INTRODUCTION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

IN THEIR GROUNDBREAKING work, McMahon and Greene (29) investigated the effects of surface stiffness (k_surf) on running mechanics. Their study sought to determine whether it was possible to build a track surface that would enhance performance and decrease injury. Their work showed that a range of k_surf values existed over which a runner's performance was enhanced by decreasing foot-ground contact time (t_c), decreasing the initial spike in peak vertical ground reaction force (f_peak), and increasing stride length. Tracks built within this enhanced performance range at Harvard University, Yale University, and Madison Square Garden have been shown to increase running speeds by 2-3% and to decrease running injuries by 50% (29). Despite the success of these "tuned tracks," the mechanisms underlying the performance enhancement are not clearly understood.

A major assumption of McMahon and Greene's (29) was that the running leg and surface could be represented as a simple spring and mass (Fig. 1). McMahon and Cheng (27) subsequently described the leg spring as having two stiffnesses: k_leg and k_vert. The k_leg is the actual leg stiffness describing the mechanical behavior of the leg's musculoskeletal system during the support phase and is calculated from the ratio of f_peak to the compression of the leg spring (l, defined in Eq. B4)

(1)

In distinction, k_vert is the effective vertical stiffness of the runner. This stiffness serves as the mechanism by which the direction of the downward velocity of the body is reversed during limb contact (27, 30). Therefore, k_vert describes the vertical motions of the center of mass during the ground contact phase (27, 30). The k_vert can be calculated from the ratio of f_peak to the maximum vertical displacement of the center of mass during contact (y_total), measured from the onset of limb contact (heel-strike) to midstep

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Farley et al. (12) and He et al. (19) determined that, for a given ground stiffness, k_leg changes little with speed. Later experiments showed that k_leg changes when animals run on surfaces of different stiffnesses (16, 18). It was specifically shown that human hoppers' k_leg adjustments were mainly due to changes in both ankle joint stiffness and leg posture (14). However, Arampatzis et al. (3) provided evidence that the knee joint is the main determinant of k_leg as a function of speed in human running. In addition, modeling efforts and experiments on humans have shown that a runner's center of mass deflections (y_total) remain nearly constant, independent of k_surf, and that this may be a general principle of running mechanics (16, 29). In other words, by adjusting their "leg spring" stiffness to adapt to different k_surf values, a runner may be able to maintain apparently uniform support mechanics.

View larger version (14K): [in this window] [in a new window]   Fig. 1.   Spring-mass model representing a runner's leg in contact with a compliant surface. lo, Uncompressed leg length; mr, mass of the runner represented as a point mass located at the hip; ytotal, maximum vertical displacement of the center of mass; l, maximum compression of the leg spring; , angle of the leg spring at first ground contact; kleg, spring constant of the runner's leg; mtrack, effective mass of the running surface; dsurf, amount the running surface deflects; ksurf, spring constant of the running surface; and fgrf, vertical ground reaction force.

Representations of the running leg as a simple spring have described the mechanics of a running leg remarkably well (2, 11, 12, 15, 16, 18, 19, 25-27). It has been shown that the physical musculoskeletal elastic components of the leg (tendons, ligaments, and muscles) are used to minimize metabolic cost while running (1, 2, 8-10). However, no one, to date, has related the performance enhancements of running on surfaces of different stiffnesses to metabolic cost. In this paper, we assume that the leg can be represented by an undamped, linear spring and examine how the energetics and mechanics of running vary on surfaces of different stiffnesses.

The goal of this study is to relate human running biomechanics to energetics on surfaces of different stiffnesses. We expect that differences in the metabolic cost of running on various surfaces are likely related to the k_leg variations observed by Farley et al. and Ferris et al. (13, 17, 18). Specifically, we expect a less flexed knee to account for a reduction in metabolic cost (30), as well as an increase in k_leg (3, 18).

In this study, we investigate the energetics and mechanics of running on surfaces having a stiffness range from 75 to 945 kN/m. This range of stiffnesses was selected to incorporate the range of McMahon and Greene's "tuned track" (29) and to extend the work of similar recent studies (16-18). We hypothesize that the metabolic cost of forward human running reaches a minimum when the k_leg of the runner is maximized on surfaces of decreased stiffness. We expect a cost reduction to result from a change in leg posture, whereby the knee is less flexed or straighter during stance (30). Running with a straighter leg should improve the limb's mechanical advantage, thereby reducing the amount of muscle force and muscle volume recruited to support body weight (5). We also anticipate that a reduction in metabolic cost could result from an increased energy return to the runner from the more compliant surfaces (14). Last, we expect that the runner's support mechanics will remain virtually unaffected across the above-defined range of k_surf.

