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The energy cost for the step-to-step transition in amputee walking
Gait & Posture 30 (2009) 35–40
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The energy cost for the step-to-step transition in amputee walking Han Houdijk a,b,*, Eveline Pollmann a, Marlies Groenewold a, Han Wiggerts c, Wojtek Polomski b a
Research Institute MOVE, Faculty of Human Movement Sciences, VU University Amsterdam, The Netherlands Heliomare Rehabilitation Centre, Wijk aan Zee, The Netherlands c Rehabilitation Centre Amsterdam, Amsterdam, The Netherlands b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 29 September 2008 Received in revised form 7 February 2009 Accepted 16 February 2009
The purpose of this study was to investigate whether the increased energy cost of amputee gait could be accounted for by an increase in the mechanical work dissipated during the step-to-step transition in walking. Eleven transtibial amputees (AMP) and 11 age-matched controls (CO) walked at both comfortable (CWS) and fixed (FWS, 1.3 m/s) walking speed, while external mechanical work of each separate leg and metabolic energy consumption were measured. At FWS the metabolic energy consumption (E˙met) was significantly higher in AMP compared to CO (3.34 J kg1 s1 vs. 2.73 J kg1 s1). At CWS, no difference in energy consumption was found (3.56 J kg1 s1 vs. 3.58 J kg1 s1) but CWS was significantly lower in AMP compared to CO (1.35 m s1 vs. 1.52 m s1). In conjunction with the higher E˙met at FWS, the negative work generated by the intact leading leg for the step-to-step transition in double support was significantly higher for AMP than CO at FWS. A moderate though significant correlation was found between negative mechanical power generated during the step-to-step transition and metabolic power (CWS: r = 0.56, p = 0.007; FWS: r = 0.50, p = 0.019). Despite the difference in negative work during the step-to-step transition, the total absolute mechanical work over a stride did not differ between groups. This could possibly be attributed to exchange of internal positive and negative work during single support, which remains unnoticed in the external work calculations. It was concluded that the increased mechanical work for the step-to-step transition from prosthetic to intact limb contributes to the increased metabolic energy cost of amputee walking. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Gait Amputee Energy cost Metabolic energy Mechanical work
1. Introduction After lower limb amputation, regaining walking ability is one of the most important goals of rehabilitation [1]. Over the years, prosthetic components have been improved to facilitate a comfortable and stable gait pattern. Nevertheless, the metabolic energy cost of amputee walking remains elevated well above the energy cost of normal walking. On average, the increase in energy cost has been found to amount to 25% for transtibial amputees to as much as 100% for transfemoral amputees [2–6]. This increase in energy cost influences the normal and independent functioning of the amputee in society. To understand the metabolic energy cost of walking total muscle work and force production should be analyzed. However, no techniques or models are currently available that allow for a valid quantification of muscle energetics or muscle work in vivo. As an alternative, external mechanical work (i.e. the mechanical work
* Corresponding author at: Department of Human Movement Sciences, Vrije Universiteit, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands. Tel.: +31 20 5988469. E-mail address: [email protected] (H. Houdijk). 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.02.009
performed on the body’s center of mass (BCM)) can be used as a global measure for muscle work [7,8]. This more global measure has the drawback that it ignores energy flows within the body (due to movement of body segments relative to the BCM, and cocontraction around joints), but it has the advantage of linking energy flows directly to comprehensible mechanical features of gait [9] and consequently it might lead to useful insights and interventions. Until now, however, none of the studies investigating external work of amputee walking have succeeded in explaining the increased metabolic energy cost. Metabolic energy cost has been shown to be uncorrelated to vertical displacement and hence the potential energy changes of the BCM [10–12]. In addition, modeling the body as an inverted pendulum and allowing exchanges between potential and kinetic energy of the BCM did not reveal a relation between external mechanical work and metabolic energy cost, nor did the recovery index (indicating the efficiency of this exchange) differ between amputee and ablebodied subjects [10–12]. Likewise, analyses of the mechanical work performed on the swing leg did not reveal differences between amputees and able-bodied subjects [13]. Recently, an extension of the inverted pendulum model was proposed that could potentially account for the increased energy
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H. Houdijk et al. / Gait & Posture 30 (2009) 35–40
Fig. 1. The double inverted pendulum model (a) describes the external mechanical work (W) generated by the leading and trailing leg to redirect the centre of mass velocity 2 þ (vcom) from v com at heel strike to vcom at toe-off during the step-to-step transition in walking. Negative work from impact impulse (S) at heel strike (W S ) is lower when the trailing leg generates a push off impulse (P) at the same time or just prior to heel strike (b), compared to a situation in which propulsion has to be generated substantially prior to heel strike by generating a hip extensor torque (c). Adapted from Donelan et al. [11].
cost of amputee walking [14–16]. This model explicitly models the step-to-step transition of walking, which is proposed to be an important determinant of the energy cost of walking. The double inverted pendulum model consists of two rigid legs and a point mass, representing the BCM, on top (Fig. 1). During the transition from one leg to the next the velocity of the BCM needs to be redirected from one circular trajectory to the next. This redirecting of BCM velocity is performed by a force generated under the leading limb directed towards the BCM, which goes at the expense of negative mechanical work performed on the BCM. It has been shown analytically [14–16] that the most efficient way to regenerate this work is to generate a push off force through ankle plantar flexion in the trailing leg at or just before heel strike of the leading leg (Fig. 1b). Alternatively, this positive work can be generated around the hip, substantially prior to heel strike. However, as shown in Fig. 1c this strategy is more costly, since it increases impact velocity and hence the negative work at heel strike [14–16]. The double inverted pendulum model predicts a potential source for the increase in the energy cost of amputee walking. Since lower limb prostheses lack the ability to actively plantar flex the ankle and generate sufficient power during the push off of walking, amputees are forced to use a more costly hip strategy to generate positive work. In this study we will test the hypothesis that walking with a lower limb prosthesis increases the mechanical work required for the step-to-step transition and that this increase is correlated with the increase in metabolic energy consumption during walking. 2. Methods 2.1. Subjects Eleven adult subjects with a unilateral transtibial prosthesis (age 46 9 years, height 1.81 0.09 m, mass 89 11 kg) and 11 agematched control subjects (age 47 11 years, height 1.82 0.08 m, mass 80 8 kg) were recruited to participate in this study. All amputee subjects were experienced in using their prosthesis for at least 1 year. All amputee subjects used their own prosthesis, all of which contained a type of dynamic foot (6 Sureflex, 3 Variflex and 2 ID10). Three of the amputee subjects suffered amputation because of vascular problems, eight were amputated following trauma. Since the three vascular amputees were relatively young and fit individuals and did not differ on these factors compared to the traumatic amputees, all amputees were treated as a single group, regardless of the cause of amputation. This study was approved by the local ethics committee and all subjects gave their written informed consent in accordance with university policy.
