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Graham E. Caldwell

The effects of relative tendon/fiber proportion and tendon elasticity on the force output of the Hill muscle model (a contractile component [CC] in series with an elastic element [SEC]) were examined through computer simulation. Three versions of the Hill model were constructed. Model 1 examined the effect of relative tendon/fiber proportion on CC kinematics and kinetics during an isometric twitch, while Model 2 compared the effect of changes in tendon compliance. These models revealed force profile differences related to alterations in CC velocity, although the reasons underlying the variation in CC kinematics were different. The relative tendon/fiber proportion and tendon compliance differences were examined in combination in Model 3. Test simulations revealed response differences among the three model versions, and therefore verified Alexander and Ker's (1990) contention that the morphology of muscle is related to design criteria. It is suggested that the implementation of generalized muscle models to represent specific units of the musculoskeletal system should be done carefully and that the implementation process itself warrants further study.

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Stephanie E. Forrester and Matthew T.G. Pain

This study aimed to identify areas of reduced surface EMG amplitude and changed frequency across the phase space of a maximal dynamic knee extension task. The hypotheses were that (1) amplitude would be lower for eccentric contractions compared with concentric contractions and unaffected by fiber length and (2) mean frequency would also be lower for eccentric contractions and unaffected by fiber length. Joint torque and EMG signals from the vasti and rectus femoris were recorded for eight athletic subjects performing maximum knee extensions at 13 preset crank velocities spanning ±300°⋅s−1. The instantaneous amplitude and mean frequency were calculated using the continuous wavelet transform time–frequency method, and the fiber dynamics were determined using a muscle model of the knee extensions. The results indicated that (1) only for the rectus femoris were amplitudes significantly lower for eccentric contractions (p = .019) and, for the vasti, amplitudes during eccentric contractions were less than maximal but this was also the case for concentric contractions due to a significant reduction in amplitude toward knee extension (p = .023), and (2) mean frequency increased significantly with decreasing fiber length for all knee extensors and contraction velocities (p = .029). Using time–frequency processing of the EMG signals and a muscle model allowed the simultaneous assessment of fiber length, velocity, and EMG.

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Mark A. King and Maurice R. Yeadon

This paper describes a method for defining the maximum torque that can be produced at a joint from isovelocity torque measurements on an individual. The method is applied to an elite male gymnast in order to calculate subject-specific joint torque parameters for the knee joint. Isovelocity knee extension torque data were collected for the gymnast using a two-repetition concentric-eccentric protocol over a 75° range of crank motion at preset crank angular velocities ranging from 20 to 250°s–1. During these isovelocity movements, differences of up to 35° were found between the angle of the dynamometer crank and the knee joint angle of the participant. In addition, faster preset crank angular velocities gave smaller ranges of isovelocity motion for both the crank and joint. The simulation of an isovelocity movement at a joint angular velocity of 150°s–1 showed that, for realistic series elastic component extensions, the angular velocity of the joint can be assumed to be the same as the angular velocity of the contractile component during most of the isovelocity trial. Fitting an 18-parameter exponential function to experimental isovelocity joint torque/ angle/ angular velocity data resulted in a surface that was well behaved over the complete range of angular velocities and within the specified range of joint angles used to calculate the surface.

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Fabien Dal Maso, Mickaël Begon and Maxime Raison

One approach to increasing the confidence of muscle force estimation via musculoskeletal models is to minimize the root mean square error (RMSE) between joint torques estimated from electromyographic-driven musculoskeletal models and those computed using inverse dynamics. We propose a method that reduces RMSE by selecting subsets of combinations of maximal voluntary isometric contraction (MVIC) trials that minimize RMSE. Twelve participants performed 3 elbow MVIC in flexion and in extension. An upper-limb electromyographic-driven musculoskeletal model was created to optimize maximum muscle stress and estimate the maximal isometric force of the biceps brachii, brachialis, brachioradialis, and triceps brachii. Maximal isometric forces were computed from all possible combinations of flexion-extension trials. The combinations producing the smallest RMSE significantly reduced the normalized RMSE to 7.4% compared with the combination containing all trials (9.0%). Maximal isometric forces ranged between 114–806 N, 64–409 N, 236–1511 N, and 556–3434 N for the brachii, brachialis, brachioradialis, and triceps brachii, respectively. These large variations suggest that customization is required to reduce the difference between models and actual participants’ maximal isometric force. While the smallest previously reported RMSE was 10.3%, the proposed method reduced the RMSE to 7.4%, which may increase the confidence of muscle force estimation.

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Mark B. Shapiro and Robert V. Kenyon

A new mechanical model of isolated muscle is proposed in which spring with variable slack length is the force-generating element. Based on the review of experimental studies in isolated muscle, it is suggested that spring slack length X0 is the control variable in the model and is a function of motor unit firing rate. In the presence of sensory feedback, the Sliding Spring model is equivalent to the Rack and Pinion model. However, sensory feedback is essential in the Rack and Pinion model but complementary in the Sliding Spring model. How the new control variable in the model of isolated muscle affects the interpretation of control processes up the motor system hierarchy is discussed in light of certain controversies associated with the Lambda and Alpha models of control of movement. It is argued that the Sliding Spring model of isolated muscle can be used as a basis for developing models of control of movement.

