A simple Hill element-nonlinear spring model of muscle contraction biomechanics

Schultz, Albert B.; Kadhiresan, V.

doi:10.1152/jappl.1991.70.2.803

Cited by 14 publications

(8 citation statements)

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“…Non-linear approximations to characterize limb mechanics often include a cubic stiffness term in addition to linear stiffness and damping terms [78] , [79] , [80] , [81] . Maintaining constant stiffness and damping parameters and as in (52), we included a cubic stiffness term so that in the matrix version of (17) .…”

Section: Methodsmentioning

confidence: 99%

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

et al. 2012

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This study presents and validates a Time-Frequency technique for measuring 2-dimensional multijoint arm stiffness throughout a single planar movement as well as during static posture. It is proposed as an alternative to current regressive methods which require numerous repetitions to obtain average stiffness on a small segment of the hand trajectory. The method is based on the analysis of the reassigned spectrogram of the arm's response to impulsive perturbations and can estimate arm stiffness on a trial-by-trial basis. Analytic and empirical methods are first derived and tested through modal analysis on synthetic data. The technique's accuracy and robustness are assessed by modeling the estimation of stiffness time profiles changing at different rates and affected by different noise levels. Our method obtains results comparable with two well-known regressive techniques. We also test how the technique can identify the viscoelastic component of non-linear and higher than second order systems with a non-parametrical approach. The technique proposed here is very impervious to noise and can be used easily for both postural and movement tasks. Estimations of stiffness profiles are possible with only one perturbation, making our method a useful tool for estimating limb stiffness during motor learning and adaptation tasks, and for understanding the modulation of stiffness in individuals with neurodegenerative diseases.

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Section: Methodsmentioning

confidence: 99%

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

et al. 2012

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“…Several models have focused at the molecular level or at the single motor unit using Hill's force-velocity equations (Lloyd and Besier 2003;Schultz et al 1991;Wexler et al 1997;Whipp and Wasserman 1969), thus providing predictions of force generating capacity but not the fatiguing aspect. The process of muscle fatiguing is dependent not only on the mechanical aspect but also on a number of factors such as neural signaling, oxygen and fuel availability, and byproduct generation.…”

Section: Introductionmentioning

confidence: 99%

An integrated exercise response and muscle fatigue model for performance decrement estimates of workloads in oxygen-limiting environments

Sih

Stuhmiller

2011

Eur J Appl Physiol

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The performance dynamic physiology model (DPM-PE) integrates a modified muscle fatigue model with an exercise physiology model that calculates the transport and delivery of oxygen to working muscles during exposures of oxygen-limiting environments. This mathematical model implements a number of physiologic processes (respiration, circulation, tissue metabolism, diffusion-limited gas transfer at the blood/gas lung interface, and ventilatory control with afferent feedback, central command and humoral chemoreceptor feedback) to replicate the three phases of ventilatory response to a variety of exertion patterns, predict the delivery and transport of oxygen and carbon dioxide from the lungs to tissues, and calculate the amount of aerobic and anaerobic work performed. The ventilatory patterns from passive leg movement, unloaded work, and stepped and ramping loaded work compare well against data. The model also compares well against steady-state ventilation, cardiac output, blood oxygen levels, oxygen consumption, and carbon dioxide generation against a range of exertion levels at sea level and at altitude, thus demonstrating the range of applicability of the exercise model. With the ability to understand and predict gas transport and delivery of oxygen to working muscle tissue for different workloads and environments, the correlation between blood oxygen measures and the recovery factor of the muscle fatigue model was explored. Endurance data sets in normoxia and hypoxia were best replicated using arterial oxygen saturation as the correlate with the recovery factor. This model provides a physiologically based method for predicting physical performance decrement due to oxygen-limiting environments.

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“…The major function of muscle is to produce force. There have been numerous attempts to model muscle force mathematically, ranging from the simplest to the most comprehensive ones that consider many physiological and mechanical factors of the muscle such as muscle length, shortening velocity, neural activation, and muscle architecture (Coggshall and Bekey, 1970;Pell and Stanfield, 1972;Christakos and Lal, 1980;Woittiez et al, 1984;Hannaford, 1990;Schultz et al, 1991;Wexler et al, 1997;Bobet and Stein, 1998;Studer et al, 1999). In most models, muscle force is calculated by summing the forces produced by individual muscle fibers.…”

Section: Introductionmentioning

confidence: 99%

A Dynamical Model of Muscle Activation, Fatigue, and Recovery

Liu

Brown

Yue

2002

Biophysical Journal

152

180

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A dynamical model is presented as a framework for muscle activation, fatigue, and recovery. By describing the effects of muscle fatigue and recovery in terms of two phenomenological parameters (F, R), we develop a set of dynamical equations to describe the behavior of muscles as a group of motor units activated by voluntary effort. This model provides a macroscopic view for understanding biophysical mechanisms of voluntary drive, fatigue effect, and recovery in stimulating, limiting, and modulating the force output from muscles. The model is investigated under the condition in which brain effort is assumed to be constant. Experimental validation of the model is performed by fitting force data measured from healthy human subjects during a 3-min sustained maximal voluntary handgrip contraction. The experimental results confirm a theoretical inference from the model regarding the possibility of maximal muscle force production, and suggest that only 97% of the true maximal force can be reached under maximal voluntary effort, assuming that all motor units can be recruited voluntarily. The effects of different motor unit types, time-dependent brain effort, sources of artifacts, and other factors that could affect the model are discussed. The applications of the model are also discussed.

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A simple Hill element-nonlinear spring model of muscle contraction biomechanics

Cited by 14 publications

References 0 publications

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

Measuring Multi-Joint Stiffness during Single Movements: Numerical Validation of a Novel Time-Frequency Approach

An integrated exercise response and muscle fatigue model for performance decrement estimates of workloads in oxygen-limiting environments

A Dynamical Model of Muscle Activation, Fatigue, and Recovery

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