{"title":"The Impact of High-Frequency-Based Stability on the Onset of Action Potentials in Neuron Models","authors":"Eduardo Cerpa, Nathaly Corrales, Matías Courdurier, Leonel E. Medina, Esteban Paduro","doi":"10.1137/24m1645632","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1910-1936, October 2024. <br/> Abstract. This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach analyzes the transient behavior of an averaged system corresponding to the FitzHugh–Nagumo neuron model using Lyapunov and quasi-static methods. The first result provides a more comprehensive understanding of the onset activation through a mathematical proof of how to avoid it using a ramp in the amplitude of the oscillatory source. The second result tests the response of the blocked system to a piecewise linear stimulus, providing a quantitative description of how the HFBS strength translates into conduction block robustness. The results of this work can provide insights for the design of electrical neurostimulation therapies.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/24m1645632","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
SIAM Journal on Applied Mathematics, Volume 84, Issue 5, Page 1910-1936, October 2024. Abstract. This paper studies the phenomenon of conduction block in model neurons using high-frequency biphasic stimulation (HFBS). The focus is investigating the triggering of undesired onset action potentials when the HFBS is turned on. The approach analyzes the transient behavior of an averaged system corresponding to the FitzHugh–Nagumo neuron model using Lyapunov and quasi-static methods. The first result provides a more comprehensive understanding of the onset activation through a mathematical proof of how to avoid it using a ramp in the amplitude of the oscillatory source. The second result tests the response of the blocked system to a piecewise linear stimulus, providing a quantitative description of how the HFBS strength translates into conduction block robustness. The results of this work can provide insights for the design of electrical neurostimulation therapies.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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