Calculation of spatially filtered signals produced by a motor unit comprising muscle fibres with non-uniform propagation

Simulation of actual muscle potentials is necessary to understand processes that underlie changes in electromyographic signals. The work reported aims to analyse existing methods and suggest new ways of calculating precisely the signals (MUS) detected by a multielectrode from motor units (MUs) consisting of homogeneous or inhomogeneous (functionally and geometrically) fibres. Simulation (based on cable equations) of intracellular action potential (IAP) in a muscle fibre with a moderate geometrical inhomogeneity demonstrates that considerable changes in propagation velocity (more than 3.5 times) are accompanied by insignificant changes in the IAP amplitude (< 5%) and IAP shape in the temporal domain. MUS can therefore be considered as the output signal of a timeshift-invariant system whose input signal is the first temporal derivative of the IAP. As a result, calculation of MUS is reduced to a single convolution in the case of muscle composed of both homogeneous and inhomogeneous fibres. The suggested approach is valid for simulation of recordings obtained with points or rectangular plates leading off surfaces from muscles consisting of fibres that are parallel or inclined to the skin surface. The MUS terminal phases are prolonged because of fibre inhomogeneities. The presence of geometrical inhomogeneities results in additional positive-negative phases in MUS.