load submaximal cycling exercise. A 4-week recombinant human erythropoietin (r-HuEPO) treatment improved participants’ aerobic capabilities, but did not elicit significant changes in LRC. The distributions of the respiratory frequency over pedalling frequency ratios were systematically bimodal, with a preferred use of 1/3 and 1/2, and a progressive shift of the higher mode from 1/3 towards 1/2 with exercise duration. These results are interpreted in the framework of the sine circle map as the result of coordination dynamics between the physiological subsystems involved in the breathing pedalling cooperation. © 2005 Elsevier Ireland Ltd. All rights reserved. Keywords: Locomotor respiratory coupling; Sine circle map; Farey tree; Exercise duration; Dynamical systems; r-HuEPO
In mammals, the capacity to sustain endurance exercises is related to their ability to efficiently integrate respiration and locomotion. Generally, this cooperation is presented as the complete entrainment of breathing cycles by the locomotion rhythm. This is especially true in quadrupeds, where galloping speed performance leads to a 1/1 ratio between stride frequency and respiratory frequency [4,5,12]. However, in less constrained locomotion tasks, like in bipedal locomotion, the analysis of locomotor respiratory coupling (LRC) showed that the two rhythmic processes of locomotion and respiration are generally frequency locked at low integer ratios (such as 1/2, 1/3 or 1/4) [5]. LRC is a generic mechanism that involves mechanical and neural interactions between the two subsystems. From the point of view of mechanics, breathing entrainment can be the results of passive interactions such as impact loading of the thorax, “visceral piston” and flexion/extension movements of the axial skeleton that tend to enhance expiration [4]. Active breathing entrainment can also be the consequence of muscles simultaneously involved in both locomotion and respi∗ Corresponding author at: EA 2991 Efficience & D´ eficience Motrice, Facult´e des Sciences du Sport, Universit´e Montpellier 1, 700, av. du Pic St Loup, 34090 Montpellier, France. Fax: +33 467415750. E-mail address: [email protected] (D. Mottet).
0304-3940/$ – see front matter © 2005 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.neulet.2005.04.047
ration, especially in tetrapods [4] and in human arm propulsion (e.g., in rowing or wheelchair locomotion) where strong couplings are reported [2,20]. As a consequence, mechanical couplings are stronger in quadrupeds than in humans, for which the upright position generates less constrains and allows larger ventilatory adaptations [5]. The observed diversity in the ratios between stride frequency and respiratory frequency in humans suggests that LRC is not simply due to a passive and active mechanical interactions between locomotor and respiratory systems. Moreover, Temprado et al. [21] recently showed that breathing was coordinated with simple repetitive wrist movements, a task where almost no mechanical coupling exists. The second mechanism that plays an important role in LRC is neurological coupling at different levels of the neural system. A common neural drive from the subthalamic and mesencephalic locomotor regions triggers an immediate increase in respiratory and cardiovascular rhythms at the onset of locomotor exercise [9]. Such a central control seems to require the activation of spinal locomotion generators [13,23], and Viala [23] proposed a model integrating several pattern generators to explain the coupling relationships between locomotion and respiration in rabbits. More recently, Morin and Viala [14] showed that proprioceptive peripheral feedback from locomotor limbs plays an important role in the modulation of LRC. All these neural
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Fig. 1. The first five levels of the Farey tree representing the hierarchy in the sine circle map. The most stable coupling occurs at level −1, when the frequency ratios are 0/1 (i.e., only one oscillator moves) or 1/1 (i.e., both oscillators move together at the same frequency).
