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J Appl Physiol 99: 2099-2107, 2005. First published July 28, 2005; doi:10.1152/japplphysiol.00103.2005
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Minimizing center of mass vertical movement increases metabolic cost in walking

Justus D. Ortega and Claire T. Farley

Locomotion Laboratory, Department of Integrative Physiology, University of Colorado, Boulder, Colorado

Submitted 28 January 2005 ; accepted in final form 22 July 2005


   ABSTRACT
TOP
 ABSTRACT
MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
A human walker vaults up and over each stance limb like an inverted pendulum. This similarity suggests that the vertical motion of a walker's center of mass reduces metabolic cost by providing a mechanism for pendulum-like mechanical energy exchange. Alternatively, some researchers have hypothesized that minimizing vertical movements of the center of mass during walking minimizes the metabolic cost, and this view remains prevalent in clinical gait analysis. We examined the relationship between vertical movement and metabolic cost by having human subjects walk normally and with minimal center of mass vertical movement ("flat-trajectory walking"). In flat-trajectory walking, subjects reduced center of mass vertical displacement by an average of 69% (P = 0.0001) but consumed approximately twice as much metabolic energy over a range of speeds (0.7–1.8 m/s) (P = 0.0001). In flat-trajectory walking, passive pendulum-like mechanical energy exchange provided only a small portion of the energy required to accelerate the center of mass because gravitational potential energy fluctuated minimally. Thus, despite the smaller vertical movements in flat-trajectory walking, the net external mechanical work needed to move the center of mass was similar in both types of walking (P = 0.73). Subjects walked with more flexed stance limbs in flat-trajectory walking (P < 0.001), and the resultant increase in stance limb force generation likely helped cause the doubling in metabolic cost compared with normal walking. Regardless of the cause, these findings clearly demonstrate that human walkers consume substantially more metabolic energy when they minimize vertical motion.

biomechanics; determinants of gait; inverted pendulum; locomotion; mechanical work

IN A CLASSIC PAPER TITLED "The Major Determinants of Normal and Pathological Gait," Saunders et al. (41) suggest that minimizing the body's vertical movements during walking minimizes mechanical work and metabolic cost. Although most researchers agree that the dynamics of walking affect metabolic cost, an alternative view suggests that the vertical movements of the center of mass allow pendulum-like exchange of mechanical energy that decreases the net external work to move the center of mass and metabolic cost of walking (2, 11). Our goal was to examine whether minimizing the vertical movements of the center of mass reduces the net external work and metabolic cost of walking.

According to Saunders et al. (41), walking with a flat center of mass trajectory reduces the muscular work required to lift the body and, consequently, reduces the metabolic cost of locomotion. Saunders et al. (41) identify six "determinants of gait" that smooth and flatten the center of mass trajectory during walking and thereby reduce the muscular work required during walking. These determinants of gait include pelvic rotation, pelvic tilt, stance phase knee flexion, foot and knee mechanics, and lateral displacement of the pelvis. Although Saunders et al.'s (41) determinants of gait view of walking has been widely accepted, particularly in clinical biomechanics (18, 30, 37, 48), it has not been rigorously tested until recently.

Although no studies have examined whether using a flat trajectory minimizes the metabolic cost of walking, several studies have provided insight into this issue. Two determinants of gait, pelvic rotation and heel lift, do indeed reduce the vertical movements of the center of mass (13, 28, 29). In contrast, stance phase knee flexion and pelvic tilt do not appreciably affect center of mass vertical displacement in normal walking (21, 22). Furthermore, individuals who naturally prefer to walk with exaggerated stance phase knee flexion perform more external work to move the center of mass (50). Although a recent simulation of walking suggests the energetic cost of raising the body's center of mass is significant (39), no study has tested the central hypothesis of Saunders et al. (41) that decreasing an individual's center of mass vertical movement minimizes mechanical work to move the center of mass and metabolic cost. Moreover, an alternative and contradictory view has emerged.

