The metabolic cost of in vivo constant muscle force production at zero net mechanical work.

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.

Inverse dynamics of mechanical multibody systems: An improved algorithm that ensures consistency between kinematics and external forces.

Inverse dynamics is a technique in which measured kinematics and, possibly, external forces are used to calculate net joint torques in a rigid body linked segment model. However, kinematics and forces are usually not consistent due to incorrect modelling assumptions and measurement errors. This is commonly resolved by introducing 'residual forces and torques' which compensate for this problem, but do not exist in reality. In this study a constrained optimization algorithm is proposed that finds the kinematics that are mechanically consistent with measured external forces and mimic the measured kinematics as closely as possible. The algorithm was tested on datasets containing planar kinematics and ground reaction forces obtained during human walking at three velocities (0.8 m/s, 1.25 and 1.8 m/s). Before optimization, the residual force and torque were calculated for a typical example. Both showed substantial values, indicating the necessity of developing a mechanically consistent algorithm. The proposed optimization algorithm converged to a solution in which the residual forces and torques were zero, without changing the ground reaction forces and with only minor changes to the measured kinematics. When using a rigid body approach, our algorithm ensures a consistent description of forces and kinematics, thereby improving the validity of calculated net joint torque and power values.

Optimizing the Distribution of Leg Muscles for Vertical Jumping.

A goal of biomechanics and motor control is to understand the design of the human musculoskeletal system. Here we investigated human functional morphology by making predictions about the muscle volume distribution that is optimal for a specific motor task. We examined a well-studied and relatively simple human movement, vertical jumping. We investigated how high a human could jump if muscle volume were optimized for jumping, and determined how the optimal parameters improve performance. We used a four-link inverted pendulum model of human vertical jumping actuated by Hill-type muscles, that well-approximates skilled human performance. We optimized muscle volume by allowing the cross-sectional area and muscle fiber optimum length to be changed for each muscle, while maintaining constant total muscle volume. We observed, perhaps surprisingly, that the reference model, based on human anthropometric data, is relatively good for vertical jumping; it achieves 90% of the jump height predicted by a model with muscles designed specifically for jumping. Alteration of cross-sectional areas-which determine the maximum force deliverable by the muscles-constitutes the majority of improvement to jump height. The optimal distribution results in large vastus, gastrocnemius and hamstrings muscles that deliver more work, while producing a kinematic pattern essentially identical to the reference model. Work output is increased by removing muscle from rectus femoris, which cannot do work on the skeleton given its moment arm at the hip and the joint excursions during push-off. The gluteus composes a disproportionate amount of muscle volume and jump height is improved by moving it to other muscles. This approach represents a way to test hypotheses about optimal human functional morphology. Future studies may extend this approach to address other morphological questions in ethological tasks such as locomotion, and feature other sets of parameters such as properties of the skeletal segments.

The Relationship between Pedal Force and Crank Angular Velocity in Sprint Cycling.

PURPOSE: Relationships between tangential pedal force and crank angular velocity in sprint cycling tend to be linear. We set out to understand why they are not hyperbolic, like the intrinsic force-velocity relationship of muscles. METHODS: We simulated isokinetic sprint cycling at crank angular velocities ranging from 30 to 150 rpm with a forward dynamic model of the human musculoskeletal system actuated by eight lower extremity muscle groups. The input of the model was muscle stimulation over time, which we optimized to maximize average power output over a cycle. RESULTS: Peak tangential pedal force was found to drop more with crank angular velocity than expected based on intrinsic muscle properties. This linearizing effect was not due to segmental dynamics but rather due to active state dynamics. Maximizing average power in cycling requires muscles to bring their active state from as high as possible during shortening to as low as possible during lengthening. Reducing the active state is a relatively slow process, and hence must be initiated a certain amount of time before lengthening starts. As crank angular velocity goes up, this amount of time corresponds to a greater angular displacement, so the instant of switching off extensor muscle stimulation must occur earlier relative to the angle at which pedal force was extracted for the force-velocity relationship. CONCLUSION: Relationships between pedal force and crank angular velocity in sprint cycling do not reflect solely the intrinsic force-velocity relationship of muscles but also the consequences of activation dynamics.

Control of position and movement is simplified by combined muscle spindle and Golgi tendon organ feedback.

