1 Title : The energy cost of swinging limbs during human running 2 Short title : Energy cost of swinging limbs

3 Authors : Eric WATELAIN123, Patrick AVOGADRO1, Fabrice PRIEUR4, Cyril GARNIER1 4 and François-Xavier LEPOUTRE13

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LAMIH, Laboratoire d’Automatique et de Mécanique et d’informatique Industrielles et

6 Humaines, Université de Valenciennes et du Hainaut-Cambrésis, Valenciennes, France; 7

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DUMPR : Département Universitaire de Médecine Physique et de Réadaptation, CHRU de

8 Lille, France ; 9

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IFR.25-IFRH Institut Fédératif de Recherches sur le Handicap, France ;

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LAMAPS, Laboratoire d'Analyse Multidisciplinaire des Activités Physiques et Sportives,

11 Université d’Artois, France.

12 Address for reprints and other correspondence: 13 E. WATELAIN 14 LAMIH UMR CNRS 8530 15 Université de Valenciennes et du Hainaut-Cambrésis 16 Le Mont Houy 17 59313 Valenciennes Cedex 9 18 E-mail: [email protected] 19 Website : http://eric.watelain.free.fr

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2The energy cost of swinging the limbs during human running 1 Abstract 2 The energetics of human running is complex. Some aspects, such as the metabolic cost of 3 swinging limbs, remain unexplained. More information about this aspect would allow the 4 natural strategies used during running to be better understood and could help athletes to 5 better prepare for competition. Instead of considering all the body segments used in 6 locomotion when calculating energy costs, the studies in the literature take only the 7 physiology of the lower limbs into account. Our study, on the other hand, measures 8 metabolic energy indirectly, using a mechanical approach to estimate the energetic cost of 9 swinging limbs. Our hypothesis is that swinging limbs while running has a non-negligible 10 metabolic cost, and that this cost can be evaluated during simulated running in reduced 11 gravity conditions without ground support. This hypothesis is strongly supported by the fact 12 that, in the absence of other mechanical expenditures, the net energetic cost from a 13 mechanical perspective can only be attributed to swinging body segments. 14 The aim of our research was first to measure the metabolic cost of swinging limbs during 15 suspended running by athletes (N=10) and then to study the relationship of this cost to swing 16 frequency. The actual metabolic cost was later compared to a mechanical estimation in 17 terms of efficiency. Three running speeds were investigated with three different swing 18 frequencies—spontaneous, minus 10% (SF-10) and plus 10% (SF+10)— introduced in random 19 order, for a total of 3*3 situations. Our results show that swinging the four limbs costs from 20 1.42±0.50 (2.77 m.s-1 SF+10) to 1.70±0.49 (3.93 m.s-1 SF+10) J.kg-1 per cycle. Depending on 21 the conditions and corrections, this cost ranges from 19.5 to 34.4% of the total metabolic 22 cost of running. The relationship between metabolic cost and swing frequency was 23 polynomial and may partially explain the spontaneous human strategy of increasing stride 24 length as speed increases rather than increasing swing frequency. The efficiency estimations 25 reveal an important and surprising ratio that requires more investigation. Two possibilities 26 must be verified: the first is that an unanticipated phenomenon, overburdens subjects with 3

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4The energy cost of swinging the limbs during human running 1 internal work when they were suspended; the second is that the internal work was 2 underestimated in the equations used in this study. 3 4 Key words: exercise; oxygen consumption; internal work; swing frequency; simulated 5 running.

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6The energy cost of swinging the limbs during human running 1 Nomenclature 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

