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Coordination patterns of walking and running at similar speed and stride frequency
Human Movement Science 18 (1999) 67±85
Coordination patterns of walking and running at similar speed and stride frequency Li Li *, Elizabeth C.H. van den Bogert, Graham E. Caldwell, Richard E.A. van Emmerik, Joseph Hamill Department of Exercise Science, University of Massachusetts, Amherst, MA 01003, USA
Abstract The present study compared walking and running constrained to one speed (2.24 m/s) and the average of preferred walking and running stride frequency. Lower extremity coordination was assessed, using phase plots, relative phase and variability analysis. Angular excursions, phase plots, patterns of relative phase and variability analysis illustrated similar segmental and joint coordination patterns for walking and running. Under the speed and stride frequency constraints, we observed topological similarity in coordination patterns between the thigh and leg in walking and running, which co-existed with functional dierences throughout the gait cycle, especially in the transition from stance to swing phase. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Biomechanics; Motor control; Gait; Dynamical systems; Kinematics
Table of variables hT : Thigh angle, de®ned as the angle between the left horizontal and the thigh segment; this angle increases as the thigh rotates clockwise around the hip joint (see Fig. 1); * Corresponding author. Department of Kinesiology, Louisiana State University, 112 Long Fieldhouse, Baton Rouge, LA 70803, USA. Tel.: +1 225 334 3046; fax: +1 225 388 3680; e-mail:[email protected].
0167-9457/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 9 4 5 7 ( 9 8 ) 0 0 0 3 4 - 7
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Fig. 1. Thigh (hT ), leg (hL ) and knee (hK ) angle were de®ned at the proximal end with respect to the left horizontal. Knee was de®ned as the angle between the thigh and leg that decreases when the knee joint ¯exes.
hL : Leg angle, de®ned as the angle between the left horizontal and the leg segment; this angle increases as the leg rotates clockwise around the knee joint (see Fig. 1); hK : Knee angle, de®ned as the angle between the thigh and leg segments on the posterior side of the body (see Fig. 1); xT , xL and xK : The angular velocity of thigh, leg and knee angles (hT , hL and hK ), respectively; u: Phase angle, de®ned from the normalized phase plot for each stride cycle as the angle formed between a line from the origin (0, 0) to the current data point (h, x) and the right horizontal. The phase angle increases in the counter-clockwise directions; CRP: Continuous relative phase, de®ned as the dierence between thigh and leg phase angles (thigh phase angle minus leg phase angle) throughout the stride cycle; VCRP: Variability of the continuous relative phase for each subject and each condition; calculated by the mean of the SD of every point on the ensemble curve. 1. Introduction The kinematic and kinetic characteristics of walking and running have been described by many researchers, with the results indicating that a walking
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stride is much dierent than a running stride (Bobbert, 1960; Cavanagh and Williams, 1982; Corcran and Brengelmann, 1970; Hagan et al., 1980; Kram and Taylor, 1990; Relston, 1958; Zarrugh et al., 1974). It has also been shown that the metabolic cost of walking a given distance reaches a minimum value at a speed of approximately 1.25 m sÿ1 and increases as speed increases, whereas the metabolic cost of running a unit distance remains relatively constant at all speeds (Carrier, 1984; Cavagna, 1978; Cavagna and Franzetti, 1986; Cavagna and Kaneko, 1977; Cavagna et al., 1976; Kram and Taylor, 1990; Margaria, 1976; Milliron and Cavanagh, 1990). Interestingly, at the speed of approximately 2.24 m sÿ1 , which is very close to the gait transition speed (Hreljac, 1995), the energy cost for a human to travel a unit distance is similar in walking and running (Cavagna et al., 1976; Hreljac, 1993). The dierent energy cost ± velocity relationships of walking and running may be due to dierent movement organization within the gait patterns. For example, the energetic cost of running is correlated with the weight that the body has to support, which may not be the case in walking (Farley and McMahon, 1992). Factors such as locomotor speed and stride frequency can aect various aspects of human locomotion. For example, Winter (1983a) reported that an increase from natural walking cadence to a 17% faster cadence was accompanied by 18% greater ankle velocity, 20% greater knee velocity and 21% greater hip velocity. Milliron and Cavanagh (1990) indicated that maximal knee ¯exion angle increased as running speed increased. In addition, peak amplitude of the vertical ground reaction force increases as the locomotion speed increases in both walking and running (Hamill et al., 1983; Nilsson and Thorstensson, 1989). Both Zarrugh et al. (1974) and Holt et al. (1991) observed that there exists an energetically optimal and preferred stride frequency for every speed of level walking. Capaday and Stein (1987) observed that the peak EMG level of the soleus was on average 2.4 times greater in running compared to walking. However, it is dicult to distinguish whether this dierence was produced by changing the gait pattern or by variation in locomotor speed or by both factors because their subjects walked at 1.11 m sÿ1 and ran at 2.22 m sÿ1 . Con®ning walking and running to the same speed and stride frequency would eliminate the in¯uence of stride length which has been shown to in¯uence energy cost (Hamill et al., 1995). The importance of progression velocity and stride frequency is especially relevant from the perspective of dynamical systems theory (SchoÈner et al., 1990). This theory views a speci®c gait pattern as an emergent behavior that arises from the collective behavior of all contributing subsystems, including
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both the central nervous and musculoskeletal systems (Diedrich and Warren, 1995). Other constraints, such as those found in the environment (e.g., gravitational forces, slippery walking surfaces) and the task itself (e.g., walking or running at dierent velocity and/or dierent stride frequency) also contribute to shaping the behavior of the system. In this perspective, dierent phase and frequency relations between limbs or body segments typify coordinative modes. These relationships or cooperativities are called ``order parameters''. Changes in the order parameter (e.g. from walk to trot to gallop in quadrupedal locomotion) occur when a speci®c control parameter (e.g. movement speed, frequency) is scaled. The advantage of using this perspective to study gait is that it provides a means of describing a high dimensional system in terms of a low dimensional representation. For instance, relative phase can be used as an order parameter to describe coordination changes between segments with the change of gait pattern (Clark and Phillips, 1993; Diedrich and Warren, 1995). In dynamical systems theory, phase plots, relative phase and their variability have been used to study gait. Phase plots, which display segmental velocity as a function of displacement, have been used to identify the coordinative pattern of the thigh and leg (Clark and Phillips, 1993). Continuous relative phase (CRP) has been used to study spatial-temporal coordination (van Emmerik and Wagenaar, 1996), while discrete relative phase has been used to study the temporal coordination (Diedrich and Warren, 1995). Variability in both continuous and discrete relative phases has been employed as an indication of system stability. In some movements, greater variability indicates that the system is closer to the point where a new pattern will emerge, while less variability will be a sign of a more stable system (Kelso et al., 1986; van Emmerik and Wagenaar, 1996). Overall, these measures have great potential for studying similarities and dierences between walking and running. Previous studies comparing the gait patterns of walking and running are equivocal because locomotor velocity was greater in running than in walking. It is not clear whether gait pattern, locomotor speed or stride frequency has the greatest in¯uence on the system. Comparing coordination patterns and variability, it is also not clear what will be the dierences and/or similarities between walking and running when the speed is controlled. In the present study, we controlled locomotor speed and stride frequency as the gait pattern was varied between walking and running. The purpose of this study was to compare lower extremity coordination in walking and running at the same speed and same stride frequency. By stabilizing other control parameters,
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such as locomotion speed and stride frequency, we were able to isolate the eects of dierent gait patterns on coordination and variability. 2. Methods 2.1. Subjects The subjects in this experiment were young, healthy, male university graduate students. Based on previous data reported by other researchers (Hreljac, 1995), a power analysis (Cohen, 1988) was performed to determine the number of subjects needed in this experiment. It was found that ®ve subjects would provide more than 80% of statistical power necessary to detect segmental angle dierences between walking and running conditions. In order to balance the condition order between subjects, a total of six subjects were chosen to perform the test. The average age, stature and body mass were: 28 4 yr; 1.79 0.07 m and 76 11 kg, respectively. Informed consent and medical clearance were obtained from each subject prior to the experiment. 2.2. Experimental procedures There were two experimental conditions: walking and running both performed at the same speed on a motorized treadmill. A speed of 2.24 m sÿ1 was selected based on the similarity of the energetic cost of walking and running at that speed (Cavagna et al., 1976; Hreljac, 1993). Prior to the start of the test session, subjects were instructed to run on the treadmill at their preferred speed for 5 min to warm up. Their preferred stride frequencies were determined while they walked and ran on the treadmill at level grade at the testing speed for 5 min. The average of preferred running and walking frequency for each individual was calculated and then imposed by a metronome in the testing sessions to help subjects maintaining their locomotor frequency. During the data collection, they either walked or ran at 2.24 m sÿ1 with this imposed stride frequency for 6 min. The order of walking and running conditions was alternated between subjects. 2.3. Data collection and processing Kinematic data were collected continuously with a high-speed (200 Hz) video camera for the last 3 min of the 6 min of walking and running. Retro-
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re¯ective markers were used to identify joint centers of the lower extremity. Ankle, knee and hip joints were de®ned by markers on the lateral malleolus, the point above the superior margin of the lateral tibia and the greater trochanter, respectively. Video data from the retro-re¯ective markers were used to determine sagittal view kinematics. Kinematic data were smoothed using a zero-lag dual pass Butterworth digital ®lter with a cut-o frequency of 18 Hz. For each subject, 5 consecutive stride cycles from the last minute of a walking or running condition were selected for analysis. Each stride cycle was de®ned from heel contact to next heel contact with heel contact identi®ed using the vertical coordinate of the ankle marker. Angle and angular velocities for the thigh (hT , xT ), leg (hL , xL ) and knee (hK , xK ) were calculated from the re¯ective marker data (Fig. 1).
