Mathematical analysis of a muscle architecture model

A computational method for the detection of activation/deactivation patterns in biological signals with three levels of electric intensity

In the present work, we develop a computational technique to approximate the changes of phase in temporal series associated to electric signals of muscles which perform activities at three different levels of intensity. We suppose that the temporal series are samples of independent, normally distributed random variables with mean equal to zero, and variance equal to one of three possible values, each of them associated to a certain degree of electric intensity. For example, these intensity levels may represent a leg muscle at rest, or active during a light activity (walking), or active during a highly demanding performance (jogging). The model is presented as a maximum likelihood problem involving discrete variables. In turn, this problem is transformed into a continuous one via the introduction of continuous variables with penalization parameters, and it is solved recursively through an iterative numerical method. An a posteriori treatment of the results is used in order to avoid the detection of relatively short periods of silence or activity. We perform simulations with synthetic data in order to assess the validity of our technique. Our computational results show that the method approximates well the occurrence of the change points in synthetic temporal series, even in the presence of autocorrelated sequences. In the way, we show that a generalization of a computational technique for the change-point detection of electric signals with two phases of activity (Esquivel-Frausto et al., 2010 [40]), may be inapplicable in cases of temporal series with three levels of intensity. In this sense, the method proposed in the present manuscript improves previous efforts of the authors.

Evaluation of motor unit placement algorithms for EMG simulation

Motor unit layout algorithms have a significant effect on motor unit fibre densities recorded. Motor unit fibre densities are affected by both the method used to place the motor unit territories, and the mechanism by which muscle fibres are assigned to motor units. The first of these should emulate the process by which separate motor neurons create overlapping territories that cover the muscle cross section, while the second should have some relation to the processes involved with axonal arborization and development of the spatial dispersion of the neuro-muscular junctions. The success of an algorithm in creating physiologically realistic motor unit layouts may be evaluated, in part, by examining the distribution of the muscle fibres assigned to the motor units. This paper examines the motor unit fibre densities found in muscles created by two recent algorithms, and explores the degree to which the concepts used by these algorithms may be shared.

Multiplicative multi-fractal modeling of electromyography signals for discerning neuropathic conditions

In this paper, we present a new method for multi-scale analysis of electromyography signals based on an interesting fractal process known as multiplicative cascade multi-fractal. Using simulated needle electromyography signals, we show this method provides a means for discrimination of normal and neuropathic electromyography signals. We also present experimental results that show the new parameters, computed using multiplicative cascade multi-fractal modeling, are more robust than the conventional signal parameter, number of turns, in the presence of additive noise. Results of multiplicative cascade multi-fractal modeling are consistent with other multi-scale approaches; advantages and differences are high lighted.

A muscle architecture model offering control over motor unit fiber density distributions

The aim of this study was to develop a muscle architecture model able to account for the observed distributions of innervation ratios and fiber densities of different types of motor units in a muscle. A model algorithm is proposed and mathematically analyzed in order to obtain an inverse procedure that allows, by modification of input parameters, control over the output distributions of motor unit fiber densities. The model's performance was tested with independent data from a glycogen depletion study of the medial gastrocnemius of the rat. Results show that the model accurately reproduces the observed physiological distributions of innervation ratios and fiber densities and their relationships. The reliability and accuracy of the new muscle architecture model developed here can provide more accurate models for the simulation of different electromyographic signals.

Activity pattern detection in electroneurographic and electromyogram signals through a heteroscedastic change-point method

In this work, we propose a heteroscedastic method in the detection of activity patterns of electroneurographic and electromyogram signals involved in rhythmic activities of nerves and muscles, respectively. The electric behavior observed in such signals is characterized by phases of activity and silence. The beginning and the length of electrically active and electrically silent phases in a signal allow us to quantitatively analyze the changes and the effects on a rhythmic activity produced by experimental changes. In order to distinguish between these two phases, signals are assumed to be a sample of a time-dependent, normally distributed random variable with non-constant variance, and that the determination of the variance at each point allows us to determine in which phase is the signal. The parameters of the model are determined by means of an iterative process which maximizes the log-likelihood under the proposed model. Moreover, we apply our method to the determination of the activity phases and silence phases in sequences of experimental and synthetic electroneurographic and electromyogram signals. The results obtained with synthetic data show that the method performs well in the determination of these activity patterns. Finally, the study of particular signals simulated under a generalized autoregressive conditional heteroscedasticity model suggests the robustness of the method with respect to the assumption of independence.