	EXPERIMENTAL METHODS

TOP ABSTRACT INTRODUCTION EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

General procedures. Eight healthy male subjects [body mass: 74.4 ± 7.1 (SD) kg; leg length: 0.96 ± 0.05 m] ran at 3.7 m/s on a level treadmill, fitted with track platforms of five different stiffnesses (see descriptions below). All subjects wore the same flat-soled running shoes. Approval was granted from Harvard University's Committee on the Use of Human Subjects in Research, and subjects provided signed, informed consent before participation. Subjects ran for 5 min on each track platform stiffness in a mirrored fashion (running on stiffest to least stiff and then least stiff to stiffest). Beaded strings hung from the ceiling to give the runner a tactile sign as to where he needed to run so that his midstep corresponded with the fore-aft center of the track platform. Video was also used to ensure that the runner was both centered and lateral enough not to be stepping on both sides of the track simultaneously. If a runner was unable to avoid the seam between tracks, he was asked to move laterally and run on one track or the other. We recorded ground reaction force (1,000 Hz) using a force plate (model OR6-5-1, Advanced Medical Technology, Newton, MA) mounted within the treadmill (22). Kinematic data were collected at 60 Hz using an infrared motion analysis system (MacReflex by Qualysis), and oxygen uptake was measured using a closed gas-collection Douglas bag setup. Oxygen and carbon dioxide contents of the collected gas samples were analyzed using Ametek (Pittsburgh, PA) S-3A O₂ and CD-3A CO₂ analyzers equipped with an Ametek CO₂ sensor (P-61B) and flow controller (R-2). The analyzers were calibrated before each run with gas by pumping several balloons of known gas mixture (16.23% O₂ and 4.00% CO₂ medical gas mixture; AGA Gas, Billerica, MA) through them. Force-plate and kinematic data were obtained simultaneously, and oxygen consumption (O₂) data were sampled during the fourth and fifth minutes of running to ensure that the subject was at a steady state. Subjects participated in two separate trials so that they ran on each platform stiffness four times. Averages were taken on each day and then averaged together for all variables measured.

Experimental platform design. We built platforms with an adjustable stiffness for our running surface. Because the experiments were conducted on a treadmill, the running surface was limited to platforms that would fit within the size limitations of the treadmill. We used a treadmill fitted with an AMTI force plate (22) that was accessible to the Douglas bag oxygen analysis setup.

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View larger version (23K): [in this window] [in a new window]   Fig. 2.   Side view (A) and top view (B) of a schematic of the experimental compliant track treadmill. The runner's foot strikes the treadmill belt (7) (note that this is cut away on top view to show underlying structures and also that the belt is longer than depicted) and exerts a vertical force (F) on the compliant running platforms (6) below. The vertical force is transmitted from the platforms via the supports (2 and 8) to the force plate (1). The stiffness of the running surface is adjusted by moving the movable support (8) in and out. The force plate (1) and entire treadmill apparatus are supported by the treadmill base (5). By moving the treadmill rollers (3) closer together, enough slack is recovered in the belt (7) to insert the track platforms (6). The belt is then redirected over the track platforms with the redirection rollers (4).

(4)

Force-plate measurements. A runner's support mechanics, defined as f_peak, t_c, duty factor, stride frequency, step length, one-half of the angle swept by a runner's leg during ground contact (), and the total vertical displacement of the center of mass, can be calculated from the force-plate data and the assumption that the leg can be represented by an undamped, linear spring (22). These parameters can then be indirectly used to calculate the mass-spring characteristics of the runner's leg. Custom LabVIEW (version 4.0.1) software was used to acquire the force-plate data. The force plate was calibrated by applying known loads to the plate before and after each set of running trials and sampling its output using the same software. The derivation of all of the above parameters is described in APPENDIX B.