Fig. 2. Typical phase plots of walking and running from an exemplar subject (left and right panel, respectively). Stance phase is indicated by solid line, swing phase by broken line. Time progresses in clockwise fashion around phase plot.
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2.4. Data analysis 2.4.1. Phase plots Phase plots of the leg, thigh and knee were employed to compare lower limb motion between walking and running. Each phase plot was determined in raw units with angular displacement on the horizontal axis and the angular velocity on the vertical axis (for example, see Fig. 2). In order to calculate phase angle (u) and to minimize the in¯uence of dierent movement amplitudes, the phase plots were normalized for each trial. The following formulae were used for phase plot normalization 2 hi ÿ min hi ÿ 1; 1 max hi ÿ min hi where h stands for joint or segment angle and i for each data point within the stride cycle. This normalization puts the origin of the horizontal axis in the middle of the range while normalizing the minimum value to ÿ1 and maximum value to 1. Horizontal axis angle: hi
2 Vertical axis angular velocity: xi xi =R; where R was calculated as: R maxfjxi jg and xi represents angular velocity at each data point i. The largest magnitude of positive and negative angular velocity values for one stride cycle was normalized to 1. The same scale then was applied to all angular velocity data in the same stride cycle. This process was repeated for each stride cycle. The phase angle ui was de®ned from the normalized phase plot for each stride cycle as the angle formed between a line from the origin (0, 0) to the current data point (hi , xi ) and the right horizontal. 2.4.2. Relative phase variables The CRP was de®ned as the dierence between thigh and leg phase angles at each point throughout the stride cycle. CRP is therefore considered to be a measure of the coordination between the thigh and leg segments. The ensemble curve was calculated from the CRP curves of ®ve strides for each subject in each condition. The results of the ensemble curve calculation are presented as the mean of the ®ve trials. 2.4.3. Variability Variability within the two gait patterns was calculated from the standard deviation of the CRP measures. The results of these calculations are an
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indication of cycle to cycle variability and can be used to compare system stability characteristics across gait patterns (see van Emmerik and Wagenaar, 1996 for a detailed explanation of the methods involved). The variation of CRP (VCRP) for each subject and each condition was calculated as the mean of the SD of every point on the ensemble curve. 2.5. Statistical analysis The phase plots and relative phase graphs were analyzed qualitatively for similarities and dierences between conditions. The degree of similarity of CRP patterns throughout the gait cycle between walking and running for each subject was evaluated by using cross correlation (Chat®eld, 1984). Repeated measures ANOVA was performed on hT , xT , hL , xL , hK , and xK at heel contact and toe-o in order to compare parameters between walking and running conditions quantitatively. Comparison of the average dierence of CRP curves between conditions was also carried out by repeated measures ANOVA. Comparison of variability between each condition was tested by paired t-test (two-tailed), using the VCRP. A statistical comparison between the CRP curves for walking and running was obtained by calculating the absolute dierence between the CRP curves in the two conditions for each subject. These comparisons were done over means of 10% intervals of the gait cycle. The dierences between each 10% bin were evaluated using 99.5% con®dence interval comparisons. 3. Results 3.1. Kinematics at heel contact and toe-o Kinematic analysis indicated that toe-o occurred at 38% (SD 3%) and 54% (SD 1%) of the gait cycle for running and walking, respectively. Summary comparisons of the lower extremity kinematic parameters at heel contact and toe-o are presented in Tables 1 and 2, respectively. At heel contact (Table 1), there was a signi®cant dierence between gait conditions for both hT and hL . Both hT and hL decreased from walking (hT mean: 113°; hL mean: 98°) to running (hT : 104°; hL : 87°). In contrast, hk and all angular velocities were not signi®cantly dierent between walking and running conditions.
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Table 1 Results of repeated measurement ANOVA for kinematic variables at heel contact Walking (MeanSD) hT (°) hL (°) hK (°) xT (°/s) xL (°/s) xK (°/s)
113 3 98 4 166 4 ÿ38 42 ÿ180 56 ÿ142 80
Running (MeanSD)
F
P-Value
77.5 43.5 1.69 5.21 0.43 0.81
0.0003 0.0012 0.2509 0.0713 0.5420 0.4106
104 4 87 3 163 3 21 31 ÿ162 60 ÿ184 74
Only F-test results that relate to the walking and running comparison are presented here. Table 2 Results of repeated measurement ANOVA for kinematic variables at toe-o Walking (Mean SD) hT (°) hL (°) hK (°) xT (°/s) xL (°/s) xK (°/s)
62 1 43 3 161 3 51 50 ÿ268 32 ÿ318 80
Running (Mean SD)
73 3 51 4 159 5 ÿ167 32 ÿ15 30 151 56
F
P-Value
62.7 63.2 0.92 102 312 192
0.0005 0.0005 0.3820 0.0002 <0.0001 <0.0001
Only F-test results that relate to the walking and running comparison are presented here.
At toe-o (Table 2), both hT and hL increased signi®cantly from walking (hT : 62°; hL : 43°) to running (hT : 73°; hL : 51°), whereas hK did not change. For the measurements of angular velocity, xT was positive in walking (51°/s) but negative in running (ÿ167°/s). This indicates that the thigh was swinging forward at toe-o in walking and backward in running. The magnitude of xL was greatly reduced in running (ÿ15°/s) compared to walking (ÿ268°/s), but the direction remained the same. These segmental velocities resulted in a negative xK (knee ¯exion) for walking (ÿ318°/s) and a positive xK (knee extension) for running (151°/s). All of these angular velocity dierences between walking and running were signi®cant at toe-o. Note that the standard deviations of all angles were relatively small compared to the standard deviation of angular velocities. 3.2. Phase plots Fig. 2 displays typical phase plots for one exemplar subject for one gait cycle (heel contact to heel contact) of walking and running, respectively.
