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A partially averaged system to model neuron responses to interferential current stimulation

View ORCID ProfileEduardo Cerpa, View ORCID ProfileMatías Courdurier, View ORCID ProfileEsteban Hernández, View ORCID ProfileLeonel E. Medina, View ORCID ProfileEsteban Paduro
doi: https://doi.org/10.1101/2022.05.23.493095
Eduardo Cerpa
‡Instituto de Ingeniería Matemática y Computacional, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860, Macul, Santiago, Chile
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Matías Courdurier
§Departamento de Matemática, Facultad de Matemáticas, Pontificia Universidad Católica de Chile. Avda. Vicuña Mackenna 4860, Macul, Santiago, Chile
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Esteban Hernández
¶Departamento de Matemáticas, Universidad Técnica Federico Santa María, Avda. España 1680, Valparaíso, Chile
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Leonel E. Medina
‖Departamento de Ingeniería Informática, Universidad de Santiago de Chile, Avda. Víctor Jara 3659, Estación Central, Santiago, Chile
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Esteban Paduro
‡Instituto de Ingeniería Matemática y Computacional, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avda. Vicuña Mackenna 4860, Macul, Santiago, Chile
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  • For correspondence: esteban.paduro@mat.uc.cl
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Abstract

The interferential current (IFC) therapy is a noninvasive electrical neurostimulation technique intended to activate deep neurons using surface electrodes. In IFC, two independent kilohertz-frequency currents purportedly intersect where an interference field is generated. However, the effects of IFC on neurons within and outside the interference field are not completely understood, and it is unclear whether this technique can reliable activate deep target neurons without side effects. In recent years, realistic computational models of IFC have been introduced to quantify the effects of IFC on brain cells, but they are often complex and computationally costly. Here, we introduce a simplified model of IFC based on the FitzHugh-Nagumo (FHN) model of a neuron. By considering a modified averaging method, we obtain a non-autonomous approximated system, with explicit representation of relevant IFC parameters. For this approximated system we determine conditions under which it reliably approximates the complete FHN system under IFC stimulation, and we mathematically prove its ability to predict nonspiking states. In addition, we perform numerical simulations that show that the interference effect is observed only for a narrow set of IFC parameters and, in particular, for a beat frequency no higher than about 100 [Hz]. Our novel model tailored to the IFC technique contributes to the understanding of neurostimulation modalities using this type of signals, and can have implications in the design of noninvasive electrical stimulation therapies.

Competing Interest Statement

The authors have declared no competing interest.

Footnotes

  • * This work has been partially supported by ANID Millennium Science Initiative Program trough Millennium Nucleus for Applied Control and Inverse Problems NCN19-161, Basal Project FB0008 AC3E, and Fondecyt 11190822.

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The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Posted May 24, 2022.
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A partially averaged system to model neuron responses to interferential current stimulation
Eduardo Cerpa, Matías Courdurier, Esteban Hernández, Leonel E. Medina, Esteban Paduro
bioRxiv 2022.05.23.493095; doi: https://doi.org/10.1101/2022.05.23.493095
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A partially averaged system to model neuron responses to interferential current stimulation
Eduardo Cerpa, Matías Courdurier, Esteban Hernández, Leonel E. Medina, Esteban Paduro
bioRxiv 2022.05.23.493095; doi: https://doi.org/10.1101/2022.05.23.493095

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