According to the alternative view, the vertical movements of the center of mass allow the exchange of mechanical energy and thereby reduce mechanical work required to move the center of mass and the metabolic cost of walking (2, 10, 11). This energy exchange and the center of mass trajectory during walking have been modeled using an inverted pendulum with the stance leg represented as a rigid strut that supports a point mass equal to body mass (2, 10, 11). Like an inverted pendulum, a human walker's center of mass rises and slows in the first half of the stance phase and then falls and accelerates during the second half of the stance phase (6, 34, 35, 38, 42). Consequently, in the first half of the stance phase, kinetic energy is converted into gravitational potential energy (11). In the second half of the stance phase, the opposite conversion occurs. Because the gravitational potential energy and kinetic energy fluctuations are nearly equal in magnitude and ~180° out of phase in walking, humans can exchange substantial mechanical energy. To achieve this exchange, muscles must generate force to maintain a stiff stance limb and prevent the center of mass from collapsing, and thus energy exchange is not a purely passive process in walking humans. Nonetheless, this model accurately represents the mechanical energy fluctuations and the pendulum-like energy exchange in an amazing variety of animals, including those in Refs. 11, 19, 20, 24, 26, 36.

According to the inverted pendulum model, the out-of-phase fluctuations in gravitational potential energy and kinetic energy represent a continuous exchange of mechanical energy. This exchange reduces the net mechanical work performed by the overall muscular system to lift and accelerate the center of mass ("net external work") by up to 65% and consequently reduces the metabolic cost in walking (9). In fact, both net external work and metabolic cost of transport are minimized at about the same intermediate walking speed where pendulum energy exchange is maximized (10). Minetti et al. (38) showed that metabolic cost and net external work are minimized at the same freely chosen stride frequencies and that recovery decreases at stride frequencies above the freely chosen stride frequency. This link between energy exchange, net external work, and metabolic cost in a number of situations (8, 10–12, 38) suggests center of mass vertical movement is advantageous because it allows pendulum-like energy exchange, reduces net external work, and reduces metabolic cost in walking.

The two divergent views regarding the relationship between center of mass vertical motion and metabolic cost have not yet been reconciled. The aim of this study is to determine how minimizing center of mass vertical motion affects inverted pendulum exchange, net external work, and metabolic cost in walking. We hypothesized that walking with a flattened center of mass trajectory does not reduce net external work performed on the center of mass because it reduces inverted pendulum energy exchange. Moreover, contrary to Saunders et al. (41), we hypothesized that metabolic cost would not decrease when humans walk with a flattened center of mass trajectory. To test our hypotheses, we examined metabolic cost, mechanical energy exchange, and net external work for humans walking with small vertical movements of the center of mass compared with walking with normal center of mass movements. In addition to testing the hypothesis of Saunders et al. (41), this study will provide insight into the fundamental mechanical determinants of metabolic cost in walking.


   MATERIALS AND METHODS
TOP
 ABSTRACT
 MATERIALS AND METHODS
RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Experimental design.   Kinetic and metabolic data were collected for eight healthy adult humans (5 women, 3 men) without any known orthopedic, neurological, or cardiovascular disease. The subjects had an average age of 26.6 yr (SD 2.6), mass of 66.1 kg (SD 10.7), and height of 1.73 m (SD 0.07). Before the experiment, all subjects gave their written, informed consent. This protocol was approved by the University of Colorado committee for the protection of human subjects.

