Modeling Needle Stimulation of Denervated Muscle Fibers: Voltage–Distance Relations and Fiber Polarization Effects

A finite-element model of the human thigh was coupled with a 1-D compartment model to simulate the excitation of denervated muscle fibers with a needle electrode. For short electrode–fiber distances, the specific characteristics of the needle geometry determined the areas of lowest threshold values. With increasing distance, these areas shifted toward the needle's center of charge. Comparison of the 1-D model with a 3-D fiber model showed that the assumption of rotational symmetry underlying the 1-D model leads to an overestimation of thresholds. For a 40- $\mu$m-diameter fiber stimulated with 50 $\mu$s pulses at electrode–fiber distances between 50 $\mu$m and 1 mm, the 1-D/3-D threshold ratios were between 1.14 and 1.35 for the muscle fiber model, and between 1.11 and 1.17 for Hodgkin–Huxley membrane properties at 20 $^{\circ}$C. For both membrane models, the deviation was more pronounced for large fiber diameters and short stimulation pulses. Qualitative results of the 1-D model like voltage–distance relations and predictions of spike initiation sites were correct.