Publications
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Herlyng, Halvor; Causemann, Marius; Einevoll, Gaute T.; Ellingsrud, Ada Johanne; Halnes, Geir & Rognes, Marie E.
(2026).
Computing for Life: Modeling and Simulation of Electrodiffusion in Dense Reconstructions of Cerebral Tissue.
In Koren, Barry & Roose, Dirk (Ed.),
Numerical Analysis and Scientific Computing: an Anthology.
Springer Nature Switzerland.
ISSN 9783032334282.
p. 512–512.
doi:
10.1007/978-3-032-33428-2_14.
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Excitable tissue is fundamental to brain function, yet its study is complicated by extreme morphological complexity and the physiological processes governing its dynamics. Consequently, detailed computational modeling of this tissue represents a formidable task, requiring both effcient numerical methods and robust implementations. Meanwhile, effcient and robust methods for image segmentation and meshing are needed to provide realistic geometries for which numerical solutions are tractable. Here, we present a computational framework that models electrodiffusion in excitable cerebral tissue, together with realistic geometries generated from electron microscopy data. To demonstrate a possible application of the framework, we simulate electrodiffusive dynamics in cerebral tissue during neuronal activity. Our results and findings highlight the numerical and computational challenges associated with modeling and simulation of electrodiffusion and other multiphysics in dense reconstructions of cerebral tissue.
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Hanssen, Kine Ødegård; Grødem, Sverre; Fyhn, Marianne; Hafting, Torkel; Einevoll, Gaute & Ness, Torbjørn V
[Show all 7 contributors for this article]
(2023).
Responses in fast-spiking interneuron firing rates to parameter variations associated with degradation of perineuronal nets.
Journal of Computational Neuroscience.
ISSN 0929-5313.
51,
p. 283–298.
doi:
10.1007/s10827-023-00849-9.
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The perineuronal nets (PNNs) are sugar coated protein structures that encapsulate certain neurons in the brain, such as parvalbumin positive (PV) inhibitory neurons. As PNNs are theorized to act as a barrier to ion transport, they may effectively increase the membrane charge-separation distance, thereby affecting the membrane capacitance. Tewari et al. (2018) found that degradation of PNNs induced a 25%-50% increase in membrane capacitance cm and a reduction in the firing rates of PV-cells. In the current work, we explore how changes in cm affects the firing rate in a selection of computational neuron models, ranging in complexity from a single compartment Hodgkin-Huxley model to morphologically detailed PV-neuron models. In all models, an increased cm lead to reduced firing, but the experimentally reported increase in cm was not alone sufficient to explain the experimentally reported reduction in firing rate. We therefore hypothesized that PNN degradation in the experiments affected not only cm, but also ionic reversal potentials and ion channel conductances. In simulations, we explored how various model parameters affected the firing rate of the model neurons, and identified which parameter variations in addition to cm that are most likely candidates for explaining the experimentally reported reduction in firing rate.
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Ellingsrud, Ada; Dukefoss, Didrik; Enger, Rune; Halnes, Geir; Pettersen, Klas & Rognes, Marie
(2022).
Validating a computational framework for ionic electrodiffusion with cortical spreading depression as a case study.
eNeuro.
9.
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Ellingsrud, Ada Johanne; Dukefoss, Didrik Bakke; Enger, Rune; Halnes, Geir; Pettersen, Klas Henning & Rognes, Marie Elisabeth
(2022).
Validating a Computational Framework for Ionic Electrodiffusion with Cortical Spreading Depression as a Case Study.
eNeuro.
9(2).
doi:
10.1523/ENEURO.0408-21.2022.
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Cortical spreading depression (CSD) is a wave of pronounced depolarization of brain tissue accompanied by substantial shifts in ionic concentrations and cellular swelling. Here, we validate a computational framework for modeling electrical potentials, ionic movement, and cellular swelling in brain tissue during CSD. We consider different model variations representing wild-type (WT) or knock-out/knock-down mice and systematically compare the numerical results with reports from a selection of experimental studies. We find that the data for several CSD hallmarks obtained computationally, including wave propagation speed, direct current shift duration, peak in extracellular K+ concentration as well as a pronounced shrinkage of extracellular space (ECS) are well in line with what has previously been observed experimentally. Further, we assess how key model parameters including cellular diffusivity, structural ratios, membrane water and/or K+ permeabilities affect the set of CSD characteristics.
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Næss, Solveig; Halnes, Geir; Hagen, Espen; Hagler, Donald J.; Dale, Anders M. & Einevoll, Gaute
[Show all 7 contributors for this article]
(2021).
Biophysically detailed forward modeling of the neural origin of EEG and MEG signals.
NeuroImage.
ISSN 1053-8119.
225.
doi:
10.1016/j.neuroimage.2020.117467.
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Electroencephalography (EEG) and magnetoencephalography (MEG) are among the most important techniques for non-invasively studying cognition and disease in the human brain. These signals are known to originate from cortical neural activity, typically described in terms of current dipoles. While the link between cortical current dipoles and EEG/MEG signals is relatively well understood, surprisingly little is known about the link between different kinds of neural activity and the current dipoles themselves. Detailed biophysical modeling has played an important role in exploring the neural origin of intracranial electric signals, like extracellular spikes and local field potentials. However, this approach has not yet been taken full advantage of in the context of exploring the neural origin of the cortical current dipoles that are causing EEG/MEG signals. Here, we present a method for reducing arbitrary simulated neural activity to single current dipoles. We find that the method is applicable for calculating extracranial signals, but less suited for calculating intracranial electrocorticography (ECoG) signals. We demonstrate that this approach can serve as a powerful tool for investigating the neural origin of EEG/MEG signals. This is done through example studies of the single-neuron EEG contribution, the putative EEG contribution from calcium spikes, and from calculating EEG signals from large-scale neural network simulations. We also demonstrate how the simulated current dipoles can be used directly in combination with detailed head models, allowing for simulated EEG signals with an unprecedented level of biophysical details. In conclusion, this paper presents a framework for biophysically detailed modeling of EEG and MEG signals, which can be used to better our understanding of non-inasively measured neural activity in humans.
