Simulation and Modeling of Nerve Impulse Propagation and Its Blockage by External Electrical Stimulation

The electric nature of biological tissues permits the transmission of signals for information and for control and is, therefore, of vital importance for life. The latest scientific achievements and nanoscale probing techniques now allow scientists to research at the subcellular level by measuring the electric current flows through a single ion channel of the cell membrane with the patch-clamp method. With the latter approach, the effects of electrical stimulation can be quantified, understood, and applied to molecular biology and the development of medical diagnostic and therapeutic methods. In this thesis, the Hodgkin-Huxley approach for unmyelinated fibers, coupled with a transmission line model, is used to analyze electrical signal transmission in nerve cells. An implicit method that is numerically stable is applied for solving the nonlinear one-dimensional equations. Our model successfully explains many important features of propagation of nerve impulse, such as voltage gating of ion channels and the generation of action potentials. Furthermore, the nerve responses to external electrical stimulation models are simulated. The study includes the impact of axonal diameter variability on the conduction velocity. An effort is also made to analyze the possibility of blocking nerve signaling by employing uniphasic and biphasic currents. For completeness, the inter dependency of axonal diameter on the threshold current required for blocking and the frequency of the impulse is also analyzed. The application of high frequency blocking signals alleviates some of the problems with DC biasing such as the "self-launch" of an action potential. Nerve blocking in this manner could bring about incapacitation, or stimulate functional neuromuscular activity for muscular therapy, or even possibly act as a localized "electrical pain reliever."