Compact Nonlinear Model of an Implantable Electrode Array for Spinal Cord Stimulation (SCS)

We describe the construction of a model of the electrode-electrolyte interface and surrounding electrolyte in the case of a platinum-electrode array intended for spinal-cord stimulation (SCS) application. We show that a finite, two-dimensional, resistor array provides a satisfactory model of the bulk electrolyte, and we identify the complexity required of that resistor array. The electrode-electrolyte interface is modelled in a fashion suitable for commonly-available, compact simulators using a nonlinear extension of the model of Franks et al. (IEEE Trans. Biomed. Eng., vol. 52, no. 7, pp. 1295-1302, Jul. 2005) that incorporates diodes and a memristor. The electrode-electrolyte interface model accounts for the nonlinear current-overpotential characteristic and diffusion-limiting effects. We characterise a commercial, implantable, electrode array, fit themodel to it, and show that the model successfully predicts subtle operational characteristics.