Kinematic measurements. To obtain information on the posture of the limb in contact with the ground, we used an infrared camera system (MacReflex; Qualysis) to follow markers that were specifically placed on the subjects. Markers were positioned on the skin overlying the greater trochanter, the lateral epicondyle of the femur, and the lateral malleolus, so that the angle that the lower leg made with the upper leg (knee angle) could be determined.

Measuring metabolic cost. To quantify the metabolic cost of human running, we used the indirect calorimetry method, as described previously. After the runners ran for 3 min, we collected the expired air for 2 min using two Douglas bags (1 per minute), a mouthpiece, and a nose clip, which were attached to the runner via a special headpiece equipped with a one-way valve. The rate of O₂ (ml/min) was then calculated using the volume of the expired air (from a dry-gas volume meter; Parkinson-Cowan), room and vapor pressure corrections, and the percentage of CO₂ and O₂ values. We converted the rate of O₂ into energy consumption using an energy equivalent of 20.1 J/ml O₂ (6) and divided by 60 s/min to obtain _metab in watts.

(5)

Statistical methods. A 1 × 5 ANOVA with a Scheffé post hoc test of condition means was used to assess the effect of k_surf on the parameters of interest: t_c, peak vertical force, stride time, stride frequency, step length, , y_total, displacement of the limb with respect to the track displacement, _metab, C₀, k_leg, k_vert, l, overall system stiffness, and knee angle. P values <0.05 were considered significant for all tests.

	RESULTS

TOP ABSTRACT INTRODUCTION EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

The runner's support mechanics were nearly invariant across the 12.5-fold change in k_surf of the experimental treadmill platform (Fig. 3), whereas their metabolic rate dropped dramatically with k_surf (Fig. 6).

View larger version (29K): [in this window] [in a new window]   Fig. 3.   When subjects ran at a constant speed (3.7 m/s) over 5 different surface stiffnesses (74-945 kN/m), their support mechanics remained essentially unchanged. As confirmed by the Scheffé post hoc test, the differences observed were due to the lowest surface stiffness only. The time that the foot is in contact with the ground [y = 0.0017 ln(x) + 0.204, R2 = 0.21] (A); the duty factor [y = 0.0063 ln(x) + 0.265, R2 = 0.58] (B); the step length (right foot to left foot) [y = 0.0065 ln(x) + 0.76, R2 = 0.22] (C); the stride (right foot to right foot) frequency [y = 0.019 ln(x) + 1.31, R2 = 0.87] (D); the angle swept by the runner's leg [y = 0.221 ln(x) + 23.44, R2 = 0.24] (E), and the peak vertical ground reaction force [y = 41.4 ln(x) + 2163.2, R2 = 0.94] (F) were all virtually constant. Values are means ± SD. Tc, period of foot-ground contact; Ta, period of foot in air.

The results of the Scheffé post hoc test revealed that, in virtually every case, the support mechanics remained essentially unchanged over the four stiffest surfaces tested. The basis for a significant difference in the ANOVA results reported below was found to be due to the data recorded for the lowest stiffness track surface.

As shown in Fig. 3, the effect of k_surf on t_c (P = 0.0001, F = 8.7), duty factor (P = 0.0001, F = 18.45), step length (P = 0.0001, F = 8.51), stride frequency (P = 0.0001, F = 15.35),  (P = 0.0001, F = 8.44), and f_peak (P = 0.009, F = 4.19) were significant. However, the data across these support mechanics showed only a small difference between the two stiffness extremes. The source of the difference occurred at the lowest stiffness, with the remaining four stiffnesses being essentially the same.

In particular, when the support mechanics means are compared, there was a 4% decrease in t_c, step length, and  between the stiffest and least stiff surfaces studied. A 7% decrease in duty factor, 3% decrease in stride frequency, and a 5% increase in f_peak were also observed between these stiffness extremes.

The post hoc test revealed that the runners also maintained a nearly constant total leg plus track platform stiffness (k_totL) over the observed range of conditions (P = 0.0207, F = 3.45) (Fig. 4C). To achieve this, the runner's k_leg increased by 29% with decreasing k_surf (P = 0.0001, F = 23.76) (Fig. 4A). Given that the runner's f_peak did not change greatly over the substrate stiffness range (Fig. 3F), the observed increase in the runner's k_leg most likely resulted from a decrease in the amount that his leg spring was compressed (P = 0.0001, F = 33.93) (Eq. 1, Figs. 1 and 4D). The l is a function of leg length, , and vertical displacement of the runner relative to the displacement of the track surface (y_limb) (Eq. B4). Because leg length and  remained essentially constant, the decrease in the l was likely due to the observed decrease in y_limb (P = 0.0001, F = 94.05) (Fig. 5B, Eq. B5).

