神经元模型中基于高频的稳定性对动作电位发生的影响

IF 1.9 4区 数学 Q1 MATHEMATICS, APPLIED
Eduardo Cerpa, Nathaly Corrales, Matías Courdurier, Leonel E. Medina, Esteban Paduro
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引用次数: 0

摘要

SIAM 应用数学杂志》,第 84 卷第 5 期,第 1910-1936 页,2024 年 10 月。 摘要本文利用高频双相刺激(HFBS)研究了模型神经元的传导阻滞现象。重点研究高频双相刺激开启时引发的非预期起始动作电位。该方法使用 Lyapunov 和准静态方法分析了与 FitzHugh-Nagumo 神经元模型相对应的平均系统的瞬态行为。第一个结果通过数学证明了如何利用振荡源振幅的斜坡来避免起始激活,从而更全面地理解了起始激活。第二项结果测试了阻滞系统对片线性刺激的响应,提供了高频振荡源强度如何转化为传导阻滞鲁棒性的定量描述。这项工作的结果可为神经电刺激疗法的设计提供启示。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Impact of High-Frequency-Based Stability on the Onset of Action Potentials in Neuron Models
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.
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来源期刊
CiteScore
3.60
自引率
0.00%
发文量
79
审稿时长
12 months
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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