Modelling extracellular electrical stimulation: IV. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

Tahayori, Bahman; Meffin, Hamish; Sergeev, Evgeni N.; Mareels, Iven; Burkitt, Anthony N.; Grayden, David B.

doi:10.1088/1741-2560/11/6/065005

Cited by 26 publications

(44 citation statements)

References 48 publications

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“…In simulations of cardiac tissue, the Bidomain approach has successfully been applied to simulate the electrophysiology, see e.g., Keener and Sneyd (2009), Franzone et al (2014), Sundnes et al (2006); Roth (2013), and Trayanova (2011). Recently, a similar approach has been applied to neural tissue, see Meffin et al (2014) and Tahayori et al (2014). Most likely, some form of homogenization process is needed to derive tractable mathematical models for neural tissue.…”

Section: Discussionmentioning

confidence: 99%

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

Tveito

Jæger

Lines

et al. 2017

Front. Comput. Neurosci.

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Two mathematical models are part of the foundation of Computational neurophysiology; (a) the Cable equation is used to compute the membrane potential of neurons, and, (b) volume-conductor theory describes the extracellular potential around neurons. In the standard procedure for computing extracellular potentials, the transmembrane currents are computed by means of (a) and the extracellular potentials are computed using an explicit sum over analytical point-current source solutions as prescribed by volume conductor theory. Both models are extremely useful as they allow huge simplifications of the computational efforts involved in computing extracellular potentials. However, there are more accurate, though computationally very expensive, models available where the potentials inside and outside the neurons are computed simultaneously in a self-consistent scheme. In the present work we explore the accuracy of the classical models (a) and (b) by comparing them to these more accurate schemes. The main assumption of (a) is that the ephaptic current can be ignored in the derivation of the Cable equation. We find, however, for our examples with stylized neurons, that the ephaptic current is comparable in magnitude to other currents involved in the computations, suggesting that it may be significant—at least in parts of the simulation. The magnitude of the error introduced in the membrane potential is several millivolts, and this error also translates into errors in the predicted extracellular potentials. While the error becomes negligible if we assume the extracellular conductivity to be very large, this assumption is, unfortunately, not easy to justify a priori for all situations of interest.

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Section: Discussionmentioning

confidence: 99%

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

Tveito

Jæger

Lines

et al. 2017

Front. Comput. Neurosci.

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“…Thresholds were determined for cathodic pulses ranging in duration from PW = 50 µs -1 ms at electrode locations throughout a 3D grid encompassing each neuron's full arborization in 100 µm steps. Electrode locations within 30 µm of the nearest neural compartment were considered too close for accurate calculation of extracellular potentials without considering the presence of the neural structures or the 3D structure of the microelectrode tip [68][69][70], and locations farther than 1 mm were outside of typical experimental ranges, so these points were removed from subsequent analysis. The chronaxie ℎ and rheobase ℎ were obtained at each location by fitting equation (2) [71] to the thresholds using non-linear least squares regression in MATLAB,…”

Section: Intracortical Microstimulationmentioning

confidence: 99%

Biophysically Realistic Neuron Models for Simulation of Cortical Stimulation

Aberra

Peterchev

Grill

2018

Preprint

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1.AbstractObjectiveWe implemented computational models of human and rat cortical neurons for simulating the neural response to cortical stimulation with electromagnetic fields.ApproachWe adapted model neurons from the library of Blue Brain models to reflect biophysical and geometric properties of both adult rat and human cortical neurons and coupled the model neurons to exogenous electric fields (E-fields). The models included 3D reconstructed axonal and dendritic arbors, experimentally-validated electrophysiological behaviors, and multiple, morphological variants within cell types. Using these models, we characterized the single-cell responses to intracortical microstimulation (ICMS) and uniform E-field with dc as well as pulsed currents.Main resultsThe strength-duration and current-distance characteristics of the model neurons to ICMS agreed with published experimental results, as did the subthreshold polarization of cell bodies and axon terminals by uniform dc E-fields. For all forms of stimulation, the lowest threshold elements were terminals of the axon collaterals, and the dependence of threshold and polarization on spatial and temporal stimulation parameters was strongly affected by morphological features of the axonal arbor, including myelination, diameter, and branching.SignificanceThese results provide key insights into the mechanisms of cortical stimulation. The presented models can be used to study various cortical stimulation modalities while incorporating detailed spatial and temporal features of the applied E-field.

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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%

“…While this simplifies the computational implementation, the interaction between the field and the membrane as well as some aspects of the membrane polarization are not captured. Also, the E-field in the first stage is obtained with macroscopic conductivity values and therefore may not reflect the detailed field distribution on cellular scales (27,28). Issues specific to magnetic stimulation are introduced in the following two sections, and these require resolution to improve the rigor and utility of magnetic stimulation models.…”

Section: Introduction Background and Motivationmentioning

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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Modelling extracellular electrical stimulation: IV. Effect of the cellular composition of neural tissue on its spatio-temporal filtering properties

Abstract: The unique features of the composite model and its simplified versions can be used to accurately estimate the spatio-temporal response of neural tissue to extracellular electrical stimulation.

Cited by 26 publications

References 48 publications

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

An Evaluation of the Accuracy of Classical Models for Computing the Membrane Potential and Extracellular Potential for Neurons

Biophysically Realistic Neuron Models for Simulation of Cortical Stimulation

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

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