View larger version (21K): [in this window] [in a new window]   Fig. 4.   When subjects ran at a constant speed (3.7 m/s) over 5 different surface stiffnesses (74-945 kN/m), there was a 29% change in their leg stiffness [y = 1.37 ln(x) + 22.4, R2 = 0.87] (A) and a 16% decrease in leg compression [y = 0.008 ln(x) + 0.091, R2 = 0.86] with decreasing surface stiffness (D). The overall stiffness of the system [y = 0.175 ln(x) + 14.46, R2 = 0.4] (C) and the effective vertical stiffness of the runner [y = 0.81 ln(x) + 29.31, R2 = 0.66] (B) remained essentially unchanged. Values are means ± SD.

View larger version (17K): [in this window] [in a new window]   Fig. 5.   A: as designed, the vertical displacement of the compliant running surface increased with decreasing surface stiffness [y = 0.01 ln(x) + 0.064, R2 = 0.91]. B: the vertical displacement of the runner's center of mass relative to the track's vertical displacement decreases with surface stiffness [y = 0.0065 ln(x) + 0.011, R2 = 0.93]. This limb displacement is used to define the leg compression (Fig. 4, Eq. B4), which in turn defines the leg stiffness of the runner (Fig. 4, Eq. 1). C: the total vertical displacement of the runner's center of mass (com) measured from midstep to take-off using the vertical displacement of the hip marker is essentially unchanged over the surface stiffnesses [y = 0.003 ln(x) + 0.076, R2 = 0.84]. This value is used to define the effective vertical stiffness (Fig. 4, Eq. 2). Values are means ± SD.

We achieved the five different k_surf by allowing the simply supported track to displace beneath the runner. Therefore, d_surf increased 12.5-fold from the stiffest to the least stiff surface (Fig. 5A). This substantial increase in surface displacement was mostly offset by y_limb so that y_total was minimally changed between the k_surf extremes (~0.8 cm) (P = 0.0001, F = 16.28). Again, the change in y_total was only significant at the lowest k_surf studied (Fig. 5C). Our finding that the k_vert (Fig. 4B) remained virtually constant (P = 0.0001, F = 11.77) over the four stiffest surfaces further supports the fact that the runners' y_total changed minimally, as k_vert is a function of f_peak and y_total. (Eq. 2).

We also found a 12% decrease in the runner's rate of _metab as k_surf decreased (P = 0.0001, F = 71.95) (Fig. 6A). The runner's mean _metab decreased from 896 to 792 W as k_surf decreased from 945 to 75 kN/m. Referring to Eq. 5 and recalling that t_c remained essentially unchanged (Fig. 3A), the observed decrease in metabolic rate suggests that the C₀ defined by Kram and Taylor (23) also decreased with decreasing k_surf (P = 0.0001, F = 32.54) (Fig. 6B).

View larger version (19K): [in this window] [in a new window]   Fig. 6.   A: the runner's metabolic rate decreased with surface stiffness [y = 41.17 ln(x) + 622.31, R2 = 0.97] over the 12.5-fold change in surface stiffness (74-945 kN/m) when running at a constant speed (3.7 m/s). B: because the contact time remained essentially constant (Fig. 3), the cost coefficient must also decrease with surface stiffness [y = 0.0142 ln(x) + 0.171, R2 = 0.91] per Eq. 5 [metab = C0 × (1/tc) × Fbw, where metab is the rate of metabolic consumption, C0 is an empirical measure of the metabolic cost of applying ground force to support the body's weight (Fbw), and tc is the period of foot-ground contact]. Values are means ± SD.

In an attempt to evaluate limb mechanical advantage, we used the kinematic data, together with the vertical ground reaction force, to calculate the limb's knee angle at midstep for running over all surfaces (Fig. 7). Knee angle increased 2.5% as k_surf decreased (P = 0.0001, F = 16.35). Thus only a slight straightening of the leg was observed.

