Gait & Posture 26 (2007) 400–406 www.elsevier.com/locate/gaitpost
Anomalous centre of mass energy fluctuations during treadmill walking in healthy individuals Johnathan Collett a,b,*, Helen Dawes a,b,c, Ken Howells a, Charlotte Elsworth a,b,d, Hooshang Izadi a,e, Cath Sackley d b
a Movement Science Group, School of Life Sciences, Oxford Brookes University, United Kingdom Rivermead Research Group, OCE, Nuffield Orthopaedic Centre NHS Trust, Oxford, United Kingdom c Department of Clinical Neurology, University of Oxford, United Kingdom d School of Health Sciences, University of Birmingham, United Kingdom e School of Technology, Oxford Brookes University, United Kingdom
Received 6 March 2006; received in revised form 12 October 2006; accepted 15 October 2006
Abstract Motorised treadmills are used to research and rehabilitate gait despite conflicting evidence that treadmill ambulation is equivalent to ground walking. It has been suggested that no mechanical differences should exist between these environments but there is little evidence to support this. During ground walking, the whole body centre of mass (COM) acts like an inverted pendulum recovering energy, thereby reducing the effort of locomotion. The energy recovery has a relationship with speed whereby maximum recovery occurs at intermediate speeds. In order to determine the relationship between energy recovery and speed during treadmill walking, we investigated estimated COM displacement in nine healthy individuals each walking on a treadmill at seven different speeds. In addition, we measured oxygen cost to determine the effort of walking. Our participants formed two distinct groups, those with normal COM energy recovery (N%R) that was similar to ground walking, and those with low COM energy recovery (L%R) that was different from typical ground walking. The low energy recovery in the L%R group was attributed to in-phase potential and kinetic energy fluctuations. Despite the low energy recovery values both groups produced the expected ‘U’-shaped oxygen cost speed curve with no significant difference between groups ( p < 0.05), however, only N%R produced a significant relationship between energy recovery and oxygen cost ( p < 0.05). Although a useful tool, walking on a treadmill may not be a true representation of ground walking and therefore not the most effective way to research or rehabilitate gait. # 2006 Elsevier B.V. All rights reserved. Keywords: Centre of mass; Treadmill; Oxygen cost; Froude; Phase shift
1. Introduction Treadmills offer a continuous-controlled environment attractive to both clinicians and researchers. They are routinely used clinically, with the aim to improve over ground gait and have been used in research to imitate ground walking [1]. However, there is a lack of evidence to support that treadmill walking is comparable to that on the ground [2]. * Corresponding author at: Movement Science Group, School of Life Sciences, Oxford Brookes University, Gypsy Lane, Headington, Oxford OX10 0SB, United Kingdom. Tel.: +44 1865 484295. E-mail address:
[email protected] (J. Collett). 0966-6362/$ – see front matter # 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2006.10.002
It has been suggested that if belt speed is used as a frame of reference no mechanical difference exists between treadmill and ground walking [3]. However, treadmill walking has been shown to differ in ground reaction force magnitude [2] and some joint kinematics and spatiotemporal gait parameters [4,5]. In addition, the evidence is conflicting whether metabolic demand is less during treadmill walking [5–8]. A primary aim during clinical interventions is to reduce the effort and to increase the efficiency of pathological gait. Optimising walking effort has shown to be dependent on speed in both clinical and healthy groups [9–11]. The criterion measure for the effort of walking is oxygen consumption [12], however it provides little insight into factors affecting this
