Theoretical Effect of DBS on Axonal Fibers of Passage: Firing Rates, Entropy, and Information Content

Abstract

Background: Deep brain stimulation (DBS) has effects on axons that originate and terminate outside the DBS target area.

Objective: We hypothesized that DBS generates action potentials (APs) in both directions in "axons of passage," altering their information content and that of all downstream cells and circuits, and sought to quantify the change in fiber information content.

Methods: We incorporated DBS parameters (fiber firing frequency and refractory time, and AP initiation location along the fiber and propagation velocity) in a filtering function determining the AP frequency reaching the postsynaptic cell. Using neural circuitry simulation software, we investigated the ability of the filtering function to predict the firing frequency of APs reaching neurons targeted by axons of passage. We calculated their entropy with and without DBS, and with the electrode applied at various distances from the cell body.

Results: The predictability of the filtering function exceeded 98%. Entropy calculations showed that the entropy ratio "without DBS" to "with DBS" was always >1.0, thus DBS reduces fiber entropy.

Conclusions: (1) The results imply that DBS effects are due to entropy reduction within fibers, i.e., a reduction in their information. (2) Where fibers of passage do not terminate in target regions, DBS may have side effects on nontargeted circuitry.

Keywords: Axons; Deep brain stimulation; Entropy; Fibers of passage; Information capacity; Mechanism; Simulation; Volume of tissue activated.