Simulation Study of Intermittent Axonal Block and Desynchronization Effect Induced by High-Frequency Stimulation of Electrical Pulses

Deep brain stimulation (DBS) has been successfully used in treating neural disorders in brain, such as Parkinson’s disease and epilepsy. However, the precise mechanisms of DBS remain unclear. Regular DBS therapy utilizes high-frequency stimulation (HFS) of electrical pulses. Among all of neuronal elements, axons are mostly inclined to be activated by electrical pulses. Therefore, the response of axons may play an important role in DBS treatment. To study the axonal responses during HFS, we developed a computational model of myelinated axon to simulate sequences of action potentials generated in single and multiple axons (an axon bundle) by stimulations. The stimulations are applied extracellularly by a point source of current pulses with a frequency of 50–200 Hz. Additionally, our model takes into account the accumulation of potassium ions in the peri-axonal spaces. Results show that the increase of extracellular potassium generates intermittent depolarization block in the axons during HFS. Under the state of alternate block and recovery, axons fire action potentials at a rate far lower than the frequency of stimulation pulses. In addition, the degree of axonal block is highly related to the distance between the axons and the stimulation point. The differences in the degree of block for individual axons in a bundle result in desynchronized firing among the axons. Stimulations with higher frequency and/or greater intensity can induce axonal block faster and increase the desynchronization effect on axonal firing. Presumably, the desynchronized axonal activity induced by HFS could generate asynchronous activity in the population of target neurons downstream thereby suppressing over-synchronized firing of neurons in pathological conditions. The desynchronization effect generated by intermittent activation of axons may be crucial for DBS therapy. The present study provides new insights into the mechanisms of DBS, which is significant for advancing the application of DBS

A fast algorithm for optimally finding partially disjoint shortest paths

The classical disjoint shortest path problem has recently recalled interests from researchers in the network planning and optimization community. However, the requirement of the shortest paths being completely vertex or edge disjoint might be too restrictive and demands much more resources in a network. Partially disjoint shortest paths, in which a bounded number of shared vertices or edges is allowed, balance between degree of disjointness and occupied network resources. In this paper, we consider the problem of finding k shortest paths which are edge disjoint but partially vertex disjoint. For a pair of distinct vertices in a network graph, the problem aims to optimally find k edge disjoint shortest paths among which at most a bounded number of vertices are shared by at least two paths. In particular, we present novel techniques for exactly solving the problem with a runtime that significantly improves the current best result. The proposed algorithm is also validated by computer experiments on both synthetic and real networks which demonstrate its superior efficiency of up to three orders of magnitude faster than the state of the art

Novel Stimulation Paradigms with Temporally-Varying Parameters to Reduce Synchronous Activity at the Onset of High Frequency Stimulation in Rat Hippocampus

Deep brain stimulation (DBS) has shown wide applications for treating various disorders in the central nervous system by using high frequency stimulation (HFS) sequences of electrical pulses. However, upon the onset of HFS sequences, the narrow pulses could induce synchronous firing of action potentials among large populations of neurons and cause a transient phase of “onset response” that is different from the subsequent steady state. To investigate the transient onset phase, the antidromically-evoked population spikes (APS) were used as an electrophysiological marker to evaluate the synchronous neuronal reactions to axonal HFS in the hippocampal CA1 region of anesthetized rats. New stimulation paradigms with time-varying intensity and frequency were developed to suppress the “onset responses”. Results show that HFS paradigms with ramp-up intensity at the onset phase could suppress large APS potentials. In addition, an intensity ramp with a slower ramp-up rate or with a higher pulse frequency had greater suppression on APS amplitudes. Therefore, to reach a desired pulse intensity rapidly, a stimulation paradigm combining elevated frequency and ramp-up intensity was used to shorten the transition phase of initial HFS without evoking large APS potentials. The results of the study provide important clues for certain transient side effects of DBS and for development of new adaptive stimulation paradigms