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Does training have consequences for the walk–run transition speed?
Human Movement Science 22 (2003) 1–12 www.elsevier.com/locate/humov
Does training have consequences for the walk–run transition speed? Helene Beaupied *, Franck Multon, Paul Delamarche Laboratoire de Physiologie et de Biom ecanique de 1ÕExercice Musculaire, UFR. APS, Universit e Rennes, 2, Avenue Charles Tillon, CS 24 414, 35044 Rennes, France
Abstract A number of authors when studying the walk–run transition phenomenon focused either on the mechanical or energy expenditure whilst only a few used both parameters concurrently. Moreover the literature demonstrates that the contribution of these variables changes along with the level and method of training. Consequently the purpose of this study is to find, by analyzing concurrently these two variables, if the walk–run transition speed is linked to the type of training. To this end we calculated two theoretical transition speeds: one based on the metabolic energy expenditure St1 and the second one based on the internal work St2 . Subjects were divided into three groups (untrained, sprint and endurance-trained men) who were required to walk and run on a treadmill at increasing speeds. Firstly we show that the relationship between St1 and St2 differs depending on the groups. Sprinters have a significantly lower St2 than St1 whereas the opposite is found for untrained subjects. We also show that the transition speed is linked to the subjectÕs type of training. To conclude it seems that acquiring running techniques through specific training has consequences for the walk–run transition phenomenon. 2002 Elsevier Science B.V. All rights reserved. PsycINFO classification: 4010; 3720 Keywords: Internal work; Energy consumption rate; Walking; Running
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Corresponding author. Tel.: +33-2-99-14-17-78; fax: +33-2-99-14-17-74. E-mail address: [email protected] (H. Beaupied).
0167-9457/03/$ - see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-9457(02)00139-2
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1. Introduction Human locomotion can be subdivided into two different modes. Walking can be characterized as an alternating sequence of single and double support phases. In contrast, running involves alternating sequences of support and nonsupport phases (Vaughan, 1984). The literature points out that a transition between walking and running occurs when walking speed is gradually increased (Hreljac, 1993a; Margaria, Cerretelli, Aghemo, & Sassi, 1963; Mercier et al., 1994; Nilsson, Thorstensson, & Halbertsma, 1985). Because of the large number of variables involved, it is difficult to specify fundamental laws governing this transition. One way of evaluating the efficiency of human motor performance is to measure energy expenditure during movement (Heglund, Fedak, Taylor, & Cavagna, 1982; Kyr€ ol€ ainen, Komi, & Belli, 1995; Pollock, Foster, Knapp, Rod, & Schmidt, 1987), and early studies tested the relation between the transition from walking to running and the metabolic energy expended during both types of locomotion. The theoretical transition speed (TTS) (St) is defined as the speed where the oxygen consumption while walking becomes greater than the consumption while running. Margaria et al. (1963) estimated the oxygen consumption as a function of both walking speed and running speed and determined the speed at which the resulting curves intersected. This speed was approximately 2.36 m s1 . Several other physiological parameters, such as heart rate, have been analyzed in a similar way resulting in about the same transition speeds (Mercier et al., 1994). These studies concluded that the transition occurs in order to decrease energy expenditure. However, some authors (Brisswalter & Mottet, 1996; Hreljac, 1993a; Mercier et al., 1994) observed that the theoretically predicted speed was generally higher than the actual transition speed. Therefore Nilsson et al. (1985) suggested that kinematic parameters might also play a role. They observed that the transition from walking to running was accompanied by a decrease in stride length and an increase in stride frequency. These observations, however, were not supplemented by an analysis in terms of mechanical work. In order to overcome these limitations new investigations have been carried out by calculating the internal work required for each mode. Just like for energy expenditure Minetti, Ardigo, and Saibene (1994) proposed to calculate the theoretical intersection point between the functions relating the internal work to speed during both walking and running, estimating the internal work on kinematic measurements. In Minetti et al.Õs experiment (1994), subjects were asked to walk at a differing range of speeds, even if they would naturally prefer to run for some of them. In order to obtain two TTSs, energy expenditure and internal work were measured simultaneously. To sum-up, with the exception of Minetti et al. (1994), previous studies focused on either energy expenditure or mechanical work. Moreover, most authors did not report if their subjects were untrained or trained. However, the energy expenditure of trained people while running is known to be less than that of untrained ones (Pollock et al., 1987), so we wondered whether the TTSs will be influenced by training. Because the kind of training (sprint or endurance training) has different influences on
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the energetic expenditure while running (Kyr€ ol€ ainen et al., 1995; Pollock et al., 1987) this might also affect the TTSs. Our study has been designed to investigate if training, and the type of training has consequences for the theoretical transition point between walking and running. To this end subjects including untrained, sprint and endurance trained people were recruited. For the subjects in each group the energetic expenditure and the internal work required while walking and running were determined. 2. Methods 2.1. Subjects Written informed consent was obtained prior to the study. The subjects, 15 males, were free of any disease that might affect gait. They were divided into three groups of five: untrained, sprinters and endurance-trained athletes. The sprinters and endurance-trained athletes trained for a minimum of 12 h per week in their respective speciality. The height and the weight of each subject are given in Table 1. Average values and standard deviations of height and weight were respectively 1:76 m 0:07 and 68:7 kg 4:7 for the untrained group, 1:84 m 0:07 and 77:9 kg 5:7 for the sprint group and 1:76 m 0:02 and 67:5 kg 3:4 for the endurance-trained group. 2.2. Experimental task Prior to the experimental procedure, subjects were familiarized with the treadmill by performing treadmill locomotion for a minimum of 15 min (Charteris & Taves, 1978). Table 1 Anthropometric data of the subjects: height (m) and mass (kg) Group
Height (m) (mean SD)
UNT1 UNT2 UNT3 UNT4 UNT5
Untrained Untrained Untrained Untrained Untrained
1.79 1.72 1.85 1.65 1.79
(1.76 0.07) (1.76 0.07) (1.76 0.07) (1.76 0.07) (1.76 0.07)
72.8 (68.7 4.7) 68 (68.7 4.7) 74 (68.7 4.7) 62.7 (68.7 4.7) 66.3 (68.7 4.7)
SP1 SP2 SP3 SP4 SP5
Sprinter Sprinter Sprinter Sprinter Sprinter
1.83 1.85 1.72 1.91 1.91
(1.84 0.07) (1.84 0.07) (1.84 0.07) (1.84 0.07) (1.84 0.07)
81 (77.9 5.7) 75 (77.9 5.7) 69.3 (77.9 5.7) 83.2 (77.9 5.7) 81 (77.9 5.7)
END1 END2 ENDS END4 END5
Endurance-trained Endurance-trained Endurance-trained Endurance-trained Endurance-trained
1.75 1.79 1.77 1.75 1.76
(1.76 0.02) (1.76 0.02) (1.76 0.02) (1.76 0.02) (1.76 0.02)
67.5 (66.6 3.4) 68 (66.6 3.4) 62.5 (66.6 3.4) 64 (66.6 3.4) 71 (66.6 3.4)
Values are mean SD.