Each subject participated in three sessions including a practice session and two testing sessions. In all sessions, subjects walked on a custom-built motorized treadmill mounted on a force platform (31). During the practice session, subjects walked for at least 20 min with a normal center of mass trajectory and 20 min with a flattened center of mass trajectory (i.e., flat-trajectory walking) at two speeds (1.3 and 1.8 m/s) to habituate subjects to the two types of walking. This session exceeded the minimum treadmill habituation time of 10 min recommended by Wall and Charteris (45). During the testing sessions, subjects walked normally and with a flattened center of mass trajectory at five speeds (0.7, 1.0, 1.3, 1.5, and 1.8 m/s) that were randomly assigned to the first testing session (3 speeds) or the second testing session (2 speeds). During the last 3 min of each 7-min trial, we collected stride frequency, rate of O2 consumption and CO2 production, and ground reaction force data. Three minutes of rest were given after each flat-trajectory walking trial. At the beginning and end of the practice session and each testing session, we collected metabolic and mechanical data at 1.3 m/s to quantify whether any habituation effect occurred.

During the flat-trajectory walking trials, subjects were provided with real-time visual feedback to help them minimize the vertical displacement of the center of mass. A reflective marker over the fourth lumbar vertebra was videotaped from a posterior view at a rate of 60 Hz and projected onto a monitor with horizontal grid lines in view of the subject. The camera was zoomed so that 1-cm displacement of the marker appeared as 4 cm on the monitor. The only instruction given to each subject was to minimize the vertical movement of the marker, and thus we did not know what strategy the subjects would use before the study. At the beginning of the practice sessions, subjects tended to experiment with a variety of techniques to achieve this goal. However, by the end of the practice session, they all converged on the strategy of increasing flexion of stance limb joints.

Metabolic cost.   We measured the rates of O2 consumption and carbon dioxide production using open-circuit indirect calorimetry (Physio-Dyne Instruments, Quogue, NY). During each trial, we gave subjects 4 min to reach metabolic steady state before collecting metabolic data for the last 3 min. Using the average O2 consumption (ml O2/min) and carbon dioxide production (ml CO2/min) for the last 3 min, we calculated average metabolic rate per kilogram body weight (W/kg) (5). For 7 min at the beginning of each session, we measured the standing metabolic rate. We subtracted standing metabolic rate from gross metabolic rate and divided by speed to calculate net metabolic cost of transport (J·kg–1·m–1).

Ground reaction force and mechanical work.   A force-sensing treadmill was used to measure the vertical, horizontal, and lateral ground reaction force components for two 10-s periods (about 20 strides total) within the last 2 min of each trial. The force treadmill consisted of a custom-built motorized treadmill mounted on a force platform (AMTI, model ZBP-7124-6-4000) and has been described in detail by Kram et al. (31). We collected force data at 1,000 Hz and low-pass filtered the data using a fourth-order zero-lag Butterworth filter with a cutoff frequency of 20 Hz. We used the ground reaction force data to calculate the acceleration of the center of mass in each direction. We then double integrated the acceleration data with respect to time for an integral number of strides to determine the instantaneous center of mass velocity and displacement in each direction (4, 7).

We determined the kinetic energy, gravitational potential energy, and total energy of the center of mass from its velocity and displacement and subsequently determined the external work performed on the center of mass. We calculated total kinetic energy (Ek,t) from body mass (m) and the resultant center of mass velocity (V) determined from its vertical, horizontal, and lateral components:

(1)
Gravitational potential energy (Ep,g) was calculated from mass (m), the acceleration due to gravity (g), and the vertical displacement of the center of mass relative to heelstrike ({Delta}h):

(2)
By taking the instantaneous sum of gravitational potential energy and kinetic energy, we calculated the total energy of the center of mass (Etot):

(3)
We determined the net external work required to lift and accelerate the center of mass by summing the positive increments in its total energy over each step (7). "Net external" work represents the net work performed by the overall muscular system to lift and accelerate the center of mass and is quantitatively identical to external work as defined by Cavagna (7). Because the two limbs and antagonist muscles can work against each other and internal work is performed to move the limbs relative to the center of mass, net external work is less than the total muscle work performed during walking (1, 43, 44, 51). Net external work was calculated using the net ground reaction force that was the instantaneous sum of ground reaction forces under both limbs. Thus this calculation involved the mathematical cancellation of simultaneous positive and negative work performed by the individual limbs during the double support phase (17). We used the term net external work to emphasize that it represents the minimum work performed to move the center of mass and does not account for the "extra" muscle work needed to move the center of mass due to opposing forces of individual limbs or of antagonist muscles.