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Data points on these phase plots follow clockwise as time progresses. At heel contact, hT was close to the maximum value with xT close to zero (see upper panels of Fig. 2). hT decreased throughout the stance phase with an almost constant angular velocity near ÿ200°/s in both gait patterns. Compared to walking, the running stance phase ended at an earlier stage in the phase plot with xT at approximately ÿ165°/s (contrasted with 25°/s for walking). During the major part of the swing phase in both walking and running, hT increased with a positive xT value until shortly before heel contact. The leg phase plot indicates that hL decreased throughout the whole stance phase and the magnitude of xL ¯uctuated but was always negative in both walking and running (see middle panels of Fig. 2). hL continued to decrease in the ®rst part of the swing phase, then increased to its maximum value at the end of the swing phase for both locomotion patterns. Finally, the knee phase plot displayed a small and a large ellipsoid associated with the stance and swing phase, respectively, in both walking and running. However, the ellipsoid associated with running stance phase was not complete when compared to the ellipsoid in walking (lower panels of Fig. 2). 3.3. Continuous relative phase Fig. 3 is a graphic representation of the ensemble CRP curves of the six subjects for both walking and running conditions. Positive CRP indicates that the leg phase angle is in the leading position relative to the thigh phase angle, while negative CRP indicates the opposite. Zero CRP is equivalent to the two segments being in phase, while both 180° and ÿ180° would mean that the two segments move in anti-phase. For both conditions, there was greater dierence observed during late stance and early swing (25±50% in walking and 15±45% in running) compared to the rest of the gait cycle. In both conditions, CRP was slightly positive at heel contact and increased immediately, reaching its peak positive value at approximately 5±10% of the gait cycle. In the walking condition, CRP crossed zero in a relatively consistent fashion, close to 15% of the gait cycle. In contrast, the crossing point of the running CRP varied between subjects (range 15± 35% of the gait cycle). CRP was dominated by negative values during swing phase for both conditions. Note that in the walking condition, CRP crossed the zero point far before toe-o occurred. In the running condition, these two events were more closely linked in time, especially for three of the six subjects. Overall, the range of CRP (between minimum and
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Fig. 3. Continuous relative phase of walking and running for six subjects. Relative phase was de®ned as the thigh phase angle minus the leg phase angle.
maximum) was smaller in the walking condition than in the running condition. Results of cross-correlation showed that the CRP trends of the two modes of locomotion were similar for each subject (R 0.75, 0.85, 0.89, 0.91, 0.96 and 0.98 for individual subjects). Dierences in CRP between conditions for each 10% portion of the gait cycle are shown in Fig. 4. The error bars in the graph indicate 99.5% con®dence intervals (overall a level controlled at 0.05 level). There were signi®cant dierences between walking and running CRP throughout the entire gait cycle, as indicated by the fact that none of the con®dence intervals crosses zero. The CRP dierence between walking and running was much greater from 20% to 40% of the gait cycle and these differences were signi®cantly dierent from the CRP dierence during the rest of the gait cycle (see Fig. 4 for the coverage of the 99.5% con®dence interval of each 10% bin). These signi®cantly greater dierences occurred in the second half of the running stance phase until toe-o, which coincided with the midstance of walking (20±40% of gait cycle).
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Fig. 4. Absolute dierences between walking and running CRP throughout the gait cycle at each tenth bin of the gait cycle with error bars indicate 99.5% con®dence interval of every bin. There are always more than 10% dierences in CRP with greater dierence observed at 20±40% of the gait cycle.
3.4. Variability The variability for continuous relative phase (VCRP) is displayed in Table 3. While some individual subject dierences are apparent, there was no clear pattern for either walking or running to have greater variability. The paired t-test also did not detect any signi®cant dierences in variability. 4. Discussion In this study we compared lower extremity coordination in the two gait modes of walking and running while controlling for speed and stride Table 3 Variability of continuous relative phase (VCRP) in walking and running Subject
Walking (°)
Running (°)
1 2 3 4 5 6
6 22 17 22 21 17
15 26 17 20 19 17
Result of paired t-test of the dierence between walking and running: p 0.4081.
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frequency. The most pronounced dierences between the two forms of locomotion were observed at toe-o including the direction of the lower extremity movement relative to the body (see xT in Table 2). In con®ning locomotion to the same speed (2.24 m/s) and stride frequency, toe-o occurred at approximately 54% of the gait cycle for walking and 38% for running. Following toe-o the swing leg moved forward relative to the body in walking, but backward relative to the body in running. The time histories of thigh and leg kinematics generated in this study were comparable to those that exist in the research literature. Time histories of hip, thigh and knee angles of walking (Fig. 5) exhibited the same pattern as the data presented by Winter (1991). The range of motion of both thigh and knee in our study was greater than in Winter (1991) due to the greater walking speed. Similar time histories for running (Fig. 5) exhibited the same
Fig. 5. Typical thigh, leg and knee angle comparison between walking and running for one cycle (from heel contact to heel contact). RTO ± running toe-o; WTO ± walking toe-o.
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patterns as the data presented by Williams (1993). The relative phase curves (Fig. 3) also displayed the same characteristics as those in the literature (Clark and Phillips, 1993), although the range of motion was dierent in our data. Hreljac (1995) has demonstrated the in¯uence of changing both speed and gait pattern on hip angle. His study illustrated the interactions produced by manipulating both speed and gait mode factors. In walking, the range of motion of the hip increased as the progression speed increased. However, as the gait pattern changed to running at the preferred transition speed, the hip range of motion actually decreased. The magnitude of the maximal hip angle was less in running (18°) than in walking (22°). However, the maximal hip angle measurement showed a similar decrease from 22° to 18° when walking speed was modi®ed to 70% of the preferred transition speed (Hreljac, 1995). Furthermore, the change of minimum hip angle caused by gait transition was similar to the change caused by increasing walking speed from 70% to 100% preferred transition speed. Thus, it was dicult to determine whether the changes in certain kinematic variables were due to the change of the gait pattern or due to the change in locomotor speed. The same argument can also be made for the in¯uence of stride frequency (Farley and GonzaÂlez, 1996). However, in the present study all observed similarities and dierences were only in¯uenced by the chosen gait pattern, because the locomotor speed and stride frequency were identical for both progression modes. The observed coordination patterns between the thigh and leg were quite similar in walking and running except during 20±40% of the gait cycle (Figs. 3 and 4). In contrast, Nilsson and Thorstensson (1989) suggested that the dierences present in walking and running are consequences of fundamental dierences in motor strategies between the two major forms of human progression. We observed both similarities and dierences at the tested speed of 2.24 m/s. It would seem that more overall dierences would be expected if there were fundamental changes in motor strategies. The fact that the alterations between the two forms of locomotion were concentrated at 20±40% of the gait cycle may indicate more subtle dierences in motor strategies rather than fundamental ones. In a subsequent study, we will examine these gait pattern similarities and dierences at a wider range of speeds including the transitional speed. The present data also suggest that the individual subject patterns of the CRP curves were more consistent in the walking condition than in the running condition (see Fig. 3). To explore these between-subject dierences of
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lower extremity coordination strategies more thoroughly would require more subjects and shall be the focus of further studies. 4.1. Similarities between the two gait modes The data demonstrate many similarities between the gait conditions. Tables 1 and 2 indicate that there were no signi®cant dierences of the knee angle hK at both heel contact and toe-o. CRP patterns in Fig. 3 indicate that similarity in coordination pattern occurs throughout the complete gait cycle, especially during early stance and for most of swing. This may indicate that, topologically, the coordination patterns between the thigh and leg were similar for walking and running, even though there were signi®cant dierences between the two conditions for hL and hT at toe-o and heel contact (Tables 1 and 2). Fig. 2 demonstrates similar patterns of thigh, leg, and knee phase plots between walking and running. The major dierence between gaits for all three pairs of phase plots are that toe-o occurred at dierent phase angles in the cycle. The CRP patterns (Fig. 3) were consistent with the phase plot data in that the overall patterns were similar for walking and running (R 0.75±98) except for the dierences exhibited at 20±40% of the gait cycle (Fig. 4). The variability data (Table 3) reveal that walking and running had similar amounts of variation. Two subjects exhibited greater variability in CRP for running and the other two exhibited greater variability for walking. As noted in the introduction, from a dynamical systems perspective, the variability of relative phase is an indicator of the stability of the coordination pattern. Diedrich and Warren (1995) observed increases in the variability of relative phase (between ankle, knee and hip joints) during transition from both walking to running and running to walking. Similar increases in variability of relative phase between motions of pelvic and thorax in the trunk were observed by van Emmerik and Wagenaar (1996). Therefore, increases in variability of relative phase can possibly identify transitions from one stable pattern to another. However, the present results suggest that both gait patterns were equally stable at the controlled stride frequency during the experiment at the test speed of 2.24 m/s (close to the walk to run transition speed). Note that the imposed stride frequency could in¯uence the characteristics of the locomotion variability. Subsequent studies are needed to determine whether similar variability characteristics also exist at other locomotor speeds and how they are aected by imposed stride frequency.
