Revisiting convolutive blind source separation for identifying spiking motor neuron activity: From theory to practice.

Objective: Identifying the spiking activity of alpha motor neurons (MNs) non-invasively is possible by decomposing signals from active muscles, e.g., obtained with surface electromyography (EMG) or ultrasound. The theoretical background of MN identification using these techniques is convolutive blind source separation (cBSS), in which different algorithms have been developed and validated. However, the existence and identifiability of inverse solutions and the corresponding estimation errors are not fully understood. In addition, the guidelines for selecting appropriate parameters are often built on empirical observations, limiting the translation to clinical applications and other modalities. Approach: We revisited the cBSS model for EMG-based MN identification, augmented it with new theoretical insights and derived a framework that can predict the existence of solutions for spike train estimates. This framework allows the quantification of source estimation errors due to the imperfect inversion of the motor unit action potentials (MUAP), physiological and non-physiological noise, and the ill-conditioning of the inverse problem. To bridge the gap between theory and practice, we used computer simulations. Main results: (1) Increasing the similarity of MUAPs or the correlation between spike trains increases the bias for detecting MN spike trains linked with high amplitude MUAPs. (2) The optimal objective function depends on the expected spike amplitude, spike amplitude statistics and the amplitude of background spikes. (3) There is some wiggle room for MN detection given non-stationary MUAPs. (4) There is no connection between MUAP duration and extension factor, in contrast to previous guidelines. (5) Source quality metrics like the silhouette score (SIL) or the pulse-to-noise ratio (PNR) are highly correlated with a source's objective function output. (6) Considering established source quality measures, SIL is superior to PNR. Significance: We expect these findings will guide cBSS algorithm developments tailored for MN identification and translation to clinical applications.