2.2. Experimental protocol and instrumentation Each subject performed the experiment at two different speeds; at comfortable walking speed (CWS) and at a fixed walking speed (FWS: 1.3 m s1). The CWS was determined by asking the subjects to walk on a 10 m flat walkway at a velocity that was comfortable and natural. The two different speeds were imposed in random order. For each speed two separate tests were performed. In the first test, subjects walked on a 10 m flat walkway with two separate force plates (custom made, size 1 by 1 m) mounted in series near the midpoint of the walkway. With these force plates the three components of the ground reaction forces under each separate leg were simultaneously collected at 200 Hz. During these trials the average walking speed was measured using an optoelectronic system (Optotrak, Nortern digital, Ontario, Canada). The average velocity of a LED, placed at the subject’s pelvis, measured over a complete stride across the force plates was available as feedback directly after each trial. Trials were discarded if the measured speed was not within 0.05 m s1 of the target speed or if the individual feet did not fall fully on the separate force plates. The data of three successful trials of each subject, with each limb being leading and trailing, at each speed were saved for further analysis. For the control data, the left and right legs were averaged into one outcome value. In the second test the subjects walked on a treadmill at the same two target speeds for 5 min while metabolic energy consumption was measured using a respirometry system (Oxycon Champion, Jaeger, Germany). Before this second test, the resting metabolic energy consumption was measured for 3 min while the subject stood quietly on the treadmill. The subjects were familiarized with walking on a treadmill if necessary before the two walking trials were executed. Cadence and step length were measured on both the walkway (from force plate data) and the treadmill (by counting the number of steps during the final minute of the test) to check for potential differences between these two separate tests. 2.3. Data analysis In order to calculate the external mechanical work performed on the BCM the individual limbs method as outlined by Donelan et al. [14] was applied. In brief, the BCM accelerations in the three orthogonal directions were obtained from the summed ground reaction forces using Newton’s second law. From these accelerations, the BCM velocity was found by integrating acceleration over time. Integration constants were chosen such that average vertical BCM velocity over a complete step was zero, average fore-aft
H. Houdijk et al. / Gait & Posture 30 (2009) 35–40
velocity was equal to the average walking speed and such that medio-lateral BCM velocity at the beginning and end of the step were equal in magnitude but opposite in sign. The mechanical power generated on the BCM by the trailing limb (Ptrail) and leading limb (Plead) individually was obtained as the dot product of the external force acting on each individual limb and the velocity of the BCM. Finally, the external mechanical work was determined using the time integral of the mechanical power profiles. For each trial one step, including a double support phase followed by a single support phase, was analyzed. For this step the mechanical work was calculated for the trailing leg during double support (WDStrail) and for the leading leg during double support (WDSlead) and during the subsequent single support phase (WSS). Since the mechanical work over a complete step is zero while walking at a steady velocity, the total work over a step (WSTEP) and over a stride (WSTRIDE; sum of left and right step) was calculated as the absolute work by integrating the absolute power profiles. To compare average external mechanical work with metabolic power, WSTRIDE was divided by stride time and body mass to obtain average mechanical power (E˙mech_tot, J kg1 s1) and divided by stride length and body mass to obtain average mechanical cost (Cmech_tot, J kg1 m1). In addition, in order to specifically compare the average negative work generated during the step-to-step transition to metabolic power, the same was done separately for the negative work during the step-to-step transition; i.e. the sum of WDSlead of both legs was divided by stride time and body mass to obtain average mechanical power lost during the collision of the step-to-step transition (E˙DSlead, J kg1 s1). The metabolic cost was derived from the oxygen uptake (VO2 (L min1)) and carbon dioxide production (VCO2 (L min1)) during the last 2 min of each trial. The energy equivalent of the oxygen consumed was calculated using the respiratory quotient (RQ) [17]. In order to exclusively obtain the metabolic cost for walking the metabolic resting values for standing were subtracted from the metabolic energy consumed during walking. The metabolic energy consumption (E˙met, J kg1 s1) and the metabolic energy cost (Cmet, J kg1 m1) for walking were calculated. 2.4. Statistics Statistical analyses were performed using SPSS (version 12.01). Descriptive statistics were calculated for basic characteristics of the subjects and presented as mean and standard deviation. Differences between the prosthetic leg or intact leg of the amputee group and the control group were tested for significance using a Student’s t-test for independent observations. Correlation between metabolic en mechanical energy consumption was analyzed using Pearson’s correlation coefficient. Statistical significance was set at p < 0.05. 3. Results Subject characteristics did not differ between groups with respect to age and body length. Only body mass of the amputee group was higher (p = 0.039). The results for external mechanical work and metabolic energy are therefore normalized to body mass. 3.1. Walking speed and metabolic energy At CWS the control group walked significantly faster than the amputees (Table 1), while the metabolic energy consumption (E˙met, J kg1 s1) did not differ between groups. The metabolic energy cost (Cmet, J kg1 m1) was on average 12% higher in the amputee group but this difference did not reach statistical significance (p = 0.102). At FWS metabolic energy consumption and energy cost were 26% higher in the amputee group, which was statistically significant.