Mass (kg) (mean SD)
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Each subject was required to walk at five different speeds (0.98, 1.53, 2.08, 2.36, 2.64 m s1 ) during a first session and then to run at six different speeds (1.53, 2.08, 2.36, 2.92, 3.88, 4.44 m s1 ) during another session. In order to reach their steady state, the subjects walked and ran at each speed during about five minutes. The choice of speeds ensured that the two modes had three speeds in common. During exercise, the oxygen consumption was measured and three-dimensional kinematic data were recorded. 2.3. Apparatus and measurements Subjects had to walk and run on a treadmill. Respiratory variables and gas exchanges were measured using a breath by breath automatic metabolic system (CPX, Cardio2, Breeze 2, Medical Graphics, St Paul, Minnesota). Briefly, expiratory airflow was measured using a pneumotachograph and expired gases were analyzed. When subjects reached steady state during exercise, we measured oxygen uptake (V_ O2 in ml min1 kg1 ), CO2 output (V_ CO2 in ml min1 kg1 ), and the respiratory exchange ratio (RER). The RER was calculated as the rate of carbon dioxide production divided by the rate of oxygen consumption. The energy consumption rate (ECR) for each subject, expressed in joules per kilogram body mass per minute was then determined for each walking and running speed (Peronnet & Massicotte, 1991). The ECR as a function of speed, permitted the estimation of regression equations for walking and running for each subject. According to previous studies (Conley & Krahenbuhl, 1980; Minetti et al., 1994; Taylor, 1994) the regression equations are quadratic for walking and linear for running. The ECR for subjects who were unable to walk at the highest speed were extrapolated on the basis of the regression equation. We then calculated the transition speed St1 for each subject by calculating the intersection of the two regression lines. In order to estimate the internal work, we used a VICON370 system (Oxford Metrics, UK). This system was composed of seven infrared cameras cadenced at 60 Hz and a set of spherical markers. The views from the cameras were gathered and processed by using a DLT algorithm that made it possible to capture the 3D position of each marker as a function of time. During exercise, 24 markers were placed over standardized anatomical landmarks (identical to those used by Winter (1979)) in order to register the motion of the body segments. The human body was modeled as 11 rigid linked segments (trunk, forearms, upper arms, thighs, shanks, feet). A second order Butterworth filter was used to smooth the position–time data for anatomical landmarks. The kinematic data were used to estimate the internal work. As human locomotion can be considered as a quasi-cyclic motion (Winter, 1990), calculations were only performed with one complete stride for all the studied speeds. The stride cycle was defined as the period from the right toe off to the same event in the following cycle. Three different global frames were used during calculations (Fig. 1). The treadmill frame Rt ðO0 ;~i;~ j; ~ k Þ in translation with the Galilean frame RðO;~i;~ j; ~ k Þ link in the laboratory, the barycentric frame was noted R ðG;~i;~ j; ~ k Þ where the center of mass G is the origin of the frame and axes are the same as for the Galilean frame. Moreover
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Fig. 1. The human body and the different frames used in the study. The Galilean frame linked to the laboratory RðO;~ i ;~ j; ~ k Þ, the frame linked to the treadmill Rt ðO0 ;~i;~ j; ~ k Þ, the barycentric frame R ðG;~i;~ j; ~ k Þ and the frames linked to the 11 body segments Ri ðGi ;~ u;~ v; ~ wÞ.
eleven local frames, one linked to each segment Si , were also used and denoted Ri ðGi ;~ u;~ v; ~ wÞ where ~ w is the longitudinal axis and ~ u is the transverse axis of each body segment. Body segment parameters were determined for each subject, based on DempsterÕs anthropometric data (Dempster, 1955). The total mechanical energy of the body is defined by the equation i¼11 X 2 E ¼ ð1=2ÞMVG=R þ ðmi ghi þ ð1=2Þmi VG2i =R þ ð1=2ÞIi w2i Þ ðJÞ t i¼1
where M is total mass, mi is mass of the ith body segment, g is gravitational acceleration, hi is height of the ith segment center of mass ðGi Þ in the Galilean frame RðO;~i;~ j; ~ k Þ, VG=Rt and VGi =R are the linear velocity of the center of mass (G) relative to Rt and the linear velocity of Gi relative to the barycentric frame R respectively, Ii is the inertial matrix of the ith segment and wi is the angular velocity of the ith segment. The calculation of the internal work was based on WinterÕs (1990) method. The internal work was calculated on the assumption of a complete energy transfer within and between all segments: Wint ¼
j¼tf X
jDEj j ðJÞ
ð1Þ
j¼t0
where Wint is the work due to the internal forces, DE is the mechanical energy variation between two successive frames and t0 and tf are the beginning and the end of the stride respectively. Then, in order to compare the different groups, for each subject the internal work was divided by the time of the complete stride for each walking and running speed.
