Dynamic performance model of an isometric muscle-joint unit

System identification of evoked mechanomyogram from abductor pollicis brevis muscle in isometric contraction

The purpose of this study is to verify the applicability of a sixth-order model to the mechanomyogram (MMG) system of the parallel-fibered muscle, which was identified from the MMG of the pennation muscle. The median nerve was stimulated, and an MMG and torque of the abductor pollicis brevis muscle were measured. The MMGs were detected with either a capacitor microphone or an acceleration sensor. The transfer functions between stimulation and the MMG and between stimulation and torque were identified by the singular value decomposition method. The torque and the MMG, which were detected with a capacitor microphone, DMMG, were approximated with a second- and a third-order model, respectively. The natural frequency of the torque, reflecting longitudinal mechanical characteristics, did not show a significant difference from that of the DMMG. The MMG detected with an acceleration sensor was approximated with a fourth-order model. The natural frequencies of the AMMG reflecting the muscle and subcutaneous tissue in the transverse direction were obtained. Both DMMG and AMMG have to be measured to investigate the model of the MMG system for parallel-fibered muscle. The MMG system of parallel-fibered muscle was also modeled with a sixth-order model.

Comparison of displacement and acceleration transducers for the characterization of mechanics of muscle and subcutaneous tissues by system identification of a mechanomyogram

The purpose of this study was to clarify the performance of transducers for the mechanical characterization of muscle and subcutaneous tissue with the aid of a system identification technique. The common peroneal nerve was stimulated, and a mechanomyogram (MMG) of the anterior tibialis muscle was detected with a laser displacement meter or an acceleration sensor. The transfer function between stimulation and the MMG was identified by the singular value decomposition method. The MMG detected with a laser displacement meter, DMMG, was approximated with a second-order model, but that detected with an acceleration sensor, AMMG, was approximated with a sixth-order model. The natural frequency of the DMMG coincided with that in the literature and was close to the lowest natural frequency of the AMMG. The highest natural frequency of the AMMG was within the range of the resonance frequencies of human soft tissue. The laser displacement meter is suitable for the precise identification of the MMG, which has a natural frequency of around 3 Hz. The acceleration transducer is suitable for the identification of the MMG with natural frequencies of tens of hertz.

Modelling the isometric force response to multiple pulse stimuli in locust skeletal muscle

An improved model of locust skeletal muscle will inform on the general behaviour of invertebrate and mammalian muscle with the eventual aim of improving biomedical models of human muscles, embracing prosthetic construction and muscle therapy. In this article, the isometric response of the locust hind leg extensor muscle to input pulse trains is investigated. Experimental data was collected by stimulating the muscle directly and measuring the force at the tibia. The responses to constant frequency stimulus trains of various frequencies and number of pulses were decomposed into the response to each individual stimulus. Each individual pulse response was then fitted to a model, it being assumed that the response to each pulse could be approximated as an impulse response and was linear, no assumption were made about the model order. When the interpulse frequency (IPF) was low and the number of pulses in the train small, a second-order model provided a good fit to each pulse. For moderate IPF or for long pulse trains a linear third-order model provided a better fit to the response to each pulse. The fit using a second-order model deteriorated with increasing IPF. When the input comprised higher IPFs with a large number of pulses the assumptions that the response was linear could not be confirmed. A generalised model is also presented. This model is second-order, and contains two nonlinear terms. The model is able to capture the force response to a range of inputs. This includes cases where the input comprised of higher frequency pulse trains and the assumption of quasi-linear behaviour could not be confirmed.

Isometric force generated by locust skeletal muscle: responses to single stimuli

A mathematical model of the locust hind leg extensor muscle is described. The model accounts for the force response of the muscle to well-separated input stimuli under isometric conditions. Experimental data was collected by stimulating the extensor muscle and measuring the force generated at the tibia. In developing a model it was assumed that the response to a single isolated stimulus was linear. A linear model was found to fit well to the response to an isolated stimulus. No assumptions were made about the model order and models of various order were fitted to data in the frequency domain, using a least squares fit. The stimulus can be approximated as an impulse, with the response to each stimulus well described by a linear second-order system. Using a third-order model provided a better fit to data, but the improvement in fit was marginal and the model uses one extra parameter. A fourth-order model, which is often used to describe the behaviour of isometric muscle was found to overfit the data. Using a second-order model provides a simpler way of describing the behaviour of an isometric twitch.

