VOLUME CONDUCTED CURRENTS AND POTENTIALS FROM EXCITABLE CELLS OF CYLINDRICAL GEOMETRY (NERVE FIBERS, SKELETAL MUSCLE)
Doctor of Philosophy thesis
The dissertation deals with the evaluation of currents and potentials from a variety of excitable cells of cylindrical geometry. Specifically, the cells considered are the unmyelinated and myelinated nerve fibers and the active skeletal muscle. The electrical behavior of these cylindrical cells is modeled in terms of a distributed parameter network resulting in a parabolic partial differential equation describing the propagation of electrical activity along the cell. The partial differential equation is numerically integrated using an implicit, finite difference technique, the Crank-Nicholson method. The immediate environment of the cell is characterized by an electromagnetic field theory model, the result of solving Laplace's equation in the medium around the cell. The field theory model is treated as an equivalent filtering problem, the one and two dimensional Fourier transforms being used to perform the resulting linear convolution. Conduction under normal and diseased states is investigated for the myelinated nerve fiber, and attempts are also made to simulate complex motor unit action potentials from motor units consisting of several individual skeletal muscle fibers. Although the core conductor model is found to be a fairly inaccurate representation of events in the extracellular medium except in cases where the volume conductor is extremely small in extent, it is a very good representation of electrical events occurring in the intracellular medium. It is possible to reconstruct the extracellular currents and potentials of the myelinated nerve fiber as functions of time using a simple and efficient filter theory approach. The resulting currents and potential waveforms correspond well with experimental values in literature. The results of the simulation indicate that electrode separation and placement are critical factors when such measurements are made. Decreasing the extent of volume conductor makes these factors less critical. The model is also shown useful in the prediction of surface electromyographic (EMG) waveforms due to the activity of bioelectric sources lying within the anisotropic muscle medium that comprises the volume conductor.