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4.2. Dierences between the two gait modes While the previous section pointed out the many similar aspects of the two gait conditions, dierences were also found. Signi®cant dierences between walking and running for xT , xL , and xK were observed at toe-o (Table 2). The lower extremity was moving forward at toe-o for walking (toe-o at 54% of stride cycle) whereas it was moving backward for running (toe-o at 38% of stride cycle). This coincides with the knee joint being in extension at toe-o in running but in ¯exion in walking (see Fig. 5). Between 38% and 54%, the phase plots of the thigh and leg demonstrated a similar path for the two gaits (Fig. 2). During this interval, the lower extremity was in contact with the ground for walking, but was in the ¯ight phase for running. During the same interval, before toe-o in walking and after toe-o in running, hip ¯exion and knee extension joint moments have been observed experimentally for both walking (Winter, 1991; Vaughan et al., 1992) and running (Winter, 1983b; Chapman et al., 1984). These joint moments result in similar kinematic performance for the thigh and the leg segments and the knee joint for both walking and running (Figs. 2±4), despite the dierent position of the foot with respect to ground contact. However, this variant foot position between gait modes may alter peripheral control during the subsequent portion of the cycle. During this time the ankle plantar ¯exors are being stretched in walking with the foot on the ground, but not in running with the foot in the air. Therefore, a stronger stretch re¯ex in walking may contribute to the dierences after toe-o between the two progression modes. 4.3. Topological invariance versus quantitative dierences The most important message from Figs. 2 and 5 is that while the overall kinematic patterns are preserved, discrete events such as the timing of toe-o change with gait modes. Interestingly, a dierent picture emerges if the CRP is divided into functional phases (early, late stance and swing, see Fig. 3). Dramatic dierences can be observed by comparing walking and running CRP within each functional phase. It is important to note that the overall coordination patterns revealed by CRP (Fig. 3 and cross correlation range from 0.75 to 0.98), are preserved in terms of topology. However, closer inspection of Fig. 3 reveals that these similar components occur throughout dierent functional phases for walking and running. For example, in walking during early stance phase, the thigh phase angle switched from leading the leg
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phase angle to lagging the leg phase angle. In running, however, the thigh leads the leg almost throughout the entire early stance phase. These data suggest that a distinction should be made between overall topology of the relative phase patterns and the timing of when in the stride cycle dierent components of this pattern emerge. This might also create potential problems for the use of discrete relative phase in comparing walking and running (e.g., Diedrich and Warren, 1995). As discrete points in the gait cycle (e.g., maximal knee or hip ¯exion) were used in the Diedrich and Warren (1995) study, these events might occur in dierent portions of the gait cycle (stance vs. swing), which might make the comparisons between walking and running more dicult. 5. Conclusion The main conclusions of the present study are that near the transition speed, when speed and stride frequency are controlled and equal, there are topological similarities in coordination patterns between the thigh and leg for walking and running. Time histories of the thigh, leg and knee displayed similar patterns throughout the gait cycle. Phase plots and CRP curves also demonstrated similar overall patterns for both walking and running. However, major dierences between the two gait patterns existed at the later part of the walking stance phase that coincides with before and after running toeo. Timing of toe-o occurrence also exhibited signi®cant dierence between the locomotor modes. Angle and angular velocity of both the thigh and leg displayed signi®cant dierences at toe-o. Relative phase curves demonstrated the most profound dierences at 20±40% of the gait cycle. In addition, although relative phase patterns between walking and running displayed topological similarity, there was evidence of clear functional dierences during the stride cycle between walking and running. References Bobbert, A.C., 1960. Energy expenditure in level and grade walking. J. Appl. Physiology 15, 1015±1021. Capaday, C., Stein, R.B., 1987. Dierence in the amplitude of human soleus H-re¯ex during walking and running. J. Physiology 392, 513±522. Carrier, D.R., 1984. The energetic paradox of human running and hominid evolution. Current Anthropology 25, 483±495. Cavagna, G.A., 1978. Aspects of eciency and ineciency of terrestrial locomotion. In: Asmussen, E., Jorgensen, K. (Eds.), Biomechanics VI-A. University Park Press, Baltimore.
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Cavagna, G.A., Franzetti, P., 1986. The determinants of the step frequency in walking in humans. J. Physiology (London) 373, 235±242. Cavagna, G.A., Kaneko, M., 1977. Mechanical work and eciency in level walking and running. J. Physiology 268, 476±481. Cavagna, G.A., Thys, H., Zamboni, A., 1976. The source of external work in level walking and running. J. Physiology 262, 639±657. Cavanagh, P.R., Williams, K.R., 1982. The eect of stride length variation on oxygen uptake during distance running. Medicine and Science in Sports and Exercise 14, 30±35. Chapman, A.E., Lonergan, R., Caldwell, G.E., 1984. Kinetic sources of lower-limb angular displacement in the recovery phase of sprinting. Medicine and Science in Sports and Exercise 16, 382±388. Chat®eld, C., 1984. The Analysis of Time Series. Chapman & Hall, New York. Clark, J.E., Phillips, S.J., 1993. A longitudinal study of intralimb coordination in the ®rst year of independent walking: A dynamical systems analysis. Child Development 64, 1143±1157. Cohen, J., 1988. Statistical Power Analysis for the Behavioral Sciences. Lawrence Erlbaum, London. Corcran, P.J., Brengelmann, G.L., 1970. Oxygen uptake in normal and handicapped subjects, in relation to speed of walking beside velocity-controlled cart. Archives of Physical Medicine 51, 78±87. Diedrich, F.J., Warren, W.H., 1995. Why change gaits? Dynamics of the walk-run transition. J. Experimental Psychology 21, 183±202. Farley, C.T., McMahon, T.A., 1992. Energetics of walking and running: insights from simulated reducedgravity experiments. J. Appl. Physiology 73, 2709±2712. Farley, C.T., Gonzalez, O., 1996. Leg stiness and stride frequency in human running. J. Biomechanics 29, 181±186. Hagan, R.D., Strathman, T., Strathman, L., Gettman, L.R., 1980. Oxygen uptake and energy expenditure during horizontal treadmill running. J. Appl. Physiology 49, 571±575. Hamill, J., Bates, B.T., Knutzen, K.M., Sawhill, J.A., 1983. Variation in ground reaction force parameters at dierent running speeds. Human Movement Science 2, 47±56. Hamill, J., Derrick, T.R., Holt, K.G., 1995. Shock attenuation and stride frequency during running. Human Movement Science 14, 45±60. Holt, K.G., Hamill, J., Andres, R.O., 1991. Predicting the minimal energy costs of human walking. Medicine and Science in Sports and Exercise 23, 491±498. Hreljac, A., 1993. Preferred and energetically optional gait transition speeds in human locomotion. Medicine and Science in Sports and Exercise 25, 1158±1162. Hreljac, A., 1995. Determinants of the gait transition speed during human locomotion: Kinematic factors. J. Biomechanics 28, 669±677. Kelso, J.A.S., Scholz, J.P., Sch oner, G., 1986. Nonequilibrium phase transition in coordinated biological motion: critical ¯uctuations. Phys. Lett. A 118, 279±284. Kram, R., Taylor, R.C., 1990. Energetics of running: A new perspective. Nature 346, 265±267. Margaria, R., 1976. Biomechanics and Energetics of Muscular Exercise. Clarendon Press, Oxford. Milliron, M.J., Cavanagh, P.R., 1990. Sagittal plane kinematics of the lower extremity during distance running. In: Cavanagh, P.R. (Ed.), Biomechanics of Distance Running, Human Kinetics, Champaign, IL. Nilsson, J., Thorstensson, A., 1989. Ground reaction forces at dierent speeds of human walking and running. Acta Physiology of Scandinavian 136, 217±227. Relston, H.J., 1958. Energy-speed relation and optimal speed during level walking. Internationale Zeischrift f ur Angewandte Physiologie Einschlesslich Arbeitsphysiologie 17, 277±283. Sch oner, G., Jiang, W.Y., Kelso, J.A.S., 1990. A synergetic theory of quadrupedal gaits and gait transitions. J. Theoret. Biol. 142, 359±391. van Emmerik, R.E.A., Wagenaar, R.C., 1996. Eect of walking velocity on relative phase dynamics in the trunk in human walking. J. Biomechanics 29, 1175±1184.