View larger version (14K): [in this window] [in a new window]   Fig. 7.   The angle formed between the runner's upper and lower legs was defined from markers placed at the greater trochanter, lateral epicondyle of the femur, and lateral malleolus. This knee angle increased 2.5% as surface stiffness decreased [y = 1.25 ln(x) + 137.29, R2 = 0.97], giving rise to a slightly straighter leg on the softer surfaces studied. Values are means ± SD.

Last, to test our hypothesis that the track itself may return significant energy to the runner, we calculated the track platform's mechanical power (E_track, Eq. 4) at each k_surf and compared this with the reduction in _metab of the runner (Eq. 5) (Fig. 8). The results show that, for every watt of mechanical power returned from the track platform, there exists the possibility of a 1.8-W _metab savings to the runner (R² = 0.99).

View larger version (20K): [in this window] [in a new window]   Fig. 8.   Change in the runner's metabolic power (metab) as a function of the change in mechanical power delivered from the track platforms (Etrack) from the stiffest surface (K5). The power delivered from the compliant track is derived from the mechanical energy due to the track spring (Eq. 4) multiplied by the runner's stride frequency. For every watt delivered from the track platforms, there exists a potential 1.8-W reduction in metabolic power (y = 1.80x, R2 = 0.99). Values are means ± SD. Kn, surface stiffness where n = 1, 2, 3, 4.

	DISCUSSION

TOP ABSTRACT INTRODUCTION EXPERIMENTAL METHODS RESULTS DISCUSSION APPENDIX A APPENDIX B REFERENCES

Our results support the hypothesis that the metabolic cost of running at an intermediate speed is progressively reduced and that the spring stiffness of the leg is progressively increased as k_surf is decreased from 945.7 to 75.4 kN/m. However, in contrast to our hypothesis that a change in limb posture is the principal factor underlying a change in both k_leg and metabolic cost, we found that only small changes in knee angle were associated with the observed 29% increase in k_leg and 12% decrease in _metab. Our data do not provide any additional insight into the mechanism for k_leg adjustment but do suggest that a reduction in metabolic cost occurs as the elastic rebound provided by a more compliant surface replaces that otherwise provided by a runner's leg.

Previous work indicated that runners adjust the stiffness of their limbs to maintain virtually constant support mechanics on surfaces of different stiffnesses (3, 14, 16, 18, 28). Although these studies provide insight into the mechanics of human running, they did not specifically examine the metabolic cost of running on compliant surfaces. One study (30) looked at deep-knee-flexed running and its effect on k_vert and O₂ but did not incorporate k_leg or compliant surfaces. Our goal was to expand on these earlier studies and examine how changes in limb-substrate stiffness interactions affect the metabolic cost of running. Consequently, we adopted a similar mechanical and experimental approach to that of these studies, focusing on the knee joint and assuming that the leg behaves as a massless, undamped linear spring.

Using this simple model of the human leg, our findings generally support those of Farley et al. (11, 13-15), indicating that human runners alter their leg spring stiffness to compensate for changes in k_surf without altering their overall support mechanics. McMahon and Greene (29), Farley et al. (14), and Ferris et al. (17) have commented that an observer looking only at the upper body of a runner would be unable to discern when the runner experienced a change in ground stiffness. This suggests that runners compensate for variable ground stiffness without affecting the fluctuations in the motion of their center of mass. This is consistent with our findings that d_surf is offset by y_limb, thus resulting in the minimal 0.8-cm change observed in y_total. Hence, utilizing preferred support mechanics might represent a general principle of running.

Kram and Taylor's (23) analysis suggests that the mass-specific metabolic rates of running animals are determined by the rate of ground-force application (1/t_c), regardless of the speed and size of the animal. Their analysis assumes that animals maintain a uniform limb mechanical advantage over a range of running speeds and gaits. This assumption is supported by previous studies of animals moving at steady speeds over a constant (high) stiffness substrate (5). As a result, the cost of force generation and the volume of muscle that must be activated to support a given unit body weight also appear to remain constant (21). However, we found a reduction in metabolic rate with virtually no change in the t_c (Figs. 3A and 6A). Thus the energetic cost of applying a ground force to support the runner's body weight can be reduced at a given rate of ground force application (1/t_c) when running on more compliant surfaces.