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Sætra, Marte Julie; Einevoll, Gaute & Halnes, Geir
(2021).
An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain.
PLoS Computational Biology.
ISSN 1553-734X.
17(7).
doi:
10.1371/journal.pcbi.1008143.
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Within the computational neuroscience community, there has been a focus on simulating the electrical activity of neurons, while other components of brain tissue, such as glia cells and the extracellular space, are often neglected. Standard models of extracellular potentials are based on a combination of multicompartmental models describing neural electrodynamics and volume conductor theory. Such models cannot be used to simulate the slow components of extracellular potentials, which depend on ion concentration dynamics, and the effect that this has on extracellular diffusion potentials and glial buffering currents. We here present the electrodiffusive neuron-extracellular-glia (edNEG) model, which we believe is the first model to combine compartmental neuron modeling with an electrodiffusive framework for intra- and extracellular ion concentration dynamics in a local piece of neuro-glial brain tissue. The edNEG model (i) keeps track of all intraneuronal, intraglial, and extracellular ion concentrations and electrical potentials, (ii) accounts for action potentials and dendritic calcium spikes in neurons, (iii) contains a neuronal and glial homeostatic machinery that gives physiologically realistic ion concentration dynamics, (iv) accounts for electrodiffusive transmembrane, intracellular, and extracellular ionic movements, and (v) accounts for glial and neuronal swelling caused by osmotic transmembrane pressure gradients. The edNEG model accounts for the concentration-dependent effects on ECS potentials that the standard models neglect. Using the edNEG model, we analyze these effects by splitting the extracellular potential into three components: one due to neural sink/source configurations, one due to glial sink/source configurations, and one due to extracellular diffusive currents. Through a series of simulations, we analyze the roles played by the various components and how they interact in generating the total slow potential. We conclude that the three components are of comparable magnitude and that the stimulus conditions determine which of the components that dominate.
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Ellingsrud, Ada Johanne; Enger, Rune; Dukefoss, Didrik Bakke; Halnes, Geir; Pettersen, Klas Henning & Rognes, Marie Elisabeth
(2021).
Validating a computational framework for ionic electrodiffusion with cortical spreading depression as a case study.
BioRxiv.
ISSN 0362-4331.
doi:
10.1101/2021.11.29.470301.
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Sætra, Marte Julie; Einevoll, Gaute & Halnes, Geir
(2020).
An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms.
PLoS Computational Biology.
ISSN 1553-734X.
16(4),
p. 1–36.
doi:
10.1371/journal.pcbi.1007661.
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In most neuronal models, ion concentrations are assumed to be constant, and effects of concentration variations on ionic reversal potentials, or of ionic diffusion on electrical potentials are not accounted for. Here, we present the electrodiffusive Pinsky-Rinzel (edPR) model, which we believe is the first multicompartmental neuron model that accounts for electrodiffusive ion concentration dynamics in a way that ensures a biophysically consistent relationship between ion concentrations, electrical charge, and electrical potentials in both the intra- and extracellular space. The edPR model is an expanded version of the two-compartment Pinsky-Rinzel (PR) model of a hippocampal CA3 neuron. Unlike the PR model, the edPR model includes homeostatic mechanisms and ion-specific leakage currents, and keeps track of all ion concentrations (Na+, K+, Ca2+, and Cl−), electrical potentials, and electrical conductivities in the intra- and extracellular space. The edPR model reproduces the membrane potential dynamics of the PR model for moderate firing activity. For higher activity levels, or when homeostatic mechanisms are impaired, the homeostatic mechanisms fail in maintaining ion concentrations close to baseline, and the edPR model diverges from the PR model as it accounts for effects of concentration changes on neuronal firing. We envision that the edPR model will be useful for the field in three main ways. Firstly, as it relaxes commonly made modeling assumptions, the edPR model can be used to test the validity of these assumptions under various firing conditions, as we show here for a few selected cases. Secondly, the edPR model should supplement the PR model when simulating scenarios where ion concentrations are expected to vary over time. Thirdly, being applicable to conditions with failed homeostasis, the edPR model opens up for simulating a range of pathological conditions, such as spreading depression or epilepsy.
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Ellingsrud, Ada Johanne; Solbrå, Andreas Våvang; Einevoll, Gaute; Halnes, Geir & Rognes, Marie Elisabeth
(2020).
Finite element simulation of ionic electrodiffusion in cellular geometries.
Frontiers in Neuroinformatics.
14,
p. 1–18.
doi:
10.3389/fninf.2020.00011.
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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.
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Mäki-Marttunen, Tuomo; Kaufmann, Tobias; Elvsåshagen, Torbjørn; Devor, Anna; Djurovic, Srdjan & Westlye, Lars Tjelta
[Show all 23 contributors for this article]
(2019).
Biophysical Psychiatry—How Computational Neuroscience Can Help to Understand the Complex Mechanisms of Mental Disorders.
Frontiers in Psychiatry.
10.
doi:
10.3389/fpsyt.2019.00534.
