Analytical Modelling of Surface EMG Signals Generated by Curvilinear Fibers With Approximate Conductivity Tensor

Mathematical modelling of surface electromyographic (EMG) signals has been proven a valuable tool to interpret experimental data and to validate signal processing techniques. Most analytical EMG models only consider muscle fibers with specific arrangements. However, the fiber orientation may change along the fiber paths and differ from fiber to fiber. Here we propose a subject-specific EMG model that simulates the fiber trajectories in muscles of the upper arm and analytically derives the action potentials assuming an approximate conductivity tensor.

Magnetic Resonance (MR) images were acquired to generate muscle fiber paths and to build the volume conductor. While the action potentials propagated along the identified curvilinear fibers, the conductivity tensor was approximated to be cylindrically anisotropic. Single fiber action potentials (SFAPs) were computed by simulating the generation, propagation, and extinction of membrane current sources. To validate the assumption of the approximate conductivity tensor, two numerical models with approximate or exact conductivity tensors were implemented.

The motor unit action potentials generated by the proposed analytical model and the two numerical models were highly similar (cross-correlation 0.98, normalized root mean square error, nRMSE ≤ 0.04, relative error in the median frequency of the simulated waveforms of approximately 3%). The proposed analytical model was also evaluated by comparing simulated and experimentally recorded compound muscle action potentials (CMAPs). Finally, the proposed model was used to test the accuracy of an EMG decomposition algorithm, providing a realistic benchmark.

The proposed analytical model generates action potentials that reflect the spatial distributions of muscle fibers with curvilinear paths.