Relationship between Neural Activation and Electric Field Distribution during Deep Brain Stimulation

Models and simulations are commonly used to study deep brain stimulation (DBS). Simulated stimulation fields are often defined and visualized by electric field isolevels or volumes of tissue activated (VTA). The aim of the present study was to evaluate the relationship between stimulation field strength as defined by the electric potential V, the electric field E, and the divergence of the electric field ∇(2) V, and neural activation. Axon cable models were developed and coupled to finite-element DBS models in three-dimensional (3-D). Field thresholds ( VT , ET, and ∇(2) VT ) were derived at the location of activation for various stimulation amplitudes (1 to 5 V), pulse widths (30 to 120 μs), and axon diameters (2.0 to 7.5 μm). Results showed that thresholds for VT and ∇(2) VT were highly dependent on the stimulation amplitude while ET were approximately independent of the amplitude for large axons. The activation field strength thresholds presented in this study may be used in future studies to approximate the VTA during model-based investigations of DBS without the need of computational axon models.