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% = percentage η = efficiency bmp = heartbeat per minute CMb = body's center of mass CMl = lower limb’s center of mass Cs = energy cost of swinging the four limbs in simulated running Csc = energy cost of swinging the four limbs after correcting the stance phase d = duty factor or ratio of the stance phase on step Emecha = mechanical energy Emeta = metabolic energy Fc = cardiac Frequency Hz = Hertz J.kg-1.cycle-1 = Joules per kilogram per running cycle J.kg-1.m-1 = Joules per kilogram per meter kg = kilogram KJ = kilojoules KJ.L-1 = kilojoules per liter [Lac] = blood lactate concentration m = meter  = total metabolic power M m.s-1 = meters per second min = minute mL = milliliter ml.min-1 = milliliters per minute mmol.L-1 = millimols per liter O2.kg-1 = oxygen per kilogram OEE = Oxygen Energy Equivalent q = compound dimensionless term accounting for limb geometry and fractional mass RER = Respiratory Exchange Ratio RF = Respiratory Frequency s = second SF = spontaneous Swing Frequency SF+10 = imposed free Swing Frequency plus 10% SF-10 = imposed free Swing Frequency minus 10% SFs2.77 = spontaneous Swing Frequency at 2.77 m.s-1 SFs3.35 = spontaneous Swing Frequency at 3.35 m.s-1 SFs3.93 = spontaneous Swing Frequency at 3.93 m.s-1 t = time v = running speed  co = rate of expired carbon dioxide production V 2 EV = Expiratory Volume  o = rate of oxygen consumption V 2 ˆ W int = estimated internal Work W.kg-1 = Watts per kilogram

8The energy cost of swinging the limbs during human running 1 Introduction 2 Over the last century, the energetics of locomotion has been widely studied in order to 3 evaluate, model, or simply better understand its underlying mechanisms. These inquiries 4 have been conducted from the perspective of metabolic energy (e.g., Lacour et al. 1990; 5 Ardigò et al. 1995), mechanical energy (e.g., Anderson, 1996 or Arampatzis et al. 2000 for 6 a review) or both (e.g., Heglund et al. 1982; Minetti et al. 2000; Avogadro et al. 2003; 7 Slawinski & Billat, 2004; Di prampero et al. 2005). Efficiency (η, the ratio of metabolic 8 energy to mechanical energy) in human running has generally been found to be between 9 40% and 50% (Fenn, 1930a; Fenn, 1930b; Cavagna et al. 1964). More recently, Cavagna & 10 Kaneko (1977) and Willems et al. (1995) found a progressive increase in η from 50% to 11 60% at running speeds around 5 m.s-1 speed, while Slawinski & Billat (2003) reported 12 efficiency rates of 83% for elite marathon runners. For a subject pool including a large 13 variety of animals as well as humans, and a wide range of speeds, Heglund et al. (1982) 14 reported that η improved with speed from 40% to 73% for speeds ranging from 0.91 to 8.89 15 m.s-1. This level of efficiency is quite surprising given that muscle efficiency is typically 16 around 25%. If we exclude experimental error, numerous mechanisms for energy 17 generation, absorption and restitution must clearly be involved. 18 It is easy to quantify the resting metabolism and the net energy consumed during exercise. 19 However, it has proved more difficult, though not impossible, to identify the relative 20 contributions of external work (the movement of the body's centre of mass, or CMb) (Fenn, 21 1930a; Fenn, 1930b; Cavagna & Kaneko, 1977)), internal work (the movement of the limbs 22 around the CMb) (Fenn, 1930a; Fenn, 1930b; Cavagna & Kaneko, 1977; Minetti & Saibene, 23 1994) and elastic energy (the energy stored and restituted by the locomotive system during 24 movement) (Cavagna et al. 1964; Cavagna et al. 1971; Williams & Cavanagh, 1983;

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10The energy cost of swinging the limbs during human running 1 Cavagna et al. 1976; Cavagna 1977; Ker et al. 1987; Sasaki & Neptune, 2006), as well as 2 the cost of cardiopulmonary and/or other physiological effort during locomotion (Åstrand & 3 Rodhal, 1986; Coast et al. 1988; Ellerby et al. 2005). The relationship between the 4 mechanical work produced by muscles and the external work produced by the body segment 5 has been studied during isolated, knee-extension movements by Sjøgaard et al. (2002) and 6 during cycling by Hansen et al. (2004). Research has also been able to differentiate between 7 the internal power generated by the muscle to overcome energy changes of the moving body 8 segment and the external power produced. For example, Sjøgaard et al. (2002) validated an 9 internal power model using metabolic measurements, noting a 3rd-order polynomial 10 relationship between the internal power and the contraction rate and metabolic consumption. 11 Hansen et al.'s graph (2004) of the internal power in relation to the pedaling rate also 12 demonstrated a polynomial relationship. 13 Some aspects of human locomotion, specifically walking and running, remain unexplained. 14 Although it has long been felt that the energetic cost of swinging limbs was negligible 15 (Kram & Taylor, 1990), some recent studies involving helmeted Guinea Fowl (Marsh et al. 16 2004; Ellerby et al. 2005) and humans (Doke et al. 2005; Modica & Kram, 2005; Gootschall 17 & Kram, 2005) have reported a substantial cost related to swinging lower limbs. Modica & 18 Kram (2005) state that swinging limbs can cost as much as one third of the total energy 19 expended during locomotion. Gottschall & Kram (2005) describe a metabolic cost of 20 initiating and propagating leg swings between 10% and 15% of the cost of human walking 21 at a speed of 1.25 m.s-1. Meyers & Steudel (1985), who studied the effect of limb mass and 22 its distribution on the energetic cost of running, also support the hypothesis that the cost of 23 swinging limbs is not negligible. Long ago, Fenn (1930; 1930b)—and later others (Cavagna 24 & Kaneko, 1977; Winter, 1979; Minetti, 1998)—offered insight into the mechanics of 25 "internal work" ( Wˆ int ). Still, to the best of our knowledge, relatively little data has been 11

