ELFENN: A Generalized Platform for Modeling Ephaptic Coupling in Spiking Neuron Models

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Objective.Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or 'whole' finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.Approach.Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.Main Results.Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.Significance.Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

Multiformity of extracellular microelectrode recordings from Aδ neurons in the dorsal root ganglia: a computational modeling study

Microelectrodes serve as a fundamental tool in electrophysiology research throughout the nervous system, providing a means of exploring neural function with a high resolution of neural firing information. We constructed a hybrid computational model using the finite element method and multicompartment cable models to explore factors that contribute to extracellular voltage waveforms that are produced by sensory pseudounipolar neurons, specifically smaller A-type neurons, and that are recorded by microelectrodes in dorsal root ganglia. The finite element method model included a dorsal root ganglion, surrounding tissues, and a planar microelectrode array. We built a multicompartment neuron model with multiple trajectories of the glomerular initial segment found in many A-type sensory neurons. Our model replicated both the somatic intracellular voltage profile of Aδ low-threshold mechanoreceptor neurons and the unique extracellular voltage waveform shapes that are observed in experimental settings. Results from this model indicated that tortuous glomerular initial segment geometries can introduce distinct multiphasic properties into a neuron's recorded waveform. Our model also demonstrated how recording location relative to specific microanatomical components of these neurons, and recording distance from these components, can contribute to additional changes in the multiphasic characteristics and peak-to-peak voltage amplitude of the waveform. This knowledge may provide context for research employing microelectrode recordings of pseudounipolar neurons in sensory ganglia, including functional mapping and closed-loop neuromodulation. Furthermore, our simulations gave insight into the neurophysiology of pseudounipolar neurons by demonstrating how the glomerular initial segment aids in increasing the resistance of the stem axon and mitigating rebounding somatic action potentials.NEW & NOTEWORTHY We built a computational model of sensory neurons in the dorsal root ganglia to investigate factors that influence the extracellular waveforms recorded by microelectrodes. Our model demonstrates how the unique structure of these neurons can lead to diverse and often multiphasic waveform profiles depending on the location of the recording contact relative to microanatomical neural components. Our model also provides insight into the neurophysiological function of axon glomeruli that are often present in these neurons.

A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields

Objective

Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or "whole" finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.

Methods

Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.

Main Results

Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh.

Significance

Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

Electrophysiological damage to neuronal membrane alters ephaptic entrainment

The brain is commonly understood as a complex network system with a particular organization and topology that can result in specific electrophysiological patterns. Among all the dynamic elements resulting from the circuits of the brain's network, ephapticity is a cellular communication mechanism that has received little attention. To understand the network's properties of ephaptic entrainment, we start investigating the ephaptic effect on a single neuron. In this study, we used numerical simulations to examine the relationship between alterations in ephaptic neuronal entrainment and impaired electrophysiological properties of the neuronal membrane, which can occur via spike field coherence (SFC). This change in frequency band amplitude is observed in some neurodegenerative diseases, such as Parkinson's or Alzheimer's. To further investigate these phenomena, we proposed a damaged model based on the impairment of both the resistance of the ion channels and the capacitance of the lipid membrane. Therefore, we simulated ephaptic entrainment with the hybrid neural model quadratic integrate-and-fire ephaptic (QIF-E), which mimics an ephaptic entrainment generated by an LFP (simulate a neuronal group). Our results indicate a link between peak entrainment (ephapticity) preference and a shift in frequency band when damage occurs mainly in ion channels. Finally, we discuss possible relationships between ephaptic entrainment and neurodegenerative diseases associated with aging factors.

Modelling neuron fiber interaction and coupling in non-myelinated bundled fiber

Understanding the local dynamics of a neural network relies heavily on local field potential and cell-field interaction. But it is still unclear how local the local potential is and what kinds of consequences the trans-membrane current flow and produced electric field have on the local neural fiber. Mimicking signal transmission in neighboring nerve fiber, a simulation model is built to analyze local behavior due to trans-membrane current, cell-field interactions, and their repercussions on the bundled fiber system. Simulation studies reveal that depending on the coupling parameters, activity in one fiber can depolarize or hyper-polarize adjacent fibers. The suggested cell-field interaction model was tested using an orientation-selective coupled retinal ganglion cell network, which was compared to its uncoupled counterpart. The proposed work has been used to model and simulate local signal dynamics in a bundled fiber system of an orientation-selective RGC network due to cell-field interaction, as well as to gain insight into the possible significance of dendritic fiber coupling in orientation selectivity bandwidth adjustment.