Whereas muscle spindles play a prominent role in current theories of human motor control, Golgi tendon organs (GTO) and their associated tendons are often neglected. This is surprising since there is ample evidence that both tendons and GTOs contribute importantly to neuromusculoskeletal dynamics. Using detailed musculoskeletal models, we provide evidence that simple feedback using muscle spindles alone results in very poor control of joint position and movement since muscle spindles cannot sense changes in tendon length that occur with changes in muscle force. We propose that a combination of spindle and GTO afferents can provide an estimate of muscle-tendon complex length, which can be effectively used for low-level feedback during both postural and movement tasks. The feasibility of the proposed scheme was tested using detailed musculoskeletal models of the human arm. Responses to transient and static perturbations were simulated using a 1-degree-of-freedom (DOF) model of the arm and showed that the combined feedback enabled the system to respond faster, reach steady state faster, and achieve smaller static position errors. Finally, we incorporated the proposed scheme in an optimally controlled 2-DOF model of the arm for fast point-to-point shoulder and elbow movements. Simulations showed that the proposed feedback could be easily incorporated in the optimal control framework without complicating the computation of the optimal control solution, yet greatly enhancing the system's response to perturbations. The theoretical analyses in this study might furthermore provide insight about the strong physiological couplings found between muscle spindle and GTO afferents in the human nervous system.

Conclusions on motor control depend on the type of model used to represent the periphery.

Within the field of motor control, there is no consensus on which kinematic and kinetic aspects of movements are planned or controlled. Perturbing goal-directed movements is a frequently used tool to answer this question. To be able to draw conclusions about motor control from kinematic responses to perturbations, a model of the periphery (i.e., the skeleton, muscle-tendon complexes, and spinal reflex circuitry) is required. The purpose of the present study was to determine to what extent such conclusions depend on the level of simplification with which the dynamical properties of the periphery are modeled. For this purpose, we simulated fast goal-directed single-joint movement with four existing types of models. We tested how three types of perturbations affected movement trajectory if motor commands remained unchanged. We found that the four types of models of the periphery showed different robustness to the perturbations, leading to different predictions on how accurate motor commands need to be, i.e., how accurate the knowledge of external conditions needs to be. This means that when interpreting kinematic responses obtained in perturbation experiments the level of error correction attributed to adaptation of motor commands depends on the type of model used to describe the periphery.

Do we use a priori knowledge of gravity when making elbow rotations?

In this study, we aim to investigate whether motor commands, emanating from movement planning, are customized to movement orientation relative to gravity from the first trial on. Participants made fast point-to-point elbow flexions and extensions in the transverse plane. We compared movements that had been practiced in reclined orientation either against or with gravity with the same movement relative to the body axis made in the upright orientation (neutral compared to gravity). For each movement type, five rotations from reclined to upright orientation were made. For each rotation, we analyzed the first trial in upright orientation and the directly preceding trial in reclined orientation. Additionally, we analyzed the last five trials of a 30-trial block in upright position and compared these trials with the first trials in upright orientation. Although participants moved fast, gravitational torques were substantial. The change in body orientation affected movement planning: we found a decrease in peak angular velocity and a decrease in amplitude for the first trials made in the upright orientation, regardless of whether the previous movements in reclined orientation were made against or with gravity. We found that these decreases disappeared after participants familiarized themselves with moving in upright position in a 30-trial block. These results indicate that participants used a general strategy, corresponding to the strategy observed in situations with unreliable or limited information on external conditions. From this, we conclude that during movement planning, a priori knowledge of gravity was not used to specifically customize motor commands for the neutral gravity condition.

Gross efficiency during rowing is not affected by stroke rate.

PURPOSE: It has been suggested that the optimal stroke rate in rowing is partly determined by the stroke-rate dependence of internal power losses. This should be reflected in a stroke-rate dependency of gross efficiency (e(gross)). The purpose of this study was to investigate if e(gross) is affected by stroke rate. A second aim was to determine whether internal power losses can be estimated by the negative power output during the stroke cycle (P(negative)). METHODS: Seventeen well-trained female rowers participated in this study. They rowed three trials on a modified rowing ergometer on slides at a submaximal intensity, with a respiratory exchange ratio of 1 or close to 1. Stroke rates were 28, 34, and 40 strokes per minute. The trials were fully randomized. Power transfer to the flywheel was kept constant whereas e(gross) was determined during each trial. RESULTS: No significant differences in e(gross) were found between conditions. This finding suggests that in rowing internal power losses are not influenced by stroke rate. Furthermore, although P(negative) increased at increasing stroke rate (P < 0.001), no relationship was found with e(gross). This suggests that P(negative) is not a reliable measure to estimate internal power losses. CONCLUSION: This study shows that within the range of stroke rates applied in competitive rowing, internal power losses are unrelated to rowing cycle frequency.

