Figure 1.

(A) The electric potential and second derivative plotted along an axon passing tangentially to the electrode. Action potentials initiate at points of sufficiently positive second derivatives: the center node closest to the electrode for cathodic stimulation and the distal nodes away from the electrode for anodic stimulation. (B) The finite element method (FEM) model consists of a tetrahedral mesh around a Medtronic 3389 lead. The Hessian was calculated on a 20 × 20 × 20mm grid with a resolution of 0.1 mm around the lead. (C) Normalized Hessian matrices visualized as 3D tensors on a subgrid given contact 1 as a cathode. Each tensor is composed of eigenvalues and eigenvectors, which represent second derivatives along principal neuron orientations. (D) A spherical coordinate system is used to describe fiber orientations throughout the paper. Orientations can be categorized into longitudinal, latitudinal, and orthogonal directions with respect to the electrode. (E) A modified neuron model was used in this paper in order to isolate firing at the location of the Hessian tensor. The active neuron is an MRG axon, and the modified neuron is an MRG axon with all compartments being passive except the center compartment.