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The mechanical transition speed (St2 ) was determined for each subject with the same method used for the ECR, implying that St2 was defined as the intersection between the two regression lines (for walking and running). After assessment of St1 and St2 for each subject, the mean values and standard deviations of these TTSs for each group were calculated. Due to the small sample size we first verified the Gaussian distribution of the data using a specific test (Shapiro–Wilk). An repeated measures one way Anova has been used to test the effect of groups on the TTSs. To test the difference between St1 and St2 values for the three groups, a single parameter analysis of variance was carried out. A value of a ¼ 0:05 was accepted as the level of statistical significance.
3. Results The transition speeds St1 and St2 were calculated for the three groups using the two methods. Figs. 2–4 show the relation between the ECR and speed while walking and running for untrained, sprinter and endurance-trained groups, respectively. The bars in the figures stand for the standard deviation calculated for each point. Untrained subjects and sprinters could not walk at the highest imposed speed (2.64 m s1 ), whereas the endurance-trained subjects succeeded in doing so. Relations between the ECR and walking speeds are quadratic with correlation coefficients 0.99 for each of the groups. These results are in accordance with the literature (Burdett, Skrinar, & Simon, 1983; Minetti et al., 1994). Relations between ECR and running speed are linear, with a correlation coefficient 0.99 for the untrained and endurance-trained groups respectively and 0.98 for the sprinters. These energy expenditure results are also compatible with the literature (Conley & Krahenbuhl, 1980; Taylor, 1994). Let us now consider the transition speeds computed for the three groups. Mean values and standard deviations of St1 are 2:29 0:04, 2:44 0:06 and 2:30 0:05 m s1 for the untrained, sprinter and endurance-trained groups, respectively. These results are in agreement with transition speeds reported earlier, which ranged from 2.16 to 2.36 m s1 (Hreljac, 1993b; Margaria et al., 1963; Mercier et al., 1994) without taking training into account. Statistical analysis shows significant differences
Fig. 2. The relation between the ECR (J kg1 min1 ) and the walking and running speeds (m s1 ) for the untrained group. Values are mean SD.
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Fig. 3. The relation between the ECR (J kg1 min1 ) and the walking and running speeds (m s1 ) for the sprinter group. Values are mean SD.
Fig. 4. The relation between the ECR (J kg1 min1 ) and the walking and running speeds (m s1 ) for the endurance-trained group. Values are mean SD.
(a < 0:05) in St1 values between the sprint and endurance-trained group and between the sprint and untrained group. The relation between internal work and walking and running speed (Figs. 5–7) was plotted for the untrained, sprint and endurance-trained group, respectively. Untrained subjects could not run at a speed higher than 3.88 m s1 . Relations between internal work and walking and running speed are quadratic for each group. The correlation coefficients are 0.99 for the three groups during walking and running. Mean values of the internal work are in agreement with previous studies (Belli, Avela, & Komi, 1993; Fukunaga & Matsuo, 1980; Kyr€ ol€ainen et al., 1995). Mean values and standard deviation of the calculated St2 are 2:65 0:07, 2:19 0:05 and 2:29 0:04 m s1 for the untrained, sprinter and endurance-trained groups, respectively. These speeds are greater than the ones obtained by considering kinematic or kinetic data (Mercier et al., 1994; Minetti et al., 1994). In general, in the literature, the speeds calculated with kinematic or kinetic data are lower than the ones calculated with the energy expenditure method. Let us consider the two transition speeds for each group of subjects. For untrained subjects, the Anova showed a St1 significantly less than St2 (a < 0:0001). The difference between St2 and St1 (St2 St1 ) was 0.36 m s1 . For the sprinter subjects St1 was significantly greater than St2 ða < 0:01Þ. The difference is )0.25 m s1 .
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Fig. 5. The relation between the internal work (J s1 kg1 ) and the walking and running speeds (m s1 ) for the untrained group. Values are mean SD.
Fig. 6. The relation between the internal work (J s1 kg1 ) and the walking and running speeds (m s1 ) for the sprinter group. Values are mean SD.
Fig. 7. The relation between the internal work (J s1 kg1 ) and the walking and running speeds (m s1 ) for the endurance-trained group. Values are mean SD.
