Muscles consume metabolic energy for active movement, particularly when performing mechanical work or producing force. Less appreciated is the cost for activating muscle quickly, which adds considerably to the overall cost of cyclic force production (Chasiotis et al., 1987). But the cost magnitude relative to mechanical work, which features in many movements, is unknown. We therefore tested whether fast activation is costly compared to performing work or producing isometric force. We hypothesized that metabolic cost would increase with a proposed measure termed force-rate (rate of increase in muscle force) in cyclic tasks, separate from mechanical work or average force level. We tested humans (N=9) producing cyclic knee extension torque against an isometric dynamometer (torque 22 N-m, cyclic waveform frequencies 0.5 – 2.5 Hz), while also quantifying quadriceps muscle force and work against series elasticity (with ultrasonography), along with metabolic rate through respirometry. Net metabolic rate increased by more than fourfold (10.5 to 46.7 W) with waveform frequency. At high frequencies, the hypothesized force-rate cost accounted for nearly half (40%) of energy expenditure. This exceeded the cost for average force (17%) and was comparable to the cost for shortening work (43%). The force-rate cost is explained by additional active calcium transport necessary for producing forces at increasing waveform frequencies, due to rate-limiting dynamics of force production. The force-rate cost could contribute substantially to the overall cost of movements that require cyclic muscle activation, such as locomotion.

Muscles consume metabolic energy for active movement, particularly when performing mechanical work or producing force. Less appreciated is the cost for activating and deactivating muscle quickly, which adds considerably to the overall cost of cyclic force production (Chasiotis et al., 1987). But the cost relative to mechanical work, which features in many movements, is unknown. We therefore tested whether fast activation-deactivation is costly compared to performing work or producing isometric force. We hypothesized that metabolic cost would increase with a proposed measure termed force-rate (rate of increase in muscle force) in cyclic tasks, separate from mechanical work or average force level. We tested humans (N = 9) producing cyclic knee extension torque against an isometric dynamometer (torque 22 N-m, cyclic waveform frequencies 0.5 to 2.5 Hz), while also quantifying the force and work of muscle fascicles against series elasticity (with ultrasonography), along with metabolic rate through respirometry. Net metabolic rate increased by more than fourfold (10.5 to 46.7 W) with waveform frequency. At high frequencies, the hypothesized force-rate cost accounted for nearly half (41%) of energy expenditure. This exceeded the cost for average force (17%) and was comparable to the cost for shortening work (42%). The energetic cost is explained by a simple first-order model of rate-limiting steps in muscle contraction, primarily crossbridge dynamics. The force-rate cost could contribute substantially to the overall cost of movements that require cyclic muscle activation, such as locomotion.

The metabolic cost per unit force is generally thought to increase with the mechanical work done by the muscle fibres. It is currently unclear how the metabolic cost of doing alternating positive and negative muscle fibre mechanical work relates to the metabolic cost of doing zero muscle fibre mechanical work at similar muscle force. The current study aimed to investigate this issue by comparing in vivo metabolic power between a dynamic and an isometric near-constant force production task. In both tasks, participants performed periodic movement about the knee joint in the gravitational field. Therefore, net external mechanical work was constrained to be zero. The tasks mainly differed from each other in average positive knee joint mechanical power, which was 4.3±0.5 W per leg during the dynamic task and 0.1±0.1 W per leg during the isometric task. Knee extension torque was near-constant around 15.2±1.7 N m during the dynamic task and around 15.7±1.7 N m during the isometric task. Owing to near-constant knee extension torque, quadriceps tendon length was presumably nearly constant during both tasks. Therefore, knee joint mechanical work was predominantly done by the muscle fibres in both tasks. Average gross metabolic power was 3.22±0.46 W kg −1 during the dynamic task and 2.13±0.36 W kg −1 during the isometric task. Because tasks differed mainly in the amount of positive muscle fibre mechanical work, these results imply that the metabolic cost of near-constant force production in vivo at zero net mechanical work can be reduced by minimizing positive muscle fibre mechanical work.

Ultrasound imaging is valuable for non-invasively estimating fascicle lengths and other features of pennate muscle, especially when performed computationally. Effective analysis techniques to date typically use optic flow to track displacements from image sequences, but are sensitive to integration drift for longer sequences. We here present an alternative algorithm that objectively estimates geometric features of pennate muscle from ultrasound images, without drift sensitivity. The algorithm identifies aponeuroses and estimates fascicle angles to derive fascicle lengths. Length estimates of human vastus lateralis and gastrocnemius fascicles in healthy subjects (N = 9 and N = 17 respectively) compared well (overall root-mean-square difference, RMSD = 0.52 cm) to manual estimates by independent observers (n = 3), with overall coefficient of multiple correlation (CMC) of 0.98. Our tests yielded accuracy (CMC, RMSD) and processing speed similar to or exceeding that of state-of-the-art algorithms. The algorithm requires minimal manual intervention and can optionally extrapolate fascicle lengths that extend beyond the image frame. It thus facilitates automated analysis of ultrasound images without drift.

