Prediction of Force Recruitment of Neuromuscular Magnetic Stimulation From 3D Field Model of the Thigh

Neuromuscular magnetic stimulation is a promising tool in neurorehabilitation due to its deeper penetration, notably lower distress, and respectable force levels compared to surface electrical stimulation. However, this method faces great challenges from a technological perspective. The systematic design of better equipment and the incorporation into modern training setups requires better understanding of the mechanisms and predictive quantitative models of the recruited forces. This article proposes a model for simulating the force recruitment in isometric muscle stimulation of the thigh extensors based on previous theoretical and experimental findings. The model couples a 3D field model for the physics with a parametric recruitment model. This parametric recruitment model is identified with a mixed-effects design to learn the most likely model based on available experimental data with a wide range of field conditions. This approach intentionally keeps the model as mathematically simple and statistically parsimonious as possible in order to avoid over-fitting. The work demonstrates that the force recruitment particularly depends on the effective, i.e., fiber-related cross section of the muscles, and that the local median electric field threshold amounts to about 65 V/m, which agrees well with values for magnetic stimulation in the brain. The coupled model is able to accurately predict key phenomena observed so far, such as a threshold shift for different distances between coil and body, the different recruiting performance of various coils with available measurement data in the literature, and the saturation behavior with its onset amplitude. The presented recruitment model could also be readily incorporated into dynamic models for biomechanics as soon as sufficient experimental data are available for calibration.