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effort. During level ground walking mechanical work is required to raise the centre of mass (COM). This work accounts for 60–75% of the total mechanical work done [13– 15] and is a reliable estimate of the work performed by muscles during walking, at intermediate speeds [13]. Furthermore, there is a reciprocal exchange of potential (PE) and kinetic (KE) energies of the COM, explained by the inverted pendulum model [16], with energy recovered through the gait cycle reducing the energy required to maintain locomotion. During each stride the COM is either behind or in front of the point of contact with the ground connected by the leg acting like a strut. When the COM is behind the point of the ground contact it decelerates as it is vertically displaced, leading to a reduction in KE and an increase in PE. As the COM moves past the point of contact with the ground it accelerates due to gravity, leading to an increase in KE and a reduction in PE [9] (Fig. 3a). The energy recovered via the inverted pendulum model is dependent on the relationship between phase and amplitude of the PE and KE curves. A recovery of 100% would require that PE and KE energy fluctuations were exactly opposite in-phase (1808) and of equal amplitude [15,17]. However, this can only occur in an ideal frictionless pendulum. When walking at higher speeds KE fluctuations are greater than PE fluctuations and at lower speeds PE fluctuations are greater than KE fluctuations [15]. In addition, at low and high speeds the phase relationship between PE and KE curves deviate from the ideal 1808 out of phase relationship [18]. Consequently, the amount of energy recovered produces an inverted U-shaped relationship with walking speed [15,17–19] with a maximum recovery of 70% occurring at intermediate speed when PE and KE energy curves approach 1808 out of phase and amplitude difference approaches zero [15,18]. Leg length can be normalised using Froude numbers (Fr) [20], a dimensionless measure relating velocity and leg length (pendulum). Maximum recovery occurs at the same equivalent speed or Fr = 0.25 in individuals through a range of leg lengths [18,21,22]. Oxygen cost (consumption per unit distance walked) elicits a U-shaped relationship with walking speed in both ground and treadmill walking with the minimum value representing optimum walking speed [10,23,24]. The optimal walking speed in terms of oxygen cost tends to correspond with the speed which individuals self-select [25] and moreover is associated with a Fr = 0.25 and maximum COM energy recovery [26]. Minetti et al. [1] alluded to in-phase KE and PE energy fluctuations during treadmill walking. Indeed previous work comparing ground and treadmill walking found significantly
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lower COM energy recovery values during treadmill walking (mean maximum recovery 26.7%) compared to normal values obtained for ground walking (mean maximum recovery 61.9%) at a range of speeds [27]. This difference was attributed to in-phase KE and PE fluctuations during treadmill walking. The present study was designed to further investigate COM energy fluctuations during treadmill walking and their effects on the inverted pendulum energy recovery model through a range of speeds.
2. Methods 2.1. Study population Four men and five women (mean: 22; S.D.: 2 years), new to treadmill walking, volunteered for the study and gave written informed consent prior to participation in accordance to the declaration of Helsinki [28] and the University Ethical Committee. The participants met the inclusion criteria of being able to walk for 28 min without stopping and had no neurological or musculoskeletal conditions affecting gait. Descriptive details of the participants are outlined in Table 1. 2.2. Gait analysis Prior to testing participants were asked to refrain from the consumption of alcohol, cigarettes, food, caffeine and medication and to avoid exercise for a period of three hours. Testing was carried out utilising the following standardised testing protocol by the same investigators, at the same time of day (room temperature, 20–25oC). Mass (Seca, CMS, London, UK) and height were measured wearing minimum clothing. Leg length was measured from anterior superior iliac spine to medial malleolus. Oxygen consumption was measured via the collection of expired air by means of a face mask (Hans Rudolf, Kansas City, USA), and a Douglas bag [24]. The composition of the expired air was determined by oxygen and carbon dioxide analysers (Servomex, East Sussex, UK) and the volume of expired air was determined by a dry gas meter (Harvard dry gas meter, Kent, UK). The gas analysers were calibrated at each testing occasion by means of gas mixtures of known concentration. Oxygen consumption was calculated using standard closed circuit methodology and the values expressed under standard conditions (STPD). COM motion was estimated from a 2.5 cm reflective marker attached over the spinous process of the fourth lumbar vertebrae (L4) [29–31]. The three-
Table 1 Group characteristics Group
n
Height (m)
Mass (kg)
Leg length (m)
SS speed (m s1)
Max % recovery
N%R L%R
3 6
1.763 0.1 1.764 0.087
74 18.3 73 12.8
0.95 0.075 0.955 0.05
1.3 0.2 1.3 0.1
72 9 18 3
Mean and standard deviation.
