Simulation of surface EMG signals for a multilayer volume conductor with triangular model of the muscle tissue

This study analytically describes surface electromyogram (sEMG) signals generated by a model of a triangular muscle, i.e., a muscle with fibers arranged in a fan shape. Examples of triangular muscles in the human body are the deltoid, the pectoralis major, the trapezius, the adductor pollicis. A model of triangular muscle is proposed. It is a sector of a cylindrical volume conductor (with the fibers directed along the radial coordinate) bounded at the muscle/fat interface. The muscle conductivity tensor reflects the fan anisotropy. Edge effects have been neglected. A solution of the nonspace invariant problem for a triangular muscle is provided in the Fourier domain. An approximate analytical solution for a two plane layer volume conductor model is obtained by introducing a homogeneous layer (modeling the fat) over the triangular muscle. The results are implemented in a complete sEMG generation model (including the finite length of the fibers), simulating single fiber action potentials. The model is not space invariant due to the changes of the volume conductor along the direction of action potential propagation. Thus the detected potentials at the skin surface change shape as they propagate. This determines problems in the extraction and interpretation of parameters. As a representative example of application of the simulation model, the influence of the inhomogeneity of the volume conductor in conduction velocity (CV) estimation is addressed (for two channels; maximum likelihood and reference point methods). Different fiber depths, electrode placements and small misalignments of the detection system with respect to the fiber have been simulated. The error in CV estimation is large when the depth of the fiber increases, when the detection system is not aligned with the fiber and close to the innervation point and to the tendons.