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Vaughan, C.L., Davis, B.L., O'Connor, J.C., 1992. Dynamics of Human Gait, Human Kinetics, Champaign, IL. Williams, K.R., 1993. Biomechanics of distance running. In: Grabiner, M.D. (Ed.), Current Issues in Biomechanics. Human Kinetics, Champaign, IL. Winter, D.A., 1983a. Biomechanical motor patterns in normal gait. J. Motor Behavior 15, 302±330. Winter, D.A., 1983b. Moments of force and mechanical power in jogging. J. Biomechanics, 16, 91±97. Winter, D.A., 1991. The Biomechanics and Motor Control of Human Gait: Normal, Elderly and Pathological, 2nd ed. University of Waterloo Press, Waterloo. Zarrugh, M.Y., Todd, F.N., Relston, H.J., 1974. Optimization of energy expenditure during level walking. European J. Appl. Physiology 33, 293±306.
Coordination patterns of walking and running at similar speed and stride frequency Li Li *, Elizabeth C.H. van den Bogert, Graham E. Caldwell, Richard E.A. van Emmerik, Joseph Hamill Department of Exercise Science, University of Massachusetts, Amherst, MA 01003, USA
Abstract The present study compared walking and running constrained to one speed (2.24 m/s) and the average of preferred walking and running stride frequency. Lower extremity coordination was assessed, using phase plots, relative phase and variability analysis. Angular excursions, phase plots, patterns of relative phase and variability analysis illustrated similar segmental and joint coordination patterns for walking and running. Under the speed and stride frequency constraints, we observed topological similarity in coordination patterns between the thigh and leg in walking and running, which co-existed with functional dierences throughout the gait cycle, especially in the transition from stance to swing phase. Ó 1999 Elsevier Science B.V. All rights reserved. Keywords: Biomechanics; Motor control; Gait; Dynamical systems; Kinematics
Table of variables hT : Thigh angle, de®ned as the angle between the left horizontal and the thigh segment; this angle increases as the thigh rotates clockwise around the hip joint (see Fig. 1); * Corresponding author. Department of Kinesiology, Louisiana State University, 112 Long Fieldhouse, Baton Rouge, LA 70803, USA. Tel.: +1 225 334 3046; fax: +1 225 388 3680; e-mail:[email protected].
0167-9457/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 - 9 4 5 7 ( 9 8 ) 0 0 0 3 4 - 7
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Fig. 1. Thigh (hT ), leg (hL ) and knee (hK ) angle were de®ned at the proximal end with respect to the left horizontal. Knee was de®ned as the angle between the thigh and leg that decreases when the knee joint ¯exes.
hL : Leg angle, de®ned as the angle between the left horizontal and the leg segment; this angle increases as the leg rotates clockwise around the knee joint (see Fig. 1); hK : Knee angle, de®ned as the angle between the thigh and leg segments on the posterior side of the body (see Fig. 1); xT , xL and xK : The angular velocity of thigh, leg and knee angles (hT , hL and hK ), respectively; u: Phase angle, de®ned from the normalized phase plot for each stride cycle as the angle formed between a line from the origin (0, 0) to the current data point (h, x) and the right horizontal. The phase angle increases in the counter-clockwise directions; CRP: Continuous relative phase, de®ned as the dierence between thigh and leg phase angles (thigh phase angle minus leg phase angle) throughout the stride cycle; VCRP: Variability of the continuous relative phase for each subject and each condition; calculated by the mean of the SD of every point on the ensemble curve. 1. Introduction The kinematic and kinetic characteristics of walking and running have been described by many researchers, with the results indicating that a walking
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stride is much dierent than a running stride (Bobbert, 1960; Cavanagh and Williams, 1982; Corcran and Brengelmann, 1970; Hagan et al., 1980; Kram and Taylor, 1990; Relston, 1958; Zarrugh et al., 1974). It has also been shown that the metabolic cost of walking a given distance reaches a minimum value at a speed of approximately 1.25 m sÿ1 and increases as speed increases, whereas the metabolic cost of running a unit distance remains relatively constant at all speeds (Carrier, 1984; Cavagna, 1978; Cavagna and Franzetti, 1986; Cavagna and Kaneko, 1977; Cavagna et al., 1976; Kram and Taylor, 1990; Margaria, 1976; Milliron and Cavanagh, 1990). Interestingly, at the speed of approximately 2.24 m sÿ1 , which is very close to the gait transition speed (Hreljac, 1995), the energy cost for a human to travel a unit distance is similar in walking and running (Cavagna et al., 1976; Hreljac, 1993). The dierent energy cost ± velocity relationships of walking and running may be due to dierent movement organization within the gait patterns. For example, the energetic cost of running is correlated with the weight that the body has to support, which may not be the case in walking (Farley and McMahon, 1992). Factors such as locomotor speed and stride frequency can aect various aspects of human locomotion. For example, Winter (1983a) reported that an increase from natural walking cadence to a 17% faster cadence was accompanied by 18% greater ankle velocity, 20% greater knee velocity and 21% greater hip velocity. Milliron and Cavanagh (1990) indicated that maximal knee ¯exion angle increased as running speed increased. In addition, peak amplitude of the vertical ground reaction force increases as the locomotion speed increases in both walking and running (Hamill et al., 1983; Nilsson and Thorstensson, 1989). Both Zarrugh et al. (1974) and Holt et al. (1991) observed that there exists an energetically optimal and preferred stride frequency for every speed of level walking. Capaday and Stein (1987) observed that the peak EMG level of the soleus was on average 2.4 times greater in running compared to walking. However, it is dicult to distinguish whether this dierence was produced by changing the gait pattern or by variation in locomotor speed or by both factors because their subjects walked at 1.11 m sÿ1 and ran at 2.22 m sÿ1 . Con®ning walking and running to the same speed and stride frequency would eliminate the in¯uence of stride length which has been shown to in¯uence energy cost (Hamill et al., 1995). The importance of progression velocity and stride frequency is especially relevant from the perspective of dynamical systems theory (SchoÈner et al., 1990). This theory views a speci®c gait pattern as an emergent behavior that arises from the collective behavior of all contributing subsystems, including
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both the central nervous and musculoskeletal systems (Diedrich and Warren, 1995). Other constraints, such as those found in the environment (e.g., gravitational forces, slippery walking surfaces) and the task itself (e.g., walking or running at dierent velocity and/or dierent stride frequency) also contribute to shaping the behavior of the system. In this perspective, dierent phase and frequency relations between limbs or body segments typify coordinative modes. These relationships or cooperativities are called ``order parameters''. Changes in the order parameter (e.g. from walk to trot to gallop in quadrupedal locomotion) occur when a speci®c control parameter (e.g. movement speed, frequency) is scaled. The advantage of using this perspective to study gait is that it provides a means of describing a high dimensional system in terms of a low dimensional representation. For instance, relative phase can be used as an order parameter to describe coordination changes between segments with the change of gait pattern (Clark and Phillips, 1993; Diedrich and Warren, 1995). In dynamical systems theory, phase plots, relative phase and their variability have been used to study gait. Phase plots, which display segmental velocity as a function of displacement, have been used to identify the coordinative pattern of the thigh and leg (Clark and Phillips, 1993). Continuous relative phase (CRP) has been used to study spatial-temporal coordination (van Emmerik and Wagenaar, 1996), while discrete relative phase has been used to study the temporal coordination (Diedrich and Warren, 1995). Variability in both continuous and discrete relative phases has been employed as an indication of system stability. In some movements, greater variability indicates that the system is closer to the point where a new pattern will emerge, while less variability will be a sign of a more stable system (Kelso et al., 1986; van Emmerik and Wagenaar, 1996). Overall, these measures have great potential for studying similarities and dierences between walking and running. Previous studies comparing the gait patterns of walking and running are equivocal because locomotor velocity was greater in running than in walking. It is not clear whether gait pattern, locomotor speed or stride frequency has the greatest in¯uence on the system. Comparing coordination patterns and variability, it is also not clear what will be the dierences and/or similarities between walking and running when the speed is controlled. In the present study, we controlled locomotor speed and stride frequency as the gait pattern was varied between walking and running. The purpose of this study was to compare lower extremity coordination in walking and running at the same speed and same stride frequency. By stabilizing other control parameters,
