Uncertainty in 1D and 3D Models of a Fiber Stimulated by an External Electrode

Abstract

One-dimensional (1D) cable model is used to study electrical excitation of nerves and muscle fibers, and to aid in the design of electrical therapies. However, approximations inherent in the cable model limit its validity. More realistic three-dimensional (3D) fiber models have been advocated but they require long computational times. This study investigates whether better accuracy of 3D models is worth the cost by computing the probability p that the difference between outputs from 3D and 1D models could have arisen from uncertainties in parameter values. The results are summarized in contour maps of probability p in the space of fiber-electrode distances and stimulus durations. The cable model is considered valid where \(p>0.05\). This region of validity depends on uncertainties in the parameters. In particular, the uncertainties must exceed 0.05 (0.02) of the nominal parameter values for the cable model to be valid in the regions where retinal (cochlear) implants operate.