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Table 1 Walking speed and metabolic energy consumption (mean S.D.) for BK amputee and control group. Amputee
Control
p
CWS
Speed (m s1) Cadence (steps s1) Step length (m) E˙met (J kg1 s1) Cmet (J kg1 m1)
1.35 0.13 1.76 0.09 0.77 0.07 3.56 0.62 2.63 0.46
1.52 0.21 1.84 0.15 0.83 0.10 3.58 0.92 2.34 0.33
0.036a 0.162 0.114 0.934 0.102
FWS
Speed (m s1) Cadence (steps s1) Step length (m) E˙met (J kg1 s1) Cmet (J kg1 m1)
1.31 0.01 1.74 0.09 0.75 0.04 3.44 0.65 2.64 0.50
1.31 0.01 1.71 0.15 0.77 0.07 2.73 0.32 2.09 0.25
0.800 0.427 0.379 0.004a 0.004a
a
Denotes significantly difference (p < 0.05).
Cadence and step length at CWS tended to be little lower in the amputee group compared to controls, but this difference was not significant (Table 1). At FWS cadence and step length were similar between amputees and controls. Cadence and step length were also found not to be different between trials on the walkway and on the treadmill for either group. 3.2. Mechanical energy The average external mechanical power profiles generated by the individual limbs during a step are displayed in Fig. 2. Data on the external mechanical work done by each leg during the different phases of a step are provided in Table 2. During double support, the positive external mechanical work of the trailing limb (WDStrail) of the amputee group was lower compared to normal when the prosthetic limb was trailing (and intact limb was leading) at both CWS and FWS. There was no difference in WDStrail between the control and amputee group when the intact limb of the amputees was trailing (and prosthetic limb was leading). The negative work performed during double support by the leading limb (WDSlead) of the amputee group was higher than normal when the intact limb was leading at FWS but not at CWS (Table 2). There was no difference in WDSlead when the prosthetic limb was leading compared to the control group. During normal walking the net external mechanical work is negative during the single support phase. At both FWS and CWS the net mechanical work during single support (WSS) in the intact limb of the amputee group was less negative compared to the control group. For CWS as well as FWS there was no difference in WSS between the prosthetic limb and the control group (Table 2). Despite the significant differences in the separate phases of the gait cycle, there was no difference in the total absolute external mechanical work generated during a step (WSTEP) between amputees and control group for either CWS or FWS (Table 2). Similarly, the average mechanical energy production (E˙mech_tot, J kg1 s1) or cost (Cmech_tot, J kg1 m1) over a complete stride did not differ between the groups at either speed (Table 2). 3.3. Metabolic vs. mechanical energy Fig. 3 displays the correlation between metabolic energy consumption and average external mechanical power generated during walking at CWS and FWS. At CWS a significant correlation was found between metabolic energy consumption (E˙met) and average total mechanical power (E˙mech_tot) (r = 0.60, p = 0.003). This correlation is, however, strongly influenced by differences in walking speed between subjects. At FWS the correlation between E˙met and E˙mech_tot was weak and not significant (r = 0.31, p = 0.161). In contrast, the correlation between metabolic energy consumption and the average negative power generated during the step-to-
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Fig. 2. The external mechanical power generated by the trailing (thin) and leading (thick) leg during a step. The group average is presented for the step of the control group (solid), the step of the amputee group when the intact leg is leading (dashed) and when the prosthetic leg is leading (dotted) for both CWS and FWS.
Table 2 Mechanical work (J kg1, mean S.D.) for BK amputee and control group. Amputee intact leada
Amputee prosthetic leadb
Control
*
CWS
WDStrail WDSlead WSS (net) WSTEP (abs) E˙mech_tot (J kg1 s1) Cmech_tot (J kg1 m1)
0.16 0.04 0.23 0.07 0.03 0.08* 0.79 0.12 1.40 0.24 1.03 0.10
0.27 0.04 0.14 0.05 0.09 0.07 0.79 0.16
0.28 0.05 0.18 0.05 0.10 0.05 0.87 0.17 1.60 0.33 1.04 0.12
FWS
WDStrail WDSlead WSS (net) WSTEP (abs) E˙mech_tot (J kg1 s1) Cmech_tot (J kg1 m1)
0.16 0.04* 0.21 0.06* 0.04 0.09* 0.74 0.08 1.30 0.14 0.99 0.10
0.25 0.07 0.13 0.06 0.10 0.08 0.76 0.12
0.28 0.05 0.12 0.05 0.14 0.05 0.74 0.17 1.24 0.15 0.95 0.11
a b *
Step in which intact limb leads, prosthetic limb trails and single support is on intact limb. Step in which prosthetic limb leads, intact limb trails and single support is on prosthetic limb. Denotes significantly difference from control group (p < 0.05).
step transition (E˙DSlead) was significant for both CWS and FWS (CWS: r = 0.56, p = 0.007; FWS: r = 0.50, p = 0.019, Fig. 3 lower panels). This means that the more negative work is performed by the leading leg during double support, the higher the metabolic energy consumption. 4. Discussion In this study it was investigated whether the mechanical work required for the step-to-step transition could explain the higher energy cost of amputee walking. In accordance with the literature [2,3,5,6] the amputee subjects in this study had a lower comfortable walking speed and higher metabolic cost during walking compared to an able-bodied control group. The difference in energy cost at CWS was a little lower than reported previously [3,5] and did not reach statistical significance. This could be due to the relatively high walking speeds that especially our control subjects self-selected over the relatively short 10 m walkway. At fixed walking speed of 1.3 m s1 a difference in energy cost of 26% was found between groups, which corresponds to previous findings [3,5].
Based on the double inverted pendulum model we hypothesized that the positive work of the prosthetic trailing leg during double support would be reduced. This would be compensated by an increase in the mechanical work generated during single support and result in an increase in mechanical energy dissipation through negative work of the intact leading leg during double support. As a consequence, the total mechanical work was expected to be higher in amputees compared to the control group. Since step-to-step transition work has been shown to be strongly dependent on walking speed, these hypotheses should especially hold when comparing groups at equal walking speeds. Therefore we will first discuss the results of the FWS condition. In accordance with our hypotheses we found a significant decrease in positive mechanical work in the prosthetic trailing leg and an increase in the mechanical energy dissipated during double support in the intact leading leg of the amputee group during the FWS condition. These observations are in line with previous studies that found a reduced ground reaction force under the prosthetic leg during push off and an increased ground reaction force under the intact leg during the loading phase of the step [18–21].