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such as locomotion speed and stride frequency, we were able to isolate the eects of dierent gait patterns on coordination and variability. 2. Methods 2.1. Subjects The subjects in this experiment were young, healthy, male university graduate students. Based on previous data reported by other researchers (Hreljac, 1995), a power analysis (Cohen, 1988) was performed to determine the number of subjects needed in this experiment. It was found that ®ve subjects would provide more than 80% of statistical power necessary to detect segmental angle dierences between walking and running conditions. In order to balance the condition order between subjects, a total of six subjects were chosen to perform the test. The average age, stature and body mass were: 28 4 yr; 1.79 0.07 m and 76 11 kg, respectively. Informed consent and medical clearance were obtained from each subject prior to the experiment. 2.2. Experimental procedures There were two experimental conditions: walking and running both performed at the same speed on a motorized treadmill. A speed of 2.24 m sÿ1 was selected based on the similarity of the energetic cost of walking and running at that speed (Cavagna et al., 1976; Hreljac, 1993). Prior to the start of the test session, subjects were instructed to run on the treadmill at their preferred speed for 5 min to warm up. Their preferred stride frequencies were determined while they walked and ran on the treadmill at level grade at the testing speed for 5 min. The average of preferred running and walking frequency for each individual was calculated and then imposed by a metronome in the testing sessions to help subjects maintaining their locomotor frequency. During the data collection, they either walked or ran at 2.24 m sÿ1 with this imposed stride frequency for 6 min. The order of walking and running conditions was alternated between subjects. 2.3. Data collection and processing Kinematic data were collected continuously with a high-speed (200 Hz) video camera for the last 3 min of the 6 min of walking and running. Retro-
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re¯ective markers were used to identify joint centers of the lower extremity. Ankle, knee and hip joints were de®ned by markers on the lateral malleolus, the point above the superior margin of the lateral tibia and the greater trochanter, respectively. Video data from the retro-re¯ective markers were used to determine sagittal view kinematics. Kinematic data were smoothed using a zero-lag dual pass Butterworth digital ®lter with a cut-o frequency of 18 Hz. For each subject, 5 consecutive stride cycles from the last minute of a walking or running condition were selected for analysis. Each stride cycle was de®ned from heel contact to next heel contact with heel contact identi®ed using the vertical coordinate of the ankle marker. Angle and angular velocities for the thigh (hT , xT ), leg (hL , xL ) and knee (hK , xK ) were calculated from the re¯ective marker data (Fig. 1).
Fig. 2. Typical phase plots of walking and running from an exemplar subject (left and right panel, respectively). Stance phase is indicated by solid line, swing phase by broken line. Time progresses in clockwise fashion around phase plot.
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2.4. Data analysis 2.4.1. Phase plots Phase plots of the leg, thigh and knee were employed to compare lower limb motion between walking and running. Each phase plot was determined in raw units with angular displacement on the horizontal axis and the angular velocity on the vertical axis (for example, see Fig. 2). In order to calculate phase angle (u) and to minimize the in¯uence of dierent movement amplitudes, the phase plots were normalized for each trial. The following formulae were used for phase plot normalization 2 hi ÿ min hi ÿ 1; 1 max hi ÿ min hi where h stands for joint or segment angle and i for each data point within the stride cycle. This normalization puts the origin of the horizontal axis in the middle of the range while normalizing the minimum value to ÿ1 and maximum value to 1. Horizontal axis angle: hi
2 Vertical axis angular velocity: xi xi =R; where R was calculated as: R maxfjxi jg and xi represents angular velocity at each data point i. The largest magnitude of positive and negative angular velocity values for one stride cycle was normalized to 1. The same scale then was applied to all angular velocity data in the same stride cycle. This process was repeated for each stride cycle. The phase angle ui was de®ned from the normalized phase plot for each stride cycle as the angle formed between a line from the origin (0, 0) to the current data point (hi , xi ) and the right horizontal. 2.4.2. Relative phase variables The CRP was de®ned as the dierence between thigh and leg phase angles at each point throughout the stride cycle. CRP is therefore considered to be a measure of the coordination between the thigh and leg segments. The ensemble curve was calculated from the CRP curves of ®ve strides for each subject in each condition. The results of the ensemble curve calculation are presented as the mean of the ®ve trials. 2.4.3. Variability Variability within the two gait patterns was calculated from the standard deviation of the CRP measures. The results of these calculations are an
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indication of cycle to cycle variability and can be used to compare system stability characteristics across gait patterns (see van Emmerik and Wagenaar, 1996 for a detailed explanation of the methods involved). The variation of CRP (VCRP) for each subject and each condition was calculated as the mean of the SD of every point on the ensemble curve. 2.5. Statistical analysis The phase plots and relative phase graphs were analyzed qualitatively for similarities and dierences between conditions. The degree of similarity of CRP patterns throughout the gait cycle between walking and running for each subject was evaluated by using cross correlation (Chat®eld, 1984). Repeated measures ANOVA was performed on hT , xT , hL , xL , hK , and xK at heel contact and toe-o in order to compare parameters between walking and running conditions quantitatively. Comparison of the average dierence of CRP curves between conditions was also carried out by repeated measures ANOVA. Comparison of variability between each condition was tested by paired t-test (two-tailed), using the VCRP. A statistical comparison between the CRP curves for walking and running was obtained by calculating the absolute dierence between the CRP curves in the two conditions for each subject. These comparisons were done over means of 10% intervals of the gait cycle. The dierences between each 10% bin were evaluated using 99.5% con®dence interval comparisons. 3. Results 3.1. Kinematics at heel contact and toe-o Kinematic analysis indicated that toe-o occurred at 38% (SD 3%) and 54% (SD 1%) of the gait cycle for running and walking, respectively. Summary comparisons of the lower extremity kinematic parameters at heel contact and toe-o are presented in Tables 1 and 2, respectively. At heel contact (Table 1), there was a signi®cant dierence between gait conditions for both hT and hL . Both hT and hL decreased from walking (hT mean: 113°; hL mean: 98°) to running (hT : 104°; hL : 87°). In contrast, hk and all angular velocities were not signi®cantly dierent between walking and running conditions.