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The brain is the most complex of human organs, and the pathophysiology underlying abnormal brain function in psychiatric disorders is largely unknown. Despite the rapid development of diagnostic tools and treatments in most areas of medicine, our understanding of mental disorders and their treatment has made limited progress during the last decades. While recent advances in genetics and neuroscience have a large potential, the complexity and multidimensionality of the brain processes hinder the discovery of disease mechanisms that would link genetic findings to clinical symptoms and behavior. This applies also to schizophrenia, for which genome-wide association studies have identified a large number of genetic risk loci, spanning hundreds of genes with diverse functionalities. Importantly, the multitude of the associated variants and their prevalence in the healthy population limit the potential of a reductionist functional genetics approach as a stand-alone solution to discover the disease pathology. In this review, we outline the key concepts of a “biophysical psychiatry,” an approach that employs large-scale mechanistic, biophysics-founded computational modelling to increase transdisciplinary understanding of the pathophysiology and strive toward robust predictions. We discuss recent scientific advances that allow a synthesis of previously disparate fields of psychiatry, neurophysiology, functional genomics, and computational modelling to tackle open questions regarding the pathophysiology of heritable mental disorders. We argue that the complexity of the increasing amount of genetic data exceeds the capabilities of classical experimental assays and requires computational approaches. Biophysical psychiatry, based on modelling diseased brain networks using existing and future knowledge of basic genetic, biochemical, and functional properties on a single neuron to a microcircuit level, may allow a leap forward in deriving interpretable biomarkers and move the field toward novel treatment options.
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Tennøe, Simen; Hodne, Kjetil; Haug, Trude; Weltzien, Finn-Arne; Einevoll, Gaute & Halnes, Geir
(2019).
[Re] Fast-Activating Voltage- and Calcium-Dependent Potassium (BK) Conductance Promotes Bursting in Pituitary Cells: A Dynamic Clamp Study.
ReScience.
ISSN 2430-3658.
5(1).
doi:
10.5281/zenodo.2611252.
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Halnes, Geir; Tennøe, Simen; Haug, Trude; Einevoll, Gaute; Weltzien, Finn-Arne & Hodne, Kjetil
(2019).
A computational model for gonadotropin releasing cells in the teleost fish medaka.
PLoS Computational Biology.
ISSN 1553-734X.
15(8),
p. 1–28.
doi:
10.1371/journal.pcbi.1006662.
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Pituitary endocrine cells fire action potentials (APs) to regulate their cytosolic Ca2+ concentration and hormone secretion rate. Depending on animal species, cell type, and biological conditions, pituitary APs are generated either by TTX-sensitive Na+ currents (INa), high-voltage activated Ca2+ currents (ICa), or by a combination of the two. Previous computational models of pituitary cells have mainly been based on data from rats, where INa is largely inactivated at the resting potential, and spontaneous APs are predominantly mediated by ICa. Unlike in rats, spontaneous INa-mediated APs are consistently seen in pituitary cells of several other animal species, including several species of fish. In the current work we develop a computational model of gonadotropin releasing cells in the teleost fish medaka (Oryzias latipes). The model stands out from previous modeling efforts by being (1) the first model of a pituitary cell in teleosts, (2) the first pituitary cell model that fires sponateous APs that are predominantly mediated by INa, and (3) the first pituitary cell model where the kinetics of the depolarizing currents, INa and ICa, are directly fitted to voltage-clamp data. We explore the firing properties of the model, and compare it to the properties of previous models that fire ICa-based APs. We put a particular focus on how the big conductance K+ current (IBK) modulates the AP shape. Interestingly, we find that IBK can prolong AP duration in models that fire ICa-based APs, while it consistently shortens the duration of the predominantly INa-mediated APs in the medaka gonadotroph model. Although the model is constrained to experimental data from gonadotroph cells in medaka, it may likely provide insights also into other pituitary cell types that fire INa-mediated APs.
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Halnes, Geir; Pettersen, Klas Henning; Øyehaug, Leiv; Rognes, Marie Elisabeth & Einevoll, Gaute
(2019).
Astrocytic Ion Dynamics: Implications for Potassium Buffering and Liquid Flow.
In Berry, Hugues & Pittà, Maurizio De (Ed.),
Computational Glioscience.
Springer Nature.
ISSN 9783030008178.
p. 363–391.
doi:
10.1007/978-3-030-00817-8_14.
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Solbrå, Andreas Våvang; Bergersen, Aslak Wigdahl; Brink, Jonas van den; Malthe-Sørenssen, Anders; Einevoll, Gaute & Halnes, Geir
(2018).
A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons.
PLoS Computational Biology.
ISSN 1553-734X.
14(10),
p. 1–26.
doi:
10.1371/journal.pcbi.1006510.
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Many pathological conditions, such as seizures, stroke, and spreading depression, are associated with substantial changes in ion concentrations in the extracellular space (ECS) of the brain. An understanding of the mechanisms that govern ECS concentration dynamics may be a prerequisite for understanding such pathologies. To estimate the transport of ions due to electrodiffusive effects, one must keep track of both the ion concentrations and the electric potential simultaneously in the relevant regions of the brain. Although this is currently unfeasible experimentally, it is in principle achievable with computational models based on biophysical principles and constraints. Previous computational models of extracellular ion-concentration dynamics have required extensive computing power, and therefore have been limited to either phenomena on very small spatiotemporal scales (micrometers and milliseconds), or simplified and idealized 1-dimensional (1-D) transport processes on a larger scale. Here, we present the 3-D Kirchhoff-Nernst-Planck (KNP) framework, tailored to explore electrodiffusive effects on large spatiotemporal scales. By assuming electroneutrality, the KNP-framework circumvents charge-relaxation processes on the spatiotemporal scales of nanometers and nanoseconds, and makes it feasible to run simulations on the spatiotemporal scales of millimeters and seconds on a standard desktop computer. In the present work, we use the 3-D KNP framework to simulate the dynamics of ion concentrations and the electrical potential surrounding a morphologically detailed pyramidal cell. In addition to elucidating the single neuron contribution to electrodiffusive effects in the ECS, the simulation demonstrates the efficiency of the 3-D KNP framework. We envision that future applications of the framework to more complex and biologically realistic systems will be useful in exploring pathological conditions associated with large concentration variations in the ECS.