mechanisms contribute to enhance the coupling between respiration and locomotion. From a dynamical systems point of view, coupling is a fundamental natural phenomenon commonly met in chemical reactions, convective fluids or electrical circuits. In biological systems, couplings have been detected from the microscopic level of synchronous firing of neurons to the macroscopic level of cooperative behaviour of animals and humans [17]. To address this issue of coupling between subsystems, the sine circle map provides a general mathematical framework for understanding the frequency-locking behaviour of two oscillators with different natural frequencies. Depending on the strength of the coupling, multiple stable r´egimes occur, where low order frequency ratios are more stable and have a wider basin of attraction (Arnold tongues) than high order ones. Moreover, the difference in stability of frequency ratios p/q and m/n that follow the unimodular rule |p × n − q × m| = 1 corresponds to the branches in the Farey tree (Fig. 1), a number theoretic organisation of the rational numbers in the unit interval that captures the hierarchical stability of the frequency ratios in the sine circle map. This approach leads to two predictions that are easy to check experimentally. The first prediction is that the most stable frequency-locking ratios should appear in the most constrained cases, when only extremely simple ratio can be performed [16]. This prediction was experimentally confirmed for LRC in galloping quadrupeds, where the 1/1 frequency locking is the rule [12], or in running humans where respiration and locomotion are frequency locked at simple ratios such as 1/2 or 1/3 [5]. The second prediction is that the switch from one ratio to another should follow the sine circle map dynamics. Unimodular transitions that characterise switches in the vicinity of the starting ratio, represent the optimal path from one frequency-locking ratio to another during efficient adaptation to task constraints. This point was well demonstrated with the paradigm of multi-frequency bimanual coordination [15,16,22]: increasing movement frequency (i.e., decreasing coupling strength for a given frequency ratio) induced unimodular switches from less stable ratios towards
more stable ones. As far as LRC is concerned, this prediction has never been explicitly tested, but indirect evidence exists. For example, Amazeen et al. [2] showed that the sine circle map hierarchy adequately characterises stable coordination patterns between locomotor and respiratory subsystems. Moreover, Bramble and Carrier [5] showed that experienced runners switch from “1/4” coordination (one respiratory cycle to four strides) to “1/2” via “1/3” coordination, which suggests that changes in LRC occurred from less to more stable ratios during exercise, and that these changes followed the unimodular rule. Finally, the general idea that simple and stable frequency ratios are associated with maximum adaptive efficiency seems easy to extend from multi-frequency bimanual coordination to LRC in humans. During high intensity running exercise, coordinating stride rate and respiratory rhythm seems related to energetic benefit [18] and endurancetrained athletes exhibit high levels of coupling at low integer ratios [3]. In cycling, the relative part of mechanical constraints is minimised, and this should enlarge the relative part of neurological mechanisms and reveal more flexible adaptations. Therefore, in the present study, we address the issue of the relations between respiratory frequency (Rf ) and pedalling frequency (Pf ) in cycling, and use the sine circle map as tool to reveal the logic of the observed changes in their ratio (Rf /Pf ). We expect switches in LRC from less stable frequency relations to more stable ones when task difficulty increases, and unimodular transitions between frequency ratios. We experimentally manipulated task difficulty in two different ways while keeping workload constant relative to participants’ capability. First, we recorded LRC at different periods of time during long duration exercise to examine fine tuned adaptations to exercise duration. Second, we artificially increased participants’ aerobic capabilities by means of recombinant human Erythropoietin (r-HuEPO) treatment. It has been shown that r-HuEPO treatment improves maximal oxygen consumption (V˙ O2 max ) by increasing haemoglobin concentration and oxygen transport to the working muscles [7,19]. As the main limiting factor in endurance exercise is the physiological coupling between respiration and locomotion (i.e., oxygen transport by the cardiovascular system [11]), an increase in oxygen transport is expected to allow a greater independence between respiration and locomotion. Twelve male national level cyclists participated in this study. They gave informed written consent after approval of the study by the legal ethics committee (Comit´e Consultatif de Protection des Personnes en Recherche Biom´edicale, Hˆopital Saint Eloi, Montpellier, France). Detailed description of the experimental protocol can be found in [7], but we summarise below the relevant aspects. The experiment started with the measurement of the reference behaviour for each participant during the first two sessions (i.e., before treatment). During session ref (day 0), participants performed an incremental exercise test to exhaustion to assess their maximal oxygen uptake (ref V˙ O2 max )