Ephaptic entrainment in hybrid neuronal model

In recent decades, there has been a growing interest in the impact of electric fields generated in the brain. Transmembrane ionic currents originate electric fields in the extracellular space and are capable of affecting nearby neurons, a phenomenon called ephaptic neuronal communication. In the present work, the Quadratic Integrated-and-Fire model (QIF-E) underwent an adjustment/improvement to include the ephaptic entrainment behavior between neurons and electric fields. Indeed, the aim of our study is to validate the QIF-E model, which is a model to estimate the influence of electric fields on neurons. For this purpose, we evaluated whether the main properties observed in an experiment by Anastassiou et al. (Nat Neurosci 14:217-223, 2011), which analyzed the effect of an electric field on cortical pyramidal neurons, are reproduced with the QIF-E model. In this way, the analysis tools are employed according to the neuronal activity regime: (i) for the subthreshold regime, the circular statistic is used to describe the phase differences between the input stimulus signal (electrode) and the modeled membrane response; (ii) in the suprathreshold regime, the Population Vector and the Spike Field Coherence are used to estimate phase preferences and the entrainment intensity between the input stimulus and Action Potentials. The results observed are (i) in the subthreshold regime the values of the phase differences change with distinct frequencies of the input stimulus; (ii) in the supra-threshold regime the preferential phase of Action Potentials changes for different frequencies. In addition, we explore other parameters of the model, such as noise and membrane characteristic-time, in order to understand different types of neurons and extracellular environment related to ephaptic communication. Such results are consistent with results observed in empirical experiments based on ephaptic phenomenon. In addition, the QIF-E model allows further studies on the physiological importance of ephaptic communication in the brain, and its simplicity may open a door to simulate the ephaptic response in neuronal networks and assess the impact of ephaptic communication in such scenarios.

Dynamics of a neuronal pacemaker in the weakly electric fish Apteronotus

The precise timing of neuronal activity is critical for normal brain function. In weakly electric fish, the medullary pacemaker network (PN) sets the timing for an oscillating electric organ discharge (EOD) used for electric sensing. This network is the most precise biological oscillator known, with sub-microsecond variation in oscillator period. The PN consists of two principle sets of neurons, pacemaker and relay cells, that are connected by gap junctions and normally fire in synchrony, one-to-one with each EOD cycle. However, the degree of gap junctional connectivity between these cells appears insufficient to provide the population averaging required for the observed temporal precision of the EOD. This has led to the hypothesis that individual cells themselves fire with high precision, but little is known about the oscillatory dynamics of these pacemaker cells. As a first step towards testing this hypothesis, we have developed a biophysical model of a pacemaker neuron action potential based on experimental recordings. We validated the model by comparing the changes in oscillatory dynamics produced by different experimental manipulations. Our results suggest that this relatively simple model can capture a large range of channel dynamics exhibited by pacemaker cells, and will thus provide a basis for future work on network synchrony and precision.

Realistic modeling of mesoscopic ephaptic coupling in the human brain

Several decades of research suggest that weak electric fields may influence neural processing, including those induced by neuronal activity and proposed as a substrate for a potential new cellular communication system, i.e., ephaptic transmission. Here we aim to model mesoscopic ephaptic activity in the human brain and explore its trajectory during aging by characterizing the electric field generated by cortical dipoles using realistic finite element modeling. Extrapolating from electrophysiological measurements, we first observe that modeled endogenous field magnitudes are comparable to those in measurements of weak but functionally relevant self-generated fields and to those produced by noninvasive transcranial brain stimulation, and therefore possibly able to modulate neuronal activity. Then, to evaluate the role of these fields in the human cortex in large MRI databases, we adapt an interaction approximation that considers the relative orientation of neuron and field to estimate the membrane potential perturbation in pyramidal cells. We use this approximation to define a simplified metric (EMOD1) that weights dipole coupling as a function of distance and relative orientation between emitter and receiver and evaluate it in a sample of 401 realistic human brain models from healthy subjects aged 16-83. Results reveal that ephaptic coupling, in the simplified mesoscopic modeling approach used here, significantly decreases with age, with higher involvement of sensorimotor regions and medial brain structures. This study suggests that by providing the means for fast and direct interaction between neurons, ephaptic modulation may contribute to the complexity of human function for cognition and behavior, and its modification across the lifespan and in response to pathology.

Finite Element Simulation of Ionic Electrodiffusion in Cellular Geometries

Mathematical models for excitable cells are commonly based on cable theory, which considers a homogenized domain and spatially constant ionic concentrations. Although such models provide valuable insight, the effect of altered ion concentrations or detailed cell morphology on the electrical potentials cannot be captured. In this paper, we discuss an alternative approach to detailed modeling of electrodiffusion in neural tissue. The mathematical model describes the distribution and evolution of ion concentrations in a geometrically-explicit representation of the intra- and extracellular domains. As a combination of the electroneutral Kirchhoff-Nernst-Planck (KNP) model and the Extracellular-Membrane-Intracellular (EMI) framework, we refer to this model as the KNP-EMI model. Here, we introduce and numerically evaluate a new, finite element-based numerical scheme for the KNP-EMI model, capable of efficiently and flexibly handling geometries of arbitrary dimension and arbitrary polynomial degree. Moreover, we compare the electrical potentials predicted by the KNP-EMI and EMI models. Finally, we study ephaptic coupling induced in an unmyelinated axon bundle and demonstrate how the KNP-EMI framework can give new insights in this setting.