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12The energy cost of swinging the limbs during human running 1 produced about the energetics of swinging limbs while running. In a study by Modica & 2 Kram (2005), the running pattern was manipulated by an external swing assist device that 3 helping the feet to return forward during aerial phase, but they did not calculate the energy 4 cost of simply swinging the four limbs (Cs). 5 Given what seems to us to be a lack of information on this subject, we felt that it would be 6 interesting to determine the energetic cost of swinging limbs in the patterns and frequencies 7 encountered in running, or at least something similar. Unfortunately, however, though a 8 swinging arm does not interact with the ground, a swinging leg does, since it provides 9 support to the body half a cycle later. This leg-ground interaction makes it difficult to 10 separate the energy expanded by swinging limbs during the swing phase of running from the 11 energy needed during one step to support and accelerate the body from the contact phase to 12 the following flight phase. However, using a simple procedure, it is possible to isolate the 13 body from the supporting ground. Though the dynamic conditions in the simulation may 14 differ slightly from those in real running, the kinematic pattern of the limbs during running 15 can be reproduced. The principle of partial or total reduced-gravity conditions—in studies of 16 humans suspended above the ground—has already been used in the literature (e.g., He et al., 17 (1991); Farley & McMahon (1992); Chang et al., (2000)). Results from this kind of studies 18 have been used in human locomotion in other environments, for example, on other planets 19 (e.g., Cavagna et al. 1999 or Minetti, 2002).

20 The present study was designed to measure the cost of swinging (Cs) during sessions of 21 simulated running and subsequently to determine the relationship between the swing 22 frequency (SF) and the energetic cost. Our hypothesis was that the energetic cost would 23 increase with SF. Given the results reported by Sjøgaard et al. (2002), we further 24 hypothesized that the relation would not be linear and that suspended running would allow

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14The energy cost of swinging the limbs during human running 1 the internal work alone to be quantified. Using the results of our simulations, we compared 2 the energetic cost of ‘swinging limbs’ to the real cost of running and to the internal work 3 value predicted using a mechanical equation. This comparison provides a starting point for a 4 preliminary discussion of the efficiency (η) of internal work in human running.

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16The energy cost of swinging the limbs during human running 1 Material and methods 2 Subjects 3 Ten subjects gave their informed consent to participate in this experiment, which was 4 approved by the local ethics committee. The entire study was conducted according to the 5 guidelines stated in the Declaration of Helsinki. Subjects were screened to correspond to the 6 various inclusion/exclusion criteria. Inclusion criteria were : male; physically active; 7 absence of important injury in the past 10 years; absence of musculo-skeletal ailments, 8 scoliosis or other deformation of the spinal column; joint replacement; recent surgery; use of 9 medication; and/or a history of neurological, pulmonary, cardiac or locomotive disorders. 10 The only exclusion criterion was the inability to run at least 30 minutes at the maximal 11 speed specified in the experimental protocol (3.93 m.s-1) tested on treadmill in the 12 laboratory.