Finally, no significant difference appeared between St1 and St2 for the endurancetrained subjects: the two speeds were about the same. 4. Discussion We studied the walk–run transition through the analysis of two variables: the energy expenditure and the internal work. From these two variables we calculated the
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crossover point (providing the TTS) between the curves corresponding respectively to walking and to running. Our results showed that the training and the type of training (sprint or endurance-training) influenced the TTS values St1 (obtained with the energy expenditure measurements) and St2 (obtained with the internal work calculations). In the present study, St1 values were equal to 2:29 0:04, 2:44 0:06 and 2:30 0:05 m s1 for the untrained, sprinter and endurance-trained groups, respectively. Literature reported values of 2.10 m s1 (Turvey, Holt, LaFiandra, & Fonseca, 1999), 2.16 m s1 (Mercier et al., 1994), 2.24 m s1 (Hreljac, 1993b) and 2.36 m s1 (Margaria et al., 1963) without accounting for the subjectsÕ training status. Hence, our results were similar to those presented in the literature. St2 values presented in this paper were 2:65 0:07 m s1 for untrained subjects, 2:19 0:05 m s1 for sprinters and 2:29 0:04 m s1 for endurance-trained subjects. Three main methods were currently used in the literature to evaluate the transition speed by considering a mechanical point of view. The first method evaluated the socalled ‘‘preferred transition speed’’ PTS (Hreljac, 1993b) which value was 2.06 m s1 . The PTS was obtained by asking the subjects to use the natural gait of walking or running, as preferred, during 30 s for selected speeds. The PTS was then defined as the minimum speed for which the subject chose to run. The second method consisted in increasing continuously the treadmill speed and to notice the one for which the subject began to run. This speed (denoted the ‘‘natural transition speed’’ NTS) was equal to 1.89 m s1 in the study by Noble et al. (1973) and to 2.17 m s1 in the study of Beuter and Lefebvre (1988). The third method required the subjects to walk or run at selected speeds during a few minutes in order to reach a steady state. The ‘‘theoretical transition speed’’ (TTS) was obtained by the crossover point method. A TTS of 2.5 m s1 was found by Grillner, Halbertsma, Nilsson, and Thorstensson (1979) by focusing on kinematic parameters, and of 1.8 m s1 by calculating internal work (Minetti et al., 1994). As presented above, the literature provided us with various transition speeds ranging from 1.8 to 2.5 m s1 . One can wonder why such results were so different. First, these differences could be due to the addition of measurement and computation inaccuracies. Especially for internal work calculations, several possible inaccuracies could occur, including the external markers displacements over the skin, anthropometrical data used to calculate mass and inertia, derivation method. Our work showed significant differences in transition speeds depending on the training status. Inaccuracies cannot be held responsible for these significant differences and can therefore consequently be neglected. Second, the previous works dealing with TTS by considering a mechanical point of view did not always focus on the same parameters and did not use the same protocol. For example, protocols requiring long measurement (to reach the steady-state) could engender different results than those carried out during short sequences. Finally, no information about the subjects training status was provided in the past works. Our main result showed that significant differences (a < 0:05) in St2 occurred between untrained, sprinters and endurance trained subjects (with both energy expenditure and internal work measurements). In previous studies, trained and
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untrained subjects may have been mixed. Because training status influenced energy consumption and internal work, techniques involving these two kinds of measurements might reflect the effect of training. In our experiment, energy expenditure and internal work were measured during the same experiment so that comparisons between these two values could be carried out. Interpreting differences between St1 values and between St2 values from different groups would be hazardous. For example, let us consider a group of subjects A and another group B. Several explanations could be proposed for the fact that AÕs St1 is higher than BÕs one. As St1 is the crossover point of two curves (one calculated while walking and the other while running), a higher AÕs St1 can be due to: • A lower energy expenditure while walking at a speed around St1 for A compared to B, that shifts the crossover point to the right, • A higher energy expenditure while running at a speed around St1 for A compared to B, that also drives to the same result, • A combination of these two possibilities. The same possibilities can be proposed for St2 . Nevertheless, the values found in the present study for St1 and St2 depending on the training status raises interesting hypotheses. St1 was the highest speed for which the energy expenditure while walking was lower than the one for running. St2 was the highest speed for which the internal work while walking was lower than the one for running. St1 was lower than St2 for untrained subjects. This relation means that, for speeds greater than St1 , running was more economic than walking from the metabolic point of view. It also means that, for speeds greater than St2 , running was more economic than walking from the mechanical point of view. Thus, for speeds between St1 and St2 , the metabolic criterion seems to induce the transition from walking to running (while walking was still economic compared to running from the mechanical point of view). We can suppose that walking at speeds ranging from St1 and St2 makes untrained subjects change of metabolism by recruiting the anaerobic (less economic than the aerobic) one instead of using the aerobic one while running. St2 was lower than St1 for sprinters. This relation means that for speeds greater than St2 running was more economic than walking from the mechanical point of view. It also means that for speeds greater than St1 , running was more economic than walking from the metabolic point of view. Thus, for speeds between St2 and St1 , the mechanical criterion might induce sprintersÕ transition from walking to running. We suppose that if the subjects reached their maximum step length they needed to transit from walking to running in order to continue with the less costly metabolism: the aerobic one. St1 was equal to St2 for endurance trained subjects. This relationship means that walking is more economic than running from both the metabolic and the mechanical point of views until St1 (or St2 ) is reached. Thus, the endurance trained subjects changed their locomotion in order to avoid changing their metabolism. To conclude, our main result was the identification of transition speeds St1 and St2 for subjects with a different training status.
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Our results raised some questions about the wide variety of parameters and protocols currently used to study the walk–run transition. For example, what was the relation between speeds obtained with methods where the subjects were forced to walk and to run at predefined speeds, and those simply measuring the natural transition speed NTS? When measuring NTS, methodological limits related to the subjectsÕ sensation of what is being comfortable while walking could not be eliminated. The subjects could force themselves walking during the protocol whereas their ‘‘real natural limit’’ was exceeded. Our results showed that there were differences in St1 and St2 depending on the training status. Future works are necessary to investigate if these differences have an effect on the NTS. Our hypothesis is that differences in natural transition speeds depending on the training status will be found as well. Competition walkers walk beyond their natural transition speed. Based on the results presented in this paper, the NTS of such subjects could be radically different from those of untrained people. Further experiments with competition walkers are necessary to verify this hypothesis.
Acknowledgements We acknowledge A. Gratas-Delamarche, J.M. Foricher, L. Fradet, C. Jaffre, R. Kulpa and H. Zouhal for their support and help. This work has been supported by the French Ministry of Sport and Youth and the French Olympic Preparation committee.
