Mechanical work accounts for most of the energetic cost in human running

The metabolic cost of human running is not well explained, in part because the amount of work performed actively by muscles is largely unknown. Series elastic tissues such as tendon can save energy by performing work passively, but there are few direct measurements of the active versus passive contributions to work in running. There are, however, indirect biomechanical measures that can help estimate the relative contributions to overall metabolic cost. We developed a simple cost estimate for muscle work in humans running (N = 8) at moderate speeds (2.2–4.6 m/s) based on measured joint mechanics and passive dissipation from soft tissue deformations. We found that even if 50% of the work observed at the lower extremity joints is performed passively, active muscle work still accounts for 76% of the net energetic cost. Up to 24% of this cost compensates for the energy lost in soft tissue deformations. The estimated cost of active work may be adjusted based on assumptions of multi-articular energy transfer, elasticity, and muscle efficiency, but even conservative assumptions yield active work costs of at least 60%. Passive elasticity can reduce the active work of running, but muscle work still explains most of the overall energetic cost.

Stability of Fixed Points in an Approximate Solution of the Spring-Mass Running Model

We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct analytical approximations of solutions in the considered model. The model itself consists of two sets of differential equations - one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a onedimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.MSC 2020 Classification: 34C20, 34D05, 37N25, 70K20, 70K42, 70K50, 70K60

Elastic energy savings and active energy cost in a simple model of running

The energetic economy of running benefits from tendon and other tissues that store and return elastic energy, thus saving muscles from costly mechanical work. The classic “Spring-mass” computational model successfully explains the forces, displacements and mechanical power of running, as the outcome of dynamical interactions between the body center of mass and a purely elastic spring for the leg. However, the Spring-mass model does not include active muscles and cannot explain the metabolic energy cost of running, whether on level ground or on a slope. Here we add explicit actuation and dissipation to the Spring-mass model, and show how they explain substantial active (and thus costly) work during human running, and much of the associated energetic cost. Dissipation is modeled as modest energy losses (5% of total mechanical energy for running at 3 m s-1) from hysteresis and foot-ground collisions, that must be restored by active work each step. Even with substantial elastic energy return (59% of positive work, comparable to empirical observations), the active work could account for most of the metabolic cost of human running (about 68%, assuming human-like muscle efficiency). We also introduce a previously unappreciated energetic cost for rapid production of force, that helps explain the relatively smooth ground reaction forces of running, and why muscles might also actively perform negative work. With both work and rapid force costs, the model reproduces the energetics of human running at a range of speeds on level ground and on slopes. Although elastic return is key to energy savings, there are still losses that require restorative muscle work, which can cost substantial energy during running.

Spatiotemporal inflection points in human running: Effects of training level and athletic modality

The effect of the different training regimes and histories on the spatiotemporal characteristics of human running was evaluated in four groups of subjects who had different histories of engagement in running-specific training; sprinters, distance runners, active athletes, and sedentary individuals. Subjects ran at a variety of velocities, ranging from slowest to fastest, over 30 trials in a random order. Group averages of maximal running velocities, ranked from fastest to slowest, were: sprinters, distance runners, active athletes, and sedentary individuals. The velocity-cadence-step length (V-C-S) relationship, made by plotting step length against cadence at each velocity tested, was analyzed with the segmented regression method, utilizing two regression lines. In all subject groups, there was a critical velocity, defined as the inflection point, in the relationship. In the velocity ranges below and above the inflection point (slower and faster velocity ranges), velocity was modulated primarily by altering step length and by altering cadence, respectively. This pattern was commonly observed in all four groups, not only in sprinters and distance runners, as has already been reported, but also in active athletes and sedentary individuals. This pattern may reflect an energy saving strategy. When the data from all groups were combined, there were significant correlations between maximal running velocity and both running velocity and step length at the inflection point. In spite of the wide variety of athletic experience of the subjects, as well as their maximum running velocities, the inflection point appeared at a similar cadence (3.0 ± 0.2 steps/s) and at a similar relative velocity (65–70%Vmax). These results imply that the influence of running-specific training on the inflection point is minimal.

Muscle-specific economy of force generation and efficiency of work production during human running

Human running features a spring-like interaction of body and ground, enabled by elastic tendons that store mechanical energy and facilitate muscle operating conditions to minimize the metabolic cost. By experimentally assessing the operating conditions of two important muscles for running, the soleus and vastus lateralis, we investigated physiological mechanisms of muscle work production and muscle force generation. We found that the soleus continuously shortened throughout the stance phase, operating as work generator under conditions that are considered optimal for work production: high force-length potential and high enthalpy efficiency. The vastus lateralis promoted tendon energy storage and contracted nearly isometrically close to optimal length, resulting in a high force-length-velocity potential beneficial for economical force generation. The favorable operating conditions of both muscles were a result of an effective length and velocity-decoupling of fascicles and muscle-tendon unit, mostly due to tendon compliance and, in the soleus, marginally by fascicle rotation.

Stability of Fixed Points in an Approximate Solution of the Spring-mass Running Model

We consider a classical spring-mass model of human running which is built upon an inverted elastic pendulum. Based on our previous results concerning asymptotic solutions for large spring constant (or small angle of attack), we construct analytical approximations of solutions in the considered model. The model itself consists of two sets of differential equations - one set describes the motion of the centre of mass of a runner in contact with the ground (support phase), and the second set describes the phase of no contact with the ground (flight phase). By appropriately concatenating asymptotic solutions for the two phases we are able to reduce the dynamics to a one-dimensional apex to apex return map. We find sufficient conditions for this map to have a unique stable fixed point. By numerical continuation of fixed points with respect to energy, we find a transcritical bifurcation in our model system.

Muscle-specific economy of force generation and efficiency of work production during human running

Human running features a spring-like interaction of body and ground, enabled by elastic tendons that store mechanical energy and facilitate muscle operating conditions to minimize the metabolic cost. By experimentally assessing the operating conditions of two important muscles for running, the soleus and vastus lateralis, we investigated physiological mechanisms of muscle energy production and muscle force generation. Results showed that the soleus continuously shortened throughout the stance phase, operating as energy generator under conditions that were found to be optimal for work production: high force-length potential and enthalpy efficiency. The vastus lateralis promoted tendon energy storage and contracted nearly isometrically close to optimal length, resulting in a high force-length-velocity potential beneficial for economical force generation. The favorable operating conditions of both muscles were a result of an effective length and velocity-decoupling of fascicles and muscle-tendon unit mostly due to tendon compliance and, in the soleus, marginally by fascicle rotation.

The extensibility of the plantar fascia influences the windlass mechanism during human running

The arch of the human foot is unique among hominins as it is compliant at ground contact but sufficiently stiff to enable push-off. These behaviours are partly facilitated by the ligamentous plantar fascia whose role is central to two mechanisms. The ideal windlass mechanism assumes that the plantar fascia has a nearly constant length to directly couple toe dorsiflexion with a change in arch shape. However, the plantar fascia also stretches and then shortens throughout gait as the arch-spring stores and releases elastic energy. We aimed to understand how the extensible plantar fascia could behave as an ideal windlass when it has been shown to strain throughout gait, potentially compromising the one-to-one coupling between toe arc length and arch length. We measured foot bone motion and plantar fascia elongation using high-speed X-ray during running. We discovered that toe plantarflexion delays plantar fascia stretching at foot strike, which probably modifies the distribution of the load through other arch tissues. Through a pure windlass effect in propulsion, a quasi-isometric plantar fascia's shortening is delayed to later in stance. The plantar fascia then shortens concurrently to the windlass mechanism, likely enhancing arch recoil at push-off.