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Table 1 Results of repeated measurement ANOVA for kinematic variables at heel contact Walking (MeanSD) hT (°) hL (°) hK (°) xT (°/s) xL (°/s) xK (°/s)
113 3 98 4 166 4 ÿ38 42 ÿ180 56 ÿ142 80
Running (MeanSD)
F
P-Value
77.5 43.5 1.69 5.21 0.43 0.81
0.0003 0.0012 0.2509 0.0713 0.5420 0.4106
104 4 87 3 163 3 21 31 ÿ162 60 ÿ184 74
Only F-test results that relate to the walking and running comparison are presented here. Table 2 Results of repeated measurement ANOVA for kinematic variables at toe-o Walking (Mean SD) hT (°) hL (°) hK (°) xT (°/s) xL (°/s) xK (°/s)
62 1 43 3 161 3 51 50 ÿ268 32 ÿ318 80
Running (Mean SD)
73 3 51 4 159 5 ÿ167 32 ÿ15 30 151 56
F
P-Value
62.7 63.2 0.92 102 312 192
0.0005 0.0005 0.3820 0.0002 <0.0001 <0.0001
Only F-test results that relate to the walking and running comparison are presented here.
At toe-o (Table 2), both hT and hL increased signi®cantly from walking (hT : 62°; hL : 43°) to running (hT : 73°; hL : 51°), whereas hK did not change. For the measurements of angular velocity, xT was positive in walking (51°/s) but negative in running (ÿ167°/s). This indicates that the thigh was swinging forward at toe-o in walking and backward in running. The magnitude of xL was greatly reduced in running (ÿ15°/s) compared to walking (ÿ268°/s), but the direction remained the same. These segmental velocities resulted in a negative xK (knee ¯exion) for walking (ÿ318°/s) and a positive xK (knee extension) for running (151°/s). All of these angular velocity dierences between walking and running were signi®cant at toe-o. Note that the standard deviations of all angles were relatively small compared to the standard deviation of angular velocities. 3.2. Phase plots Fig. 2 displays typical phase plots for one exemplar subject for one gait cycle (heel contact to heel contact) of walking and running, respectively.
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Data points on these phase plots follow clockwise as time progresses. At heel contact, hT was close to the maximum value with xT close to zero (see upper panels of Fig. 2). hT decreased throughout the stance phase with an almost constant angular velocity near ÿ200°/s in both gait patterns. Compared to walking, the running stance phase ended at an earlier stage in the phase plot with xT at approximately ÿ165°/s (contrasted with 25°/s for walking). During the major part of the swing phase in both walking and running, hT increased with a positive xT value until shortly before heel contact. The leg phase plot indicates that hL decreased throughout the whole stance phase and the magnitude of xL ¯uctuated but was always negative in both walking and running (see middle panels of Fig. 2). hL continued to decrease in the ®rst part of the swing phase, then increased to its maximum value at the end of the swing phase for both locomotion patterns. Finally, the knee phase plot displayed a small and a large ellipsoid associated with the stance and swing phase, respectively, in both walking and running. However, the ellipsoid associated with running stance phase was not complete when compared to the ellipsoid in walking (lower panels of Fig. 2). 3.3. Continuous relative phase Fig. 3 is a graphic representation of the ensemble CRP curves of the six subjects for both walking and running conditions. Positive CRP indicates that the leg phase angle is in the leading position relative to the thigh phase angle, while negative CRP indicates the opposite. Zero CRP is equivalent to the two segments being in phase, while both 180° and ÿ180° would mean that the two segments move in anti-phase. For both conditions, there was greater dierence observed during late stance and early swing (25±50% in walking and 15±45% in running) compared to the rest of the gait cycle. In both conditions, CRP was slightly positive at heel contact and increased immediately, reaching its peak positive value at approximately 5±10% of the gait cycle. In the walking condition, CRP crossed zero in a relatively consistent fashion, close to 15% of the gait cycle. In contrast, the crossing point of the running CRP varied between subjects (range 15± 35% of the gait cycle). CRP was dominated by negative values during swing phase for both conditions. Note that in the walking condition, CRP crossed the zero point far before toe-o occurred. In the running condition, these two events were more closely linked in time, especially for three of the six subjects. Overall, the range of CRP (between minimum and
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Fig. 3. Continuous relative phase of walking and running for six subjects. Relative phase was de®ned as the thigh phase angle minus the leg phase angle.
maximum) was smaller in the walking condition than in the running condition. Results of cross-correlation showed that the CRP trends of the two modes of locomotion were similar for each subject (R 0.75, 0.85, 0.89, 0.91, 0.96 and 0.98 for individual subjects). Dierences in CRP between conditions for each 10% portion of the gait cycle are shown in Fig. 4. The error bars in the graph indicate 99.5% con®dence intervals (overall a level controlled at 0.05 level). There were signi®cant dierences between walking and running CRP throughout the entire gait cycle, as indicated by the fact that none of the con®dence intervals crosses zero. The CRP dierence between walking and running was much greater from 20% to 40% of the gait cycle and these differences were signi®cantly dierent from the CRP dierence during the rest of the gait cycle (see Fig. 4 for the coverage of the 99.5% con®dence interval of each 10% bin). These signi®cantly greater dierences occurred in the second half of the running stance phase until toe-o, which coincided with the midstance of walking (20±40% of gait cycle).
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Fig. 4. Absolute dierences between walking and running CRP throughout the gait cycle at each tenth bin of the gait cycle with error bars indicate 99.5% con®dence interval of every bin. There are always more than 10% dierences in CRP with greater dierence observed at 20±40% of the gait cycle.
3.4. Variability The variability for continuous relative phase (VCRP) is displayed in Table 3. While some individual subject dierences are apparent, there was no clear pattern for either walking or running to have greater variability. The paired t-test also did not detect any signi®cant dierences in variability. 4. Discussion In this study we compared lower extremity coordination in the two gait modes of walking and running while controlling for speed and stride Table 3 Variability of continuous relative phase (VCRP) in walking and running Subject
Walking (°)
Running (°)
1 2 3 4 5 6
6 22 17 22 21 17
15 26 17 20 19 17
Result of paired t-test of the dierence between walking and running: p 0.4081.
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frequency. The most pronounced dierences between the two forms of locomotion were observed at toe-o including the direction of the lower extremity movement relative to the body (see xT in Table 2). In con®ning locomotion to the same speed (2.24 m/s) and stride frequency, toe-o occurred at approximately 54% of the gait cycle for walking and 38% for running. Following toe-o the swing leg moved forward relative to the body in walking, but backward relative to the body in running. The time histories of thigh and leg kinematics generated in this study were comparable to those that exist in the research literature. Time histories of hip, thigh and knee angles of walking (Fig. 5) exhibited the same pattern as the data presented by Winter (1991). The range of motion of both thigh and knee in our study was greater than in Winter (1991) due to the greater walking speed. Similar time histories for running (Fig. 5) exhibited the same
Fig. 5. Typical thigh, leg and knee angle comparison between walking and running for one cycle (from heel contact to heel contact). RTO ± running toe-o; WTO ± walking toe-o.
