Computationally efficient simulation of electrical activity at cell membranes interacting with self-generated and externally imposed electric fields

Agudelo-Toro, Andres; Neef, Andreas

doi:10.1088/1741-2560/10/2/026019

Cited by 67 publications

(85 citation statements)

References 67 publications

(115 reference statements)

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“…For simplicity, we assumed that that there was no feedback from the ECS dynamics to the neurons. That is, we did not account for changes in neural reversal potentials due to changes in ECS ion concentrations [9, 12], or ephaptic effects of ECS potentials on neuronal membrane potentials [53, 80–82]. Such feedback mechanisms would likely influence the neurodynamics.…”

Section: Discussionmentioning

confidence: 99%

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

et al. 2016

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Recorded potentials in the extracellular space (ECS) of the brain is a standard measure of population activity in neural tissue. Computational models that simulate the relationship between the ECS potential and its underlying neurophysiological processes are commonly used in the interpretation of such measurements. Standard methods, such as volume-conductor theory and current-source density theory, assume that diffusion has a negligible effect on the ECS potential, at least in the range of frequencies picked up by most recording systems. This assumption remains to be verified. We here present a hybrid simulation framework that accounts for diffusive effects on the ECS potential. The framework uses (1) the NEURON simulator to compute the activity and ionic output currents from multicompartmental neuron models, and (2) the electrodiffusive Kirchhoff-Nernst-Planck framework to simulate the resulting dynamics of the potential and ion concentrations in the ECS, accounting for the effect of electrical migration as well as diffusion. Using this framework, we explore the effect that ECS diffusion has on the electrical potential surrounding a small population of 10 pyramidal neurons. The neural model was tuned so that simulations over ∼100 seconds of biological time led to shifts in ECS concentrations by a few millimolars, similar to what has been seen in experiments. By comparing simulations where ECS diffusion was absent with simulations where ECS diffusion was included, we made the following key findings: (i) ECS diffusion shifted the local potential by up to ∼0.2 mV. (ii) The power spectral density (PSD) of the diffusion-evoked potential shifts followed a 1/f2 power law. (iii) Diffusion effects dominated the PSD of the ECS potential for frequencies up to several hertz. In scenarios with large, but physiologically realistic ECS concentration gradients, diffusion was thus found to affect the ECS potential well within the frequency range picked up in experimental recordings.

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Section: Discussionmentioning

confidence: 99%

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

et al. 2016

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“…EMI computations are typically much more CPU demanding than solving the Cable equation, but the model faithfully represents the physics of the neuron and its surroundings. Variants of the EMI model have been studied previously by e.g., Krassowska and Neu (1994), Ying and Henriquez (2007), Henríquez et al (2013), Agudelo-Toro and Neef (2013), and Agudelo-Toro (2012). For linear membrane currents and specialized geometries, analytical solutions are available; see e.g., Rall (1962), Rall (1969), Klee and Rall (1977), Krassowska and Neu (1994), Ying and Henriquez (2007), and Agudelo-Toro and Neef (2013).…”

Section: Introductionmentioning

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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“…Mortar finite element methods ( [51]; see also [4] for the application of the method in simulations of cell membranes) allow for the coupling of different types of variational problems posed over non-overlapping domains by weakly (in an integral sense) enforcing interface conditions on common boundaries. For the EMI system, the Poisson problems (1) and (2) are coupled by the conditions (4) and (5) and the conditions (7) and (8).…”

Section: Mortar Finite Element Methods For Solving the Emi Pdesmentioning

confidence: 99%

“…For this reason, we consider an operator splitting approach to solve the EMI model defined by (1)(2)(3)(4)(5)(6)(7)(8)(9). The system (1-9) is solved by first applying given initial conditions for v and w. Then, for each time step n, we assume that the solutions v n−1 and w n−1 are known for t = t n−1 on Ŵ and Ŵ 1,2 respectively.…”

Section: Operator Splitting Schemementioning

confidence: 99%

“…This approach has been applied in several earlier papers (e.g., [1][2][3][4][5][6][7]), which used the EMI framework (or related approaches) for detailed simulations of a single cell or a small number of cells. Indeed, the presentation here is very much motivated by the formulation presented by Stinstra et al [5] and by Agudelo-Toro and Neef [4]. Furthermore, the EMI approach was used to study the effect of the ephaptic coupling of neurons in Tveito et al [8].…”

Section: Introductionmentioning

confidence: 99%

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A Cell-Based Framework for Numerical Modeling of Electrical Conduction in Cardiac Tissue

et al. 2017

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In this paper, we study a mathematical model of cardiac tissue based on explicit representation of individual cells. In this EMI model, the extracellular (E) space, the cell membrane (M), and the intracellular (I) space are represented as separate geometrical domains. This representation introduces modeling flexibility needed for detailed representation of the properties of cardiac cells including their membrane. In particular, we will show that the model allows ion channels to be non-uniformly distributed along the membrane of the cell. Such features are difficult to include in classical homogenized models like the monodomain and bidomain models frequently used in computational analyses of cardiac electrophysiology. The EMI model is solved using a finite difference method (FDM) and two variants of the finite element method (FEM). We compare the three schemes numerically, reporting on CPU-efforts and convergence rates. Finally, we illustrate the distinctive capabilities of the EMI model compared to classical models by simulating monolayers of cardiac cells with heterogeneous distributions of ionic channels along the cell membrane. Because of the detailed representation of every cell, the computational problems that result from using the EMI model are much larger than for the classical homogenized models, and thus represent a computational challenge. However, our numerical simulations indicate that the FDM scheme is optimal in the sense that the computational complexity increases proportionally to the number of cardiac cells in the model. Moreover, we present simulations, based on systems of equations involving ∼117 million unknowns, representing up to ∼16,000 cells. We conclude that collections of cardiac cells can be simulated using the EMI model, and that the EMI model enable greater modeling flexibility than the classical monodomain and bidomain models.

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Computationally efficient simulation of electrical activity at cell membranes interacting with self-generated and externally imposed electric fields

Cited by 67 publications

References 67 publications

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue

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

A Cell-Based Framework for Numerical Modeling of Electrical Conduction in Cardiac Tissue

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