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Tennøe, Simen; Halnes, Geir & Einevoll, Gaute
(2018).
Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis in computational neuroscience.
Frontiers in Neuroinformatics.
12:49,
p. 1–29.
doi:
10.3389/fninf.2018.00049.
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Computational models in neuroscience typically contain many parameters that are poorly constrained by experimental data. Uncertainty quantification and sensitivity analysis provide rigorous procedures to quantify how the model output depends on this parameter uncertainty. Unfortunately, the application of such methods is not yet standard within the field of neuroscience. Here we present Uncertainpy, an open-source Python toolbox, tailored to perform uncertainty quantification and sensitivity analysis of neuroscience models. Uncertainpy aims to make it quick and easy to get started with uncertainty analysis, without any need for detailed prior knowledge. The toolbox allows uncertainty quantification and sensitivity analysis to be performed on already existing models without needing to modify the model equations or model implementation. Uncertainpy bases its analysis on polynomial chaos expansions, which are more efficient than the more standard Monte-Carlo based approaches. Uncertainpy is tailored for neuroscience applications by its built-in capability for calculating characteristic features in the model output. The toolbox does not merely perform a point-to-point comparison of the “raw” model output (e.g., membrane voltage traces), but can also calculate the uncertainty and sensitivity of salient model response features such as spike timing, action potential width, average interspike interval, and other features relevant for various neural and neural network models. Uncertainpy comes with several common models and features built in, and including custom models and new features is easy. The aim of the current paper is to present Uncertainpy to the neuroscience community in a user-oriented manner. To demonstrate its broad applicability, we perform an uncertainty quantification and sensitivity analysis of three case studies relevant for neuroscience: the original Hodgkin-Huxley point-neuron model for action potential generation, a multi-compartmental model of a thalamic interneuron implemented in the NEURON simulator, and a sparsely connected recurrent network model implemented in the NEST simulator.
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Mäki-Marttunen, Tuomo; Halnes, Geir; Devor, Anna; Metzner, Christoph; Dale, Anders M. & Andreassen, Ole Andreas
[Show all 7 contributors for this article]
(2018).
A stepwise neuron model fitting procedure designed for recordings with high spatial resolution: Application to layer 5 pyramidal cells.
Journal of Neuroscience Methods.
ISSN 0165-0270.
293,
p. 264–283.
doi:
10.1016/j.jneumeth.2017.10.007.
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Background Recent progress in electrophysiological and optical methods for neuronal recordings provides vast amounts of high-resolution data. In parallel, the development of computer technology has allowed simulation of ever-larger neuronal circuits. A challenge in taking advantage of these developments is the construction of single-cell and network models in a way that faithfully reproduces neuronal biophysics with subcellular level of details while keeping the simulation costs at an acceptable level. New method In this work, we develop and apply an automated, stepwise method for fitting a neuron model to data with fine spatial resolution, such as that achievable with voltage sensitive dyes (VSDs) and Ca2+ imaging. Result We apply our method to simulated data from layer 5 pyramidal cells (L5PCs) and construct a model with reduced neuronal morphology. We connect the reduced-morphology neurons into a network and validate against simulated data from a high-resolution L5PC network model. Comparison with existing methods Our approach combines features from several previously applied model-fitting strategies. The reduced-morphology neuron model obtained using our approach reliably reproduces the membrane-potential dynamics across the dendrites as predicted by the full-morphology model. Conclusions The network models produced using our method are cost-efficient and predict that interconnected L5PCs are able to amplify delta-range oscillatory inputs across a large range of network sizes and topologies, largely due to the medium after hyperpolarization mediated by the Ca2+-activated SK current.
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Martínez-Cañada, Pablo; Mobarhan, Milad; Halnes, Geir; Fyhn, Marianne; Morillas, Christian & Pelayo, Francisco
[Show all 7 contributors for this article]
(2018).
Biophysical network modeling of the dLGN circuit: Effects of cortical feedback on spatial response properties of relay cells.
PLoS Computational Biology.
ISSN 1553-734X.
14(1),
p. 1–45.
doi:
10.1371/journal.pcbi.1005930.
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Despite half-a-century of research since the seminal work of Hubel and Wiesel, the role of the dorsal lateral geniculate nucleus (dLGN) in shaping the visual signals is not properly understood. Placed on route from retina to primary visual cortex in the early visual pathway, a striking feature of the dLGN circuit is that both the relay cells (RCs) and interneurons (INs) not only receive feedforward input from retinal ganglion cells, but also a prominent feedback from cells in layer 6 of visual cortex. This feedback has been proposed to affect synchronicity and other temporal properties of the RC firing. It has also been seen to affect spatial properties such as the center-surround antagonism of thalamic receptive fields, i.e., the suppression of the response to very large stimuli compared to smaller, more optimal stimuli. Here we explore the spatial effects of cortical feedback on the RC response by means of a a comprehensive network model with biophysically detailed, single-compartment and multicompartment neuron models of RCs, INs and a population of orientation-selective layer 6 simple cells, consisting of pyramidal cells (PY). We have considered two different arrangements of synaptic feedback from the ON and OFF zones in the visual cortex to the dLGN: phase-reversed (‘push-pull’) and phase-matched (‘push-push’), as well as different spatial extents of the corticothalamic projection pattern. Our simulation results support that a phase-reversed arrangement provides a more effective way for cortical feedback to provide the increased center-surround antagonism seen in experiments both for flashing spots and, even more prominently, for patch gratings. This implies that ON-center RCs receive direct excitation from OFF-dominated cortical cells and indirect inhibitory feedback from ON-dominated cortical cells. The increased center-surround antagonism in the model is accompanied by spatial focusing, i.e., the maximum RC response occurs for smaller stimuli when feedback is present.
