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1Concord Field Station, Department of Organismic and Evolutionary Biology, Harvard University; Bedford, Massachusetts 01730; 2Department of Integrative Physiology, University of Colorado, Boulder, Colorado 80309; 3Department of Zoology, Oregon State University, Corvallis, Oregon 97331; and 4Department of Organismal Biology and Anatomy, University of Chicago, Chicago, Illinois 60637
Submitted 5 January 2004 ; accepted in final form 9 July 2004
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ABSTRACT |
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 TOP ABSTRACT METHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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gait; muscle mechanical advantage; muscle force; metabolic cost
Although limb muscle mechanical advantage increases significantly with body size in quadrupedal mammals (1, 2), changes in limb mechanical advantage as a function of gait and speed have not been observed. Data for quadrupedal mammals, however, have been largely limited to comparisons of trotting and galloping. The distinctive kinematics (17) and mechanics (9–11, 27) of human walking vs. running suggest that changes in limb mechanical advantage may play a role in determining the energy cost of transport at each gait. In studies comparing a quadruped and biped of similar size, Roberts and coworkers (31, 32) showed that their similar metabolic costs are related to the relative size of limb muscles and the volume of muscle that must be recruited to support body weight during locomotion on four vs. two limbs.
We also seek to evaluate how the generally erect bipedal posture of humans and possible gait-related changes in limb mechanical advantage may relate to comparisons of the energy cost of transport in humans compared with quadrupedal mammals. Early work on the scaling of the energetic cost of transport (40) showed that the transport cost of human running exceeds that for quadrupeds of similar size. This would predict that human runners have a lower limb EMA, requiring them to recruit a larger volume of muscle and generate more force for their weight compared with similar-sized quadrupeds.
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METHODS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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Muscle moment arms (r) were determined by palpation of muscle attachments relative to estimates of joint centers of rotation for each subject. These were found to compare well with direct measurements made on fresh cadavers (Table 2) and mounted skeletons of similar stature, as well as values reported in the literature (35, 36, 41, 42). Because we used the same r values for analyzing walking and running, any error in these values will not affect our main goal of comparing posture-related effects on muscle force-generation requirements during these two gaits. In addition to each subject's weight, the following data were also obtained: stature, thigh length, leg length, and foot length. These data (Table 2) were used to calculate the mass and moments of inertia of individual limb segments of each of the subjects by using published anthropometric data (44).
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The EMA (1) of muscle extensors to generate a given force on the ground was calculated as the ratio (r/R) of the agonist muscle group's weighted mean moment arm (r) to the moment arm (R) of the GRF acting about the joint (Fig. 1). R is calculated on the basis of the resultant GRF over at any instant in time relative to a joint's center of rotation, and r is calculated on the basis of the moment arms of individual agonist muscles, each being weighted relative to the fiber cross-sectional area (A) of each muscle (r = r1*A1/Atot + r2*A2/Atot + ... ri*Ai/Atot, where Atot = A1 + A2 + ... Ai). Measurements of r for individual muscle agonists were only obtained when reliable differences in moment arm could be assessed by palpation (e.g., for the hamstrings: semimembranosus, semitendinosus, and biceps femoris, but not for the quadriceps, which were assumed to have the samer). Muscle moment arms were measured at joint angles corresponding to peak MGRF. Although this may underestimate or overestimate muscle forces if r increases or decreases at other joint angles, no systematic effect among limb joints or with respect to joint kinematics as a function of speed and gait is assumed (r is likely to vary most at the knee because of gait-related changes in joint angle, but this cannot be reliably distinguished by palpation). Whole limb EMA was calculated as the average of hip, knee, and ankle EMA. Active agonist muscles during limb support were considered to be the triceps surae at the ankle, the quadriceps at the knee, and the hamstrings and gluteus maximus at the hip. This approach assumes that each agonist muscle generates an equivalent stress (force per fiber cross-sectional area).
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Time-integrated muscle force (muscle impulse) and estimates of active muscle volume.
