Energetics of Human Running: A Mechanistic Perspective

Abstract

There are conflicting explanations for the metabolic cost of energy in human motion. Mechanical work can be measured at each joint, but both muscles and tendons act across joints, and several decades of studies show tendon can perform substantial work elastically, thereby confounding estimates of muscle work. This has motivated the prevailing “mass-spring” model of running, which incorporates a point mass bouncing atop a compliant spring, with no explicit need for muscles. Dispensing with mechanical work as measurement and explanation, the mass-spring model has led to the alternative “cost of generating force” hypothesis, where body weight and ground contact time appear to determine metabolic cost for a variety of animals and running speeds. Although the correlations are quite good, such a cost does not readily admit a mechanistic explanation. I propose that the mass-spring model has fundamental limitations in explaining energetics, and that mechanical work merits re-consideration as a basic mechanism. I introduce refinements to the experimental evaluation of work, new models for the action of muscle and elastic tendon, and experimental procedures that help to explain how mechanical work contributes substantially to the overall metabolic cost of running.

This dissertation first re-examines the experimental measures of mechanical work. Whereas past literature has estimated the work performed by body joints on rigid body segments, our measures include the work of soft-tissue deformations, not previously appreciated as a substantial contribution. I evaluated the aggregate work of soft-tissues in running, and found that they behaved in a manner similar to a damped spring-mass system. I show that damped vibrations, and the active work necessary to compensate for them, may account for 29% of the net metabolic cost for running at 5 m/s. Another issue is that the most directly measurable quantity, joint work, does not account for how multi-articular muscles transfer energy between joints, and the degree to which tendons perform passive elastic work. Despite the lack of objective information, these phenomena may nevertheless be incorporated into a parametric estimation of the likely contribution of active mechanical work to running. I show that, applying basic parameter values derived from the literature, mechanical work may account for 74% of the net metabolic cost of running.

I then use experiment-based models to re-examine two other aspects of running mechanics. One is the regulation of running speed, which is not considered in most steady-state analyses. Applying mechanical perturbations in the forward and backward directions, I show that runners immediately apply corrections that dissipate or restore kinetic energy in the first step following perturbation. A simple actuated model reproduces the experimental work-loop, whereas the mass-spring model cannot account for such corrections. I also re-examine the role of the foot, which is ignored in mass-spring models, and thought to be dissipative in rigid body models. I use a simple model to show that the apparent dissipation could instead be explained by multi-articular energy transfer across the foot arch and metatarsophalangeal joint via plantar fascia and other tissues. The model shows how energy could be saved, and how features such as foot’s length could contribute to economical running.