A numerically stable model for simulating high frequency conduction block in nerve fiber

Abstract

Previous studies performed on myelinated nerve fibers have shown that a high frequency alternating current stimulus can block impulse conduction. The current threshold at which block occurs increases as the blocking frequency increases. Cable models based on the Hodgkin-Huxley model are consistent with these results.

Recent experimental studies on unmyelinated nerve have shown that at higher frequencies, the block threshold decreases. When the block threshold is plotted as a function of frequency the resulting graph is distinctly nonmonotonic. Currently, all published models do not explain this behavior and the physiological mechanisms that create it are unknown. This difference in myelinated vs. unmyelinated block thresholds at high frequencies could have numerous clinical applications, such as chronic pain management.

A large body of literature has shown that the specific capacitance of biological tissue decreases at frequencies in the kHz range or higher. Prior research has shown that introducing a frequency-dependent capacitance (FDC) to the Hodgkin-Huxley model will attenuate the block threshold at higher frequencies, but not to the extent that was seen in the experiments. This model was limited by the methods used to solve its higher order partial differential equation. The purpose of this thesis project is to develop a numerically stable method of incorporating the FDC into the model and to examine its effect on block threshold. The final, modified model will also be compared to the original model to ensure that the fundamental characteristics of action potential propagation remain unchanged.