In addition to measurements of muscle EMA, agonist extensor muscle forces were calculated and integrated over the time course of limb support (
Fm dt) to determine agonist muscle impulses. Muscle impulses were determined to provide an estimate of how changes in force-generating requirements during stance at different speeds and gaits might correlate with differences in energy cost, given that the energy (ATP) utilization of skeletal muscle is dependent on the magnitude and duration of force development (26, 34), in addition to rates of length change and work performed (16, 20). By using inverse dynamics and GRF recordings, muscle forces were calculated during ground contact for each image frame on the basis of analysis of inertial, gravitational, and external moments exerted about each limb joint, accounting for the transmission of force by multisegmental muscles (3, 44). Agonist muscle forces were determined on the basis of a free-body analysis of joint moments required to generate ground force [MGRF at the ankle (Ma), knee (Mk), and hip (Mh)] by using the following equations (5, 41)
 | (1) |
 | (2) |
 | (3) |
In addition to assuming that agonist muscle forces were distributed based on equal stress, we assumed no coactivation of monoarticular muscle antagonists, other than that associated with the action of two-joint muscles acting to extend one joint and flex the other. For example, the gastrocnemius extends the ankle but, in doing so, flexes the knee. Consequently, its antagonist flexor moment was included in calculating the net moment produced at the knee and the extensor moment produced by the quadriceps (Eq. 2). This allows the component of force exerted by the gastrocnemius muscle (FG) to be determined from the total force exerted by the triceps surae (FTS) and the component of force exerted by the rectus femoris (FRF) from the quadriceps force (FQ). These force components were solved simultaneously from Eqs. 2 and 3 after Eq. 1 was solved.
Muscle impulses were then normalized to the ground reaction impulse (F dt)/(GRF dt) to evaluate how much muscle force was required to support a given force on the ground over the duration of limb support at the different speeds within each gait. In effect, this normalized impulse provided a measure of the average muscle force required to exert one body weight of force on the ground. It also corresponds to the inverse (r/R) of the relationship described by muscle EMA (Fig. 1) and has the advantage of allowing a comparison of muscle force-generation requirements with respect to ground force over the entire period of limb support, including those instances when the GRF passes through the joint's center of rotation and MGRF 
0, which are ignored in the determination of muscle EMA as defined above.
Because the metabolic cost of locomotion is likely linked to volume of muscle that must be recruited to support an animal's weight while it is running (25, 32), we also estimated the volume of active muscle at each joint. This is important to consider because differences in muscle fiber length affect the volume of muscle needed to generate a given force. Our measurements, however, ignore the cost associated with muscles activated during the swing phase of gait. To estimate the volume of actively recruited muscle at each joint during stance, we used morphological data obtained from fresh lower extremity muscles of four male human cadavers (Table 2; all cadavers were in good musculoskeletal health at the time of their death; however, given their age, substantial muscle wastage had likely occurred). This was done by assuming that muscles exert an equivalent force per cross-sectional area of active fibers (constant muscle stress, 
), irrespective of differences in the velocity of muscle contraction at differing joints. Given this assumption (i.e., that active fiber cross-sectional area of a muscle, A* = F/), the volume of active muscle (V*, cm3) was defined as
 | (4) |
Although our values for muscle area are substantially less than those reported for younger adults (41), any differences in the absolute measures of muscle mass, fascicle length, and fiber area obtained from the cadavers vs. actual values for the four experimental subjects are not likely to affect our conclusions. Our analysis of how the recruitment of active muscle volume during stance varies as a function of gait depends on the relative size and architecture of the muscles within the limb, which are less likely to differ among groups of subjects than absolute size and architecture. Also, our comparisons of walking and running use the same muscle data for both gaits.
Comparisons between gaits were analyzed using two-way factorial ANOVA. Results were considered significant at a P < 0.05 level.
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RESULTS |
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F), normalized to ground impulse (GRF), increased 5.2 ± 1.0-fold at the knee (P < 0.001, F = 21.71), decreased 37 ± 7% at the hip (P < 0.05, F = 6.42), and remained unchanged at the ankle (P > 0. 5, F = 0.01) (Fig. 6). In addition to the reduced knee EMA during running, the increase in knee impulse ratio (F/GRF) was enhanced by a 32% lower ground reaction impulse during running (265 ± 48 Ns) vs. during walking (389 ± 67 Ns; means of all four subjects averaged for all speed trials within each gait, n = 12). Whereas only 9% of total extensor muscle impulse was produced at the knee during walking, knee extensors generated 39% of total extensor impulse during running, nearly matching that generated by the ankle extensors.