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and power output (refPOWmax ). The measured ref V˙ O2 max of each participant was used to adapt the load during session REF (day 2), where participants performed for 50 min at a constant load corresponding to 65% of their ref V˙ O2 max . Then, following a double-blind procedure, participants received either 50 U/kg r-HuEPO (EPO group) or 1 ml NaCl 0.9% (PLA group) subcutaneously three times a week for 4 weeks. After the treatment, during session trt (day 25), participants performed a second incremental exercise test to exhaustion to assess their new maximal oxygen uptake (trt V˙ O2 max ) and power output (trtPOWmax ). Next, participants performed two 50-min constant-load exercises (ABS and REL). During session ABS (same absolute power as before treatment), participants performed for 50 min at a constant load corresponding to 65% of ref V˙ O2 max . During session REL (same relative power as before treatment), participants performed for 50 min at a constant load corresponding to 65% of trt V˙ O2 max (i.e., their new V˙ O2 max after treatment). To minimise sequencing effects, the order of the ABS and REL sessions was randomly chosen for each participant (day 27 or 29). Each exercise was performed on cycle ergometer (Ergoline 800S, Hoechberg, Germany) at preferred pedalling frequency. Breathing and pedalling were continuously sampled breath by breath and analyzed by an automated system (Jaeger Oxycon Alpha, Hoechberg, Germany). Incremental exercises consisted of a 3-min warm-up at 60 W, followed by an increase in load by steps of 30 W every minute until exhaustion. Constant-load exercises consisted of a 4-min resting baseline, followed by a 50-min plateau at the experimentally chosen load. During constant-load exercises, participants were allowed to take off the mouthpiece of the recording system for about 5–7 min in the first and second part of the exercise. As a consequence, constant-load exercises were divided in three parts for data analysis: from minutes 10 to 15 (Begin), from minutes 25 to 30 (Middle) and from minutes 45 to 50 (End). For the Begin, Middle and End parts, Rf /Pf was computed for each individual breathing cycle and mapped in a level 3 Farey tree1 : each observed Rf /Pf ratio was assigned to a Farey interval bounded by the corresponding ratios at level 4. This mapping in the Farey tree (Fig. 1) allowed calculation of (i) the percentage of each Farey ratio; (ii) the percentage of unimodular transitions among all observed transitions; and (iii) the average number of consecutive cycles that stay within each Farey interval. The latter variable is a local measure of stability which is an indication of the effective attractiveness of the Farey interval of interest: even if perturbed by random fluctuations always present in biological systems, the system 1 As the number of Farey ratios depends on the size of the tree (Fig. 1), we first needed to select the size of the Farey tree. Here, we used a brute force strategy to determine the size of Farey tree that best fitted the distribution of the observed ratios: we systematically tested all the Farey trees from level −1 to level 13 for each trial. As no significant differences were found, the average value (i.e., level 3 tree) was used in all analyses.
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should remain longer within a deeply attractive Farey interval than within a less attractive one. Analysis of variance (ANOVA) was used to test the effects of the experimental factors on pedalling related dependent variables (frequency, Pf ; power output, POW), respiratory related dependent variables (frequency, Rf ; oxygen uptake, V˙ O2 ; tidal volume, VT ; ventilatory flow, V˙ E ), and LRC related dependent variables (frequency ratio, Rf /Pf , percentage and local stability of each Farey ratio and percentage of unimodular transitions). For maximal tests, the experimental factors were between group treatment (EPO versus PLA) and repeated measures before and after (ref versus trt). For long duration exercises, the experimental factors were between group treatment (EPO versus PLA) and repeated measures during sessions (REF, ABS and REL) and during parts (Begin, Middle, End). Experimental effects were considered significant when the α risk probability was lower than 0.05 after Greenhouse–Geisser correction. To assess the amount of variance attributed to each significant effect, effect size (ES) was also determined [1]. A first expected result was that r-HuEPO administration resulted in a significant increase in V˙ O2 max (+8.5%) and POWmax (+9.1%) in the EPO group (group × before/after interaction: respectively, F(1, 10) = 13.36, p = 0.0044, ES = 48.50%, and F(1, 10) = 12.79, p = 0.005, ES = 68.97%). However, as far as the relations between respiration and locomotion are concerned, in constant-load exercises, no significant effects of the r-HuEPO treatment were found: Pf , Rf and Rf /Pf did not change significantly (respectively: F(2, 20) = 0.42, p = 0.659; F(2, 20) = 2.80, p = 0.085 and F(2, 20) = 2.64, p = 0.096). These results confirms that the rHuEPO treatment improves aerobic capacity in maximal tests [7], but the present contribution revealed that these changes did not elicit significant changes in LRC during submaximal long duration exercises. A second and more important part of the present results concerns the effects of exercise duration. Oxygen consumption (V˙ O2 ) was found to decrease as exercise progressed (F(2,
Fig. 2. Average oxygen gain (i.e., ratio of consumed oxygen over produced power) as a function of exercise duration. The linear decrease in oxygen gain with exercise duration reveals an increased energetic efficiency with exercise duration.
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Fig. 3. Effects of exercise duration on respiratory frequency Rf (top left panel), pedalling frequency Pf (bottom left panel) and their ratio Rf /Pf (right panel). Respiratory frequency increased with exercise duration while pedalling frequency decreased, which resulted in a progressive change in LRC towards 1/2.