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dimensional position of the markers was acquired via a twocamera motion analysis system sampling at 100 Hz (Qualysis, Sweden). Participants were asked to walk on the treadmill (Woodway PPS 55, Germany) while the speed display was obscured. An investigator adjusted the treadmill speed so that the participant experienced a range of walking speeds up to and including ‘walk–run transition’ speed. After this the participant was ask to find a ‘‘natural comfortable walking speed’’ by adjusting the treadmill speed control themselves; ‘‘self-selected walking speed’’ (SS). Once SS was determined, speeds of 20%, 40% and 60% above and below the SS were used. If the 60% above the self-selected speed was greater than 90% of the ‘‘walk–run transition’’ speed, then 90% of the ‘‘walk–run transition’’ was used. Each participant walked for 4 min at the seven different speeds, incrementally. Expired air was collected in minutes 3–4 of each speed to ensure physiological steady state; during this period the motion analysis was also performed. 2.3. Data analysis STPD oxygen cost (ml kg1 m1) was calculated from expired air. The efficiency of energy recovery according to the inverted pendulum model (% recovery) was calculated using the methods of Wang et al. [32]. Our methods differed as we calculated the energy fluctuations of the COM from the motion of the L4 marker in horizontal (x), lateral (y) and vertical (z) directions and not from ground reaction forces. Displacement (x, y, z) of the COM marker was obtained from the motion capture system (Q track 2.77, Qualysis, Sweden). Velocity (x, y, z) was then calculated from displacement between each time point (distance/time). Potential (PE) and kinetic energies (PE) of the estimated COM could then be then derived from the displacement and velocity of the L4 marker using the equations: PE ¼ mgh
(1a)
KE ¼ 12mv2
(1b)
where m is mass, g the acceleration due to gravity, h the height of COM (z) and v is velocity of COM (x, y, z) (incorporating treadmill x velocity). The amplitude of the fluctuations of the energies (DPE, DKE) were then averaged over four consecutive strides and % recovery calculated using the equation: % recovery ¼ 100
ðDPE þ DKEÞ DðPE þ KEÞ DPE þ DKE
(2)
The dynamic similarity of participants was calculated using Froude numbers: Fr ¼
v2 gL
(3)
where v is walking velocity, g the acceleration due to gravity and L is leg length.
To further investigate energy transductions of the COM phase and amplitude, relationships between PE and KE fluctuations were calculated. Phase shift was calculated as the point at which the KE cycle started in relation to the PE cycle. Positive KE fluctuations occurring at 18 or 3598 of the PE cycle represent the same magnitude of phase shift. We therefore calculated a phase shift based on the methods of Cavagna et al. [33] as the degrees of difference between the KE positive fluctuation and 1808 of the PE cycle. A phase shift of a = 08 represents perfectly out of phase PE and KE fluctuations and a = 1808 perfectly in-phase PE and KE fluctuations. The equality of PE and KE fluctuation amplitude was determined as the percentage difference from the larger fluctuation over a stride. 2.4. Statistical analysis To investigate the relationship among several different variables in the study, a regression method of analysis was performed. Linear and quadratic equations were fitted to the data and relationships determined on the basis of the strength of correlation coefficient (R2) together with the significance of slope coefficients. Repeated Measures ANOVA was used to explore the within-subjects effects for the Fr measurements and between-subject differences in the two groups.