13 Material 14 Subjects were seated on a custom-designed saddle and wore a safety harness designed to 15 stabilize the body and to prevent falls during the sessions. The saddle was supported by two 16 straps attached to a rigid, heavy-gauge steel frame (3 x 3 x 3m) and one strap attached to the 17 ground. The harness was itself attached to the steel frame by one strap on the subject's back 18 (at the level of the 4th dorsal vertebra) and by two straps attached to a wooden beam above 19 the subject's head that kept the shoulders level (Fig. 1). Between sessions, two chairs (one 20 for each foot) were provided to allow the subject to rise up off the saddle and thus avoid any 21 potential pain resulting from prolonged contact between the ischium and the saddle. 22 Cardiac frequency (Fc) was recorded using a cardiofrequency meter (Polar Electro S710i, 23 Kempele, Finland). Using an expired gas analyzer (CPX/D Medical Graphics, St Paul,  o in ml.min-1), respiratory frequency (RF), 24 USA), the oxygen consumption rate ( V 2

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18The energy cost of swinging the limbs during human running  co and 1 expiratory volume (EV), and respiratory exchange ratio (RER, the ratio between V 2  o ) were measured. The values of Fc, V  o , RF, RER for the last 30s of each session were 2 V 2 2  o measured during the 3 averaged. In addition, in order to obtain net values, the value for V 2 o 4 initial rest period (subject in a suspended position) was subtracted from the average V 2 5 value for each session. 6 During the initial rest period and immediately at the end of each session, blood samples 7 were taken by pricking subject fingertips; these samples were analyzed within the hour. 8 Blood lactate concentrations ([Lac]) were measured using a Dr Lange Miniphotometer Plus 9 LP20 (Lange GmbH, Berlin, Germany). 10 The spontaneous SF of each subject was measured in the laboratory on a Proform 785 11 treadmill, (Proform, Logan, USA). The speed error induced by the treadmill was less 12 than 1%. A metronome (MA-30, Korg Inc, Tokyo, Japon) was also used to demonstrate the 13 appropriate running frequency to the subject, who was asked to match this frequency as 14 closely as possible.

15 Methods  o using the O2 energy 16 The metabolic energy (Emeta) was calculated as the product of V 2 17 equivalent (OEE), which was calculated as shown in Eqn 1 (Åstrand & Rodhal, 1986; 18 Medbo et al. 1986).   1 − RER   RER − 0.7    + 21.13 ⋅    , 19 OEE (KJ)= 19.6 ⋅  0.3  0.3    

20 where RER 1, OEE was assumed to be 21.13 KJ.L-1

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(1)

20The energy cost of swinging the limbs during human running 1 The first [Lac] value was determined from a blood sample taken during the initial suspended 2 rest period. To determine the energy derived from the lactic pathway, the [Lac] value at the 3 end of the intial session was subtracted from the value measured at the end of the following 4 session. Then the value from this session was subtracted from the value for the next session, 5 and so on. It was assumed that an increase of 1 mmol.L-1 in the [Lac] value provided as 6 much energy as 3.3 mL O2.kg-1 (Margaria & Aghemo, 1971). Despite the important new 7 functions and uses of lactates in body that have been identified for the lactates since 1971 8 (see Brooks, 2002a et b; Gladden, 2004; or Phils et al., 2005 for reviews), the use of lactates 9 to estimate anaerobic pathways has not been totally excluded. The total metabolic power (  , W.kg-1) was subsequently calculated with, and without, the energy derived from oxygen 10 M 11 consumption and the energy derived from the lactic pathway for one second of time (Eqn 2). 12 These two estimations were then compared.

13 M (W.kg-1) =

E meta + [ Lac ] ∗ 0.033 * 21.13 , t

(2)

14 where t= acquisition time in s (see protocol).

 to SF for each subject and 15 The value of Cs (J.kg-1.cycle-1) was calculated as the ratio M 16 each session (Eqn 3), and Wˆ int (in J.kg-1.m-1) was estimated using the equation proposed by 17 Minetti (1998), presented in Eqn 4. 18 Cs (J.kg-1.cycle-1) =

M SF

  d 2    * q , 19 Wˆ int (J.kg .m )= SF * v * 1 +  1 − d     -1

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-1

(3)

(4)

