Stretching Your Energetic Budget: How Tendon Compliance Affects the Metabolic Cost of Running.

Muscles attach to bones via tendons that stretch and recoil, affecting muscle force generation and metabolic energy consumption. In this study, we investigated the effect of tendon compliance on the metabolic cost of running using a full-body musculoskeletal model with a detailed model of muscle energetics. We performed muscle-driven simulations of running at 2-5 m/s with tendon force-strain curves that produced between 1 and 10% strain when the muscles were developing maximum isometric force. We computed the average metabolic power consumed by each muscle when running at each speed and with each tendon compliance. Average whole-body metabolic power consumption increased as running speed increased, regardless of tendon compliance, and was lowest at each speed when tendon strain reached 2-3% as muscles were developing maximum isometric force. When running at 2 m/s, the soleus muscle consumed less metabolic power at high tendon compliance because the strain of the tendon allowed the muscle fibers to operate nearly isometrically during stance. In contrast, the medial and lateral gastrocnemii consumed less metabolic power at low tendon compliance because less compliant tendons allowed the muscle fibers to operate closer to their optimal lengths during stance. The software and simulations used in this study are freely available at simtk.org and enable examination of muscle energetics with unprecedented detail

Data from: Muscle-tendon mechanics explain unexpected effects of exoskeleton assistance on metabolic rate during walking

The goal of this study was to gain insight into how ankle exoskeletons affect the behavior of the plantarflexor muscles during walking. Using data from previous experiments, we performed electromyography-driven simulations of musculoskeletal dynamics to explore how changes in exoskeleton assistance affected plantarflexor muscle–tendon mechanics, particularly for the soleus. We used a model of muscle energy consumption to estimate individual muscle metabolic rate. As average exoskeleton torque was increased, while no net exoskeleton work was provided, a reduction in tendon recoil led to an increase in positive mechanical work performed by the soleus muscle fibers. As net exoskeleton work was increased, both soleus muscle fiber force and positive mechanical work decreased. Trends in the sum of the metabolic rates of the simulated muscles correlated well with trends in experimentally observed whole-body metabolic rate (R2=0.9), providing confidence in our model estimates. Our simulation results suggest that different exoskeleton behaviors can alter the functioning of the muscles and tendons acting at the assisted joint. Furthermore, our results support the idea that the series tendon helps reduce positive work done by the muscle fibers by storing and returning energy elastically. We expect the results from this study to promote the use of electromyography-driven simulations to gain insight into the operation of muscle–tendon units and to guide the design and control of assistive devices

OpenSim Moco: Musculoskeletal optimal control.

Musculoskeletal simulations are used in many different applications, ranging from the design of wearable robots that interact with humans to the analysis of patients with impaired movement. Here, we introduce OpenSim Moco, a software toolkit for optimizing the motion and control of musculoskeletal models built in the OpenSim modeling and simulation package. OpenSim Moco uses the direct collocation method, which is often faster and can handle more diverse problems than other methods for musculoskeletal simulation. Moco frees researchers from implementing direct collocation themselves-which typically requires extensive technical expertise-and allows them to focus on their scientific questions. The software can handle a wide range of problems that interest biomechanists, including motion tracking, motion prediction, parameter optimization, model fitting, electromyography-driven simulation, and device design. Moco is the first musculoskeletal direct collocation tool to handle kinematic constraints, which enable modeling of kinematic loops (e.g., cycling models) and complex anatomy (e.g., patellar motion). To show the abilities of Moco, we first solved for muscle activity that produced an observed walking motion while minimizing squared muscle excitations and knee joint loading. Next, we predicted how muscle weakness may cause deviations from a normal walking motion. Lastly, we predicted a squat-to-stand motion and optimized the stiffness of an assistive device placed at the knee. We designed Moco to be easy to use, customizable, and extensible, thereby accelerating the use of simulations to understand the movement of humans and other animals

Simulating Ideal Assistive Devices to Reduce the Metabolic Cost of Running.

Tools have been used for millions of years to augment the capabilities of the human body, allowing us to accomplish tasks that would otherwise be difficult or impossible. Powered exoskeletons and other assistive devices are sophisticated modern tools that have restored bipedal locomotion in individuals with paraplegia and have endowed unimpaired individuals with superhuman strength. Despite these successes, designing assistive devices that reduce energy consumption during running remains a substantial challenge, in part because these devices disrupt the dynamics of a complex, finely tuned biological system. Furthermore, designers have hitherto relied primarily on experiments, which cannot report muscle-level energy consumption and are fraught with practical challenges. In this study, we use OpenSim to generate muscle-driven simulations of 10 human subjects running at 2 and 5 m/s. We then add ideal, massless assistive devices to our simulations and examine the predicted changes in muscle recruitment patterns and metabolic power consumption. Our simulations suggest that an assistive device should not necessarily apply the net joint moment generated by muscles during unassisted running, and an assistive device can reduce the activity of muscles that do not cross the assisted joint. Our results corroborate and suggest biomechanical explanations for similar effects observed by experimentalists, and can be used to form hypotheses for future experimental studies. The models, simulations, and software used in this study are freely available at simtk.org and can provide insight into assistive device design that complements experimental approaches

Average whole-body metabolic power consumed during running as tendon compliance varies.

