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

In Vivo Dynamics of the Musculoskeletal System Cannot Be Adequately Described Using a Stiffness-Damping-Inertia Model

Background: Visco-elastic properties of the (neuro-)musculoskeletal system play a fundamental role in the control of posture and movement. Often, these properties are described and identified using stiffness-damping-inertia (KBI) models. In such an approach, perturbations are applied to the (neuro-)musculoskeletal system and subsequently KBI-model parameters are optimized to obtain a best fit between simulated and experimentally observed responses. Problems with this approach may arise because a KBI-model neglects critical aspects of the real musculoskeletal system. Methodology/Principal Findings: The purpose of this study was to analyze the relation between the musculoskeletal properties and the stiffness and damping estimated using a KBI-model, to analyze how this relation is affected by the nature of the perturbation and to assess the sensitivity of the estimated stiffness and damping to measurement errors. Our analyses show that the estimated stiffness and damping using KBI-models do not resemble any of the dynamical parameters of the underlying system, not even when the responses are very accurately fitted by the KBI-model. Furthermore, the stiffness and damping depend non-linearly on all the dynamical parameters of the underlying system, influenced by the nature of the perturbation and the time interval over which the KBI-model is optimized. Moreover, our analyses predict a very high sensitivity of estimated parameters to measurement errors. Conclusions/Significance: The results of this study suggest that the usage of stiffness-damping-inertia models t

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. © 2013 the American Physiological Society

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 α-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 (

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

The Metabolic Cost of Walking in healthy young and older adults: A Systematic Review and Meta Analysis

The Metabolic Cost of Walking (MCoW) is an important variable of daily life that has been studied extensively. Several studies suggest that MCoW is higher in Older Adults (OA) than in Young Adults (YA). However, it is difficult to compare values across studies due to differences in the way MCoW was expressed, the units in which it was reported and the walking speed at which it was measured. To provide an overview of MCoW in OA and YA and to investigate the quantitative effect of age on MCoW, we have conducted a literature review and performed two meta-analyses. We extracted data on MCoW in healthy YA (18–41 years old) and healthy OA (≥59 years old) and calculated, if not already reported, the Gross (GCoW) and Net MCoW (NCoW) in J/kg/m. If studies reported MCoW measured at multiple speeds, we selected those values for YA and OA at which MCoW was minimal. All studies directly comparing YA and OA were selected for meta-analyses. From all studies reviewed, the average GCoW in YA was 3.4 ± 0.4 J/kg/m and 3.8 ± 0.4 J/kg/m in OA (~12% more in OA), and the average NCoW in YA was 2.4 ± 0.4 J/kg/m and 2.8 ± 0.5 J/kg/m in OA (~17% more in OA). Our meta-analyses indicated a statistically significant elevation of both GCoW and NCoW (p < 0.001) for OA. In terms of GCoW, OA expended about 0.3 J/kg/m more metabolic energy than YA and about 0.4 J/kg/m more metabolic energy than YA in terms of NCoW. Our study showed a statistically significant elevation in MCoW of OA over YA. However, from the literature it is unclear if this elevation is directly caused by age or due to an interaction between age and methodology. We recommend further research comparing MCoW in healthy OA and YA during “natural” over-ground walking and treadmill walking, after sufficient familiarization time

Limiting radial pedal forces greatly reduces maximal power output and efficiency in sprint cycling: an optimal control study

A cyclist's performance depends critically on the generated average mechanical power output (AMPO). The instantaneous mechanical power output equals the product of crank angular velocity, crank length, and the tangential pedal force. Radial pedal forces do not contribute to mechanical power. It has been suggested that radial pedal forces arise from suboptimal pedaling technique and that limiting these would increase AMPO and efficiency. Here, we presented an optimal control musculoskeletal model of a cyclist (consisting of five segments driven by nine Hill-type muscle-tendon units) to predict maximal AMPO during sprint cycling at different levels of allowed radial pedal forces. Our findings showed that limiting radial pedal forces has a detrimental effect on maximal AMPO; it dropped from 1,115 W without a limit on radial forces to 528 W when no radial forces were allowed (both at 110 rpm). We explained that avoiding radial pedal forces causes ineffective use of muscles: muscles deliver less positive power and have a higher muscle power dissipation ratio (average mechanical power dissipated per unit of average positive power delivered). We concluded that radial pedal forces are an unavoidable by-product when optimizing for maximal AMPO and that limiting these leads to a performance decrease.NEW & NOTEWORTHY In the literature, but also in the "cycling field" [e.g., trainers, coaches, and (professional) cyclists], it is often suggested that trying to limit/avoid radial pedal forces enhances cycling technique and with that maximal average power output and efficiency. In this paper, we introduce an optimal control model of a human cyclists (consisting of five segments and driven by nine Hill-type muscle-tendon complex models). With that we not only show, but also explain why limiting radial forces is a bad idea: it will decrease maximal attainable AMPO and will decrease efficiency