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A model for transcutaneous current stimulation: simulations and experiments

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Abstract

Complex nerve models have been developed for describing the generation of action potentials in humans. Such nerve models have primarily been used to model implantable electrical stimulation systems, where the stimulation electrodes are close to the nerve (near-field). To address if these nerve models can also be used to model transcutaneous electrical stimulation (TES) (far-field), we have developed a TES model that comprises a volume conductor and different previously published non-linear nerve models. The volume conductor models the resistive and capacitive properties of electrodes, electrode-skin interface, skin, fat, muscle, and bone. The non-linear nerve models were used to conclude from the potential field within the volume conductor on nerve activation. A comparison of simulated and experimentally measured chronaxie values (a measure for the excitability of nerves) and muscle twitch forces on human volunteers allowed us to conclude that some of the published nerve models can be used in TES models. The presented TES model provides a first step to more extensive model implementations for TES in which e.g., multi-array electrode configurations can be tested.

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Abbreviations

TES:

Transcutaneous electrical stimulation

AP:

Action potential

PD:

Pulse duration

FE:

Finite element

TP:

Transmembrane potential

V FE(t):

Electric scalar potential

σ:

Conductivity

ρ:

Resistivity

ɛr :

Permittivity

V n (t):

Transmembrane potential at node n and time t

V e,n (t):

Extracellular potential at node n and time t

I i,n (t):

Ionic current at node n and time t

C m :

Membrane capacitance

G a :

Conductance of the axoplasm

I rh :

Rheobase

T ch :

Chronaxie

I th :

Threshold current

τsim :

Time constant of simulated recruitment-duration curve

τexp :

Time constant of measured recruitment-duration curve

Rec:

Recruitment

Recsat :

Saturation value of recruitment

g L :

Nodal leakage conductance

\(\varrho_i\) :

Axoplasmatic resistivity

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Acknowledgments

The project was supported by the Swiss National Science Foundation (SNF) No. 205321-107904/1.

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Authors and Affiliations

  1. Automatic Control Laboratory, ETH Zurich, Physikstrasse 3, 8092, Zurich, Switzerland

    Andreas Kuhn, Thierry Keller, Marc Lawrence & Manfred Morari

  2. Sensory-Motor Systems Laboratory, ETH Zurich, 8092, Zurich, Switzerland

    Andreas Kuhn & Marc Lawrence

  3. Biorobotics Department, Fatronik-Tecnalia, 2009 Donostia-San Sebastian, Spain

    Thierry Keller

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  1. Andreas Kuhn
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Correspondence to Andreas Kuhn.

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Kuhn, A., Keller, T., Lawrence, M. et al. A model for transcutaneous current stimulation: simulations and experiments. Med Biol Eng Comput 47, 279–289 (2009). https://doi.org/10.1007/s11517-008-0422-z

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