22The energy cost of swinging the limbs during human running 1 where SF is expressed in Hz and v (the speed), in m.s-1; where d (the duty factor) is the ratio 2 of the stance phase to the step phase, and q (compound dimensionless term) = 0.1. 3 4 Because in this study, the subjects never touched the ground, the raw data slightly 5 overestimates the real internal work. In fact, when the lower limbs touch the ground during 6 real running, the internal work during the stance phase is necessarily lower than during the 7 swing phase because the segment speed is lower. In addition, the subject does not have to 8 work to sustain the lower limb and thus does not generate force against gravity. Based on 9 the estimations of mechanical work (Slawinski (2003); Slawinski & Billat (2004); Slawinski 10 & Billat, 2005) on all running cycles, the lower limb's internal work during the stance phase 11 and during the swing phase were estimated separately, and the lower limb's internal work 12 overestimation during the stance phase was subtracted from the estimation. For this, the 13 internal work during the stance phase corresponds to around 10% of all cycles for 38% of 14 the gait cycle. We examined the equivalent physiological energy used during all the gait 15 cycles and then created correction ratios based on the mechanical differences. After 16 correction, the internal work ranges from 76.6% to 79.7% of the raw internal work. This 17 correction allowed a corrected Cs (Csc) to be determined. 18 The Emeta values for real running—found in studies by Le Bris et al. (2005), Heise & Martin 19 (1998), Martin (1985) and Minetti et al. (1994), whose study populations were very similar 20 to ours and who used the same running speeds that we did—were compared with those from 21 our simulations. For similar conditions, the Emeta values were consistent with those in these 22 studies. The means values used were 33.82, 37.41 and 44.93 ml.m-1.kg-1, respectively, for 23 2.77, 3.35 and 3.93 m.s-1.

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24The energy cost of swinging the limbs during human running 1 Protocol 2 Subjects completed 3 sessions, each separated by at least 24 hours. During the two first 3 sessions, subjects were asked to run on a motorized treadmill for 10-15 min (Schieb, 1986) 4 to familiarize themselves with the desired pattern, and were then asked to reproduce the 5 same running pattern while sitting on the saddle. During the first of these training sessions, 6 the subject was given oral feedback about how he swung his limbs while sitting on the 7 saddle, as compared to while running on the treadmill. Transferring the pattern clearly 8 requires a lot of time: from 30-70 minutes for the subjects of this study. In the second 9 session, the spontaneous swing frequencies of each subject were measured while running at 10 2.77 (SFs2.77), 3.35 (SFs3.35) and 3.93 m.s-1 (SFs3.93), by counting the number of steps taken in 11 one minute. 12 The third session included no time on the treadmill except for a five-minute warm-up 13 period. The subjects were then asked to seat themselves directly on the saddle and the safety 14 harness was put in place and adjusted. Then, with only the time necessary to become 15 correctly suspended (at least 5 min), the subjects were asked to remain stationary, suspended  o at rest was measured. After that, a blood sample was 16 in the apparatus, for 2 min. while V 2 17 taken to establish [Lac] at rest. 18 Subjects were then asked to mimic their individual running patterns, as they did during the 19 training sessions, at paces corresponding to SFs, SFs-10% (SF-10) and SFs+10% (SF+10) ; 20 These paces are similar to those used in the 1997 study by Cavagna et al.. Since, in addition 21 to the 3 different SF values, there were also 3 different velocities, each subject had to swing 22 his limbs in 9 frequencies conditions, in random order. Subjects were asked to follow the 23 pace set by a metronome producing a given swing frequency so that the time between two 24 consecutive beeps corresponded to one step. The time elapsed between 40 steps was 25 measured during each trial in order to calculate the effective swing frequency. Each

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26The energy cost of swinging the limbs during human running  o to stabilize. A rest of 4 minutes was 1 frequency condition run lasted 4 minutes to allow V 2 2 allowed between runs, in order to avoid possible pain and/or fatigue.

3 Statistics 4 Statistical analyses were conducted. Student t-tests for identifying emerging groups were 5 applied to compare total power with and without a lactate pathway. A one-way ANOVA for  o , [Lac], Fc, M  and 6 repeated measurements was used to test the differences between the V 2 7 Cs for each frequency condition run. Repeated ANOVA measurements were also completed 8 to test the Fc, EV and [Lac] values for the nine successive frequency conditions. The 9 Scheffe test, the most conservative of the post-hoc tests, was chosen, and the regression  and SF was calculated and verified statistically. Any value attaining p