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patterns as the data presented by Williams (1993). The relative phase curves (Fig. 3) also displayed the same characteristics as those in the literature (Clark and Phillips, 1993), although the range of motion was dierent in our data. Hreljac (1995) has demonstrated the in¯uence of changing both speed and gait pattern on hip angle. His study illustrated the interactions produced by manipulating both speed and gait mode factors. In walking, the range of motion of the hip increased as the progression speed increased. However, as the gait pattern changed to running at the preferred transition speed, the hip range of motion actually decreased. The magnitude of the maximal hip angle was less in running (18°) than in walking (22°). However, the maximal hip angle measurement showed a similar decrease from 22° to 18° when walking speed was modi®ed to 70% of the preferred transition speed (Hreljac, 1995). Furthermore, the change of minimum hip angle caused by gait transition was similar to the change caused by increasing walking speed from 70% to 100% preferred transition speed. Thus, it was dicult to determine whether the changes in certain kinematic variables were due to the change of the gait pattern or due to the change in locomotor speed. The same argument can also be made for the in¯uence of stride frequency (Farley and GonzaÂlez, 1996). However, in the present study all observed similarities and dierences were only in¯uenced by the chosen gait pattern, because the locomotor speed and stride frequency were identical for both progression modes. The observed coordination patterns between the thigh and leg were quite similar in walking and running except during 20±40% of the gait cycle (Figs. 3 and 4). In contrast, Nilsson and Thorstensson (1989) suggested that the dierences present in walking and running are consequences of fundamental dierences in motor strategies between the two major forms of human progression. We observed both similarities and dierences at the tested speed of 2.24 m/s. It would seem that more overall dierences would be expected if there were fundamental changes in motor strategies. The fact that the alterations between the two forms of locomotion were concentrated at 20±40% of the gait cycle may indicate more subtle dierences in motor strategies rather than fundamental ones. In a subsequent study, we will examine these gait pattern similarities and dierences at a wider range of speeds including the transitional speed. The present data also suggest that the individual subject patterns of the CRP curves were more consistent in the walking condition than in the running condition (see Fig. 3). To explore these between-subject dierences of
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lower extremity coordination strategies more thoroughly would require more subjects and shall be the focus of further studies. 4.1. Similarities between the two gait modes The data demonstrate many similarities between the gait conditions. Tables 1 and 2 indicate that there were no signi®cant dierences of the knee angle hK at both heel contact and toe-o. CRP patterns in Fig. 3 indicate that similarity in coordination pattern occurs throughout the complete gait cycle, especially during early stance and for most of swing. This may indicate that, topologically, the coordination patterns between the thigh and leg were similar for walking and running, even though there were signi®cant dierences between the two conditions for hL and hT at toe-o and heel contact (Tables 1 and 2). Fig. 2 demonstrates similar patterns of thigh, leg, and knee phase plots between walking and running. The major dierence between gaits for all three pairs of phase plots are that toe-o occurred at dierent phase angles in the cycle. The CRP patterns (Fig. 3) were consistent with the phase plot data in that the overall patterns were similar for walking and running (R 0.75±98) except for the dierences exhibited at 20±40% of the gait cycle (Fig. 4). The variability data (Table 3) reveal that walking and running had similar amounts of variation. Two subjects exhibited greater variability in CRP for running and the other two exhibited greater variability for walking. As noted in the introduction, from a dynamical systems perspective, the variability of relative phase is an indicator of the stability of the coordination pattern. Diedrich and Warren (1995) observed increases in the variability of relative phase (between ankle, knee and hip joints) during transition from both walking to running and running to walking. Similar increases in variability of relative phase between motions of pelvic and thorax in the trunk were observed by van Emmerik and Wagenaar (1996). Therefore, increases in variability of relative phase can possibly identify transitions from one stable pattern to another. However, the present results suggest that both gait patterns were equally stable at the controlled stride frequency during the experiment at the test speed of 2.24 m/s (close to the walk to run transition speed). Note that the imposed stride frequency could in¯uence the characteristics of the locomotion variability. Subsequent studies are needed to determine whether similar variability characteristics also exist at other locomotor speeds and how they are aected by imposed stride frequency.
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4.2. Dierences between the two gait modes While the previous section pointed out the many similar aspects of the two gait conditions, dierences were also found. Signi®cant dierences between walking and running for xT , xL , and xK were observed at toe-o (Table 2). The lower extremity was moving forward at toe-o for walking (toe-o at 54% of stride cycle) whereas it was moving backward for running (toe-o at 38% of stride cycle). This coincides with the knee joint being in extension at toe-o in running but in ¯exion in walking (see Fig. 5). Between 38% and 54%, the phase plots of the thigh and leg demonstrated a similar path for the two gaits (Fig. 2). During this interval, the lower extremity was in contact with the ground for walking, but was in the ¯ight phase for running. During the same interval, before toe-o in walking and after toe-o in running, hip ¯exion and knee extension joint moments have been observed experimentally for both walking (Winter, 1991; Vaughan et al., 1992) and running (Winter, 1983b; Chapman et al., 1984). These joint moments result in similar kinematic performance for the thigh and the leg segments and the knee joint for both walking and running (Figs. 2±4), despite the dierent position of the foot with respect to ground contact. However, this variant foot position between gait modes may alter peripheral control during the subsequent portion of the cycle. During this time the ankle plantar ¯exors are being stretched in walking with the foot on the ground, but not in running with the foot in the air. Therefore, a stronger stretch re¯ex in walking may contribute to the dierences after toe-o between the two progression modes. 4.3. Topological invariance versus quantitative dierences The most important message from Figs. 2 and 5 is that while the overall kinematic patterns are preserved, discrete events such as the timing of toe-o change with gait modes. Interestingly, a dierent picture emerges if the CRP is divided into functional phases (early, late stance and swing, see Fig. 3). Dramatic dierences can be observed by comparing walking and running CRP within each functional phase. It is important to note that the overall coordination patterns revealed by CRP (Fig. 3 and cross correlation range from 0.75 to 0.98), are preserved in terms of topology. However, closer inspection of Fig. 3 reveals that these similar components occur throughout dierent functional phases for walking and running. For example, in walking during early stance phase, the thigh phase angle switched from leading the leg
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phase angle to lagging the leg phase angle. In running, however, the thigh leads the leg almost throughout the entire early stance phase. These data suggest that a distinction should be made between overall topology of the relative phase patterns and the timing of when in the stride cycle dierent components of this pattern emerge. This might also create potential problems for the use of discrete relative phase in comparing walking and running (e.g., Diedrich and Warren, 1995). As discrete points in the gait cycle (e.g., maximal knee or hip ¯exion) were used in the Diedrich and Warren (1995) study, these events might occur in dierent portions of the gait cycle (stance vs. swing), which might make the comparisons between walking and running more dicult. 5. Conclusion The main conclusions of the present study are that near the transition speed, when speed and stride frequency are controlled and equal, there are topological similarities in coordination patterns between the thigh and leg for walking and running. Time histories of the thigh, leg and knee displayed similar patterns throughout the gait cycle. Phase plots and CRP curves also demonstrated similar overall patterns for both walking and running. However, major dierences between the two gait patterns existed at the later part of the walking stance phase that coincides with before and after running toeo. Timing of toe-o occurrence also exhibited signi®cant dierence between the locomotor modes. Angle and angular velocity of both the thigh and leg displayed signi®cant dierences at toe-o. Relative phase curves demonstrated the most profound dierences at 20±40% of the gait cycle. In addition, although relative phase patterns between walking and running displayed topological similarity, there was evidence of clear functional dierences during the stride cycle between walking and running. References Bobbert, A.C., 1960. Energy expenditure in level and grade walking. J. Appl. Physiology 15, 1015±1021. Capaday, C., Stein, R.B., 1987. Dierence in the amplitude of human soleus H-re¯ex during walking and running. J. Physiology 392, 513±522. Carrier, D.R., 1984. The energetic paradox of human running and hominid evolution. Current Anthropology 25, 483±495. Cavagna, G.A., 1978. Aspects of eciency and ineciency of terrestrial locomotion. In: Asmussen, E., Jorgensen, K. (Eds.), Biomechanics VI-A. University Park Press, Baltimore.
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