3. Results Initial analysis of the data revealed that individuals formed two distinct groups, those with normal % recovery values through the range of speeds and those with low values. Therefore, we dichotomously grouped participants according to whether normal pendulum-walking mechanics were maintained during treadmill walking. Participants with maximum % recovery values within 15% of the normal maximum value (70% [17]) were deemed to have maintained pendulum-walking mechanics and formed the N%R group [34]. Participants with maximum % recovery that did not meet this criterion were placed in L%R group. Descriptive details of the groups are found in Table 1. N%R was made up of three participants (one male, two females) and the L%R of six (three males, three females). Repeated measures ANOVA confirmed a significantly greater % recovery for N%R over all percentages of SS speed ( p < 0.01), with no significant difference in Fr ( p > 0.05) between groups. T-tests showed no significant difference ( p > 0.05) in height, mass, leg length or speed. Oxygen cost elicited the U-shaped curve with Fr expected from the literature (Fig. 1). Both groups had a significant quadratic relationship ( p < 0.01) with R2 values of 0.617 and 0.738, respectively, for N%R and L%R. Repeated measures ANOVA showed there was no significant difference in oxygen cost between groups ( p > 0.05), with minimum oxygen cost calculated from the regression equations occurring at
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Fig. 1. The oxygen cost Fr relationship. The data reported is for all individuals at all speeds, the solid line represents the quadratic oxygen cost Fr relationship in N%R (unfilled) with the dashed line representing L%R (filled). The slope of the N%R regression line is equal to: y = 2.0825x2 1.1454x + 2.774 with an R2 = 0.617 ( p < 0.01) from the equation minimum VO2 (0.149 ml kg1 m1) was calculated at Fr = 0.25. The equation of the L%R regression line is: y = 1.7416x2 0.9347x + 0.0730 (R2 = 0.738, p < 0.01) with a minimum VO2 of 0.148 ml kg1 m1 at Fr = 0.27.
Fr = 0.25 (VO2 = 0.149 ml kg1 m1) for N%R and Fr = 0.27 (VO2 = 0.148 ml kg1 m1) for L%R. Quadratic relationships were also found for % recovery and Fr (Fig. 2): N%R elicited an inverted U relationship which was significant ( p < 0.05) with R2 = 0.34 and maximum % recovery (66.85%) calculated at Fr = 0.19. The opposite was found in L%R with a significant U-shaped relationship (R2 = 0.24, p < 0.01) between % recovery and
Fig. 3. COM energy fluctuations. Examples of KE (solid line) and PE (dashed line) fluctuation of the COM during walking at self-selected speeds. Normalised to the gait cycle maximum vertical displacement occurs at approximately 30% and 80% of the cycle during single support and minimum displacement occurring at approximately 0% and 50% during double support. (a) An example of out of phase energy fluctuations in one participant during treadmill walking (a = 388). (b) An example of in-phase energy fluctuations in one participant during treadmill walking (a = 1398). Fig. 2. The % recovery Fr relationship. Reported are the data for all individuals at all speeds, the solid line represents the quadratic % recovery Fr relationship for N%R (unfilled) with the dashed line representing group L%R (filled). Maximum % recovery was calculated as 66.85% at Fr = 0.19 from the regression line y = 296.19x2 + 114.594x + 55.7667 (R2 = 0.34, p < 0.05) for N%R. It was not possible to calculate maximum % recovery from the L%R regression line (y = 151.627x2 50.621x + 10.3373, R2 = 0.24, p < 0.01).
Fr, therefore the Fr at which maximum % recovery occurred could not be determined. (Minimum % recovery (6.11%) was calculated at Fr = 0.17.) When further inspecting pendular energy transduction, N%R participants walked with out of phase KE and PE fluctuations (Fig. 3a). Participants in L%R walked with
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Fig. 4. The oxygen cost % recovery relationship. Reported are data for all individuals at all speeds, the black line represents the linear % recovery oxygen cost relationship for N%R (unfilled data points) (y = 0.0021x + 0.3029, R2 = 0.249, p < 0.05) with the grey line representing L%R (filled data points) (y = 0.0007x + 0.1843, R2 = 0.016, p > 0.05).
When considering the metabolic and mechanical data N%R had a weak but significant negative linear correlation between oxygen cost and % recovery (R2 = 0.249, p < 0.05) with L%R showing no correlation (R2 = 0.016, p > 0.05) (Fig. 4). Further analysing the % recovery with phase shift relationship showed a significant negative linear correlation for L%R (R2 = 0.507, p < 0.01) with N%R having a non significant relationship (R2 = 0.065, p > 0.05) (Fig. 5). Interestingly, when the data were not divided into groups a strong significant linear relationship was produced between % recovery and phase shift (R2 = 0.856, p < 0.01,) with xintercept occurring at 68.4% recovery and y-intercept at a phase shift of a = 179.3. There was a significant inverse linear relationship between % recovery and amplitude difference (R2 = 0.572, p < 0.01) with N%R and significant linear relationship with L%R (R2 = 0.202, p < 0.01). In N%R, x-intercept occurred at 89.4% recovery and yintercept at an amplitude difference of 98.4%.