To evaluate the potential for inverted pendulum energy exchange, we examined the relative magnitudes and timing of the kinetic energy and gravitational potential energy fluctuations. Gravitational potential energy and kinetic energy each fluctuated once per step, and {Delta}Ep,g and {Delta}Ek,t corresponded to the magnitudes of these fluctuations normalized to body mass and speed (J·kg–1·m–1) to compare to net external work values. We compared the magnitudes of {Delta}Ep,g and {Delta}Ek,t by taking their ratio, and we quantified their relative timing by calculating phase angle (9):

(4)
where {Delta}t represents the time interval between minimum {Delta}Ek,t and maximum {Delta}Ep,g and T represents the time interval between consecutive heelstrikes. Thus, when the minimum {Delta}Ek,t and the maximum in {Delta}Ep,g occurred simultaneously, phase angle was 180°.

Finally, we evaluated how much inverted pendulum energy exchange reduced the net external work required to lift and accelerate the center of mass by calculating the mechanical energy recovery (11):

(5)
where Wp,g was calculated as the sum of the positive increments in gravitational potential energy over a step and was the work required to lift the center of mass and Wext is net external work. We calculated the work required to accelerate the center of mass (Wk,t) as the sum of the positive increments in the kinetic energy over a step. All mechanical work values are expressed per kilogram body mass and per meter traveled.

Kinematics.   We measured sagittal plane kinematics of the right lower limb using high-speed video (200 fields/s, JC Labs, Mountain View, CA) and reflective markers on the iliac crest, greater trochanter, lateral femoral condyle, lateral malleolus, and lateral border of the fifth metatarsal head. We digitized the video (Peak Performance Technologies, Englewood, CO) and filtered the position data using a fourth-order zero-lag Butterworth filter with a cutoff frequency of 6 Hz (49). From the position data, we calculated the hip, knee, and ankle angles during the stance phase of walking. Each joint angle was defined as the acute angle between adjacent segments. We determined the average angle and minimum angle for each joint during the stance phase. We focused on the stance phase because stance limb action is the primary determinant of the motion of the center of mass.

Statistical analyses.   The effects of walking condition on metabolic cost and walking mechanics were tested using a two-way mixed repeated-measures ANOVA and Student-Newman-Keuls post hoc tests where appropriate. For the habituation data, we tested the effects of habituation on vertical displacement, stride frequency, and metabolic cost using one-way repeated-measures ANOVA. We tested the effects of habituation between trials within each session as well as across all sessions. All statistical analyses were performed using SPSS 11.5 (SPSS) software and an {alpha} level of 0.05.


   RESULTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
The metabolic cost and kinematics of normal and flat-trajectory walking remained constant within and among testing sessions, suggesting that subjects were fully habituated to both types of walking at the end of the practice session. Metabolic cost remained constant across the practice and testing sessions for normal and flat-trajectory walking (P = 0.63 and P = 0.76, respectively), and stride frequency also did not change (P = 0.97 for both types of walking). Moreover, in normal walking, subjects maintained a nearly constant vertical displacement of 3.0 cm (SD 0.4) for all practice and testing sessions (P = 0.99). In flat-trajectory walking, subjects reduced the vertical displacement from 1.5 cm (SD 0.3) to 1.0 cm (SD 0.2) between the beginning and end of the practice session (P = 0.002) but then maintained a constant vertical displacement over the testing sessions (P = 0.92). Although most subjects experimented with a variety of techniques for flat-trajectory walking at the beginning of the practice session, all subjects appeared to consistently use one technique by the end of the practice session.