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Fig. 3. Correlation between mean metabolic power (E˙met) and mechanical power during walking at CWS and FWS. Correlation is displayed for total absolute external mechanical (E˙mech_tot) power in the upper panels, and the average negative mechanical power (the mechanical energy dissipated during the step-to-step transition (E˙DSlead)) in the lower panels. Control subjects are displayed as squares, amputee subjects as diamonds.
For single support, it was hypothesized that extra mechanical work needs to be generated to compensate for the reduced output of the prosthetic trailing leg during double support and for the extra energy dissipated by the leading leg. In this study, net work during single support on the intact leg was shown to increase at FWS in the sense that the net negative work found in this phase was lower for amputees compared to the control group. This observation is also in accordance with previous studies that found a compensational power output at the hip during single support for transtibial [22,23] and transfemoral [24] amputees. Despite the fact that the external mechanical work done by the separated legs, during the separate phases of the stride followed our hypotheses, the total absolute external mechanical work over a complete stride did not appear to differ between groups. This results from the fact that the hypothesized increase in external work during single support appeared as a reduction of the net negative work in this phase (which when taken absolute results in a reduced total work). It could be suggested that the amputee group found a clever strategy to compensate for the extra energy loss for the step-to-step transition by somehow reducing negative work during single support. However, probably we are confronted with a limitation of the external work calculation here. External (BCM) work represents the net summation of muscle work in the body affecting the BCM energy content. Consequently, the reduction of net negative work found during single support in this study could be the result of an increase in positive muscle work, a reduction in negative muscle work or a combination of both somewhere in the musculoskeletal system. Especially, during the single support phase, where substantial work is generated around the joints of the separate stance and swing leg and also trunk and arms, the net work appearing as external BCM work cannot be interpreted without difficulty. To that extent the individual limbs method appears to be no better (nor worse) than the conventional combined limbs methods for calculating external BCM work [14]. This problem could possibly be solved by using more elaborate musculoskeletal models. However, inverse dynamics calculations of net joint work have been shown not to
solve this problem easily [11] and the current validity of more elaborate musculoskeletal models does not warrant success with such an approach either. Nevertheless, despite the lack of difference in total absolute external mechanical work, the clear increase in energy dissipated during double support in the intact leading leg of the amputees suggests that the step-to-step transition can play a role in the higher energy cost of amputee walking. It is not likely that this negative work can be stored or transferred effectively in the body and hence it will be lost and needs to be re-generated. This is further supported by the significant correlation between metabolic energy consumption and the average mechanical power dissipated during the step-to-step transition by the leading leg (Fig. 3, lower panels). Although this correlation is moderate, the step-to-step transition cost still explains 25% of the difference in metabolic energy consumption between subjects in the FWS condition. The CWS condition was included since it is resembles normal walking behavior more realistically. However, since the leading leg’s negative work during double support strongly depends on walking velocity, as Donelan et al. [14] demonstrated, the difference in comfortable walking speed between groups obscure a clear interpretation of the results. Nevertheless, the results for the CWS condition seem to be in line with conclusions drawn above. Despite a lower walking speed, metabolic energy consumption was equal for the amputee group and controls. Concurrently, the negative work in the leading leg during the step-to-step transition did not differ between groups, despite differences in walking speed. Hence amputees walk at lower speed with relatively high collision cost, which might explain equal metabolic energy consumption per unit of time and higher metabolic energy cost per unit distance traveled in amputees. This conclusion is supported by the fact that (independent of speed differences between subjects) step-to-step transition cost remained a significant predictor of the metabolic energy consumption in the CWS condition (Fig. 3). Based on these results it can be concluded that the mechanical work for the step-to-step transition can account for at least part of
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the increased metabolic cost of amputee walking. This is a unique finding since the double inverted pendulum model, on which the step-to-step transition cost is based, is the only model so far that has succeeded in relating part of the extra metabolic cost of amputee gait to a distinct mechanical feature [11–13,25]. The moderate correlation between step-to-step work and metabolic cost, however, also suggests that other factors should be considered. These factors should not necessarily be limited to the mechanics directly related to propulsion. One other important factor could be the increased muscle activity for balance control, for instance through muscle co-contraction or movement variability, which will go unnoticed in biomechanical analyses of average steps. The issue of balance control could become extra apparent when subjects are required to walk on a treadmill, as used in this study [26,27]. This issue deserves further attention In conclusion, it was found that the increased energy consumption during amputee walking is associated with a decrease in the push off work of the prosthetic leg and a concomitant increase in the mechanical energy lost during the step-to-step transition. This finding supports the development of prosthetic feet capable of storing and returning elastic energy for enhancing positive work in the prosthetic leg during double support. Moreover, it motivates the development of actively powered prosthetic feet [28] to really restore push off and reduce step-to-step transition cost. Testing differences in step-to-step transition cost between prosthetic feet was not the aim of the present study and not possible because of the heterogeneous sample of prosthetic feet used by our participants, but this would be an interesting next step. Conflict of interest None. References [1] Rommers GM, Vos LD, Groothoff JW, Schuiling CH, Eisma WH. Epidemiology of lower limb amputees in the north of The Netherlands: aetiology, discharge destination and prosthetic use. Prosthet Orthot Int 1997;21(2):92–9. [2] Fisher SV, Gullickson GJ. Energy cost of ambulation in health and disability: a literature review. Arch Phys Med Rehabil 1978;59(3):124–33. [3] Pinzur MS. The metabolic cost of lower extremity amputation. Clin Podiatr Med Surg 1997;14(4):599–602. [4] Ward KH, Meyers MC. Exercise performance of lower-extremity amputees. Sports Med 1995;20(4):207–14. [5] Waters RL, Mulroy S. The energy expenditure of normal and pathologic gait. Gait Posture 1999;9:207–31.