A model of open-loop control of equilibrium position and stiffness of the human elbow joint.

According to the equilibrium point theory, the control of posture and movement involves the setting of equilibrium joint positions (EP) and the independent modulation of stiffness. One model of EP control, the alpha-model, posits that stable EPs and stiffness are set open-loop, i.e. without the aid of feedback. The purpose of the present study was to explore for the elbow joint the range over which stable EPs can be set open-loop and to investigate the effect of co-contraction on intrinsic low-frequency elbow joint stiffness (K (ilf)). For this purpose, a model of the upper and lower arm was constructed, equipped with Hill-type muscles. At a constant neural input, the isometric force of the contractile element of the muscles depended on both the myofilamentary overlap and the effect of sarcomere length on the sensitivity of myofilaments to [Ca2+] (LDCS). The musculoskeletal model, for which the parameters were chosen carefully on the basis of physiological literature, captured the salient isometric properties of the muscles spanning the elbow joint. It was found that stable open-loop EPs could be achieved over the whole range of motion of the elbow joint and that K (ilf), which ranged from 18 to 42 N m.rad(-1), could be independently controlled. In the model, LDCS contributed substantially to K (ilf) (up to 25 N m.rad(-1)) and caused K (ilf) to peak at a sub-maximal level of co-contraction.

Is equilibrium point control feasible for fast goal-directed single-joint movements?

Several types of equilibrium point (EP) controllers have been proposed for the control of posture and movement. EP controllers are appealing from a computational perspective because they do not require solving the "inverse dynamic problem" (i.e., computation of the torques required to move a system along a desired trajectory). It has been argued that EP controllers are not capable of controlling fast single-joint movements. To refute this statement, several extensions have been proposed, although these have been tested using models in which only the tendon compliance, force-length-velocity relation, and mechanical interaction between tendon and contractile element were not adequately represented. In the present study, fast elbow-joint movements were measured and an attempt was made to reproduce these using a realistic musculoskeletal model of the human arm. Three types of EP controllers were evaluated: an open-loop alpha-controller, a closed-loop lambda-controller, and a hybrid open- and closed-loop controller. For each controller we considered a continuous version and a version in which the control signals were sent out intermittently. Only the intermittent hybrid EP controller was capable of generating movements that were as fast as those of the subjects. As a result of the nonlinear muscle properties, the hybrid EP controller requires a more detailed representation of static muscle properties than generally assumed in the context of EP control. In sum, this study shows that fast single-joint movements can be realized without explicitly solving the inverse dynamics problem, but in a less straightforward manner than implied by proponents of conventional EP controllers.

The relationship of the kicking action in soccer and anterior ankle impingement syndrome. A biomechanical analysis.

Two different hypotheses have been advanced to explain the formation of talotibial osteophytes in the anterior ankle impingement syndrome. We investigated how frequently hyperplantar flexion occurs during kicking and whether the site of impact of the ball coincides with the reported location of the osteophytes. We also measured the magnitude of the impact force. We studied 150 kicking actions performed by 15 elite soccer players by using mobile sensors and high-speed video. In 39% of the kicking actions, the plantar flexion angle exceeded the maximum static plantar flexion angle. Ball impact was predominantly made with the anteromedial aspect of the foot and ankle, with impact between the ball and the base of the first metatarsal bone in 89% of the kicking actions and between the ball and the anterior part of the medial malleolus in 76%. Postimpact ball velocity averaged 24.6 m/s, with a corresponding average contact force of 1025 N. Hyperplantar flexion was reached in only the minority of the kicking actions. The data on impact location and impact force support the hypothesis that spur formation in anterior ankle impingement syndrome is related to recurrent ball impact, which can be regarded as repetitive microtrauma to the anteromedial aspect of the ankle.