Huxley-type cross-bridge models in largeish-scale musculoskeletal models; an evaluation of computational cost

A Huxley-type cross-bridge model is attractive because it is inspired by our current understanding of the processes underlying muscle contraction, and because it provides a unified description of muscle's mechanical behavior and metabolic energy expenditure. In this study, we determined the computational cost for task optimization of a largeish-scale musculoskeletal model in which muscles are represented by a 2-state Huxley-type cross-bridge model. Parameter values defining the rate functions of the Huxley-type cross-bridge model could be chosen such that the steady-state force-velocity relation resembled that of a Hill-type model. Using these parameter values, maximum-height squat jumping was used as the example task to evaluate the computational cost of task optimization for a skeletal model driven by a Huxley-type cross-bridge model. The optimal solutions for the Huxley- and Hill-type muscle models were similar for all mechanical variables considered. Computational cost of the Huxley-type cross-bridge model was much higher than that of the Hill-type model. Compared to the Hill-type model, the number of state variables per muscle was large (2 vs about 18,000), the integration step size had to be about 100 times smaller, and the computational cost per integration step was about 100 times higher

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

Effect of stroke rate on the distribution of net mechanical power in rowing

The aim of this study was to assess the effect of manipulating stroke rate on the distribution of mechanical power in rowing. Two causes of inefficient mechanical energy expenditure were identified in rowing. The ratio between power not lost at the blades and generated mechanical power (P

Spontaneous kicking behavior in infants:age-related effects of unilateral weighting

The age-related effects of unilateral weighting on spontaneously generated kicks in 18 healthy, full-term infants were investigated. The main question was whether infants during the first half-year after birth reveal changes in how they adjust to unilateral weighting. At 6 weeks, infants reduced the frequency of the weighted leg and increased that of the unweighted leg whereas at 12 weeks the frequency of kicking increased in both legs. At both ages, unilateral weighting also resulted in differences on a number of kinematic parameters. By 18 and 26 weeks, such frequency and kinematic effects were no longer present. With regard to interlimb couplings, a clear pattern of bilateral coordination was only present at 26 weeks; these results suggest that the effects of unilateral weighting are not directly related to the rightness of interlimb couplings. The implications of these age-related differences for understanding developmental changes in the control of leg movements are discussed. It is suggested that the infants' improved ability to act in a task-specific manner as well as nonlinear changes in the musculo-skeletal system and fine-tuning processes at a neural level might be factors of importance. (C) 2000 John Wiley & Sons, Inc

Natural Frequency Method: estimating the preferred walking speed of <italic toggle="yes">Tyrannosaurus rex</italic> based on tail natural frequency

Locomotor energetics are an important determinant of an animal's ecological niche. It is commonly assumed that animals minimize locomotor energy expenditure by selecting gait kinematics tuned to the natural frequencies of relevant body parts. We demonstrate that this allows estimation of the preferred step frequency and walking speed of Tyrannosaurus rex, using an approach we introduce as the Natural Frequency Method. Although the tail of bipedal dinosaurs was actively involved in walking, it was suspended passively by the caudal interspinous ligaments. These allowed for elastic energy storage, thereby reducing the metabolic cost of transport. In order for elastic energy storage to be high, step and natural frequencies would have to be matched. Using a 3D morphological reconstruction and a spring-suspended biomechanical model, we determined the tail natural frequency of T. rex (0.66 s−1, range 0.41–0.84), and the corresponding walking speed (1.28 m s−1, range 0.80–1.64), which we argue to be a good indicator of preferred walking speed (PWS). The walking speeds found here are lower than earlier estimations for large theropods, but agree quite closely with PWS of a diverse group of extant animals. The results are most sensitive to uncertainties regarding ligament moment arms, vertebral kinematics and ligament composition. However, our model formulation and method for estimation of walking speed are unaffected by assumptions regarding muscularity, and therefore offer an independent line of evidence within the field of dinosaur locomotion

Mechanical power output in rowing should not be determined from oar forces and oar motion alone

Mechanical power output is a key performance-determining variable in many cyclic sports. In rowing, instantaneous power output is commonly determined as the dot product of handle force moment and oar angular velocity. The aim of this study was to show that this commonly used proxy is theoretically flawed and to provide an indication of the magnitude of the error. To obtain a consistent dataset, simulations were performed using a previously proposed forward dynamical model. Inputs were previously recorded rower kinematics and horizontal oar angle, at 20 and 32 strokes∙min−1. From simulation outputs, true power output and power output according to the common proxy were calculated. The error when using the common proxy was quantified as the difference between the average power output according to the proxy and the true average power output (P̅residual), and as the ratio of this difference to the true average power output (ratiores./rower). At stroke rate 20, P̅residual was 27.4 W and ratiores./rower was 0.143; at stroke rate 32, P̅residual was 44.3 W and ratiores./rower was 0.142. Power output in rowing appears to be underestimated when calculated according to the common proxy. Simulations suggest this error to be at least 10% of the true power output