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Active muscle volume. Because of the differences in mean fascicle length (L, Eq. 4) among hip (12.1 cm), knee (7.5 cm), and ankle (4.2 cm) extensor muscles (adjusted for differences in subject limb length compared with cadaver data reported in Table 2), changes in muscle force-generation requirements resulted in significant shifts in the estimated volume of actively recruited fibers when gait changed from walking to running (Fig. 7). When summed for all three muscle groups, the volume of active muscle estimated to generate force on the ground to counter MGRF increased 2.26-fold when gait changed from a walk (2,237 cm3) to a run (5,066 cm3). At a walk, active muscle volume required to generate MGRF was greatest at the hip, being 46 ± 4% of total, compared with 31 ± 2% at the ankle and 23 ± 4% at the knee (Fig. 7A). When gait changed to run, however, the knee extensors represented 49 ± 8% of the estimated total, compared with 15 ± 2% at the ankle and 36 ± 6% at the hip. The greater estimated volume of active muscle at the knee results from the knee extensors having longer fibers than the ankle extensors, despite generating comparable levels of force at a run. The 4.9-fold increase in the active volume of the knee extensors resulted from the decrease in knee EMA and the increase in knee extensor force and impulse at a run vs. a walk.
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DISCUSSION |
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The decrease in knee EMA at a run corresponds to previously defined differences in the mechanics of body weight support during walking vs. running, or trotting, and hopping gaits (8). During walking, the knee is extended throughout most of the stance phase of the stride to provide a flexible strut (27) that the body vaults over, exchanging potential and kinetic energy of the body's center of mass to conserve mechanical energy (10). This strategy allows the knee (and hip) to remain more closely aligned with the GRF, lowering the external moment developed at the knee. During running, the knee is held in a more flexed position, associated with the limb's function as a spring (11, 15, 27), which absorbs the impact of the body's weight during landing and allows for the storage of elastic energy at the ankle, within the foot (23), and probably at other sites throughout the leg. This shift in limb function, however, requires a substantial increase in the magnitude of force and total extensor impulse at the knee required to generate the GRF. Because our analysis and results neglect the contribution of force-generation requirements in the frontal plane, our results may differ from those obtained for women and obese runners, whose requirements in the frontal plane are likely greater than those for lean male runners.
At least partly because of these changes in knee joint mechanics in the parasagittal plane, the energy cost of transport in humans is 50–80% greater during running than during walking (15, 28). To assess how the decrease in extensor mechanical advantage may affect this increase in energy cost, we estimated the volume of actively recruited fibers within each agonist muscle group, assuming that all recruited fibers are activated similarly and generate equivalent force per fiber cross-sectional area (equal stress) in the different muscles. We adopted this approach because, in general, longer fibered muscles can be expected to consume more energy to generate a given force per unit time than shorter fibered muscles (31). Although the specific contractile conditions under which a muscle generates force (i.e., its speed of shortening and whether it shortens, lengthens, or remains isometric) will affect the energy cost of force generation (26), our approach represents a rough first approximation for estimating the volume of actively recruited fibers within a muscle during stance. A similar approach has also been taken by Griffin et al. (19) to examine the metabolic cost of generating force in human walking. Consequently, although the magnitude and rate of muscle force development required to support the body's weight at a particular speed and gait have been shown to underlie the energy cost of locomotion (25, 37), the volume of actively recruited muscle fibers underlying force-generation requirements within the limb during stance is also likely to be a critical influence on energy cost. Consistent with this, Griffin et al. found that the active muscle volume required to generate force on the ground (associated with MGRF) and the rate of generating this force accounted for >85% of the increase in net metabolic rate across moderate walking speeds and load-carrying conditions.
In the present study, when adjusted for differences in muscle fiber length and compared across the gait transition, the knee extensors showed the greatest increase in the active muscle volume needed to generate force on the ground (MGRF), increasing 4.9-fold from 512 ± 170 cm3 at a walk to 2,486 ± 277 cm3 at a run (23–49% of the total active volume of the three agonist groups combined). In comparison, the hip extensors, which accounted for 1,030 ± 202 cm3 of the active muscle volume at a walk (46% of total), increased by 1.77-fold to 1,822 ± 281 cm3 at a run (36% of total); and the ankle extensors increased by 1.10-fold from 695 ± 97 cm3 at a walk (36% of total) to 761 ± 81 cm3 at run (16% of total). These results differ from those reported by Griffin et al. (19), who found that active muscle volume at the ankle (50% of total) exceeded that at the hip (32% of total) at all walking speeds examined. However, this reflects a difference in how we estimated active muscle volume here [based on peak muscle force (F, Eq. 4)] vs. Griffin et al.'s use of time-integrated muscle force normalized to ground impulse (Fm/GRF, or the inverse of limb EMA) during limb support. Given the several assumptions involved in estimating active muscle volume by either approach, it is difficult to assess which method provides the better estimate of the volume of active muscle recruitment and energy use.