The close relationship between the reductions in metabolic rates and the increased mechanical power returned by the track to the runner in the latter portion of foot-ground contact (Fig. 8) offers a straightforward explanation. This close relationship strongly suggests that, when a greater share of the elastic rebound elevating the center of mass in the latter portion of the contact phase is provided by the elastic recoil of the running surface rather than the biological springs in the runner's leg, the metabolic cost of running is reduced. We believe that these reductions in the metabolic cost of operating leg springs are probably explained by decreases in the mechanical work and shortening velocity performed by the muscles active during foot-ground contact.

Although we had hypothesized that reductions in metabolic cost and increases in k_leg would be achieved predominantly via changes in knee angle, it seems evident that this mechanism cannot fully account for these changes. The change in k_leg is likely due to a combination of local joint stiffness variation and overall limb posture adjustment (15). Whereas our study provided some indication that the leg becomes straighter at midstep on less stiff surfaces (Fig. 7), the change at the knee was small and would require a large sensitivity to have an effect on externally developed knee torque. Therefore, this small change in knee angle could only account for a minority of the reductions in metabolic cost and increases in k_leg that we observed on more compliant surfaces.

Our hypothesis also anticipated that the decrease in _metab might well be explained by an enhanced energy return from the more compliant track platforms. The elastic surface could actually be assisting the runner by assuming some of the cost necessary to operate the leg spring, reducing the amount of mechanical work required, and thereby allowing the leg muscles to operate more isometrically. Reductions in relative shortening velocities would reduce metabolic cost in two ways. First, the increased force per unit area of active muscle would reduce the volume of muscle required to support the body's weight. Second, the _metab consumed per unit of active muscle is also reduced when the muscles shorten through a lesser distance (20).

To lend support for these ideas, experiments were conducted to characterize the track-runner interaction. The dynamic calibration of the four most compliant experimental track platforms showed a linear relationship between force and displacement (R² = 0.96, 0.97, 0.95, and 0.94 from least to most stiff) with little hysteresis (damping ratio <0.1). Hence, the track can indeed be considered an elastic substrate capable of storing and returning mechanical energy. Also, by calculating the resonant period of the track-plus-runner system at the least stiff surface (~0.2 s) and comparing the result to the contact times of the runners at this same stiffness (0.21 ± 0.02 s), we conclude that the track has sufficient time to return its stored energy to the runner. Last, our results show a consistent linear relationship between the reduction in _metab and track mechanical power output across all surfaces studied (Fig. 8). These results suggest that the track has the capacity to save the runner 1.8 W of _metab for every watt of mechanical power that it returns.

Although our results support the fact that running on a decreased k_surf results in a reduction of metabolic cost and an increase in k_leg without affecting support mechanics, future studies need to be done to find a true metabolic minimum. Our measurements were designed to examine surfaces that were within a stiffness range that had already demonstrated an enhanced running performance (29). However, support mechanics are progressively altered to accommodate extreme decreases in k_surf. As mentioned above, our results support our hypothesis that these support mechanics would remain fairly constant over the 12.5-fold change in k_surf but also show a significant change in these variables at the lowest k_surf studied. This raises the possibility of a trend in data as k_surf goes even lower. McMahon and Greene's (29) work supports this speculation. We also anticipate that, as k_surf decreases even further and the virtual consistency of the support mechanics seen at the higher stiffnesses is lost, there would exist a true metabolic minimum. Studies that looked at running on surfaces with extremely low stiffness, such as a trampoline and pillows (30) or sand (24), which also have high damping ratios, indicate that runners likely increase the amount of center-of-mass work that they perform and thus substantially increase their cost of locomotion (24). We propose that a study be done to examine lower k_surf values than were studied here to determine at what substrate stiffness a true metabolic minimum exists as a relation of speed. We believe that there exists an optimal ratio of t_c to surface resonant period that can be used for the future design of tracks and even running shoes to minimize the cost of running.

Summary. Our study sought to link the mechanics and energetics of human running on surfaces of different stiffnesses. The results show that both metabolic cost and k_leg change when k_surf is manipulated. The metabolic reduction is largely due to the track's elastic energy return assisting the runner's leg spring. Although the mechanism for k_leg adjustment still remains unclear, our results support the hypothesis that human runners adjust k_leg to maintain consistent support mechanics across different surfaces.