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

Abstract

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 in 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.