On the power spectrum of motor unit action potential trains synchronized with mechanical vibration

This study provides a definitive analysis of the spectrum of a motor unit action potential train (MUAPT) elicited by mechanical vibratory stimulation via a detailed and concise mathematical formulation. Experimental studies demonstrated that MUAPs are not exactly synchronized with the vibratory stimulus but show a variable latency jitter, whose effects have not been investigated yet. Synchronized action potential train was represented as a quasi-periodic sequence of a given MU waveform. The latency jitter of action potentials was modeled as a Gaussian stochastic process, in accordance to the previous experimental studies. A mathematical expression for power spectrum of a synchronized MUAPT has been derived. The spectrum comprises a significant continuous component and discrete components at the vibratory frequency and its harmonics. Their relevance is correlated to the level of synchronization: the weaker the synchronization the more relevant is the continuous spectrum. Electromyography (EMG) rectification enhances the discrete components. The derived equations have general validity and well describe the power spectrum of actual EMG recordings during vibratory stimulation. Results are obtained by appropriately setting the level of synchronization and vibration frequency. This paper definitively clarifies the nature of changes in spectrum of raw EMG recordings from muscles undergoing vibratory stimulation. Results confirm the need of motion artifact filtering for raw EMG recordings during stimulation and strongly suggest to avoid EMG rectification that significantly alters the spectrum characteristics.