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Gait & Posture journal homepage: www.elsevier.com/locate/gaitpost
The energy cost for the step-to-step transition in amputee walking Han Houdijk a,b,*, Eveline Pollmann a, Marlies Groenewold a, Han Wiggerts c, Wojtek Polomski b a
Research Institute MOVE, Faculty of Human Movement Sciences, VU University Amsterdam, The Netherlands Heliomare Rehabilitation Centre, Wijk aan Zee, The Netherlands c Rehabilitation Centre Amsterdam, Amsterdam, The Netherlands b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 29 September 2008 Received in revised form 7 February 2009 Accepted 16 February 2009
The purpose of this study was to investigate whether the increased energy cost of amputee gait could be accounted for by an increase in the mechanical work dissipated during the step-to-step transition in walking. Eleven transtibial amputees (AMP) and 11 age-matched controls (CO) walked at both comfortable (CWS) and fixed (FWS, 1.3 m/s) walking speed, while external mechanical work of each separate leg and metabolic energy consumption were measured. At FWS the metabolic energy consumption (E˙met) was significantly higher in AMP compared to CO (3.34 J kg1 s1 vs. 2.73 J kg1 s1). At CWS, no difference in energy consumption was found (3.56 J kg1 s1 vs. 3.58 J kg1 s1) but CWS was significantly lower in AMP compared to CO (1.35 m s1 vs. 1.52 m s1). In conjunction with the higher E˙met at FWS, the negative work generated by the intact leading leg for the step-to-step transition in double support was significantly higher for AMP than CO at FWS. A moderate though significant correlation was found between negative mechanical power generated during the step-to-step transition and metabolic power (CWS: r = 0.56, p = 0.007; FWS: r = 0.50, p = 0.019). Despite the difference in negative work during the step-to-step transition, the total absolute mechanical work over a stride did not differ between groups. This could possibly be attributed to exchange of internal positive and negative work during single support, which remains unnoticed in the external work calculations. It was concluded that the increased mechanical work for the step-to-step transition from prosthetic to intact limb contributes to the increased metabolic energy cost of amputee walking. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Gait Amputee Energy cost Metabolic energy Mechanical work
1. Introduction After lower limb amputation, regaining walking ability is one of the most important goals of rehabilitation [1]. Over the years, prosthetic components have been improved to facilitate a comfortable and stable gait pattern. Nevertheless, the metabolic energy cost of amputee walking remains elevated well above the energy cost of normal walking. On average, the increase in energy cost has been found to amount to 25% for transtibial amputees to as much as 100% for transfemoral amputees [2–6]. This increase in energy cost influences the normal and independent functioning of the amputee in society. To understand the metabolic energy cost of walking total muscle work and force production should be analyzed. However, no techniques or models are currently available that allow for a valid quantification of muscle energetics or muscle work in vivo. As an alternative, external mechanical work (i.e. the mechanical work
* Corresponding author at: Department of Human Movement Sciences, Vrije Universiteit, Van der Boechorststraat 9, 1081 BT Amsterdam, The Netherlands. Tel.: +31 20 5988469. E-mail address: [email protected] (H. Houdijk). 0966-6362/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.gaitpost.2009.02.009
performed on the body’s center of mass (BCM)) can be used as a global measure for muscle work [7,8]. This more global measure has the drawback that it ignores energy flows within the body (due to movement of body segments relative to the BCM, and cocontraction around joints), but it has the advantage of linking energy flows directly to comprehensible mechanical features of gait [9] and consequently it might lead to useful insights and interventions. Until now, however, none of the studies investigating external work of amputee walking have succeeded in explaining the increased metabolic energy cost. Metabolic energy cost has been shown to be uncorrelated to vertical displacement and hence the potential energy changes of the BCM [10–12]. In addition, modeling the body as an inverted pendulum and allowing exchanges between potential and kinetic energy of the BCM did not reveal a relation between external mechanical work and metabolic energy cost, nor did the recovery index (indicating the efficiency of this exchange) differ between amputee and ablebodied subjects [10–12]. Likewise, analyses of the mechanical work performed on the swing leg did not reveal differences between amputees and able-bodied subjects [13]. Recently, an extension of the inverted pendulum model was proposed that could potentially account for the increased energy
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Fig. 1. The double inverted pendulum model (a) describes the external mechanical work (W) generated by the leading and trailing leg to redirect the centre of mass velocity 2 þ (vcom) from v com at heel strike to vcom at toe-off during the step-to-step transition in walking. Negative work from impact impulse (S) at heel strike (W S ) is lower when the trailing leg generates a push off impulse (P) at the same time or just prior to heel strike (b), compared to a situation in which propulsion has to be generated substantially prior to heel strike by generating a hip extensor torque (c). Adapted from Donelan et al. [11].
cost of amputee walking [14–16]. This model explicitly models the step-to-step transition of walking, which is proposed to be an important determinant of the energy cost of walking. The double inverted pendulum model consists of two rigid legs and a point mass, representing the BCM, on top (Fig. 1). During the transition from one leg to the next the velocity of the BCM needs to be redirected from one circular trajectory to the next. This redirecting of BCM velocity is performed by a force generated under the leading limb directed towards the BCM, which goes at the expense of negative mechanical work performed on the BCM. It has been shown analytically [14–16] that the most efficient way to regenerate this work is to generate a push off force through ankle plantar flexion in the trailing leg at or just before heel strike of the leading leg (Fig. 1b). Alternatively, this positive work can be generated around the hip, substantially prior to heel strike. However, as shown in Fig. 1c this strategy is more costly, since it increases impact velocity and hence the negative work at heel strike [14–16]. The double inverted pendulum model predicts a potential source for the increase in the energy cost of amputee walking. Since lower limb prostheses lack the ability to actively plantar flex the ankle and generate sufficient power during the push off of walking, amputees are forced to use a more costly hip strategy to generate positive work. In this study we will test the hypothesis that walking with a lower limb prosthesis increases the mechanical work required for the step-to-step transition and that this increase is correlated with the increase in metabolic energy consumption during walking. 2. Methods 2.1. Subjects Eleven adult subjects with a unilateral transtibial prosthesis (age 46 9 years, height 1.81 0.09 m, mass 89 11 kg) and 11 agematched control subjects (age 47 11 years, height 1.82 0.08 m, mass 80 8 kg) were recruited to participate in this study. All amputee subjects were experienced in using their prosthesis for at least 1 year. All amputee subjects used their own prosthesis, all of which contained a type of dynamic foot (6 Sureflex, 3 Variflex and 2 ID10). Three of the amputee subjects suffered amputation because of vascular problems, eight were amputated following trauma. Since the three vascular amputees were relatively young and fit individuals and did not differ on these factors compared to the traumatic amputees, all amputees were treated as a single group, regardless of the cause of amputation. This study was approved by the local ethics committee and all subjects gave their written informed consent in accordance with university policy.
