FORWARD AND INVERSE MODELS IN ELECTRONEUROLOGY (SPINAL STIMULATION, NEUROGRAPHY, CIRCULAR LIMB, NEUROLOGY, ELECTROPHYSIOLOGY)
WILSON, OWEN BLAKE
Doctor of Philosophy thesis
Understanding the behavior of electric fields in animal tissues is essential to a number of clinical topics, including electric stimulation of nerves or muscles, and sensing of nerve potentials for diagnostic purposes. These applications represent, respectively, the so-called "forward" and "inverse" problems of electroneurology. To date, most modeling efforts in this field have concentrated on situations with simple geometry. This study demonstrates that similar techniques can be developed to describe much more complex physiology. A mathematical model of the forward problem is developed for an idealized long circular limb. The model equations, which predict electric field potentials arising from nerve activity within the limb, are solved analytically and expressed in terms of an equivalent 2-dimensional digital filter. The effects of limb structures are then interpreted in terms of their influence on the filter characteristics. The associated inverse problem consists of estimating Compound Action Potentials (CAPs) on an active nerve using potential measurements taken on the skin, and its solution is obtained by inverting the forward filter. This approach is computationally efficient compared with other numerical techniques traditionally employed in electrophysiology. Conventional signal processing methods give a solution which reduces the effects of measurement noise and minimizes the number of surface potential measurements required. A sensitivity analysis identifies the effects of varying important model parameters. It is shown that the inverse solution is independent of many assumptions in the forward model. The idealizations underlying both forward and inverse models are discussed in light of these results, and some of the initial geometric and electrical modeling restrictions are relaxed. Finally, it is shown that the same forward and inverse modeling technique can be extended to describe electric fields in and around the human spinal cord. Epidural stimulation and sensing of the spinal cord are considered, and the geometric and electrical parameters which most strongly influence these problems are discussed. A favorable comparison is made with the results of an extensive finite element modeling study from the literature.