In flat-trajectory walking, the center of mass moved vertically by 69% (SD 4) less than in normal walking (P < 0.0001), whereas other aspects of the center of mass dynamics remained similar (Fig. 1). The average vertical displacement of the center of mass in flat-trajectory walking was 0.9 cm (SD 0.1) for all speeds and was independent of speed (P = 0.32; Fig. 1A). In contrast, in normal walking, the vertical displacement increased from 1.8 cm (SD 0.1) to 4.2 cm (SD 0.2) across the range of speeds (P = 0.0001). Thus, in flat-trajectory walking, the center of mass moved vertically by 54–78% less than in normal walking at the slowest and fastest speeds, respectively. Despite reducing the vertical displacement of the center of mass to <1 cm during flat-trajectory walking, subjects did not substantially change lateral displacement (P = 0.26) or stride frequency (P = 0.17). Specifically, in flat-trajectory walking, subjects maintained center of mass lateral displacement within 0.4 cm (Fig. 1B) and stride frequency within 0.04 Hz (Fig. 1C) of the values in normal walking.



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  		Fig. 1. Center of mass vertical displacement (A), center of mass lateral displacement (B), and stride frequency (C) vs. speed during normal walking ({bullet}) and flat-trajectory walking ({triangleup}). Values are means ± SD. In flat-trajectory walking, vertical displacement of the center of mass was smaller than in normal walking, and lateral displacement of the center of mass was similar in both types of walking. Stride frequency was similar in both types of walking. Lines are least squares regressions. *Significant differences (P < 0.05) between flat-trajectory walking and normal walking.

 
Subjects used substantially more flexed stance limbs during flat-trajectory walking than during normal walking. Average joint angle for the stance phase decreased by 10° (SD 4) at the hip (P < 0.001), 18° (SD 5) at the knee (P < 0.001), and 7° (SD 2) at the ankle (P < 0.001) between flat-trajectory walking and normal walking. Average stance phase joint angles did not change with walking speed (P = 0.409, 0.179, and 0.848, respectively) (Figs. 2 and 3).



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  		Fig. 2. Representative joint angles at the hip (A), knee (B), and ankle (C) during the stance phase of normal walking (solid lines) and flat-trajectory walking (broken lines) vs. time for a single stance phase at 1.3 m/s. Time is expressed as a percent of the stance phase duration. Throughout the stance phase of flat-trajectory walking, subjects had greater flexion at the hip, knee, and ankle (P < 0.001).

 


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  		Fig. 3. Average stance phase joint angles for the hip (A), knee (B), and ankle (C) vs. speed during normal walking ({bullet}) and flat-trajectory walking ({circ}). Values are means ± SD. In flat-trajectory walking, the hip, knee, and ankle were more flexed during stance than in normal walking. Lines are least squares regressions. *Significant differences (P < 0.05) between flat-trajectory walking and normal walking.

 
Despite the minimal vertical movements of the center of mass during flat-trajectory walking, subjects consumed, on average, twice as much metabolic energy to travel a meter than during normal walking (P < 0.0001) (Fig. 4). During flat-trajectory walking, subjects consumed the least metabolic energy to travel a meter at the intermediate speed of 1.0 m/s (3.74 J·kg–1·m–1, SD 0.45) and consumed 4 and 8% more at the slowest and fastest speeds, respectively (P = 0.01). During normal walking, subjects consumed the least metabolic energy at the intermediate speed of 1.3 m/s (1.8 J·kg–1·m–1, SD 0.1) and consumed 17 and 27% more at the slowest and fastest speeds, respectively (P = 0.01). Even at those extreme speeds, the cost of transport was on average 1.8-fold greater in flat-trajectory walking than in normal walking.



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  		Fig. 4. Net metabolic cost of transport vs. speed for normal walking ({bullet}) and flat-trajectory walking ({triangleup}). Values are means ± SD. In flat-trajectory walking, subjects consumed about twice as much metabolic energy per kilogram of body weight to travel a given distance than in normal walking. Lines are least squares regressions. *Significant differences (P < 0.05) between flat-trajectory walking and normal walking.

