Nerve Activation Model

A cable model of myelinated axons by McNeal [2] was used for analysis of the electric field from the electrode. An equivalent driving function, as defined by Warmen et al. [3] was used to predict axon excitation. The solution to the cable equation gave the transmembrane potential Vm induced at a node of Ranvier.
Using parameters of the cable based on properties of mammalian myelinated axons [4], threshold current for a 100µsec pulse from a point source was determined. The equivalent driving force DF(i) was calculated for 10 micron and 20 micron diameter axons at nodes of Ranvier in the X-Y plane. DF(i) being independent of fiber diameter and distance from elecrode. An axon was considered to be activated when DF(i) was equal to or greater than threshold.

Activation Contour Plots

A reference point ‘A’ was located midway between the center of the nerve and the center of the cathode (1.25 mm radially from the center). The driving function at point A due to a stimulus of –1 V at the cathode was calculated. The threshold current density was determined to be 4.88 mA/sq. cm.
V thr (A/10µm) was defined to be the threshold voltage stimulus required to activate a 10 µm axon at point A and was calculated by scaling –1 Volt, with the ratio of 4.88 mA/sq.cm. to the driving function DF(i). If the value of the driving function for a 10 µm diameter axon at location ‘A’ was half of threshold with a stimulus of V volts, then a stimulus of 2V volts would be needed to activate the axon.
The threshold stimulus was found to be lowest at nodes of Ranvier in the X-Y plane passing through the center of the cathode. Finite element solutions were found for stimulus of –1 V at the cathode. In the figure, equivalent driving function DF (i) contours for threshold current density of 4.88 mA/sq. cm (J) and for 2.44 mA/sq. cm (2J) are shown for 10 µm and 20 µm axons.
All the axons of a particular diameter are activated in the region between the Jth contour line and the nerve surface towards the electrode. A voltage of twice threshold is required to activate fibers in the region between contour lines 2Jth and the surface of the nerve towards the electrode.

[1] Chintalacharuvu, R., Ksienski, D., & J.T. Mortimer (1991) A numerical analysis of the electric field generated by a nerve cuff electrode. Proc. of the IEEE-Eng. Med. Biol. Soc. 13th Ann. Conf., 13(2), 912-913.
and Chintalacharuvu, Rekha Rani, (1991)“A numerical analysis of the electric field generated by the nerve cuff electrode”, MS Thesis, Dept of Electrical Engineering and Applied Physics, Case Western Reserve University, Cleveland, OH, USA.
[2] McNeal, D.R. (1976) Analysis of a model for excitation of myelinated nerve. IEEE Trans. Biomed. Engg. Vol.23, pp 329 – 337.
[3] Warman, E., Grill, W. & D. Durand (1999) Modeling the effects of electric fields on nerve fibers: Estimation of excitation. IEEE Trans. Biomed. Engg.
[4] Sweeney, J.D., Mortimer, J.T. & D. Durand (1987) Modelling of mammalian myelinated nerves for functional neuromuscular stimulation. Proc. 9th. Ann. Conf. IEEE-EBMS. pp. 1578 – 1579.