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Does training have consequences for the walk–run transition speed? Helene Beaupied *, Franck Multon, Paul Delamarche Laboratoire de Physiologie et de Biom ecanique de 1ÕExercice Musculaire, UFR. APS, Universit e Rennes, 2, Avenue Charles Tillon, CS 24 414, 35044 Rennes, France
Abstract A number of authors when studying the walk–run transition phenomenon focused either on the mechanical or energy expenditure whilst only a few used both parameters concurrently. Moreover the literature demonstrates that the contribution of these variables changes along with the level and method of training. Consequently the purpose of this study is to find, by analyzing concurrently these two variables, if the walk–run transition speed is linked to the type of training. To this end we calculated two theoretical transition speeds: one based on the metabolic energy expenditure St1 and the second one based on the internal work St2 . Subjects were divided into three groups (untrained, sprint and endurance-trained men) who were required to walk and run on a treadmill at increasing speeds. Firstly we show that the relationship between St1 and St2 differs depending on the groups. Sprinters have a significantly lower St2 than St1 whereas the opposite is found for untrained subjects. We also show that the transition speed is linked to the subjectÕs type of training. To conclude it seems that acquiring running techniques through specific training has consequences for the walk–run transition phenomenon. 2002 Elsevier Science B.V. All rights reserved. PsycINFO classification: 4010; 3720 Keywords: Internal work; Energy consumption rate; Walking; Running
*
Corresponding author. Tel.: +33-2-99-14-17-78; fax: +33-2-99-14-17-74. E-mail address: [email protected] (H. Beaupied).
0167-9457/03/$ - see front matter 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0167-9457(02)00139-2
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1. Introduction Human locomotion can be subdivided into two different modes. Walking can be characterized as an alternating sequence of single and double support phases. In contrast, running involves alternating sequences of support and nonsupport phases (Vaughan, 1984). The literature points out that a transition between walking and running occurs when walking speed is gradually increased (Hreljac, 1993a; Margaria, Cerretelli, Aghemo, & Sassi, 1963; Mercier et al., 1994; Nilsson, Thorstensson, & Halbertsma, 1985). Because of the large number of variables involved, it is difficult to specify fundamental laws governing this transition. One way of evaluating the efficiency of human motor performance is to measure energy expenditure during movement (Heglund, Fedak, Taylor, & Cavagna, 1982; Kyr€ ol€ ainen, Komi, & Belli, 1995; Pollock, Foster, Knapp, Rod, & Schmidt, 1987), and early studies tested the relation between the transition from walking to running and the metabolic energy expended during both types of locomotion. The theoretical transition speed (TTS) (St) is defined as the speed where the oxygen consumption while walking becomes greater than the consumption while running. Margaria et al. (1963) estimated the oxygen consumption as a function of both walking speed and running speed and determined the speed at which the resulting curves intersected. This speed was approximately 2.36 m s1 . Several other physiological parameters, such as heart rate, have been analyzed in a similar way resulting in about the same transition speeds (Mercier et al., 1994). These studies concluded that the transition occurs in order to decrease energy expenditure. However, some authors (Brisswalter & Mottet, 1996; Hreljac, 1993a; Mercier et al., 1994) observed that the theoretically predicted speed was generally higher than the actual transition speed. Therefore Nilsson et al. (1985) suggested that kinematic parameters might also play a role. They observed that the transition from walking to running was accompanied by a decrease in stride length and an increase in stride frequency. These observations, however, were not supplemented by an analysis in terms of mechanical work. In order to overcome these limitations new investigations have been carried out by calculating the internal work required for each mode. Just like for energy expenditure Minetti, Ardigo, and Saibene (1994) proposed to calculate the theoretical intersection point between the functions relating the internal work to speed during both walking and running, estimating the internal work on kinematic measurements. In Minetti et al.Õs experiment (1994), subjects were asked to walk at a differing range of speeds, even if they would naturally prefer to run for some of them. In order to obtain two TTSs, energy expenditure and internal work were measured simultaneously. To sum-up, with the exception of Minetti et al. (1994), previous studies focused on either energy expenditure or mechanical work. Moreover, most authors did not report if their subjects were untrained or trained. However, the energy expenditure of trained people while running is known to be less than that of untrained ones (Pollock et al., 1987), so we wondered whether the TTSs will be influenced by training. Because the kind of training (sprint or endurance training) has different influences on
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the energetic expenditure while running (Kyr€ ol€ ainen et al., 1995; Pollock et al., 1987) this might also affect the TTSs. Our study has been designed to investigate if training, and the type of training has consequences for the theoretical transition point between walking and running. To this end subjects including untrained, sprint and endurance trained people were recruited. For the subjects in each group the energetic expenditure and the internal work required while walking and running were determined. 2. Methods 2.1. Subjects Written informed consent was obtained prior to the study. The subjects, 15 males, were free of any disease that might affect gait. They were divided into three groups of five: untrained, sprinters and endurance-trained athletes. The sprinters and endurance-trained athletes trained for a minimum of 12 h per week in their respective speciality. The height and the weight of each subject are given in Table 1. Average values and standard deviations of height and weight were respectively 1:76 m 0:07 and 68:7 kg 4:7 for the untrained group, 1:84 m 0:07 and 77:9 kg 5:7 for the sprint group and 1:76 m 0:02 and 67:5 kg 3:4 for the endurance-trained group. 2.2. Experimental task Prior to the experimental procedure, subjects were familiarized with the treadmill by performing treadmill locomotion for a minimum of 15 min (Charteris & Taves, 1978). Table 1 Anthropometric data of the subjects: height (m) and mass (kg) Group
Height (m) (mean SD)
UNT1 UNT2 UNT3 UNT4 UNT5
Untrained Untrained Untrained Untrained Untrained
1.79 1.72 1.85 1.65 1.79
(1.76 0.07) (1.76 0.07) (1.76 0.07) (1.76 0.07) (1.76 0.07)
72.8 (68.7 4.7) 68 (68.7 4.7) 74 (68.7 4.7) 62.7 (68.7 4.7) 66.3 (68.7 4.7)
SP1 SP2 SP3 SP4 SP5
Sprinter Sprinter Sprinter Sprinter Sprinter
1.83 1.85 1.72 1.91 1.91
(1.84 0.07) (1.84 0.07) (1.84 0.07) (1.84 0.07) (1.84 0.07)
81 (77.9 5.7) 75 (77.9 5.7) 69.3 (77.9 5.7) 83.2 (77.9 5.7) 81 (77.9 5.7)
END1 END2 ENDS END4 END5
Endurance-trained Endurance-trained Endurance-trained Endurance-trained Endurance-trained
1.75 1.79 1.77 1.75 1.76
(1.76 0.02) (1.76 0.02) (1.76 0.02) (1.76 0.02) (1.76 0.02)
67.5 (66.6 3.4) 68 (66.6 3.4) 62.5 (66.6 3.4) 64 (66.6 3.4) 71 (66.6 3.4)
Values are mean SD.