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Mobarhan, Milad; Halnes, Geir; Martínez-Cañada, Pablo; Hafting, Torkel; Fyhn, Marianne & Einevoll, Gaute
(2018).
Firing-rate based network modeling of the dLGN circuit: Effects of cortical feedback on spatiotemporal response properties of relay cells.
PLoS Computational Biology.
ISSN 1553-734X.
14(5).
doi:
10.1371/journal.pcbi.1006156.
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Visually evoked signals in the retina pass through the dorsal geniculate nucleus (dLGN) on the way to the visual cortex. This is however not a simple feedforward flow of information: there is a significant feedback from cortical cells back to both relay cells and interneurons in the dLGN. Despite four decades of experimental and theoretical studies, the functional role of this feedback is still debated. Here we use a firing-rate model, the extended difference-of-Gaussians (eDOG) model, to explore cortical feedback effects on visual responses of dLGN relay cells. For this model the responses are found by direct evaluation of two- or three-dimensional integrals allowing for fast and comprehensive studies of putative effects of different candidate organizations of the cortical feedback. Our analysis identifies a special mixed configuration of excitatory and inhibitory cortical feedback which seems to best account for available experimental data. This configuration consists of (i) a slow (long-delay) and spatially widespread inhibitory feedback, combined with (ii) a fast (short-delayed) and spatially narrow excitatory feedback, where (iii) the excitatory/inhibitory ON-ON connections are accompanied respectively by inhibitory/excitatory OFF-ON connections, i.e. following a phase-reversed arrangement. The recent development of optogenetic and pharmacogenetic methods has provided new tools for more precise manipulation and investigation of the thalamocortical circuit, in particular for mice. Such data will expectedly allow the eDOG model to be better constrained by data from specific animal model systems than has been possible until now for cat. We have therefore made the Python tool pyLGN which allows for easy adaptation of the eDOG model to new situations.
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Gratiy, Sergey L.; Halnes, Geir; Denman, Daniel; Hawrylycz, Michael J; Koch, Christof & Einevoll, Gaute
[Show all 7 contributors for this article]
(2017).
From Maxwell's equations to the theory of current-source density analysis.
European Journal of Neuroscience.
ISSN 0953-816X.
45(8),
p. 1013–1023.
doi:
10.1111/ejn.13534.
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Despite the widespread use of current‐source density (CSD) analysis of extracellular potential recordings in the brain, the physical mechanisms responsible for the generation of the signal are still debated. While the extracellular potential is thought to be exclusively generated by the transmembrane currents, recent studies suggest that extracellular diffusive, advective and displacement currents—traditionally neglected—may also contribute considerably toward extracellular potential recordings. Here, we first justify the application of the electro‐quasistatic approximation of Maxwell's equations to describe the electromagnetic field of physiological origin. Subsequently, we perform spatial averaging of currents in neural tissue to arrive at the notion of the CSD and derive an equation relating it to the extracellular potential. We show that, in general, the extracellular potential is determined by the CSD of membrane currents as well as the gradients of the putative extracellular diffusion current. The diffusion current can contribute significantly to the extracellular potential at frequencies less than a few Hertz; in which case it must be subtracted to obtain correct CSD estimates. We also show that the advective and displacement currents in the extracellular space are negligible for physiological frequencies while, within cellular membrane, displacement current contributes toward the CSD as a capacitive current. Taken together, these findings elucidate the relationship between electric currents and the extracellular potential in brain tissue and form the necessary foundation for the analysis of extracellular recordings.
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Tveito, Aslak; Jæger, Karoline Horgmo; Lines, Glenn Terje; Paszkowski, Lukasz; Sundnes, Joakim & Edwards, Andrew
[Show all 9 contributors for this article]
(2017).
An evaluation of the accuracy of classical models for computing the membrane potential and extracellular potential for neurons.
Frontiers in Computational Neuroscience.
11.
doi:
10.3389/fncom.2017.00027.
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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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Halnes, Geir; Mäki-Marttunen, Tuomo; Pettersen, Klas; Andreassen, Ole Andreas & Einevoll, Gaute
(2017).
Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis.
Journal of Neurophysiology.
ISSN 0022-3077.
118(1),
p. 114–120.
doi:
10.1152/jn.00976.2016.
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Current-source density (CSD) analysis is a well-established method for analyzing recorded local field potentials (LFPs), that is, the low-frequency part of extracellular potentials. Standard CSD theory is based on the assumption that all extracellular currents are purely ohmic, and thus neglects the possible impact from ionic diffusion on recorded potentials. However, it has previously been shown that in physiological conditions with large ion-concentration gradients, diffusive currents can evoke slow shifts in extracellular potentials. Using computer simulations, we here show that diffusion-evoked potential shifts can introduce errors in standard CSD analysis, and can lead to prediction of spurious current sources. Further, we here show that the diffusion-evoked prediction errors can be removed by using an improved CSD estimator which accounts for concentration-dependent effects.
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Halnes, Geir; Mäki-Marttunen, Tuomo; Keller, Daniel; Pettersen, Klas; Andreassen, Ole Andreas & Einevoll, Gaute
(2016).
Effect of Ionic Diffusion on Extracellular Potentials in Neural Tissue.
PLoS Computational Biology.
ISSN 1553-734X.
12(11).
doi:
10.1371/journal.pcbi.1005193.
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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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Heiberg, Thomas; Hagen, Espen; Halnes, Geir & Einevoll, Gaute
(2016).
Biophysical Network Modelling of the dLGN Circuit: Different Effects of Triadic and Axonal Inhibition on Visual Responses of Relay Cells.
PLoS Computational Biology.
ISSN 1553-734X.
12(5).
doi:
10.1371/journal.pcbi.1004929.