A comparison of models of force production during stimulated isometric ankle dorsiflexion in humans

In this paper, we compare seven models on their ability to fit isometric muscle force. We stimulated the ankle dorsiflexors of eight subjects at seven ankle angles (85 degrees-120 degrees). Three different stimulation patterns (twitch, triangular, and random) were applied at all ankle angles. Four additional patterns (doublets, steady rates, "catch property," and walking-like) were applied at 95 degrees. Parameter values were optimized for each model at each angle. Parameters for the general linear model were calculated using a novel least-squares algorithm. A linear, second-order critically damped model gave the poorest fits (average root mean square (rms) error: 15 N). The models of Ding et al. (2002) and Bobet and Stein (1998) gave the best fits (average rms errors: 9.2 and 9.4 N). The other models (general linear second-order model, Wiener model, Zhou et al. (1995) model, general linear model) gave intermediate results. Results were similar at all ankle angles. We conclude that the Ding and Bobet-Stein models are the best overall for isometric contractions, that no linear model of any kind will give an error less than 9% of maximum force, and that the models tested are consistent across lengths.

The functional form of the lognormal distribution as a sum of decaying exponential and sinusoidal terms applied to the isometric pinch force of human fingers

The transient data of the pinch force produced between the human forefinger and thumb have been shown to fit the functional form of the well-known lognormal density function. Isometeric force generation is achieved by the stochastic recruitment of individual motor units, which sum together. Evidence from animal and human experiments demonstrates that the force generation can be modelled by underdamped terms. It is shown that a lognormal time series (distribution) can be fitted to a sum of exponential decaying sinusoidal terms.

Frequency domain-based models of skeletal muscle

Models of skeletal muscle based on its response to sinusoidal stimulation have been in use since the late 1960s. In these methods, cyclic excitation at varying frequencies is used to determine force or muscle length amplitude and phase as functions of excitation frequency. These functions can then be approximated by models consisting of combinations of poles and zeros and pure time delays without the need to combine force-length or force-velocity relationships. The major findings of a series of frequency response studies undertaken in our laboratory revealed that: The frequency response models for isometric force including orderly recruitment of motor units were relatively invariant of the particular strategy or oscillation level employed. A critically damped second order model with corner frequency near 2 Hz and a pure time delay best described the relationship between input stimulation and output isometric force. The frequency response models for load-moving muscles consisted of an overall gain which is a function of mass, dependent mostly on the width of the length-force relation at a given load (force), and a frequency-dependent gain component independent of load mass. The phase lag between input and output was also independent of load. Muscle function and architecture are the primary determinants of its isometric force frequency response. Tendon viscoelasticity (excluding the aponeurosis) has no significant effect on isometric force dynamic response, but does have a minor effect on load-moving dynamic response. The effect of tendon in reducing or augmenting the load-moving muscle response bandwidth is muscle-dependent. The joint produces decreased high frequency gain and uniformly increased phase lags between input excitation and output force in isometric conditions. The joint acts as a lag network in load-moving conditions, increasing the phase lag without significant effect on the gain. Despite its inherent non-linear properties, the joint does not significantly deteriorate output signal quality in either isometric or load-moving conditions. Co-contraction strategy has a significant effect on the dynamic response of the joint. These frequency-based models have shown to be robust as long as the excitation type and mechanical conditions under which they are obtained are not varied. They are particularly useful for the design of neuroprostheses, where a dynamic description of muscle output as a function of stimulus input under given conditions is desirable.

The influence of antagonist muscle control strategies on the isometric frequency response of the cat's ankle joint

This study investigated the effect of various strategies to control the interaction between agonist and antagonist muscles on the frequency response of the isometric cat ankle joint actuated by the tibialis anterior (TA) and soleus (SOL) muscles. Some strategies were based on the physiologic need for increasing joint stability during forceful contractions; with these strategies, the proportional rate of physiologic antagonist activity was termed antagonist gain. Other strategies were based on the electrical stimulation literature, which advocates co-contraction at low force levels. The range of crossover of antagonist activity to the agonist's domain was termed overlap. Strategies consisting of 0%, 10%, and 20% antagonist gain were combined with 0%, 50%, and 100% overlap for a total of nine strategies. These were applied to the TA and SOL using sinusoidal input signals varying in frequency from 0.4 to 6 Hz. Gain and phase Bode plots were constructed through the use of the fast Fourier transforms (FFT's); and analysis of variance determined the significance of differences in gain and phase across frequencies. Best-fit models consisting of four poles and two zeroes were used to fit the experimental data and compared against an analytical model of muscles acting independently across the joint. Harmonic distortion was calculated to evaluate signal quality. It was found that changing the overlap and the antagonist gain produces significant changes in the dynamic response of the two-muscle joint system. The analytical approach to modeling such a system tends to consistently overestimate gain. It is suggested that signal quality is optimal when a moderate amount of antagonist gain (10%) is engaged, with overlap of 50% to smooth transitions between opposing movements. It is expected that this type of strategy will achieve optimum signal quality while preserving the long-term integrity of the joint.