Mass (kg) (mean SD)
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Each subject was required to walk at five different speeds (0.98, 1.53, 2.08, 2.36, 2.64 m s1 ) during a first session and then to run at six different speeds (1.53, 2.08, 2.36, 2.92, 3.88, 4.44 m s1 ) during another session. In order to reach their steady state, the subjects walked and ran at each speed during about five minutes. The choice of speeds ensured that the two modes had three speeds in common. During exercise, the oxygen consumption was measured and three-dimensional kinematic data were recorded. 2.3. Apparatus and measurements Subjects had to walk and run on a treadmill. Respiratory variables and gas exchanges were measured using a breath by breath automatic metabolic system (CPX, Cardio2, Breeze 2, Medical Graphics, St Paul, Minnesota). Briefly, expiratory airflow was measured using a pneumotachograph and expired gases were analyzed. When subjects reached steady state during exercise, we measured oxygen uptake (V_ O2 in ml min1 kg1 ), CO2 output (V_ CO2 in ml min1 kg1 ), and the respiratory exchange ratio (RER). The RER was calculated as the rate of carbon dioxide production divided by the rate of oxygen consumption. The energy consumption rate (ECR) for each subject, expressed in joules per kilogram body mass per minute was then determined for each walking and running speed (Peronnet & Massicotte, 1991). The ECR as a function of speed, permitted the estimation of regression equations for walking and running for each subject. According to previous studies (Conley & Krahenbuhl, 1980; Minetti et al., 1994; Taylor, 1994) the regression equations are quadratic for walking and linear for running. The ECR for subjects who were unable to walk at the highest speed were extrapolated on the basis of the regression equation. We then calculated the transition speed St1 for each subject by calculating the intersection of the two regression lines. In order to estimate the internal work, we used a VICON370 system (Oxford Metrics, UK). This system was composed of seven infrared cameras cadenced at 60 Hz and a set of spherical markers. The views from the cameras were gathered and processed by using a DLT algorithm that made it possible to capture the 3D position of each marker as a function of time. During exercise, 24 markers were placed over standardized anatomical landmarks (identical to those used by Winter (1979)) in order to register the motion of the body segments. The human body was modeled as 11 rigid linked segments (trunk, forearms, upper arms, thighs, shanks, feet). A second order Butterworth filter was used to smooth the position–time data for anatomical landmarks. The kinematic data were used to estimate the internal work. As human locomotion can be considered as a quasi-cyclic motion (Winter, 1990), calculations were only performed with one complete stride for all the studied speeds. The stride cycle was defined as the period from the right toe off to the same event in the following cycle. Three different global frames were used during calculations (Fig. 1). The treadmill frame Rt ðO0 ;~i;~ j; ~ k Þ in translation with the Galilean frame RðO;~i;~ j; ~ k Þ link in the laboratory, the barycentric frame was noted R ðG;~i;~ j; ~ k Þ where the center of mass G is the origin of the frame and axes are the same as for the Galilean frame. Moreover
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Fig. 1. The human body and the different frames used in the study. The Galilean frame linked to the laboratory RðO;~ i ;~ j; ~ k Þ, the frame linked to the treadmill Rt ðO0 ;~i;~ j; ~ k Þ, the barycentric frame R ðG;~i;~ j; ~ k Þ and the frames linked to the 11 body segments Ri ðGi ;~ u;~ v; ~ wÞ.
eleven local frames, one linked to each segment Si , were also used and denoted Ri ðGi ;~ u;~ v; ~ wÞ where ~ w is the longitudinal axis and ~ u is the transverse axis of each body segment. Body segment parameters were determined for each subject, based on DempsterÕs anthropometric data (Dempster, 1955). The total mechanical energy of the body is defined by the equation i¼11 X 2 E ¼ ð1=2ÞMVG=R þ ðmi ghi þ ð1=2Þmi VG2i =R þ ð1=2ÞIi w2i Þ ðJÞ t i¼1
where M is total mass, mi is mass of the ith body segment, g is gravitational acceleration, hi is height of the ith segment center of mass ðGi Þ in the Galilean frame RðO;~i;~ j; ~ k Þ, VG=Rt and VGi =R are the linear velocity of the center of mass (G) relative to Rt and the linear velocity of Gi relative to the barycentric frame R respectively, Ii is the inertial matrix of the ith segment and wi is the angular velocity of the ith segment. The calculation of the internal work was based on WinterÕs (1990) method. The internal work was calculated on the assumption of a complete energy transfer within and between all segments: Wint ¼
j¼tf X
jDEj j ðJÞ
ð1Þ
j¼t0
where Wint is the work due to the internal forces, DE is the mechanical energy variation between two successive frames and t0 and tf are the beginning and the end of the stride respectively. Then, in order to compare the different groups, for each subject the internal work was divided by the time of the complete stride for each walking and running speed.