 
At all speeds of flat-trajectory walking, gravitational potential energy fluctuated much less than kinetic energy, and this mismatch led to reduced energy exchange by the inverted pendulum mechanism than in normal walking. In flat-trajectory walking, gravitational potential energy fluctuated an average of 63% (SD 16) less than kinetic energy fluctuated over the range of speeds (Figs. 5B and Fig. 6C). This mismatch occurred because gravitational potential energy fluctuated minimally (0.13 J·kg–1·m–1, SD 0.01) (Fig. 6A), whereas kinetic energy fluctuated only slightly less than in normal walking (0.39 J·kg–1·m–1, SD 0.10) (Fig. 6B). Moreover, the relative timing of these energy fluctuations (i.e., phase angle) tended to deviate more from the ideal value for pendulum-like energy exchange (180°) in flat-trajectory walking (256°, SD 22) than in normal walking (P = 0.0004) (Fig. 7A). In contrast, in normal walking, gravitational potential and kinetic energy fluctuated nearly out of phase (199°, SD 9) and approximately equally at all speeds (0.42 J·kg–1·m–1, SD 0.06, and 0.44 J·kg–1·m–1, SD 0.14, for {Delta}Ep,g and {Delta}Ek,t, respectively) (Figs. 5A and 6, A–C). Thus the energy fluctuation magnitudes and timing were close to ideal for energy exchange in normal walking but not in flat-trajectory walking.



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  		Fig. 5. Representative data for total energy (Etot), kinetic energy (Ek,t), and gravitational potential energy (Ep,g) of center of mass vs. time at 1.3 m/s for normal walking (A) and flat-trajectory walking (B). A single step from heel strike of one foot to heel strike of opposite foot is shown. All energy values are normalized to body mass. In flat-trajectory walking, Ep,g fluctuated much less than in normal walking. Total energy fluctuations were not smaller in flat-trajectory walking than in normal walking due to lack of energy exchange.

 


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  		Fig. 6. Magnitude of Ep,g ({Delta}Ep,g; A), magnitude of Ek,t ({Delta}Ek,t; B), and ratio of Ep,g fluctuation to Ek,t ({Delta}Ep,g/{Delta}Ek,t; C) vs. speed (means ± SD) in normal walking ({bullet}) and flat-trajectory walking ({triangleup}). In flat-trajectory walking, {Delta}Ep,g/{Delta}Ek,t was smaller than in normal walking primarily because Ep,g fluctuated less than in normal walking. Lines are least squares regressions, and energy fluctuation values are normalized to body mass and expressed per meter to facilitate comparisons to net external work. *Significant differences (P < 0.05) between flat-trajectory walking and normal walking.

 


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  		Fig. 7. Phase angle between Ep,g maximum and Ek,t minimum (A), inverted pendulum recovery of mechanical energy (B), and net external work (C) vs. speed (means ± SD) for normal walking ({bullet}) and flat-trajectory walking ({triangleup}). To maximize inverted pendulum energy exchange, Ep,g and Ek,t should be out of phase (i.e., phase angle of 180°). In flat-trajectory walking, phase angle deviated more from 180° and varied more than in normal walking. Recovery was much greater in normal walking than in flat-trajectory walking, but net external work per kilogram body mass was similar. Lines are least squares regressions. *Significant differences (P < 0.05) between flat-trajectory walking and normal walking.

 
In flat-trajectory walking at moderate speeds, subjects recovered only about one-half as much mechanical energy by the inverted pendulum mechanism as in normal walking (P < 0.0001) (Fig. 7B). In flat-trajectory walking, mechanical energy recovery by the inverted pendulum mechanism decreased from 41% (SD 3) to 21% (SD 4) as subjects walked faster (P = 0.04), whereas in normal walking, recovery remained 63% (SD 2) over the range of speeds (P = 0.24). Recovery was low in flat-trajectory walking primarily because the decrease in gravitational potential energy was less than the increase in kinetic energy in the second half of stance (Fig. 5B). Consequently, the conversion of gravitational potential energy to kinetic energy was lower in flat-trajectory walking than in normal walking.