2.2. Experimental protocol and instrumentation Each subject performed the experiment at two different speeds; at comfortable walking speed (CWS) and at a fixed walking speed (FWS: 1.3 m s1). The CWS was determined by asking the subjects to walk on a 10 m flat walkway at a velocity that was comfortable and natural. The two different speeds were imposed in random order. For each speed two separate tests were performed. In the first test, subjects walked on a 10 m flat walkway with two separate force plates (custom made, size 1 by 1 m) mounted in series near the midpoint of the walkway. With these force plates the three components of the ground reaction forces under each separate leg were simultaneously collected at 200 Hz. During these trials the average walking speed was measured using an optoelectronic system (Optotrak, Nortern digital, Ontario, Canada). The average velocity of a LED, placed at the subject’s pelvis, measured over a complete stride across the force plates was available as feedback directly after each trial. Trials were discarded if the measured speed was not within 0.05 m s1 of the target speed or if the individual feet did not fall fully on the separate force plates. The data of three successful trials of each subject, with each limb being leading and trailing, at each speed were saved for further analysis. For the control data, the left and right legs were averaged into one outcome value. In the second test the subjects walked on a treadmill at the same two target speeds for 5 min while metabolic energy consumption was measured using a respirometry system (Oxycon Champion, Jaeger, Germany). Before this second test, the resting metabolic energy consumption was measured for 3 min while the subject stood quietly on the treadmill. The subjects were familiarized with walking on a treadmill if necessary before the two walking trials were executed. Cadence and step length were measured on both the walkway (from force plate data) and the treadmill (by counting the number of steps during the final minute of the test) to check for potential differences between these two separate tests. 2.3. Data analysis In order to calculate the external mechanical work performed on the BCM the individual limbs method as outlined by Donelan et al. [14] was applied. In brief, the BCM accelerations in the three orthogonal directions were obtained from the summed ground reaction forces using Newton’s second law. From these accelerations, the BCM velocity was found by integrating acceleration over time. Integration constants were chosen such that average vertical BCM velocity over a complete step was zero, average fore-aft
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velocity was equal to the average walking speed and such that medio-lateral BCM velocity at the beginning and end of the step were equal in magnitude but opposite in sign. The mechanical power generated on the BCM by the trailing limb (Ptrail) and leading limb (Plead) individually was obtained as the dot product of the external force acting on each individual limb and the velocity of the BCM. Finally, the external mechanical work was determined using the time integral of the mechanical power profiles. For each trial one step, including a double support phase followed by a single support phase, was analyzed. For this step the mechanical work was calculated for the trailing leg during double support (WDStrail) and for the leading leg during double support (WDSlead) and during the subsequent single support phase (WSS). Since the mechanical work over a complete step is zero while walking at a steady velocity, the total work over a step (WSTEP) and over a stride (WSTRIDE; sum of left and right step) was calculated as the absolute work by integrating the absolute power profiles. To compare average external mechanical work with metabolic power, WSTRIDE was divided by stride time and body mass to obtain average mechanical power (E˙mech_tot, J kg1 s1) and divided by stride length and body mass to obtain average mechanical cost (Cmech_tot, J kg1 m1). In addition, in order to specifically compare the average negative work generated during the step-to-step transition to metabolic power, the same was done separately for the negative work during the step-to-step transition; i.e. the sum of WDSlead of both legs was divided by stride time and body mass to obtain average mechanical power lost during the collision of the step-to-step transition (E˙DSlead, J kg1 s1). The metabolic cost was derived from the oxygen uptake (VO2 (L min1)) and carbon dioxide production (VCO2 (L min1)) during the last 2 min of each trial. The energy equivalent of the oxygen consumed was calculated using the respiratory quotient (RQ) [17]. In order to exclusively obtain the metabolic cost for walking the metabolic resting values for standing were subtracted from the metabolic energy consumed during walking. The metabolic energy consumption (E˙met, J kg1 s1) and the metabolic energy cost (Cmet, J kg1 m1) for walking were calculated. 2.4. Statistics Statistical analyses were performed using SPSS (version 12.01). Descriptive statistics were calculated for basic characteristics of the subjects and presented as mean and standard deviation. Differences between the prosthetic leg or intact leg of the amputee group and the control group were tested for significance using a Student’s t-test for independent observations. Correlation between metabolic en mechanical energy consumption was analyzed using Pearson’s correlation coefficient. Statistical significance was set at p < 0.05. 3. Results Subject characteristics did not differ between groups with respect to age and body length. Only body mass of the amputee group was higher (p = 0.039). The results for external mechanical work and metabolic energy are therefore normalized to body mass. 3.1. Walking speed and metabolic energy At CWS the control group walked significantly faster than the amputees (Table 1), while the metabolic energy consumption (E˙met, J kg1 s1) did not differ between groups. The metabolic energy cost (Cmet, J kg1 m1) was on average 12% higher in the amputee group but this difference did not reach statistical significance (p = 0.102). At FWS metabolic energy consumption and energy cost were 26% higher in the amputee group, which was statistically significant.
