Mathematical modeling and simulation of motor unit action potencials. / Modelagem matemática e simulação de potenciais de ação de unidades motoras.

AUTOR(ES)
DATA DE PUBLICAÇÃO

2006

RESUMO

This work presents the mathematical model and simulation of motor unit action potentials of vertebrate muscles aiming at after simulation of the electromyogram. To obtain this, initially, it was made a compilation of several data about the distribution of muscle fibers (FBs) in motor units (MUs) of many muscles, and the mathematical models of the action potential of a single FB (SFAP) and MU (MUAP), reported in previous works. On the basis of this physiological data, first, the FB was located in a muscle, using an approximation in which the FBs are encircled with other six FBs in the muscle. To reach this, concentric hexagons were constructed to build the surface of the MU, and later the FBs were situated in the MU, covering a range between 75 and 2000 FBs, corresponding to mammals extremity muscles. Later, a new approximation were was madein order to distribute the 170000 FBs in the 272 MUs of the medial head of muscle medialis gastrocnemius (MG) of the cat, reaching, in a first simulation, the localization of almost 70% of the FBs at each MU. With the FBs lalready allocated in the muscle, and based in data of previous works, their axonal delay were approximated by a gaussian distribution, with mean of 2 ms (cat) or 10 ms (man) and standard deviation of less than 0,5 ms, discarding the axonal delay in the axonal branching, that were estimated to affectup to 29 times less. To SFAP generation, two models were used, the first analytical, resulting in delayed numerical simulations, and the other based on convolution of the second derivate of the current with a weight function, where the length of the FBs was imaginarily duplicated, in order to consider the end fiber effect. Using this, a simulation time 30 times lesser than the analytical one was obtained. Additionally, so as to simulate the external recording (i.e. in the skin), it was made an approximation to the function that models the circular shape surface electrodes located at distances greater than 1,79 mm of the FBs, showing a similar spectrum reported. Finally, the waves and spectrum of the simulated MUAPs resulted similar to the ones reported in the literature. Beyond this, in certain cases, MUAPs were simulated with some tuned, either locating the neuromuscular junctions with thickness bands of 1 mm, or, when the axonal delay and the FB muscle fiber conduction velocity were considered as a function of the square root fiber diameter. This was simulated for MUAPs of MG and biceps brachii muscles of human beings, in the last case it has reached the waveforms and tuned found in heath subjects, and it was visualized the mean frequency of firing rate at the spectrum. In order to know how much affects grouping for the FBs to waves a MU, they were not found significant differences with FBs located homogeneously and randomly, except a little variation in the amplitude of the MUAP. However, they presented a change in the spectral bandwidth when the FBs are more concentrated.

ASSUNTO(S)

unidade motora (mu) motor unit (mu) potencial de ação de unidade motora (muap) muscle fiber (fb) motor unit action potential (muap) fibra muscular (fb)

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