20) = 6.84, p = 0.0187, ES = 18.91%). As the power output was constant during the whole exercise, this lower oxygen uptake for a given power output (Fig. 2) indicates a better energetic efficiency at the end of the exercise. As shown in Fig. 3, average respiratory frequency Rf increased with exercise duration (F(2, 20) = 42.51, p = 0.0001, ES = 57.12%) while average pedalling frequency Pf decreased (F(2, 20) = 8.38, p = 0.0097, ES = 41.54%). This combined change in the numerator and denominator resulted in an increase in the average Rf /Pf ratio (F(2, 20) = 41.6, p = 0.0001, ES = 73.89%), which evolved from about 3/8 to about 1/2 during exercise (Fig. 3, right panel) while its standard deviation was getting larger (F(2, 20) = 14.27, p = 0.0026, ES = 83.28%). We also noted that, due to a decrease in VT (F(2, 20) = 31.53, p = 0.0026, ES = 80.19%), V˙ E did not change significantly (F(2, 20) = 0.99, p = 0.387) when respiratory frequency increased with exercise duration. A detailed analysis of the mapping of the Rf /Pf ratios in the Farey tree (Fig. 4) revealed a bimodal distribution, where 1/2 and 1/3 systematically occurred more frequently than any other ratios. This result is important because it clearly indicates that the distribution of the Rf /Pf ratios is not the result of fluctuations around the mean value, and that the mean is actually a poor indicator of the effective distribution. Indeed, the bimodal distributions in Fig. 4 suggest that the observed Rf /Pf ratios result from a delicate balance between 1/2, 1/3 and the other ratios. Moreover, exercise duration changed this balance. This qualitative result was confirmed with the analysis of the occurrence of the distribution modes, showing a raising use of 1/2 from Begin to End (F(2, 20) = 7.65, p = 0.0097, ES = 34.50%) and the opposite phenomenon for the less stable 1/3, which was more frequent at the beginning than at the end of exercise (F(2, 20) = 8.28, p = 0.0087, ES = 45.05%). Hence, exercise duration induced a shift in the distribution of LRC ratios, where the mode progressively varied from 1/3 to 1/2. This change towards a ratio located higher in the Farey tree hierarchy should be accompanied
by an increase in stability and we tested this prediction by focusing on the transitions between ratios. The analysis revealed that 48% of the breathing cycles resulted in a transition to a higher or lower level in the tree and that 80% of these transitions followed the unimodular rule, yet without significant changes with exercise duration (respectively, F(2, 20) = 2.77, p = 0.7154 and F(2, 20) = 3.27, p = 0.4424). When focusing on effective local stability after a transition, a four ways ANOVA2 (i.e., treatment × session × part × mode: 1/2, 1/3) revealed that 1/3 became less attractive with exercise duration while the inverse was true for 1/2 (part × mode interaction: F(2, 18) = 9.18, p = 0.0018, ES = 23.42% as illustrated in Fig. 5). Hence, exercise duration induced a shift from a 1/3 LRC at the beginning of the exercise towards a 1/2 LRC at the end, and this shift was accompanied with an exchange in local dynamic stability (i.e., deepness of the basin of attraction), the most frequent LRC being the most stable after a transition. The aim of this study was to address LRC from a phenomenological point of view, where a collective variable such as the Rf /Pf ratio is supposed to summarise the numerous interactions among the multiple neural, muscular and physiological mechanisms involved in the regulation of locomotion and respiration. According to the hierarchy in the sine circle map, we expected higher order LRC under r-HuEPO treatment and a shift toward lower order ratios with exercise duration. A first result of the present study is the lack of change in LRC regulation after r-HuEPO treatment. The greater aerobic performance after r-HuEPO treatment did not result in significant changes in the coordination between respiration and locomotion during long duration exercise at 65% of V˙ O2 max . One possible explanation is that exercise intensity was not high enough to trigger visible adaptations. Indeed, 2 One participant (for whom transitions occurred in only 6% of the cycles) was excluded from this analysis.
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Fig. 4. Typical distributions of the LRC frequency ratios mapped in a level 3 Farey tree, for the part Begin, Middle and End of the 50-min constant-load exercises. Distributions are bimodal and progressively shift towards 1/2 (i.e., a more stable level 0 ratio) with exercise duration.
Fig. 5. Local stability index for the two modes of the Rf /Pf distribution (1/2 and 1/3) and for the part Begin, Middle and End of the 50-min exercise. An exchange of stability occurred between 1/2 and 1/3 with exercise duration: 1/3 is locally more stable at the beginning of the exercise and 1/2 is locally more stable at the end.