Although recovery was low in flat-trajectory walking, a similar amount of net external work was needed to move the center of mass as in normal walking (P = 0.31) (Fig. 7C). In flat-trajectory walking, the gravitational potential energy fluctuations were on average 69% smaller than in normal walking (P < 0.0001), and, consequently, substantially less net work was needed to lift the center of mass in the first half of stance. However, substantially more net work was needed to accelerate the center of mass in the second half of stance than in normal walking. Specifically, gravitational potential energy decreased so little in flat-trajectory walking that inverted pendulum energy exchange supplied only a small portion of the energy needed for the simultaneous increase in kinetic energy. In contrast, energy exchange provided the majority of the energy needed to accelerate the center of mass in normal walking (Figs. 5A and 6C). Because minimizing vertical displacement increased the net work required for reacceleration, net external work was not lower in flat-trajectory walking (0.35 J·kg–1·m–1, SD 0.09) compared with normal walking (0.32 J·kg–1·m–1, SD 0.07) (P = 0.31) (Fig. 7C).


   DISCUSSION
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 
Contrary to the view of Saunders et al. (41) and in agreement with our hypothesis, minimizing the vertical motion of the center of mass during walking does not reduce the mechanical work required to move the center of mass and approximately doubles the metabolic cost. Although some evidence suggests that the metabolic cost of lifting the center of mass is substantial (39), the results of this study emphasize that vertical motion allows inverted pendulum energy exchange and therefore reduces the mechanical work required to accelerate the center of mass in normal walking. In accordance with the determinants of gait view, the mechanical work required to lift the center of mass decreases in flat-trajectory walking. However, because little gravitational potential energy is available to be converted to kinetic energy, the work required to accelerate the center of mass increases in flat-trajectory walking. Due to these offsetting effects, minimizing vertical motion does not change the net external work required to move the center of mass. Therefore, other factors probably contribute to the high metabolic cost of flat-trajectory walking, including greater muscle force generation to support body weight and greater positive muscle work performed to compensate for co-contraction.

The high metabolic cost of flat-trajectory walking may be explained by greater muscle force generation to support body weight due to increased stance leg flexion (25, 32). Because our subjects uniformly chose to flatten the center of mass trajectory by increasing stance leg flexion, it is likely that the ground reaction force had longer moment arms about the joints and the effective mechanical advantage of the stance limb extensor muscles decreased (3). Consequently, subjects likely had to generate greater muscle force to support body weight in flat-trajectory walking than in normal walking. Several studies on human walking demonstrate that exaggerated hip and knee flexion leads to greater muscle activation, muscle force, and metabolic cost (14, 23, 25, 46, 47). However, in the extreme case of human walkers maintaining a knee angle of <135° during the stance phase, metabolic cost increases by only 38% (47). Given that metabolic cost doubled in our study, it is likely that other factors contribute to doubling metabolic cost in flat-trajectory walking.

Although unlikely to be a major contributor, another factor that could underlie the high metabolic cost of flat-trajectory walking is the opposing actions of the individual limbs during double support (17, 33). In the double-support phase of walking, the two limbs work against each other as the body transitions from one inverted pendulum arc to the next. The leading limb performs negative work to change the direction of the center of mass while the trailing limb simultaneously performs positive work to accelerate the center of mass upward and forward. This simultaneous limb work is not fully reflected in net external work because the opposing components of the forces under the two limbs mathematically cancel each other. In flat-trajectory walking, the center of mass changes direction during double support less dramatically than in normal walking because it follows a flatter arc in each single-support phase. Because the negative work by the leading limb primarily acts to change the direction of the center of mass during double support, the leading limb likely performs less negative work in flat-trajectory walking. As a result, the simultaneous positive work performed by the trailing limb that compensates for the negative work by the leading limb should also be less than in normal walking. Therefore, the total individual limb work performed by the leading and trailing limbs during double support is likely not greater and may even be less than in normal walking.