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Maurice R. Yeadon and Mark A. King

The use of computer simulation models in studies of human movement is now widespread. Most of these models, however, have not been evaluated in a quantitative manner in order to establish the level of accuracy that may be expected. Without such an evaluation, little credence should be given to the published results and conclusions. This paper presents a simulation model of tumbling takeoffs which is evaluated by comparing the simulation output with an actual performance of an elite gymnast. A five-segment planar model was developed to simulate tumbling takeoffs. The model comprised rigid foot, leg, thigh, trunk + head, and arm segments with two damped linear springs to represent the elasticity of the tumbling track/ gymnast interface. Torque generators were included at the ankle, knee, hip, and shoulder joints in order to allow each joint to open actively during the takeoff. The model was customized to the elite gymnast by determining subject-specific inertia and torque parameters. Good agreement was found between actual and simulated tumbling performances of a double layout somersault with 1% difference in the linear and angular momenta at takeoff. Allowing the activation timings of the four torque generators to vary resulted in an optimized simulation that was some 0.32 m higher than the evaluation simulation. These simulations suggest the model is a realistic representation of the elite gymnast, since otherwise the model would either fail to reproduce the double layout somersault or would produce a very different optimized solution.

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Markus Tilp, Simon Steib, Gudrun Schappacher-Tilp and Walter Herzog

Force enhancement following muscle stretching and force depression following muscle shortening are well-accepted properties of skeletal muscle contraction. However, the factors contributing to force enhancement/depression remain a matter of debate. In addition to factors on the fiber or sarcomere level, fiber length and angle of pennation affect the force during voluntary isometric contractions in whole muscles. Therefore, we hypothesized that differences in fiber lengths and angles of pennation between force-enhanced/depressed and reference states may contribute to force enhancement/depression during voluntary contractions. The purpose of this study was to test this hypothesis. Twelve subjects participated in this study, and force enhancement/depression was measured in human tibialis anterior. Fiber lengths and angles of pennation were quantified using ultrasound imaging. Neither fiber lengths nor angles of pennation were found to differ between the isometric reference contractions and any of the force-enhanced or force-depressed conditions. Therefore, we rejected our hypothesis and concluded that differences in fiber lengths or angles of pennation do not contribute to the observed force enhancement/depression in human tibialis anterior, and speculate that this result is likely true for other muscles too.

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Filipe Conceição, Mark A. King, Maurice R. Yeadon, Martin G.C. Lewis and Stephanie E. Forrester

This study aimed to determine whether subject-specific individual muscle models for the ankle plantar flexors could be obtained from single joint isometric and isovelocity maximum torque measurements in combination with a model of plantar flexion. Maximum plantar flexion torque measurements were taken on one subject at six knee angles spanning full flexion to full extension. A planar three-segment (foot, shank and thigh), two-muscle (soleus and gastrocnemius) model of plantar flexion was developed. Seven parameters per muscle were determined by minimizing a weighted root mean square difference (wRMSD) between the model output and the experimental torque data. Valid individual muscle models were obtained using experimental data from only two knee angles giving a wRMSD score of 16 N m, with values ranging from 11 to 17 N m for each of the six knee angles. The robustness of the methodology was confirmed through repeating the optimization with perturbed experimental torques (±20%) and segment lengths (±10%) resulting in wRMSD scores of between 13 and 20 N m. Hence, good representations of maximum torque can be achieved from subject-specific individual muscle models determined from single joint maximum torque measurements. The proposed methodology could be applied to muscle-driven models of human movement with the potential to improve their validity.

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John W. Chow, Warren G. Darling, James G. Hay and James G. Andrews

The purpose of this study was to propose and evaluate a method for the in vivo determination of the force-length-velocity relations of individual quadriceps muscles. One female subject performed maximum effort knee extensions on an isokinetic dynamometer. The gravitational and inertial effects were taken into consideration when determining the resultant knee torque. Selected anatomical and geometric parameters of the quadriceps muscles were obtained from radiography and magnetic resonance imaging (MRI). Hill’s (1938) mechanical model was used to represent the force-velocity relation of a muscle at a given length, and the constants in Hill’s model were assumed to vary with muscle length. Experimentally determined knee torque and muscle shortening velocity data were used to determine the unknown parameters in the muscle model. The relation between each muscle parameter and muscle length for each muscle was obtained using regression analysis. On average, the muscle model overestimated the knee torque by 15.5 ± 5.1%. The overestimations may have resulted from the lack of low torque-high velocity data for the determination of muscle model parameters. When a set of fixed Hill constants was used, the knee torque was underestimated by 29.0 ± 10.6%. The results demonstrate the feasibility of the method proposed in this study.

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Kenneth Meijer, Peter Bosch, Maarten F. Bobbert, Arthur J. van Soest and Peter A. Huijing

The influence of parameter values (i.e., fiber optimum lengths and moment arms) and simplification of the geometry of a Hill-type muscle model on the prediction of normalized maximal isometric knee extension moment to knee joint angle relationship was studied. For that purpose, the geometry of m. quadriceps femoris was modeled in considerable detail, and all parameter values were determined on one set of cadaver specimens that had been selected for muscular appearance. The predicted relationship was compared to that measured in human subjects over the full range of physiological knee angles, and a good correspondence was found (r = .96). The good correspondence could be attributed to the substitution of realistic parameter values into the model. Incorporating complex muscle geometry into the model resulted in a small additional improvement of the prediction. It was speculated that the variation in results of cadaver measurements among studies reflects true differences caused by individuals' levels of physical activity in the period preceding death.