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oxygen deficit due to high exercise intensity seems to play a key role in fatigue resistance [8], but faster V˙ O2 kinetics after r-HuEPO supplementation tends to minimise this oxygen deficit [7]. Hence, increasing oxygen deficit with higher workload might be necessary to reveal adaptations in LRC after r-HuEPO treatment, but would make a 50-min exercise extremely difficult to sustain. A second and more important result is the significant changes in LRC that exercise duration brought out. Simultaneously with an increased energetic efficiency (Fig. 2), we observed a shift in Rf /Pf that was the consequence of a change in both Rf and Pf (Fig. 3). The increase in Rf was combined with a decrease in VT , with the result that V˙ E did not change with exercise duration. This lack of change in the global ventilatory response during exercise indicates that the reasons for the changes in Rf should be looked for elsewhere. Indeed, the starting point of the observed LRC regulations seems to be the necessary optimisation of energetic efficiency to postpone fatigue. Slowing down Pf is known to minimise the wasted internal energy due to tissues viscosity and co-contractions [10]. Hence, the better energetic efficiency gained by decreasing pedalling rate accounts for the observed changes in Pf which, in turn, result in changes in Rf , probably due to an entrainment of locomotion on respiration. The final result of this increase in energetic efficiency by decreasing Pf along with exercise duration resulted in parallel changes towards simpler LRC ratios. A third important point concerns the dynamic stability of the observed LRC ratios during exercise. About one half of the breathing cycles were followed by a transition towards a different Rf /Pf ratio, which is rather surprising for a submaximal constant-load exercise where the physiological constraints on the respiratory system remain globally invariant (i.e., steady state for ventilation [7]). The bimodal distribution of the Rf /Pf ratios indicates that the global physiological demand on the cooperation between the respiratory and locomotor systems is reached by a more subtle distribution than Gaussian variations around the mean. This observation suggests that the effective distribution of the Rf /Pf ratios is the result of a combined process, where the physiological demand acts as a global guide for the LRC in the landscape provided by the sine circle map. In other words, it seems that the observed distribution of the Rf /Pf ratios emerges from the dynamic stability principles defined by the sine circle map, which accounts locally for the multimodal distributions favouring simple ratios, and the physiological demand that globally drives the average LRC value. Based on the coupled dynamical systems perspective, the observed changes in the distribution of LRC ratios with exercise duration (Fig. 4) can be explained by the loss of stability of the higher order frequency-locking r´egimes due to raising the task difficulty [16,22]. Such a loss of stability induces transitions to wider Arnold tongues, which accounts rather well for the preferential use of the 1/2 coordination with exercise duration (Fig. 4). The present results suggest that the same dynamical principles are at work in bimanual coordination and in
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LRC, two systems with different structural properties, but where the sine circle map captures the dynamics of coupling at a macroscopic level. Although the precise nature of the coupling cannot be determined on the basis of the present contribution, the use of a pedalling task minimises the role of mechanical constraints and puts to the fore neurophysiologic reasons for LRC. As the role of spinal control, via central pattern generators and reflex loops, is essential in the generation and coordination of rhythmical behaviours in vertebrates [13], we suggest that the observed shift towards a simpler frequency locking with exercise duration might be due to a progressively rising influence of the spinal circuitry in the control of LRC. Spinal influences tend to synchronise rhythmical behaviours in a very stable 1/1 frequency locking [14,23] or in-phase coordination [6]. In this contribution, the qualitative changes in LRC observed during a 50-min cycling exercise were interpreted as the use of more stable coordination patterns according to the dynamics of the sine circle map. As in many systems of coupled nonlinear oscillators, such changes in coupling relations also characterise a more efficient response to task constrains: our results are qualitatively similar to [18] showing that runners with more stable LRC (1/1 frequency ratio) were also more efficient. In this way, more stable coordination patterns might improve efficiency to postpone fatigue in long duration exercise. Acknowledgements We wish to thank the participants in the present study and the whole staff from the “Service de Physiologie Clinique” (Prof. C. Pr´efaut) at the Hˆopital Arnaud de Villeneuve (Montpellier, France). Special thanks go to P. Connes and C. Caillaud for their support and experienced consulting. References [1] H. Abdi, Introduction au traitement statistique des donn´ees exp´erimentales, Presses Universitaires de Grenoble, 1987. [2] P.G. Amazeen, E.L. Amazeen, P.J. Beek, Coupling of breathing and movement during manual wheelchair propulsion, J. Exp. Psychol. Hum. Percept. Perform. 27 (2001) 1243–1259. [3] P. Bernasconi, P. Burki, A. Buhrer, E.A. Koller, J. Kohl, Running training and co-ordination between breathing and running rhythms during aerobic and anaerobic conditions in humans, Eur. J. Appl. Physiol. Occup. Physiol. 70 (1995) 387–393. [4] D. Boggs, Interactions between locomotion and ventilation in tetrapods, Comp. Biochem. Physiol. A: Mol. Integr. Physiol. 133 (2002) 269.
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