Partitioning the metabolic cost of human running: a task-by-task approach

Abstract

Compared with other species, humans can be very tractable and thus an ideal "model system" for investigating the metabolic cost of locomotion. Here, we review the biomechanical basis for the metabolic cost of running. Running has been historically modeled as a simple spring-mass system whereby the leg acts as a linear spring, storing, and returning elastic potential energy during stance. However, if running can be modeled as a simple spring-mass system with the underlying assumption of perfect elastic energy storage and return, why does running incur a metabolic cost at all? In 1980, Taylor et al. proposed the "cost of generating force" hypothesis, which was based on the idea that elastic structures allow the muscles to transform metabolic energy into force, and not necessarily mechanical work. In 1990, Kram and Taylor then provided a more explicit and quantitative explanation by demonstrating that the rate of metabolic energy consumption is proportional to body weight and inversely proportional to the time of foot-ground contact for a variety of animals ranging in size and running speed. With a focus on humans, Kram and his colleagues then adopted a task-by-task approach and initially found that the metabolic cost of running could be "individually" partitioned into body weight support (74%), propulsion (37%), and leg-swing (20%). Summing all these biomechanical tasks leads to a paradoxical overestimation of 131%. To further elucidate the possible interactions between these tasks, later studies quantified the reductions in metabolic cost in response to synergistic combinations of body weight support, aiding horizontal forces, and leg-swing-assist forces. This synergistic approach revealed that the interactive nature of body weight support and forward propulsion comprises ∼80% of the net metabolic cost of running. The task of leg-swing at most comprises ∼7% of the net metabolic cost of running and is independent of body weight support and forward propulsion. In our recent experiments, we have continued to refine this task-by-task approach, demonstrating that maintaining lateral balance comprises only 2% of the net metabolic cost of running. In contrast, arm-swing reduces the cost by ∼3%, indicating a net metabolic benefit. Thus, by considering the synergistic nature of body weight support and forward propulsion, as well as the tasks of leg-swing and lateral balance, we can account for 89% of the net metabolic cost of human running.

Fig. 1.

The net rate of oxygen consumption increases linearly across human running speed (solid line), and as a consequence, the net cost of transport (dashed line) remains independent of speed (m/s). The lines are developed from the classic data published by Margaria et al. (1963). It is important to note that Margaria et al. (1963) found that the extrapolation of the regression line relating gross and running speed crossed the zero-speed intercept at a value that was similar to his subjects’ resting metabolism. After subtracting this value from gross , Margaria et al. (1963) referred to this quantity using the term “net”.

Fig. 2.

Spring-mass model characterizes the mechanics of human running. The model consists of a mass and a single leg-spring that connects the foot (not shown) and COM. This model depicts the runner transversing along the ground from the beginning (left-most position), middle (leg-spring is oriented vertically), and to the end of stance phase (right-most position). The leg-spring has an initial length, L_o, at the beginning, and ΔL represents its maximal compression at mid-stance. The dashed spring-mass model shows the length of the uncompressed leg-spring. Thus, the difference between the length of the dashed leg-spring and maximally compressed leg-spring represents the maximum compression of the leg-spring, ΔL. The downward vertical displacement of the mass during stance is represented by Δy, which is substantially smaller than ΔL. Half of the angle swept by the leg-spring during contact with the ground is denoted by θ. Figure reprinted and caption adapted and modified from Farley and Gonzalez (1996) with permission from Elsevier.

Fig. 3.

The individual tasks of body weight support, forward propulsion, and leg-swing exacts a metabolic cost, leading to an overestimation for explaining the net metabolic cost of running. (A) To reduce the amount of body weight than the subject must support, a rolling trolley apparatus applies a relatively constant upward force via a modified climbing harness to the subject’s waist. As a result, the net metabolic cost of running decreased in less than direct proportion to the level of body weight support. When extrapolating to zero body weight support, the regression value suggests that the task of body weight support exacts ∼74% of the net metabolic cost of running. (B) On the left, the apparatus applies a relatively constant horizontal force about the subject’s waist in the forward direction, thus reducing the need to generate forward propulsive forces along the ground. An optimal aiding force of 15% body weight suggests that the task of forward propulsion exacts ∼37% of the net metabolic cost of running. (C) On the left, an external leg-swing-assist apparatus applies anterior pulling forces to each foot to initiate and propagate the leg forward during swing. An optimal, external leg swing-assist force of 4% body weight suggests that the task of leg-swing exacts ∼20% of the net metabolic cost of running. The data (mean ± SEM) and least-squares regression lines are derived from the studies noted on each figure.

Fig. 4.

When considering their interactive nature, the synergistic tasks of body weight support, forward propulsion, and leg-swing exact a metabolic cost that is less than physiologically possible, thus providing a more coherent explanation for the metabolic cost of running. The experimental set-up consists of strategic combinations of BWS, an optimal aiding horizontal force about the waist (AHF), and an optimal leg-swing assistive force at the feet (LSA). The regression lines represent changes in the net metabolic cost of running when applying BWS, BWS + AHF, and BWS + AHF + LSA. The BWS condition demonstrates that the net metabolic cost of running decreased in less than direct proportion to the level of BWS. When extrapolating the BWS line to zero body weight, the regression value suggests that the task of body weight support exacts ∼65% of the net metabolic cost of running. When extrapolating the BWS + AHF line to zero body weight, the regression value suggests that the synergistic tasks of body weight support and forward propulsion exacts ∼80% of the net metabolic cost of running. When extrapolating the BWS + AHF + LSW line to zero body weight, the regression value suggests that synergistic tasks of body weight support and forward propulsion along with the independent task of leg-swing exacts ∼87% of the net metabolic cost of running. The data (mean ± SEM) and least-squares regression lines are derived from the study noted in the figure.

Fig. 5.

The task of maintaining lateral balance exacts a net metabolic cost during human running. When provided with external lateral support (LS, solid and dashed lines), the net metabolic cost of running decreased by ∼2% (significant external LS effect, P = 0.032). When eliminating arm-swing (no arm swing, open circles; arm swing, filled circles), the net metabolic cost of running increased by ∼8% (significant arm swing effect, P < 0.001). The lack of a significant interaction effect between external LS and arm-swing indicates that external LS resulted in a similar reduction in net metabolic cost of running with or without arm-swing. The data (mean ± SEM) are derived from the authors noted in the figure.

Fig. 6.

Swinging the arms reduces the net metabolic cost of human running. We measured net metabolic cost (mean ± SEM) as subjects ran while holding the hands on top of the head (HEAD), holding the arms across the chest (CHEST), holding the hands with the arms behind the back in a relaxed position (BACK), and while swinging their arms normally (NORMAL). The data demonstrate that running without arm-swing (compared with the control, * indicates P < 0.05 and ** indicates P < 0.01) increases net metabolic cost, indicating that arm-swing provides a small, but significant metabolic benefit during human running.

Fig. 7.

The (A) cost of generating force, (B) individual task-by-task, and (C) synergistic task-by-task approach partition the net metabolic cost of human running into its biomechanical constituents. The cost of generating force approach and the individual task-by-task approach both illustrate that body weight support is the primary determinant of the net metabolic cost of human running. In the individual task-by-task approach, forward propulsion represents the second largest determinant. The individual task-by-task approach leads to an overestimation while the synergistic task-by-task approach suggests that the synergistic tasks of body weight support and forward propulsion are the primary determinant of the net metabolic cost of human running. Note that leg-swing and lateral balance exact a relatively small net metabolic cost. If we sum all the biomechanical tasks, the synergistic task-by-task approach accounts for 89% of the net metabolic cost of human running.