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Despite its prominent placement between the retina and primary visual cortex in the early visual pathway, the role of the dorsal lateral geniculate nucleus (dLGN) in molding and regulating the visual signals entering the brain is still poorly understood. A striking feature of the dLGN circuit is that relay cells (RCs) and interneurons (INs) form so-called triadic synapses, where an IN dendritic terminal can be simultaneously postsynaptic to a retinal ganglion cell (GC) input and presynaptic to an RC dendrite, allowing for so-called triadic inhibition. Taking advantage of a recently developed biophysically detailed multicompartmental model for an IN, we here investigate putative effects of these different inhibitory actions of INs, i.e., triadic inhibition and standard axonal inhibition, on the response properties of RCs. We compute and investigate so-called area-response curves, that is, trial-averaged visual spike responses vs. spot size, for circular flashing spots in a network of RCs and INs. The model parameters are grossly tuned to give results in qualitative accordance with previous in vivo data of responses to such stimuli for cat GCs and RCs. We particularly investigate how the model ingredients affect salient response properties such as the receptive-field center size of RCs and INs, maximal responses and center-surround antagonisms. For example, while triadic inhibition not involving firing of IN action potentials was found to provide only a non-linear gain control of the conversion of input spikes to output spikes by RCs, axonal inhibition was in contrast found to substantially affect the receptive-field center size: the larger the inhibition, the more the RC center size shrinks compared to the GC providing the feedforward excitation. Thus, a possible role of the different inhibitory actions from INs to RCs in the dLGN circuit is to provide separate mechanisms for overall gain control (direct triadic inhibition) and regulation of spatial resolution (axonal inhibition) of visual signals sent to cortex.
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Mäki-Marttunen, Tuomo; Halnes, Geir; Devor, Anna; Witoelar, Aree; Bettella, Francesco & Djurovic, Srdjan
[Show all 10 contributors for this article]
(2016).
Functional effects of schizophrenia-linked genetic variants on intrinsic single-neuron excitability: a modeling study.
Biological Psychiatry: Cognitive Neuroscience and Neuroimaging.
ISSN 2451-9022.
1(1),
p. 49–59.
doi:
10.1016/j.bpsc.2015.09.002.
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BACKGROUND: Recent genome-wide association studies have identified a large number of genetic risk factors for
schizophrenia (SCZ) featuring ion channels and calcium transporters. For some of these risk factors, independent
prior investigations have examined the effects of genetic alterations on the cellular electrical excitability and calcium
homeostasis. In the present proof-of-concept study, we harnessed these experimental results for modeling of
computational properties on layer V cortical pyramidal cells and identified possible common alterations in behavior
across SCZ-related genes.
METHODS: We applied a biophysically detailed multicompartmental model to study the excitability of a layer V
pyramidal cell. We reviewed the literature on functional genomics for variants of genes associated with SCZ and used
changes in neuron model parameters to represent the effects of these variants.
RESULTS: We present and apply a framework for examining the effects of subtle single nucleotide polymorphisms
in ion channel and calcium transporter-encoding genes on neuron excitability. Our analysis indicates that most of the
considered SCZ-related genetic variants affect the spiking behavior and intracellular calcium dynamics resulting from
summation of inputs across the dendritic tree.
CONCLUSIONS: Our results suggest that alteration in the ability of a single neuron to integrate the inputs and scale
its excitability may constitute a fundamental mechanistic contributor to mental disease, alongside the previously
proposed deficits in synaptic communication and network behavior.
Keywords: Biophysical modeling, Functional genomics, Genome-wide association studies, Layer V pyramidal cell,
Neuron excitability, Schizophrenia
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Halnes, Geir; Østby, Ivar; Pettersen, Klas; Omholt, Stig William & Einevoll, Gaute
(2015).
An Electrodiffusive Formalism for Ion Concentration Dynamics in Excitable Cells and the Extracellular Space Surrounding Them.
In Liljenstrøm, Hans (Eds.),
Advances in Cognitive Neurodynamic (IV). Proceedings of the Fourth International Conference on Cognitive Neurodynamics - 2013.
Springer Science+Business Media B.V..
ISSN 9789401795487.
p. 353–360.
doi:
10.1007/978-94-017-9548-7_50.
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Allken, Vaneeda; Chepkoech, Joy-Loi; Einevoll, Gaute & Halnes, Geir
(2014).
The Subcellular Distribution of T-Type Ca2+ Channels in Interneurons of the Lateral Geniculate Nucleus.
PLOS ONE.
9(9).
doi:
10.1371/journal.pone.0107780.
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Inhibitory interneurons (INs) in the lateral geniculate nucleus (LGN) provide both axonal and dendritic GABA output to thalamocortical relay cells (TCs). Distal parts of the IN dendrites often enter into complex arrangements known as triadic synapses, where the IN dendrite plays a dual role as postsynaptic to retinal input and presynaptic to TC dendrites. Dendritic GABA release can be triggered by retinal input, in a highly localized process that is functionally isolated from the soma, but can also be triggered by somatically elicited Ca2+-spikes and possibly by backpropagating action potentials. Ca2+-spikes in INs are predominantly mediated by T-type Ca2+-channels (T-channels). Due to the complex nature of the dendritic signalling, the function of the IN is likely to depend critically on how T-channels are distributed over the somatodendritic membrane (T-distribution). To study the relationship between the T-distribution and several IN response properties, we here run a series of simulations where we vary the T-distribution in a multicompartmental IN model with a realistic morphology. We find that the somatic response to somatic current injection is facilitated by a high T-channel density in the soma-region. Conversely, a high T-channel density in the distal dendritic region is found to facilitate dendritic signalling in both the outward direction (increases the response in distal dendrites to somatic input) and the inward direction (the soma responds stronger to distal synaptic input). The real T-distribution is likely to reflect a compromise between several neural functions, involving somatic response patterns and dendritic signalling.
