A Static Distributed-parameter Circuit Model Explains Electrical Stimulation on the Neuromuscular System

Abstract: Finite Element Modeling (FEM) has been widely used to model the electric field distribution, to study the interaction between stimulation electrodes and neural tissue. However, due to the insufficient computational capability to represent neural tissue down to an atom-level, the existing FEM fails to model the real electric field that is perpendicular to neuron membrane to initiate an action potential. Thus, to reveal the real electrode-tissue interactions, we developed a circuit to model transmembrane voltage waveforms. Here, we show a distributed-parameter circuit model to systematically study how electrode-tissue interaction is affected by electrode position, input current waveform, and biological structures in the neuromuscular system. Our model explains and predicts various phenomena in neuromuscular stimulation, guides new stimulation electrode and method design, and more importantly, facilitates a fundamental understanding of the physical process during electrode-tissue interaction. In our model, myelin is assumed to be inductive. The voltage waveform resonance caused by this inductive myelin accounts for the much lower stimulation threshold to activate motoneurons than muscle fibers, which is observed with in vivo measurements. These findings confirmed the feasibility of studying electrode-tissue interaction using a proper distributed-parameter circuit. Our current application on the neuromuscular system also raises the possibility that this distributed-parameter circuit model could potentially be applied to study other neural tissues, including the Peripheral Nervous System (PNS) and the Central Nervous System (CNS).