All three joints also showed increases in estimated active muscle volume due to increased inertia during stance as speed increased and gait changed, with the knee and hip being most important. It seems likely, therefore, that a substantial fraction of the observed increase in the energy cost of transport at a run vs. a walk is linked to the increase in muscle impulse and the volume of active muscle at the knee, with a smaller contribution due to inertia at the hip during stance. However, it is important to emphasize that our approach ignores both the cost associated with muscles that are active during the swing phase of gait and how differences in limb support time (or duty factor) affect the cost of muscle force generation. Although increased energy use can be expected with increased motor unit recruitment to generate greater muscle force, energy cost is also likely reduced when the muscles are activated for shorter periods of time. Thus the interacting effects of increased muscle recruitment but decreased activation duration on energy cost, when humans increase speed and change gait from a walk to a run, remains an important challenge to sort out.
Because our estimate of active muscle volume also ignores changes in the contractile state of the different muscle groups, other factors, such as stride frequency, also likely influence the energy cost of running vs. walking. The increase in stride frequency when humans increase speed and change gait from a walk to a run (preferred walk 0.91 ± 0.07 Hz vs. preferred run 1.37 ± 0.08 Hz) presumably requires the recruitment of faster contracting fibers to develop force more rapidly and shorten at higher velocities. This likely increases the cost of force generation, increasing the overall cost of transport of the body (22, 25). Griffin et al. (19) similarly observed a significant effect of an increase in the rate of force development (based on ground contact time) in relation to the net metabolic cost of walking. In addition, there is evidence that more work may be performed to move the body per unit distance during running than during walking (9, 21), although increased elastic energy storage and return by tendons in running likely supplies some of the increased work (8, 23). Taken together, these factors also likely explain much of the difference in the observed increase in the cost of transport of running vs. walking. Nevertheless, our results here suggest that the metabolic cost of generating a substantial increase in quadriceps muscle force during the stance phase of gait likely contributes a major fraction of the increased energy cost of running vs. walking.
Muscle EMA and energy cost vs. size.
The mechanical advantage of limb muscles (r/R) increases with body mass in quadrupedal mammals (
M0.27, 1, 2). The increase in muscle EMA is associated with a size-dependent change to more upright locomotor posture in larger mammals, which reduces mass-specific muscle forces and, thus, peak muscle and bone stress. When compared with that of quadrupedal mammals, the EMA of humans during walking (0.71 ± 0.29, n = 104, pooled for all trials and subjects and averaged for the three joints) fell within the 95% confidence interval (0.592–1.081 at 70 kg body mass) of the regression for the quadruped hindlimb (Fig. 8). However, because of the decrease in knee EMA, average muscle EMA of humans during running (0.52 ± 0.16, n = 99) was significantly less (34%) than that predicted for the hindlimb of a quadruped of similar size (predicted EMA = 0.78). Because the quadruped data are based on mean EMA values obtained for each species over a range of trotting and galloping speeds (for which no discernable change in EMA was observed), the comparison with human walking may be influenced by the difference in gait.
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Although an erect bipedal posture and change in muscle gearing at the ankle joint (7) suggests improved locomotor economy during walking (33) and endurance during running (7), the reduced limb mechanical advantage observed here in running humans supports previous results showing that running incurs a greater cost of transport compared with walking at a preferred speed. Consequently, improved running economy or transport cost was unlikely a key selective factor favoring the evolution of erect bipedalism in humans (7). Furthermore, although differences in the time course of muscle force generation and the rate of force development appear to explain speed- and size-related differences in the energy cost of locomotion within mammals (22, 25), changes in energy cost of transport between walking and running within humans are also likely determined by changes in the magnitude of muscle force generation and recruited volume of active muscle during limb support.
We conclude, therefore, that the greater energy cost during running in humans may be explained in part by the decrease in limb mechanical advantage resulting from the use of more flexed knee joint during running vs. walking. Whether changes in limb mechanical advantage occur in other species between the mechanically dissimilar gaits of walking vs. running, trotting, or galloping awaits further investigation. To date, such gait-related changes in limb mechanical advantage have not been observed (1, 31). This may reflect the evolution of a unique erect bipedal gait within hominids, which distinguishes modern humans from avian bipeds and mammalian quadrupeds.
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GRANTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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ACKNOWLEDGMENTS |
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TOPABSTRACTMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
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FOOTNOTES |
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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.
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REFERENCES |
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