4. Discussion in-phase KE and PE fluctuation (Fig. 3b). There was no relationship between phase shift and Fr number and therefore speed when taking dynamic similarity into account and phase shift did not significantly change with Fr ( p > 0.05) in either group. However, phase shift was significantly less in N%R and therefore closer to perfectly out of phase for this group ( p < 0.01). Amplitude difference also had no relationship with Fr N%R (R2 = 0.161, p > 0.05) but did elicit a significant relationship quadratic with L%R (R2 = 0.224, p < 0.05). There was also significantly less amplitude difference in L%R ( p < 0.05).
Fig. 5. The phase shift % recovery relationship. Reported is the linear relationship between % recovery and phase shift for N%R (solid black line, unfilled data points), L%R (solid grey line, filled data points) and for all the data (dashed line, all data points). The equations of the regression lines: y = 0.2784x + 66.876 (R2 = 0.065, p > 0.05), y = 0.2889x + 53.575 (R2 = 0.507, p < 0.01) and y = 0.3815x + 68.403 (R2 = 0.856, p < 0.01), for N%R, L%R and all data, respectively.
We found that the majority of the participants (L%R) used a walking strategy on the treadmill that resulted in low percentage recovery values that elicited a U-shaped relationship with Fr (speed when taking into account dynamic similarity) contrary to the inverted U relationship found in typical, mechanically efficient, walking. However, no difference in oxygen cost was found between groups. The evidence that metabolic energy consumption is the same for treadmill and ground walking is equivocal, with some studies showing that treadmill and ground walking elicit the same metabolic demand [5,6] and others that metabolic demand is reduced on the treadmill [7,8]. Our results suggest that there was no difference in oxygen cost between individuals that adopted a strategy that is mechanically similar to inverted pendulum ground walking and those who used a different strategy. In addition, we found a weak but significant inverse linear relationship between oxygen cost and % recovery in N%R (R2 = 0.249, p < 0.05), in agreement with previous studies [9,26]. When we further examined the components that determine % recovery, phase shift was significantly greater in L%R than N%R ( p < 0.01). The N%R group had a mean phase of a = 25.38 (S.D. 29.38) across all speeds. Cavagna et al. [33] found a mean phase shift (the degrees of difference between observed and the ideal 1808 out of phase PE and KE fluctuations) of a = 11.58 (S.D. 8.88) in ground walking at self-selected speed. In our study, phase shift did not relate to Fr in either group, however when all the data were considered phase shift had a significant inverse linear relationship with % recovery (R2 = 0.856, p < 0.01). Moreover, regression analysis found that the x-axis intercepted (1808 out of phase) at a % recovery value of 68%, comparable to the maximum % recovery of 70% reported by Cavagna et al. [17]. In addition, the y-intercept
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(0% recovery) occurred at a phase shift of a = 179.38 that would indicate an exactly in-phase relationship between KE and PE fluctuations. The other component of % recovery analysed was amplitude difference. Amplitude difference was significantly less in L%R than N%R ( p < 0.05), however this did not lead to high % recovery values and therefore the low % recovery observed in the group can be attributed to the phase shift. A walking style that results in in-phase PE and KE energy fluctuation was observed by Wang et al. [32] when a ‘bent hip bent knee’ gait was imposed that produced low % recovery values (27%). Knee and hip flexion was not measured in this study, although the knee tends to be more flexed in stance and at the end of swing during treadmill walking [5] and significantly more hip flexion has also been observed [4]. These differences in joint angle are not comparable to the bent knee bent hip gait imposed by Wang et al. [32]. However, greater hip and knee flexion could contribute to the in-phase COM energy fluctuations seen in participants in L%R. Our results suggest that if this is the case it does not increase oxygen cost as might be expected. To our knowledge the effect of the treadmill environment on the inverted pendulum model of walking has not been specifically addressed in the literature. Zijlstra and Hof [35] tested a compass gait model of COM displacement through a range of walking speeds and stride length and cadence using treadmill locomotion and the pelvis to indicate COM displacement. They found the model was generally in good agreement with the amplitude of pelvic (COM) displacement. However, it was noted that the phase of COM velocity change was ‘slightly advanced’ to what is predicted (1808) for 100% recovery. Minetti