Increased co-contraction of antagonist stance limb muscles may also contribute to the high metabolic cost of flat-trajectory walking. When antagonistic extensors and flexors of the stance limb are simultaneously active, the flexors absorb some of the positive work performed by the extensors, and thus the net work performed by the combined active muscles is less than the positive work performed by the extensors. Consequently, if there is co-contraction of antagonists in the stance limb, the net external work will differ from the total work performed by individual muscles. Co-contraction of antagonist muscles may increase in flat-trajectory walking because it is an unfamiliar task. Grasso et al. (23) found that walking with exaggerated knee flexion increases co-contraction of stance limb muscles. However, co-contraction might have been especially high in that study (23) because it did not familiarize subjects to bent-posture walking before the experimental trials. Our study included a practice session, and the constant metabolic cost over the practice and experimental sessions suggests that subjects had become familiar with flat-trajectory walking. Nonetheless, it would be useful for a future study to measure electromyogram of the stance limb muscles during flat-trajectory walking to examine the role of co-contraction in increasing metabolic cost.

It is important to note that our study focuses on the effect of reducing vertical displacement but does not encompass the vertical displacement range above normal. Saunders et al. (41) believed that the large vertical displacement associated with vaulting over strut-like legs (i.e., compass gait) would lead to a very high metabolic cost. However, an alternative view is that a compass gait, if physically possible, may conceivably be more economical than normal walking due to more inverted pendulum energy exchange and better mechanical advantage of the muscles supporting body weight. However, these effects might be offset by a greater cost of redirecting the center of mass between inverted pendulum arcs during double support (16). Moreover, in a pilot experiment conducted in our laboratory, we attempted to measure metabolic cost during compass-like gait. Although most subjects could maintain a rigid stance limb during support, they also kept their lower limbs rigid during the swing phase. As a result, they altered numerous factors including stride frequency, step length, and swing limb kinematics. The remaining subjects simply could not walk at a constant speed without stance limb flexion. Therefore, we chose to focus on reducing the vertical motion of the center of mass and testing the central hypothesis of Saunder et al. (41) that minimizing center of mass vertical movement reduces energetic cost of walking.

In conclusion, our results show that minimizing the vertical motion of the center of mass doubles metabolic cost but does not affect net external work in human walking. Our findings emphasize that net external work is not the main determinant of the metabolic cost of walking and suggest that the cost of generating muscle force to support body weight plays a key role. These findings have clinical implications for therapies aiming to improve walking economy in patients with gait disorders that affect center of mass motion and metabolic cost such as hip joint replacement, lower limb amputation, stroke, and cerebral palsy (15, 27, 40). Indeed, Detrembler et al. (15) suggest impaired inverted pendulum recovery of mechanical energy is an important factor in the increased metabolic cost during stroke-induced hemiparetic walking. However, based on Saunders et al. (1953), some literature suggests that patients with gait disorders should be trained to walk with little vertical motion of the trunk to reduce metabolic cost (18, 30, 37, 48). Our findings suggest that maintaining normal levels of vertical center of mass motion and an extended stance limb are important factors in reducing the metabolic cost of walking.


   GRANTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
ACKNOWLEDGMENTS
 REFERENCES
 
This study was supported by National Institute on Aging Grant AG-00279.


   ACKNOWLEDGMENTS
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
REFERENCES
 
The authors thank the members of the Locomotion Laboratory for help with this study.


   FOOTNOTES
 

Address for reprint requests and other correspondence: J. D. Ortega, Locomotion Laboratory, Dept. of Integrative Physiology, 354 UCB, Boulder, CO 80309-0354 (e-mail: ortegajd{at}colorado.edu)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MATERIALS AND METHODS
 RESULTS
 DISCUSSION
 GRANTS
 ACKNOWLEDGMENTS
 REFERENCES
 

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