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Halnes, Geir; Østby, Ivar; Pettersen, Klas; Omholt, Stig W & Einevoll, Gaute Tomas
(2013).
Electrodiffusive Model for Astrocytic and Neuronal Ion Concentration Dynamics.
PLoS Computational Biology.
ISSN 1553-734X.
9(12).
doi:
10.1371/journal.pcbi.1003386.
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Halnes, Geir; Augustinaite, Sigita; Heggelund, Paul; Einevoll, Gaute Tomas & Migliore, Michele
(2011).
A Multi-Compartment Model for Interneurons in the Dorsal Lateral Geniculate Nucleus.
PLoS Computational Biology.
ISSN 1553-734X.
7(9).
doi:
10.1371/journal.pcbi.1002160.
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Hauge, Eirill; Sætra, Marte; Einevoll, Gaute; Rognes, Marie & Halnes, Geir
(2023).
Neuronal synchronization through electrochemical ephaptic coupling.
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Neuronal synchronization plays an important role in memory formation, while deviations in the synchrony are seen in a wide range of neuropsychiatric disorders. Neuronal networks synchronize primarily through synapses, though contributions from indirect neuronal communication through the extracellular space (ECS), known as ephaptic coupling, are observed under certain conditions. Furthering our knowledge of the dynamics between the neuronal network activity and the ECS is vital to better understand brain function, especially in neurodegenerative diseases associated with deviations from baseline extracellular ion concentrations. In-silico studies often focus on ephaptic coupling via local field potentials, as most computational models assume that ion concentrations in the ECS are constant. The chemical ephaptic effects, caused by changes in ECS ion concentrations due to transmembrane fluxes, remain largely unexplored. In this study, we extend an ion-conserving electrodiffusive two-compartment model of a neuron to describe a small network of excitatory pyramidal neurons sharing a common extracellular space. The model predicts the time evolution of the intracellular and extracellular concentrations of key ion species (Na+, K+, Cl-, and Ca2+), as well as the intracellular and extracellular potentials. With this model, we may simultaneously account for the effects that synaptic, and both electric and chemical ephaptic coupling have on neural synchrony. We quantify and compare the contribution to ephaptic effects made by changes in ionic concentrations versus variations in the electric potentials. Our studies provide insight into changes in network spike patterns due to the interplay between membrane currents and the ECS under various conditions.
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Hagen, Espen; Ness, Torbjørn Vefferstad; Halnes, Geir & Einevoll, Gaute
(2022).
Brain signal predictions from multi-scale networks using a linearized framework.
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Ness, Torbjørn V; Halnes, Geir; Næss, Solveig; Pettersen, Klas Henning & Einevoll, Gaute
(2022).
Computing Extracellular Electric Potentials from Neuronal Simulations.
In Negrello, M (Eds.),
Computational Modelling of the Brain..
Springer.
ISSN 9783030894399.
p. 179–199.
doi:
10.1007/978-3-030-89439-9_8.
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Halnes, Geir
(2021).
Ion concentration dynamics in brain tissue: Effects on neurodynamics and extracellular potentials.
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Sætra, Marte Julie; Einevoll, Gaute T. & Halnes, Geir
(2019).
A two-compartment neuron model with ion conservation and ion pumps.
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Halnes, Geir; Tennøe, Simen; Haug, Trude Marie; Einevoll, Gaute T.; Weltzien, Finn-Arne & Hodne, Kjetil
(2019).
A computational model of the spontaneous activity of gonadotropin-releasing cells in the teleost fish medaka.
Full text in Research Archive
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Halnes, Geir; Tennøe, Simen; Einevoll, Gaute; Haug, Trude; Weltzien, Finn-Arne & Hodne, Kjetil
(2019).
A computational model of the spontaneous activity of gonadotrophin-releasing cells in the teleost fish models.
Full text in Research Archive
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Sætra, Marte Julie; Einevoll, Gaute & Halnes, Geir
(2019).
A two-compartment neuron model with ion conservation and ion pumps.
Full text in Research Archive
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Tennøe, Simen; Halnes, Geir & Einevoll, Gaute
(2018).
Uncertainpy: A Python toolbox for uncertainty quantification and sensitivity analysis of computational neuroscience models.
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Solbrå, Andreas Våvang; Bergersen, Aslak Wigdahl; Brink, Jonas van den; Malthe-Sørenssen, Anders; Einevoll, Gaute & Halnes, Geir
(2018).
Modeling electrodiffusion in the extracellular space around a morphologically detailed neuron.
Full text in Research Archive
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Halnes, Geir; Mäki-Marttunen, Tuomo; Pettersen, Klas; Andreassen, Ole Andreas & Einevoll, Gaute T.
(2017).
Extracellular diffusion can introduce errors in current source density estimates.
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Næss, Solveig; Ness, Torbjørn V; Halnes, Geir; Halgren, Eric; Dale, Anders M. & Einevoll, Gaute
(2017).
Biophysical modeling of single-neuron contributions to ECoG and EEG signals.
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Mobarhan, Milad; Halnes, Geir; Martínez-Cañada, Pablo; Hafting, Torkel; Fyhn, Marianne & Einevoll, Gaute
(2017).
Firing-rate Based Network Modeling of the dLGN Circuit: Effects of Cortical Feedback on Spatiotemporal Response Properties of Relay Cells.
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Næss, Solveig; Ness, Torbjørn V; Halnes, Geir; Halgren, Eric; Dale, Anders M. & Einevoll, Gaute
(2017).
Biophysical modeling of single neuron contributions to ECoG and EEG signals.
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Næss, Solveig; Ness, Torbjørn V; Halnes, Geir; Halgren, Eric; Dale, Anders & Einevoll, Gaute
(2017).
Biophysical modeling of single-neuron contributions toECoG, EEG and MEG signals.