et al. [1] alluded to the in-phase style adopted by L%R. They calculated % recovery during treadmill walking, however it was acknowledged that very low % recovery values were eliminated from the results and only strides where PE and KE, in the x-axis (horizontal) were out of phase were accepted for analysis. They observed that at medium-high speed and step frequencies those PE and KE fluctuations were not perfectly out of phase and that when PE was increasing there was also an increase in KE. Considering the L%R in-phase energy fluctuations illustrated in Fig. 3b the COM motion can be described. During each stride when the COM is behind the point of the treadmill contact (foot) the COM accelerates as it is vertically displaced whilst the foot is moved backwards by the treadmill, leading to an increase in KE coinciding with the PE increase (0–30% of the gait cycle). The COM is then decelerated as it is lowered in order to maintain a constant speed with the treadmill, leading to KE decreasing with PE and therefore the in-phase fluctuations (30–50% of the gait cycle). The actuator for the deceleration of the COM when it is lowered is unclear, however, it could possibly be due to the greater hip and knee flexion observed during treadmill walking [4,5]. The reason for the acceleration of the COM when it is vertically displaced is
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also unclear. However, Minetti et al. [1] proposed that contraction of plantar flexor muscles might be accelerating the COM forward during treadmill walking. Although to date there is no direct evidence, indirect evidence supports this thesis. An electromyography (EMG) study of treadmill versus ground walking found that calf muscle activity begins earlier in stance phase during treadmill walking in some subjects, walking at selected comfortable, slow and fast speeds, which could cause the COM to accelerate as it is vertically displaced [5]. Another possibility is interaction between the treadmill and the subject. Savelberg et al. [36] suggested that kinematic differences between ground and treadmill locomotion were caused by energy exchange between the treadmill and the subject. They found a variation in treadmill belt velocity during walking that produced a sinusoidal wave. Interestingly the sinusoidal wave was the same frequency and approximately opposite in-phase to the sinusoidal wave produced during COM vertical displacement. Indeed it has been proposed that the treadmill motor may provide some of the energy needed to raise the COM [7]. Further examination of the energy exchange between the individual and the treadmill may help explain the % recovery with Fr relationship found in L%R and why oxygen cost seems not to be affected. Humans self-select optimal walking strategies [1,10,14,15,18,34]. Therefore, altered COM motion during treadmill walking in L%R could be a result of selfoptimisation. Our oxygen cost data does not support this, however previous studies have found less oxygen utilisation during treadmill compared to ground walking [7,8]. Participants in group N%R may have used a walking style comparable to ground walking as they were new to treadmill walking. Whether the style is adopted after treadmill familiarisation needs to be investigated, as much as one hour has been suggested for treadmill habituation [37]. If an inphase walking style is adopted on a treadmill after habituation in clinical populations, treadmill gait training may not be the most effective form of rehabilitation for mechanical aspects of walking, although our results suggest that cardiovascular befits would be unaffected. Although there is limited evidence comparing the two modes of training, treadmill training with support has been shown to be less effective than ground training at improving gait symmetry after brain injury [38].
5. Conclusion The inverted pendulum energy recovery model does not accurately represent treadmill walking in all individuals. This is true over a range of speeds and does not have a detrimental effect on metabolic energy cost. The continuous-controlled environment the treadmill provides makes it a valuable tool in research and rehabilitation. However, it may not provide true a representation of ground walking.
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Conflict of interest The authors (J. Collett, H. Dawes, K. Howells, C. Elsworth, H. Izadi and C. Sackley) have no conflict of interest regarding the content of the manuscript. ‘‘Anomalous centre of mass energy fluctuations during treadmill walking in healthy individuals’’. The research was solely funded by Oxford Brookes University and The University of Birmingham.
Acknowledgements This study was funded by Oxford Brookes University and the University of Birmingham.
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