While ultrasound is a useful tool for visualizing muscle in vivo, traditional analysis involves substantial manual labor. Semi-automated algorithms have been introduced in recent years, reducing the amount of time required for extracting pennation angles and fascicle lengths from ultrasound images. Unfortunately, semi-automated algorithms still require some user actions and thereby subjective decision making. We here present a freely available, fully automated feature detection algorithm that involves Hessian filtering to highlight line-like objects within the ultrasound image. Hough transform is used to determine muscle fascicle angles and feature detection is used to determine the location and angle of aponeuroses. As a demonstration, we test the algorithm on ultrasound images obtained from vastus lateralis muscle in healthy individuals (N = 9) during isometric knee extension moment production (0 – 45 N-m) at three knee angles (15-25 deg). Pennation angle, muscle thickness and fascicle length vary with knee moment and knee angle in line with previous observations. Specifically, fascicle length decreases with larger knee moments and increases towards knee flexion. We expect the proposed algorithm to be useful for estimating muscle fascicle lengths during cyclic movements like human locomotion.

Humans perform mechanical work during walking, some by leg joints actuated by muscles, and some by passive, dissipative soft tissues. Dissipative losses must be restored by active muscle work, potentially in amounts sufficient to cost substantial metabolic energy. The most dissipative, and therefore costly, walking conditions might be predictable from the pendulum-like dynamics of the legs. If this behavior is systematic, it may also predict the work distribution between active joints and passive soft tissues. We therefore tested whether the overall negative work of walking, and the fraction due to soft tissue dissipation, are both predictable by a simple dynamic walking model across a wide range of conditions. The model predicts whole-body negative work from the leading leg's impact with ground (termed the Collision), to increase with the squared product of walking speed and step length. We experimentally tested this in humans (N=9) walking in 26 different combinations of speed (0.7 – 2.0 m·s−1) and step length (0.5 – 1.1 m), with recorded motions and ground reaction forces. Whole-body negative Collision work increased as predicted (R2=0.73), with a consistent fraction of about 63% (R2=0.88) due to soft tissues. Soft tissue dissipation consistently accounted for about 56% of the variation in total whole-body negative work, across a wide range of speed and step length combinations. During typical walking, active work to restore dissipative losses could account for 31% of the net metabolic cost. Soft tissue dissipation, not included in most biomechanical studies, explains most of the variation in negative work of walking, and could account for a substantial fraction of the metabolic cost.

The biomechanics of human walking are well documented for standard conditions such as for self-selected step length and preferred speed. However, humans can and do walk with a variety of other step lengths and speeds during daily living. The variation of biomechanics across gait conditions may be important for describing and determining the mechanics of locomotion. To address this, we present an open biomechanics dataset of steady walking at a broad range of conditions, including 33 experimentally-controlled combinations of speed (0.7–2.0 m·s−1), step length (0.5–1.1 m), and step width (0–0.4 m). The dataset contains ground reaction forces and motions from healthy young adults (N = 10), collected using split-belt instrumented treadmill and motion capture systems respectively. Most trials also include pre-computed inverse dynamics, including 3D joint positions, angles, torques and powers, as well as intersegmental forces. Apart from raw data, we also provide five strides of good quality data without artifacts for each trial, and sample software for visualization and analysis.

Humans perform mechanical work during walking, some by leg joints actuated by muscles, and some by passive, dissipative soft tissues. Dissipative losses must be restored by active muscle work, potentially in amounts sufficient to cost substantial metabolic energy. The most dissipative, and therefore costly, walking conditions might be predictable from the pendulum-like dynamics of the legs. If pendulum behavior is systematic, it may also predict the work distribution between active joints and passive soft tissues. We therefore tested whether the overall negative work of walking, and the fraction due to soft tissue dissipation, are both predictable by a pendulum model across a wide range of conditions. The model predicts whole-body negative work from the leading leg's impact with ground (termed the Collision), to increase with the squared product of walking speed and step length. We experimentally tested this in humans (N = 9) walking in 26 different combinations of speed (0.7 - 2.0 m/s) and step length (0.5 - 1.1 m), with recorded motions and ground reaction forces. Whole-body negative Collision work increased as predicted (R2 = 0.73), with a consistent fraction of about 63% (R2 = 0.88) due to soft tissues. Soft tissue dissipation consistently accounted for about 56% of the variation in total whole-body negative work. During typical walking, active work to restore dissipative losses could account for 31% of the net metabolic cost. Soft tissue dissipation, not included in most biomechanical studies, explains most of the variation in negative work of walking, and could account for a substantial fraction of the metabolic cost.