Modeling extracellular electrical stimulation: II. Computational validation and numerical results

Tahayori, Bahman; Meffin, Hamish; Dokos, Socrates; Burkitt, Anthony N.; Grayden, David B.

doi:10.1088/1741-2560/9/6/065006

Cited by 30 publications

(33 citation statements)

References 27 publications

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“…The exclusion of the response potential is justified theoretically in the conventional CE because the membrane potential it describes is the mean value averaged around the circumference of the cable and not directly affected by the response field (36,37). However, the response field needs to be included to describe the behavior of the neural cable in the transverse dimension and/or ephaptic interactions with neighboring membranes (27,28,(36)(37)(38)(39)(40). The vector potential is used together with the scalar potential, especially the transmembrane potential, assuming that the latter behaves the same with a non-conservative E-field present (29).…”

Section: Coupling Of E-field To Neuronal Membrane In Magnetic Stimulamentioning

confidence: 99%

Coupling magnetically induced electric fields to neurons: longitudinal and transverse activation

Wang

Grill

Peterchev

2018

Preprint

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We present a theory and computational models to couple the electric field induced by magnetic stimulation to neuronal membranes. The response of neuronal membranes to induced electric fields is examined under different time scales, and the characteristics of the primary and secondary electric fields from electromagnetic induction and charge accumulation on conductivity boundaries, respectively, are analyzed. Based on the field characteristics and decoupling of the longitudinal and transverse field components along the neural cable, quasi-potentials are a simple and accurate approximation for coupling of magnetically induced electric fields to neurons and a modified cable equation provides theoretical consistency for magnetic stimulation. The conventional and modified cable equations are used to simulate magnetic stimulation of long peripheral nerves by circular and figure-8 coils. Activation thresholds are obtained over a range of lateral and vertical coil positions for two nonlinear membrane models representing unmyelinated and myelinated axons and also for undulating myelinated axons. For unmyelinated straight axons, the thresholds obtained with the modified cable equation are significantly lower due to transverse polarization, and the spatial distributions of thresholds as a function of coil position differ significantly from predictions by the activating function. For myelinated axons, the transverse field contributes negligibly to activation thresholds, whereas axonal undulation can increase or decrease thresholds depending on coil position. The analysis provides a rigorous theoretical foundation and implementation methods for the use of the cable equation to model neuronal response to magnetically induced electric fields. Experimentally observed stimulation with the electric fields perpendicular to the nerve trunk cannot be explained by transverse polarization alone and is likely due to nerve fiber undulation and other geometrical inhomogeneities.

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Section: Coupling Of E-field To Neuronal Membrane In Magnetic Stimulamentioning

confidence: 99%

Coupling magnetically induced electric fields to neurons: longitudinal and transverse activation

Wang

Grill

Peterchev

2018

Preprint

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“…In particular, an upper‐threshold stimulation voltage with a Gaussian distribution is applied on Fiber #3 along its length (see Figure ), while the other fibers are activated only if the diffused charges from Fiber #3 generate an input voltage higher than the modulated threshold . The 3D distribution of charges on Fiber #3 modulates the activation of the other fibers .…”

Section: Methodsmentioning

confidence: 99%

Effects of nerve bundle geometry on neurotrauma evaluation

Cinelli

Destrade

McHugh

et al. 2018

Numer Methods Biomed Eng

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“…The equations describing the subthreshold membrane potential under voltage and current density boundary conditions are given below and were derived in [9], [10]. They involve two modes of stimulation: a longitudinal mode, which is the conventional mode described by a classical cable equation, and a transverse mode, which is often neglected and is described by an ordinary differential equation in time.…”

Section: B Stage 2: Calculation Of Subthreshold Membrane Potentialmentioning

confidence: 99%

“…We do this by considering the simple example of a cylindrical neurite in a homogeneous volume conductor with stimulation by a point source electrode. The two stage model described above is followed: Stage 1 uses the standard expression for the electrical potential in a homogeneous volume conductor; Stage 2 uses the equations derived in [9], [10] for subthreshold membrane potential under the two types of boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Internal inconsistencies in models of electrical stimulation in neural tissue

Meffin

Tahayori

Grayden

et al. 2013

2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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Calculating the membrane potential of a neurite under extracellular electrical stimulation is important in the design of some recent stimulation strategies for neuroprosthetic devices including retinal implants, cochlear implants, deep brain stimulation. A common approach, widely used in the electrical stimulation literature uses a volume conductor model to calculate the electrical potential in the tissue and then extracts the voltage or current density on the surface of a neuron, which is used as input to the cable equation to calculate the neuron's response. However this approach ignores the effect of the neuron itself as well as surrounding neurons on the extracellular potential. Here we highlight that this leads to an internal inconsistency in the overall model because the result depends on whether the voltage or current density is used to calculate the neural response. The magnitude of this discrepancy is calculated for the example of a point source electrode in a homogeneous medium and is shown to be up to several hundred percent under some stimulus conditions. The inconsistency can be resolved by ensuring that the voltage is related to the current density by the transimpedance of the neurite. Deriving a volume conductor model that satisfies this relationship requires further work.

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Modeling extracellular electrical stimulation: II. Computational validation and numerical results

Cited by 30 publications

References 27 publications

Coupling magnetically induced electric fields to neurons: longitudinal and transverse activation

Coupling magnetically induced electric fields to neurons: longitudinal and transverse activation

Effects of nerve bundle geometry on neurotrauma evaluation

Internal inconsistencies in models of electrical stimulation in neural tissue

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