A computer model to predict strength-duration curve parameters from measured data

Tarek Z Elabbady, Purdue University

Abstract

The threshold strength for an electric or magnetic (electrodeless) stimulus is related to its duration by the strength-duration (s-d) curve. Two common mathematical expressions are used to describe the s-d curve; the first is exponential in form while the second is hyperbolic in form. Classically, the rectangular pulse has been used to determine strength-duration curves. However, recent applications have required the use of more complex waveforms, and the ability of these s-d curves to adequately describe tissue response to more complex waveforms has been questioned. Single-axon and single-cell models, first introduced by Hodgkin and Huxley (1952), were used in several computer models to simulate the process of tissue excitation. The single-cell models contain parameters empirically derived from voltage-clamped measurements on single-cells. It may be inappropriate to use the parameters derived from single-cells to model excitation in more complex geometry tissue. These observations have caused us to re-examine the classical view of stimulation, and in particular, to appreciate the need for a more sophisticated framework in which to interpret results. Our goal is to simplify the existing models based on single-cell and single-axon responses and use it to extend the s-d model in its exponential form to enable prediction of the s-d curve for non-rectangular stimuli. Our new model is called "The Extended and Simplified Non-Linear (ESN) model for tissue stimulation". The ESN model contains parameters, analogous to those forming the basis of the single-cell and single-axon models, but differs from the existing models in that the value of key parameters are calculated directly from data measured in complex vital systems. In a subsequent effort we adapt the parameters extracted from the experimental data to build a computer program to predict thresholds for complex stimulus waveforms. A view of the proposed model can be divided in two sections, the first is a backward direction one in which values for the parameters are extracted from measured data. The second part of the model is a forward direction model, in which the parameters from the first part have been adapted in a special formulation to be used in predicting stimulation thresholds for complex waveforms.

Degree

Ph.D.

Advisors

Nyenhuis, Purdue University.

Subject Area

Electrical engineering

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