Submyelin potassium accumulation may functionally block subsets of local axons during deep brain stimulation: a modeling study

Deep brain stimulation has been used for over a decade to relieve the symptoms of Parkinson's disease, although its mechanism of action remains poorly understood. To better understand the direct effects of DBS on central neurons, a computational model of a myelinated axon has been constructed which includes the effects of K+ accumulation within the peri-axonal space. Using best estimates of anatomic and electrogenic model parameters for ill vivo STN axons, the model predicts a functional block along the axon due to K+ accumulation in the submyelin space. The functional block occurs for a range of model parameters: high stimulation frequencies (> 130 Hz); high extracellular K+ concentrations (> 3 x 10(-3) M); low maximum Na+/K+ ATPase current densities (< 0.026 A m(-2)); low diffusion coefficients for K+ diffusion out of the submyelin space (< 2.4 x 10(-9) m(2) s(-1)); small periaxonal space widths of the myelin attachment sections (< 2.7 x 10(-9) m) and perinodal/internodal sections (< 8.4 x 10(-9) m). These results suggest that therapeutic DBS of the STN likely results in a functional block for many STN axons, although a subset of STN axons may also be activated at the stimulating frequency.