<p>The mean (line) and standard deviation (vertical bars) predicted by our simulations at each speed and tendon compliance are shown in (a); the mean increase in average metabolic power from the lowest average power at each speed is shown in (b), expressed as a percentage of the lowest average power at each speed. Filled circles in (a) indicate the lowest value at each speed; open circles denote values that are not significantly greater than these minima (<i>p</i> < 0.05, matched pairs t-test). The “experimental range” indicated in (b) is 4.9±1% strain at <i>F</i>_max, the mean and standard deviation reported by Maganaris and Paul [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150378#pone.0150378.ref031" target="_blank">31</a>]. The optimal tendon compliance was near this range for all running speeds; less compliant tendons were substantially more favorable when running at 2 m/s.</p

Dynamics and metabolics of the medial gastrocnemius and soleus muscles during running at 2 m/s.

<p>Simulated muscle activations, fiber lengths, and fiber velocities (top row) and outputs from our model of muscle energetics (bottom row) for the right medial gastrocnemius (a) and soleus (b) muscles are shown over the gait cycle. Our model of muscle energetics predicted the rate of heat generation due to sarcoplasmic reticular ion transport and actin–myosin interaction (activation and maintenance heat rate), the rate of heat generation due to shortening and lengthening of the fibers, and the mechanical power of the fibers [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150378#pone.0150378.ref037" target="_blank">37</a>]. The mean (line) and standard deviation (shaded region) are shown for the seven rearfoot-striking subjects when low (2% strain at <i>F</i>_max; orange) and high (10% strain at <i>F</i>_max; blue) tendon compliances were used. When tendons were very compliant, the soleus fibers were operating nearly isometrically during stance, thereby reducing the average shortening and lengthening heat rate predicted by the energetics model (from 128 to 61 mW/kg). In contrast, the medial gastrocnemius fibers were operating far from their optimal lengths during stance when tendons were very compliant, thereby requiring greater activation to generate a similar plantarflexion moment and increasing the average activation and maintenance heat rate (from 38 to 57 mW/kg).</p

Muscle activations and positive fiber mechanical power during running as tendon compliance varies.

<p>The mean (line) and standard deviation (vertical bars) at each speed and tendon compliance are shown. Filled circles indicate the lowest value at each speed; open circles denote values that are not significantly greater than these minima (<i>p</i> < 0.05, matched pairs t-test). Although the sum of squared activations (a) reveals similar trends as average metabolic power at the whole-body level, activation-based metrics may disagree with metabolics at the muscle level (e.g., see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150378#pone.0150378.g006" target="_blank">Fig 6(b)</a>). Comparison of Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150378#pone.0150378.g003" target="_blank">3(a)</a> and 7(b) reveals that average positive fiber mechanical power achieved minima at greater tendon compliances than average whole-body metabolic power consumption, suggesting that positive fiber mechanical power is a poor surrogate for metabolic power.</p

Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies

Physics-based predictive simulations of human movement have the potential to support personalized medicine, but large computational costs and difficulties to model control strategies have limited their use. We have developed a computationally efficient optimal control framework to predict human gaits based on optimization of a performance criterion without relying on experimental data. The framework generates three-dimensional muscle-driven simulations in 36 min on average-more than 20 times faster than existing simulations-by using direct collocation, implicit differential equations and algorithmic differentiation. Using this framework, we identified a multi-objective performance criterion combining energy and effort considerations that produces physiologically realistic walking gaits. The same criterion also predicted the walk-to-run transition and clinical gait deficiencies caused by muscle weakness and prosthesis use, suggesting that diverse healthy and pathological gaits can emerge from the same control strategy. The ability to predict the mechanics and energetics of a broad range of gaits with complex three-dimensional musculoskeletal models will allow testing novel hypotheses about gait control and hasten the development of optimal treatments for neuro-musculoskeletal disorders.status: publishe

Tendon force–strain relationship measured experimentally and used in our simulations.

<p>The model curves (solid black lines) produced tendon strains of 1–10% when the muscles were developing maximum isometric force (<i>F</i>_max). The curve labeled “E” is one physiologically plausible curve based on the experimental data reported by Maganaris and Paul [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150378#pone.0150378.ref031" target="_blank">31</a>] and Magnusson et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0150378#pone.0150378.ref030" target="_blank">30</a>] (shaded regions).</p

Simulating ideal assistive devices to reduce the metabolic cost of walking with heavy loads

<div><p>Wearable robotic devices can restore and enhance mobility. There is growing interest in designing devices that reduce the metabolic cost of walking; however, designers lack guidelines for which joints to assist and when to provide the assistance. To help address this problem, we used musculoskeletal simulation to predict how hypothetical devices affect muscle activity and metabolic cost when walking with heavy loads. We explored 7 massless devices, each providing unrestricted torque at one degree of freedom in one direction (hip abduction, hip flexion, hip extension, knee flexion, knee extension, ankle plantarflexion, or ankle dorsiflexion). We used the Computed Muscle Control algorithm in OpenSim to find device torque profiles that minimized the sum of squared muscle activations while tracking measured kinematics of loaded walking without assistance. We then examined the metabolic savings provided by each device, the corresponding device torque profiles, and the resulting changes in muscle activity. We found that the hip flexion, knee flexion, and hip abduction devices provided greater metabolic savings than the ankle plantarflexion device. The hip abduction device had the greatest ratio of metabolic savings to peak instantaneous positive device power, suggesting that frontal-plane hip assistance may be an efficient way to reduce metabolic cost. Overall, the device torque profiles generally differed from the corresponding net joint moment generated by muscles without assistance, and occasionally exceeded the net joint moment to reduce muscle activity at other degrees of freedom. Many devices affected the activity of muscles elsewhere in the limb; for example, the hip flexion device affected muscles that span the ankle joint. Our results may help experimentalists decide which joint motions to target when building devices and can provide intuition for how devices may interact with the musculoskeletal system. The simulations are freely available online, allowing others to reproduce and extend our work.</p></div