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Solbrå, Andreas Våvang; Malthe-Sørenssen, Anders; Einevoll, Gaute & Halnes, Geir
(2016).
A novel electrodiffusive scheme for modeling ion dynamics in neural tissue.
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Tennøe, Simen; Feinberg, Jonathan; Langtangen, Hans Petter; Einevoll, Gaute & Halnes, Geir
(2016).
UncertainPy: A Python toolbox for uncertainty quantification of computational neuroscience models.
Full text in Research Archive
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Næss, Solveig; Ness, Torbjørn Vefferstad; Halnes, Geir; Halgren, Eric; Dale, Anders M. & Einevoll, Gaute
(2016).
Biophysical modeling of single-neuron contributions to EEG and ECoG signals.
Full text in Research Archive
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Solbrå, Andreas Våvang; Einevoll, Gaute; Malthe-Sørenssen, Anders & Halnes, Geir
(2016).
A novel electrodiffusive scheme for modeling ion dynamics in neural tissue.
Full text in Research Archive
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Tennøe, Simen; Halnes, Geir; Lepperød, Mikkel Elle; Feinberg, Jonathan; Einevoll, Gaute & Langtangen, Hans Petter
(2016).
UncertainPy: A Python toolbox for uncertainty quantification in neural and neural-network models.
Full text in Research Archive
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Halnes, Geir; Mäki-Marttunen, Tuomo; Pettersen, Klas; Keller, Daniel; Andreassen, Ole Andreas & Einevoll, Gaute
(2016).
Effects of ionic diffusion on power spectra of local field potentials (LFP).
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Tennøe, Simen; Langtangen, Hans Petter; Einevoll, Gaute & Halnes, Geir
(2015).
How uncertain are predictions from neuroscience models?
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Tennøe, Simen; Langtangen, Hans Petter; Einevoll, Gaute & Halnes, Geir
(2015).
When things go wrong: Uncertainty in neuroscience.
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Halnes, Geir; Mäki-Marttunen, Tuomo; Pettersen, Klas Henning; Keller, Daniel; Andreassen, Ole Andreas & Einevoll, Gaute
(2015).
Can ionic diffusion have an effect on extracellular potentials?
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Einevoll, Gaute & Halnes, Geir
(2013).
LGN Models.
In Jaeger, Dieter & Jung, Ranu (Ed.),
Encyclopedia of Computational Neuroscience.
Springer Science+Business Media B.V..
ISSN 9781461466741.
Full text in Research Archive
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Halnes, Geir; Østby, Ivar; Pettersen, Klas; Omholt, Stig W & Einevoll, Gaute Tomas
(2013).
An electrodiffusive model for neuronal and astrocytic ion concentration dynamics.
Full text in Research Archive
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Halnes, Geir; Østby, Ivar; Pettersen, Klas; Omholt, Stig W & Einevoll, Gaute Tomas
(2013).
Electrodiffusive model for neuronal and astrocytic ion concentration dynamics.
Full text in Research Archive
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Halnes, Geir; Østby, Ivar; Pettersen, Klas; Omholt, Stig W & Einevoll, Gaute Tomas
(2013).
An electrodiffusive model for neuronal and astrocytic ion concentration dynamics.
Full text in Research Archive
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Heiberg, Thomas; Hagen, Espen; Halnes, Geir; Plesser, Hans Ekkehard & Einevoll, Gaute Tomas
(2013).
Biophysically detailed network model for area summation in LGN relay cells.
Full text in Research Archive
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Halnes, Geir; Østby, Ivar; Pettersen, Klas Henning; Omholt, Stig W & Einevoll, Gaute Tomas
(2012).
An electrodiffusive model for investigation of spatial buffering of potassium by glial cells.
Full text in Research Archive
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Halnes, Geir; Østby, Ivar; Pettersen, Klas Henning; Omholt, Stig W & Einevoll, Gaute Tomas
(2012).
Electrodiffusion in neural tissue at long timescales.
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Halnes, Geir; Østby, Ivar; Pettersen, Klas Henning; Omholt, Stig W & Einevoll, Gaute Tomas
(2012).
Electrodiffusion in neural tissue at long timescales.
Full text in Research Archive
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Halnes, Geir; Augustinaite, Sigita; Heggelund, Paul; Einevoll, Gaute Tomas & Migliore, Michele
(2011).
A multi-compartment model for interneurons in the dorsal lateral geniculate nucleus.
Full text in Research Archive
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Halnes, Geir; Augustinaite, Sigita; Heggelund, Paul; Einevoll, Gaute & Migliore, Michele
(2010).
A compartmental model of an LGN interneuron.
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Halnes, Geir; Augustinaite, Sigita; Heggelund, Paul; Migliore, Michele & Einevoll, GT
(2009).
Compartmental modeling of LGN interneurons.
Scandinavian Journal of Optometry and Visual Science.
ISSN 1891-0882.
2,
p. 9–9.
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Halnes, Geir; Sætra, Marte Julie & Birkeland, Birk Thorbjørnssønn
(2023).
Comparing different techniques for stimulating neurons : a computational study.
Norges miljø- og biovitenskapelige universitet (NMBU).
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A comparison of different techniques for stimulating neurons using a computational model. The computational model is an expanded version of the electrodiffusive Pinsky-Rinzel model from Sætra et al. (2020) referenced in the thesis. The explicit modeling of ion concentrations allows for comparison of which ions are used for stimulation. The expansion of the model allows for comparison of stimulation currents coming from inside and outside the system. In conclusion, both the ion mix in the stimulation current and the stimulation technique can have an effect on the response of the model. In particular, there is an effect of potassium ions in the stimulation current.
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Nov. 16, 2023 2:05 PM
- Last modified
Nov. 16, 2023 2:05 PM