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Table 1 Walking speed and metabolic energy consumption (mean S.D.) for BK amputee and control group. Amputee
Control
p
CWS
Speed (m s1) Cadence (steps s1) Step length (m) E˙met (J kg1 s1) Cmet (J kg1 m1)
1.35 0.13 1.76 0.09 0.77 0.07 3.56 0.62 2.63 0.46
1.52 0.21 1.84 0.15 0.83 0.10 3.58 0.92 2.34 0.33
0.036a 0.162 0.114 0.934 0.102
FWS
Speed (m s1) Cadence (steps s1) Step length (m) E˙met (J kg1 s1) Cmet (J kg1 m1)
1.31 0.01 1.74 0.09 0.75 0.04 3.44 0.65 2.64 0.50
1.31 0.01 1.71 0.15 0.77 0.07 2.73 0.32 2.09 0.25
0.800 0.427 0.379 0.004a 0.004a
a
Denotes significantly difference (p < 0.05).
Cadence and step length at CWS tended to be little lower in the amputee group compared to controls, but this difference was not significant (Table 1). At FWS cadence and step length were similar between amputees and controls. Cadence and step length were also found not to be different between trials on the walkway and on the treadmill for either group. 3.2. Mechanical energy The average external mechanical power profiles generated by the individual limbs during a step are displayed in Fig. 2. Data on the external mechanical work done by each leg during the different phases of a step are provided in Table 2. During double support, the positive external mechanical work of the trailing limb (WDStrail) of the amputee group was lower compared to normal when the prosthetic limb was trailing (and intact limb was leading) at both CWS and FWS. There was no difference in WDStrail between the control and amputee group when the intact limb of the amputees was trailing (and prosthetic limb was leading). The negative work performed during double support by the leading limb (WDSlead) of the amputee group was higher than normal when the intact limb was leading at FWS but not at CWS (Table 2). There was no difference in WDSlead when the prosthetic limb was leading compared to the control group. During normal walking the net external mechanical work is negative during the single support phase. At both FWS and CWS the net mechanical work during single support (WSS) in the intact limb of the amputee group was less negative compared to the control group. For CWS as well as FWS there was no difference in WSS between the prosthetic limb and the control group (Table 2). Despite the significant differences in the separate phases of the gait cycle, there was no difference in the total absolute external mechanical work generated during a step (WSTEP) between amputees and control group for either CWS or FWS (Table 2). Similarly, the average mechanical energy production (E˙mech_tot, J kg1 s1) or cost (Cmech_tot, J kg1 m1) over a complete stride did not differ between the groups at either speed (Table 2). 3.3. Metabolic vs. mechanical energy Fig. 3 displays the correlation between metabolic energy consumption and average external mechanical power generated during walking at CWS and FWS. At CWS a significant correlation was found between metabolic energy consumption (E˙met) and average total mechanical power (E˙mech_tot) (r = 0.60, p = 0.003). This correlation is, however, strongly influenced by differences in walking speed between subjects. At FWS the correlation between E˙met and E˙mech_tot was weak and not significant (r = 0.31, p = 0.161). In contrast, the correlation between metabolic energy consumption and the average negative power generated during the step-to-
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Fig. 2. The external mechanical power generated by the trailing (thin) and leading (thick) leg during a step. The group average is presented for the step of the control group (solid), the step of the amputee group when the intact leg is leading (dashed) and when the prosthetic leg is leading (dotted) for both CWS and FWS.
Table 2 Mechanical work (J kg1, mean S.D.) for BK amputee and control group. Amputee intact leada
Amputee prosthetic leadb
Control
*
CWS
WDStrail WDSlead WSS (net) WSTEP (abs) E˙mech_tot (J kg1 s1) Cmech_tot (J kg1 m1)
0.16 0.04 0.23 0.07 0.03 0.08* 0.79 0.12 1.40 0.24 1.03 0.10
0.27 0.04 0.14 0.05 0.09 0.07 0.79 0.16
0.28 0.05 0.18 0.05 0.10 0.05 0.87 0.17 1.60 0.33 1.04 0.12
FWS
WDStrail WDSlead WSS (net) WSTEP (abs) E˙mech_tot (J kg1 s1) Cmech_tot (J kg1 m1)
0.16 0.04* 0.21 0.06* 0.04 0.09* 0.74 0.08 1.30 0.14 0.99 0.10
0.25 0.07 0.13 0.06 0.10 0.08 0.76 0.12
0.28 0.05 0.12 0.05 0.14 0.05 0.74 0.17 1.24 0.15 0.95 0.11
a b *
Step in which intact limb leads, prosthetic limb trails and single support is on intact limb. Step in which prosthetic limb leads, intact limb trails and single support is on prosthetic limb. Denotes significantly difference from control group (p < 0.05).
step transition (E˙DSlead) was significant for both CWS and FWS (CWS: r = 0.56, p = 0.007; FWS: r = 0.50, p = 0.019, Fig. 3 lower panels). This means that the more negative work is performed by the leading leg during double support, the higher the metabolic energy consumption. 4. Discussion In this study it was investigated whether the mechanical work required for the step-to-step transition could explain the higher energy cost of amputee walking. In accordance with the literature [2,3,5,6] the amputee subjects in this study had a lower comfortable walking speed and higher metabolic cost during walking compared to an able-bodied control group. The difference in energy cost at CWS was a little lower than reported previously [3,5] and did not reach statistical significance. This could be due to the relatively high walking speeds that especially our control subjects self-selected over the relatively short 10 m walkway. At fixed walking speed of 1.3 m s1 a difference in energy cost of 26% was found between groups, which corresponds to previous findings [3,5].
Based on the double inverted pendulum model we hypothesized that the positive work of the prosthetic trailing leg during double support would be reduced. This would be compensated by an increase in the mechanical work generated during single support and result in an increase in mechanical energy dissipation through negative work of the intact leading leg during double support. As a consequence, the total mechanical work was expected to be higher in amputees compared to the control group. Since step-to-step transition work has been shown to be strongly dependent on walking speed, these hypotheses should especially hold when comparing groups at equal walking speeds. Therefore we will first discuss the results of the FWS condition. In accordance with our hypotheses we found a significant decrease in positive mechanical work in the prosthetic trailing leg and an increase in the mechanical energy dissipated during double support in the intact leading leg of the amputee group during the FWS condition. These observations are in line with previous studies that found a reduced ground reaction force under the prosthetic leg during push off and an increased ground reaction force under the intact leg during the loading phase of the step [18–21].
