Precise and fast calculation of the motor unit potentials detected by a point and rectangular plate electrode

To reduce the time of computation of a motor unit potential (MUP), the shape of intracellular action potential (IAP) and (or) MU anatomy are generally simplified. A method of MUP presentation is suggested. It provides accuracy of the MUPs calculated for any distance and size of rectangular electrodes together with considerably reduced computational load and time. No simplification of the IAP shape or location of muscle fibres of different diameters and lengths is required. The MUP generated by N temporally and spatially dispersed single fibre action potentials is considered to be the output signal of a linear time-shift invariant system for potential generation. The input signal is the first temporal derivative of the IAP. The common impulse response (CIR) is the sum of potentials produced at the electrode by N pairs of dipoles propagating from the motor end-plates to the ends of the corresponding fibres. The potentials of each dipole at the rectangular plate electrode are determined analytically. Thus, the MUP is calculated as a single convolution between the input signal and CIR for a rectangular electrode of any size.