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The mechanical transition speed (St2 ) was determined for each subject with the same method used for the ECR, implying that St2 was defined as the intersection between the two regression lines (for walking and running). After assessment of St1 and St2 for each subject, the mean values and standard deviations of these TTSs for each group were calculated. Due to the small sample size we first verified the Gaussian distribution of the data using a specific test (Shapiro–Wilk). An repeated measures one way Anova has been used to test the effect of groups on the TTSs. To test the difference between St1 and St2 values for the three groups, a single parameter analysis of variance was carried out. A value of a ¼ 0:05 was accepted as the level of statistical significance.
3. Results The transition speeds St1 and St2 were calculated for the three groups using the two methods. Figs. 2–4 show the relation between the ECR and speed while walking and running for untrained, sprinter and endurance-trained groups, respectively. The bars in the figures stand for the standard deviation calculated for each point. Untrained subjects and sprinters could not walk at the highest imposed speed (2.64 m s1 ), whereas the endurance-trained subjects succeeded in doing so. Relations between the ECR and walking speeds are quadratic with correlation coefficients 0.99 for each of the groups. These results are in accordance with the literature (Burdett, Skrinar, & Simon, 1983; Minetti et al., 1994). Relations between ECR and running speed are linear, with a correlation coefficient 0.99 for the untrained and endurance-trained groups respectively and 0.98 for the sprinters. These energy expenditure results are also compatible with the literature (Conley & Krahenbuhl, 1980; Taylor, 1994). Let us now consider the transition speeds computed for the three groups. Mean values and standard deviations of St1 are 2:29 0:04, 2:44 0:06 and 2:30 0:05 m s1 for the untrained, sprinter and endurance-trained groups, respectively. These results are in agreement with transition speeds reported earlier, which ranged from 2.16 to 2.36 m s1 (Hreljac, 1993b; Margaria et al., 1963; Mercier et al., 1994) without taking training into account. Statistical analysis shows significant differences
Fig. 2. The relation between the ECR (J kg1 min1 ) and the walking and running speeds (m s1 ) for the untrained group. Values are mean SD.
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Fig. 3. The relation between the ECR (J kg1 min1 ) and the walking and running speeds (m s1 ) for the sprinter group. Values are mean SD.
Fig. 4. The relation between the ECR (J kg1 min1 ) and the walking and running speeds (m s1 ) for the endurance-trained group. Values are mean SD.
(a < 0:05) in St1 values between the sprint and endurance-trained group and between the sprint and untrained group. The relation between internal work and walking and running speed (Figs. 5–7) was plotted for the untrained, sprint and endurance-trained group, respectively. Untrained subjects could not run at a speed higher than 3.88 m s1 . Relations between internal work and walking and running speed are quadratic for each group. The correlation coefficients are 0.99 for the three groups during walking and running. Mean values of the internal work are in agreement with previous studies (Belli, Avela, & Komi, 1993; Fukunaga & Matsuo, 1980; Kyr€ ol€ainen et al., 1995). Mean values and standard deviation of the calculated St2 are 2:65 0:07, 2:19 0:05 and 2:29 0:04 m s1 for the untrained, sprinter and endurance-trained groups, respectively. These speeds are greater than the ones obtained by considering kinematic or kinetic data (Mercier et al., 1994; Minetti et al., 1994). In general, in the literature, the speeds calculated with kinematic or kinetic data are lower than the ones calculated with the energy expenditure method. Let us consider the two transition speeds for each group of subjects. For untrained subjects, the Anova showed a St1 significantly less than St2 (a < 0:0001). The difference between St2 and St1 (St2 St1 ) was 0.36 m s1 . For the sprinter subjects St1 was significantly greater than St2 ða < 0:01Þ. The difference is )0.25 m s1 .
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Fig. 5. The relation between the internal work (J s1 kg1 ) and the walking and running speeds (m s1 ) for the untrained group. Values are mean SD.
Fig. 6. The relation between the internal work (J s1 kg1 ) and the walking and running speeds (m s1 ) for the sprinter group. Values are mean SD.
Fig. 7. The relation between the internal work (J s1 kg1 ) and the walking and running speeds (m s1 ) for the endurance-trained group. Values are mean SD.