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Fig. 3. Correlation between mean metabolic power (E˙met) and mechanical power during walking at CWS and FWS. Correlation is displayed for total absolute external mechanical (E˙mech_tot) power in the upper panels, and the average negative mechanical power (the mechanical energy dissipated during the step-to-step transition (E˙DSlead)) in the lower panels. Control subjects are displayed as squares, amputee subjects as diamonds.
For single support, it was hypothesized that extra mechanical work needs to be generated to compensate for the reduced output of the prosthetic trailing leg during double support and for the extra energy dissipated by the leading leg. In this study, net work during single support on the intact leg was shown to increase at FWS in the sense that the net negative work found in this phase was lower for amputees compared to the control group. This observation is also in accordance with previous studies that found a compensational power output at the hip during single support for transtibial [22,23] and transfemoral [24] amputees. Despite the fact that the external mechanical work done by the separated legs, during the separate phases of the stride followed our hypotheses, the total absolute external mechanical work over a complete stride did not appear to differ between groups. This results from the fact that the hypothesized increase in external work during single support appeared as a reduction of the net negative work in this phase (which when taken absolute results in a reduced total work). It could be suggested that the amputee group found a clever strategy to compensate for the extra energy loss for the step-to-step transition by somehow reducing negative work during single support. However, probably we are confronted with a limitation of the external work calculation here. External (BCM) work represents the net summation of muscle work in the body affecting the BCM energy content. Consequently, the reduction of net negative work found during single support in this study could be the result of an increase in positive muscle work, a reduction in negative muscle work or a combination of both somewhere in the musculoskeletal system. Especially, during the single support phase, where substantial work is generated around the joints of the separate stance and swing leg and also trunk and arms, the net work appearing as external BCM work cannot be interpreted without difficulty. To that extent the individual limbs method appears to be no better (nor worse) than the conventional combined limbs methods for calculating external BCM work [14]. This problem could possibly be solved by using more elaborate musculoskeletal models. However, inverse dynamics calculations of net joint work have been shown not to
solve this problem easily [11] and the current validity of more elaborate musculoskeletal models does not warrant success with such an approach either. Nevertheless, despite the lack of difference in total absolute external mechanical work, the clear increase in energy dissipated during double support in the intact leading leg of the amputees suggests that the step-to-step transition can play a role in the higher energy cost of amputee walking. It is not likely that this negative work can be stored or transferred effectively in the body and hence it will be lost and needs to be re-generated. This is further supported by the significant correlation between metabolic energy consumption and the average mechanical power dissipated during the step-to-step transition by the leading leg (Fig. 3, lower panels). Although this correlation is moderate, the step-to-step transition cost still explains 25% of the difference in metabolic energy consumption between subjects in the FWS condition. The CWS condition was included since it is resembles normal walking behavior more realistically. However, since the leading leg’s negative work during double support strongly depends on walking velocity, as Donelan et al. [14] demonstrated, the difference in comfortable walking speed between groups obscure a clear interpretation of the results. Nevertheless, the results for the CWS condition seem to be in line with conclusions drawn above. Despite a lower walking speed, metabolic energy consumption was equal for the amputee group and controls. Concurrently, the negative work in the leading leg during the step-to-step transition did not differ between groups, despite differences in walking speed. Hence amputees walk at lower speed with relatively high collision cost, which might explain equal metabolic energy consumption per unit of time and higher metabolic energy cost per unit distance traveled in amputees. This conclusion is supported by the fact that (independent of speed differences between subjects) step-to-step transition cost remained a significant predictor of the metabolic energy consumption in the CWS condition (Fig. 3). Based on these results it can be concluded that the mechanical work for the step-to-step transition can account for at least part of
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the increased metabolic cost of amputee walking. This is a unique finding since the double inverted pendulum model, on which the step-to-step transition cost is based, is the only model so far that has succeeded in relating part of the extra metabolic cost of amputee gait to a distinct mechanical feature [11–13,25]. The moderate correlation between step-to-step work and metabolic cost, however, also suggests that other factors should be considered. These factors should not necessarily be limited to the mechanics directly related to propulsion. One other important factor could be the increased muscle activity for balance control, for instance through muscle co-contraction or movement variability, which will go unnoticed in biomechanical analyses of average steps. The issue of balance control could become extra apparent when subjects are required to walk on a treadmill, as used in this study [26,27]. This issue deserves further attention In conclusion, it was found that the increased energy consumption during amputee walking is associated with a decrease in the push off work of the prosthetic leg and a concomitant increase in the mechanical energy lost during the step-to-step transition. This finding supports the development of prosthetic feet capable of storing and returning elastic energy for enhancing positive work in the prosthetic leg during double support. Moreover, it motivates the development of actively powered prosthetic feet [28] to really restore push off and reduce step-to-step transition cost. Testing differences in step-to-step transition cost between prosthetic feet was not the aim of the present study and not possible because of the heterogeneous sample of prosthetic feet used by our participants, but this would be an interesting next step. Conflict of interest None. References [1] Rommers GM, Vos LD, Groothoff JW, Schuiling CH, Eisma WH. Epidemiology of lower limb amputees in the north of The Netherlands: aetiology, discharge destination and prosthetic use. Prosthet Orthot Int 1997;21(2):92–9. [2] Fisher SV, Gullickson GJ. Energy cost of ambulation in health and disability: a literature review. Arch Phys Med Rehabil 1978;59(3):124–33. [3] Pinzur MS. The metabolic cost of lower extremity amputation. Clin Podiatr Med Surg 1997;14(4):599–602. [4] Ward KH, Meyers MC. Exercise performance of lower-extremity amputees. Sports Med 1995;20(4):207–14. [5] Waters RL, Mulroy S. The energy expenditure of normal and pathologic gait. Gait Posture 1999;9:207–31.
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