Stabilization of Weakly Unstable Fixed Points as a Common Dynamical Mechanism of High-Frequency Electrical Stimulation

Dan Wilson

doi:10.1038/s41598-020-62839-6

Abstract

While high-frequency electrical stimulation often used to treat various biological diseases, it is generally difficult to understand its dynamical mechanisms of action. In this work, high-frequency electrical stimulation is considered in the context of neurological and cardiological systems. Despite inherent differences between these systems, results from both theory and computational modeling suggest identical dynamical mechanisms responsible for desirable qualitative changes in behavior in response to high-frequency stimuli. Specifically, desynchronization observed in a population of periodically firing neurons and reversible conduction block that occurs in cardiomyocytes both result from bifurcations engendered by stimulation that modifies the stability of unstable fixed points. Using a reduced order phase-amplitude modeling framework, this phenomenon is described in detail from a theoretical perspective. Results are consistent with and provide additional insight for previously published experimental observations. Also, it is found that sinusoidal input is energy-optimal for modifying the stability of weakly unstable fixed points using periodic stimulation.

Highlights

IntroductionThe mechanisms underlying the observed response to HFES are usually reasonably well understood
From a physiological perspective, the mechanisms underlying the observed response to HFES are usually reasonably well understood
Emerging evidence suggests that HFES could be used as an intervention for cardiac arrest[10,11,12] and could be used to develop new strategies for pain management[8,9]

Summary

Introduction

The mechanisms underlying the observed response to HFES are usually reasonably well understood. Theoretical analysis and supporting computational simulations suggest that the influence of HFES in various applications can be characterized by a common dynamical mechanism. In different high-dimensional computational models describing cardiological and neurological electrophysiology, high-frequency stimulation is found to induce qualitative changes in the stability of fixed points with linearizations that have near-zero principle eigenvalues. In the results to follow, the ability of periodic, charge-balanced electrical stimulation to stabilize a weakly unstable fixed point, thereby engendering changes in the qualitative dynamical behavior is investigated. Computational simulations and subsequent theoretical analysis provides evidence that desynchronization in a large population of neural oscillators and repolarization block in individual cardiomyocites in response to high-frequency stimulation may be governed by the stabilization of underlying unstable fixed points. This work suggests a novel dynamical mechanism that is consistent across a wide variety of applications under which HFES operates; this framework could be used to develop new treatments that incorporate HFES

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Conclusion