Finally, no significant difference appeared between St1 and St2 for the endurancetrained subjects: the two speeds were about the same. 4. Discussion We studied the walk–run transition through the analysis of two variables: the energy expenditure and the internal work. From these two variables we calculated the
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crossover point (providing the TTS) between the curves corresponding respectively to walking and to running. Our results showed that the training and the type of training (sprint or endurance-training) influenced the TTS values St1 (obtained with the energy expenditure measurements) and St2 (obtained with the internal work calculations). In the present study, St1 values were equal to 2:29 0:04, 2:44 0:06 and 2:30 0:05 m s1 for the untrained, sprinter and endurance-trained groups, respectively. Literature reported values of 2.10 m s1 (Turvey, Holt, LaFiandra, & Fonseca, 1999), 2.16 m s1 (Mercier et al., 1994), 2.24 m s1 (Hreljac, 1993b) and 2.36 m s1 (Margaria et al., 1963) without accounting for the subjectsÕ training status. Hence, our results were similar to those presented in the literature. St2 values presented in this paper were 2:65 0:07 m s1 for untrained subjects, 2:19 0:05 m s1 for sprinters and 2:29 0:04 m s1 for endurance-trained subjects. Three main methods were currently used in the literature to evaluate the transition speed by considering a mechanical point of view. The first method evaluated the socalled ‘‘preferred transition speed’’ PTS (Hreljac, 1993b) which value was 2.06 m s1 . The PTS was obtained by asking the subjects to use the natural gait of walking or running, as preferred, during 30 s for selected speeds. The PTS was then defined as the minimum speed for which the subject chose to run. The second method consisted in increasing continuously the treadmill speed and to notice the one for which the subject began to run. This speed (denoted the ‘‘natural transition speed’’ NTS) was equal to 1.89 m s1 in the study by Noble et al. (1973) and to 2.17 m s1 in the study of Beuter and Lefebvre (1988). The third method required the subjects to walk or run at selected speeds during a few minutes in order to reach a steady state. The ‘‘theoretical transition speed’’ (TTS) was obtained by the crossover point method. A TTS of 2.5 m s1 was found by Grillner, Halbertsma, Nilsson, and Thorstensson (1979) by focusing on kinematic parameters, and of 1.8 m s1 by calculating internal work (Minetti et al., 1994). As presented above, the literature provided us with various transition speeds ranging from 1.8 to 2.5 m s1 . One can wonder why such results were so different. First, these differences could be due to the addition of measurement and computation inaccuracies. Especially for internal work calculations, several possible inaccuracies could occur, including the external markers displacements over the skin, anthropometrical data used to calculate mass and inertia, derivation method. Our work showed significant differences in transition speeds depending on the training status. Inaccuracies cannot be held responsible for these significant differences and can therefore consequently be neglected. Second, the previous works dealing with TTS by considering a mechanical point of view did not always focus on the same parameters and did not use the same protocol. For example, protocols requiring long measurement (to reach the steady-state) could engender different results than those carried out during short sequences. Finally, no information about the subjects training status was provided in the past works. Our main result showed that significant differences (a < 0:05) in St2 occurred between untrained, sprinters and endurance trained subjects (with both energy expenditure and internal work measurements). In previous studies, trained and
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untrained subjects may have been mixed. Because training status influenced energy consumption and internal work, techniques involving these two kinds of measurements might reflect the effect of training. In our experiment, energy expenditure and internal work were measured during the same experiment so that comparisons between these two values could be carried out. Interpreting differences between St1 values and between St2 values from different groups would be hazardous. For example, let us consider a group of subjects A and another group B. Several explanations could be proposed for the fact that AÕs St1 is higher than BÕs one. As St1 is the crossover point of two curves (one calculated while walking and the other while running), a higher AÕs St1 can be due to: • A lower energy expenditure while walking at a speed around St1 for A compared to B, that shifts the crossover point to the right, • A higher energy expenditure while running at a speed around St1 for A compared to B, that also drives to the same result, • A combination of these two possibilities. The same possibilities can be proposed for St2 . Nevertheless, the values found in the present study for St1 and St2 depending on the training status raises interesting hypotheses. St1 was the highest speed for which the energy expenditure while walking was lower than the one for running. St2 was the highest speed for which the internal work while walking was lower than the one for running. St1 was lower than St2 for untrained subjects. This relation means that, for speeds greater than St1 , running was more economic than walking from the metabolic point of view. It also means that, for speeds greater than St2 , running was more economic than walking from the mechanical point of view. Thus, for speeds between St1 and St2 , the metabolic criterion seems to induce the transition from walking to running (while walking was still economic compared to running from the mechanical point of view). We can suppose that walking at speeds ranging from St1 and St2 makes untrained subjects change of metabolism by recruiting the anaerobic (less economic than the aerobic) one instead of using the aerobic one while running. St2 was lower than St1 for sprinters. This relation means that for speeds greater than St2 running was more economic than walking from the mechanical point of view. It also means that for speeds greater than St1 , running was more economic than walking from the metabolic point of view. Thus, for speeds between St2 and St1 , the mechanical criterion might induce sprintersÕ transition from walking to running. We suppose that if the subjects reached their maximum step length they needed to transit from walking to running in order to continue with the less costly metabolism: the aerobic one. St1 was equal to St2 for endurance trained subjects. This relationship means that walking is more economic than running from both the metabolic and the mechanical point of views until St1 (or St2 ) is reached. Thus, the endurance trained subjects changed their locomotion in order to avoid changing their metabolism. To conclude, our main result was the identification of transition speeds St1 and St2 for subjects with a different training status.
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Our results raised some questions about the wide variety of parameters and protocols currently used to study the walk–run transition. For example, what was the relation between speeds obtained with methods where the subjects were forced to walk and to run at predefined speeds, and those simply measuring the natural transition speed NTS? When measuring NTS, methodological limits related to the subjectsÕ sensation of what is being comfortable while walking could not be eliminated. The subjects could force themselves walking during the protocol whereas their ‘‘real natural limit’’ was exceeded. Our results showed that there were differences in St1 and St2 depending on the training status. Future works are necessary to investigate if these differences have an effect on the NTS. Our hypothesis is that differences in natural transition speeds depending on the training status will be found as well. Competition walkers walk beyond their natural transition speed. Based on the results presented in this paper, the NTS of such subjects could be radically different from those of untrained people. Further experiments with competition walkers are necessary to verify this hypothesis.
Acknowledgements We acknowledge A. Gratas-Delamarche, J.M. Foricher, L. Fradet, C. Jaffre, R. Kulpa and H. Zouhal for their support and help. This work has been supported by the French Ministry of Sport and Youth and the French Olympic Preparation committee.
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