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Li D, Li S, Pan M, Li Q, Song J, Zhang R. The role of extracellular glutamate homeostasis dysregulated by astrocyte in epileptic discharges: a model evidence. Cogn Neurodyn 2024; 18:485-502. [PMID: 38699615 PMCID: PMC11061099 DOI: 10.1007/s11571-023-10001-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2023] [Revised: 07/26/2023] [Accepted: 08/13/2023] [Indexed: 05/05/2024] Open
Abstract
Glutamate (Glu) is a predominant excitatory neurotransmitter that acts on glutamate receptors to transfer signals in the central nervous system. Abnormally elevated extracellular glutamate levels is closely related to the generation and transition of epileptic seizures. However, there lacks of investigation regarding the role of extracellular glutamate homeostasis dysregulated by astrocyte in neuronal epileptic discharges. According to this, we propose a novel neuron-astrocyte computational model (NAG) by incorporating extracellular Glu concentration dynamics from three aspects of regulatory mechanisms: (1) the Glu uptake through astrocyte EAAT2; (2) the binding and release Glu via activating astrocyte mGluRs; and (3) the Glu free diffusion in the extracellular space. Then the proposed model NAG is analyzed theoretically and numerically to verify the effect of extracellular Glu homeostasis dysregulated by such three regulatory mechanisms on neuronal epileptic discharges. Our results demonstrate that the neuronal epileptic discharges can be aggravated by the downregulation expression of EAAT2, the aberrant activation of mGluRs, and the elevated Glu levels in extracellular micro-environment; as well as various discharge states (including bursting, mixed-mode spiking, and tonic firing) can be transited by their combination. Furthermore, we find that such factors can also alter the bifurcation threshold for the generation and transition of epileptic discharges. The results in this paper can be helpful for researchers to understand the astrocyte role in modulating extracellular Glu homeostasis, and provide theoretical basis for future related experimental studies.
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Affiliation(s)
- Duo Li
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Sihui Li
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Min Pan
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Qiang Li
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Jiangling Song
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
| | - Rui Zhang
- The Medical Big Data Research Center and The School of Mathematics, Northwest University, Xi’an, 710127 China
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2
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Verardo C, Mele LJ, Selmi L, Palestri P. Finite-element modeling of neuromodulation via controlled delivery of potassium ions using conductive polymer-coated microelectrodes. J Neural Eng 2024; 21:026002. [PMID: 38306702 DOI: 10.1088/1741-2552/ad2581] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 02/02/2024] [Indexed: 02/04/2024]
Abstract
Objective. The controlled delivery of potassium is an interesting neuromodulation modality, being potassium ions involved in shaping neuron excitability, synaptic transmission, network synchronization, and playing a key role in pathological conditions like epilepsy and spreading depression. Despite many successful examples of pre-clinical devices able to influence the extracellular potassium concentration, computational frameworks capturing the corresponding impact on neuronal activity are still missing.Approach. We present a finite-element model describing a PEDOT:PSS-coated microelectrode (herein, simplyionic actuator) able to release potassium and thus modulate the activity of a cortical neuron in anin-vitro-like setting. The dynamics of ions in the ionic actuator, the neural membrane, and the cellular fluids are solved self-consistently.Main results. We showcase the capability of the model to describe on a physical basis the modulation of the intrinsic excitability of the cell and of the synaptic transmission following the electro-ionic stimulation produced by the actuator. We consider three case studies for the ionic actuator with different levels of selectivity to potassium: ideal selectivity, no selectivity, and selectivity achieved by embedding ionophores in the polymer.Significance. This work is the first step toward a comprehensive computational framework aimed to investigate novel neuromodulation devices targeting specific ionic species, as well as to optimize their design and performance, in terms of the induced modulation of neural activity.
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Affiliation(s)
- Claudio Verardo
- Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy
- BioRobotics Institute and Department of Excellence in Robotics and AI, Scuola Superiore Sant'Anna, Pisa, Italy
| | - Leandro Julian Mele
- Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy
- Department of Materials Science and Engineering, Stanford University, Stanford, CA, United States of America
| | - Luca Selmi
- Department of Engineering "Enzo Ferrari", Università degli Studi di Modena e Reggio Emilia, Modena, Italy
| | - Pierpaolo Palestri
- Polytechnic Department of Engineering and Architecture, Università degli Studi di Udine, Udine, Italy
- Department of Engineering "Enzo Ferrari", Università degli Studi di Modena e Reggio Emilia, Modena, Italy
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3
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Idumah G, Somersalo E, Calvetti D. A spatially distributed model of brain metabolism highlights the role of diffusion in brain energy metabolism. J Theor Biol 2023; 572:111567. [PMID: 37393987 DOI: 10.1016/j.jtbi.2023.111567] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Revised: 06/20/2023] [Accepted: 06/22/2023] [Indexed: 07/04/2023]
Abstract
The different active roles of neurons and astrocytes during neuronal activation are associated with the metabolic processes necessary to supply the energy needed for their respective tasks at rest and during neuronal activation. Metabolism, in turn, relies on the delivery of metabolites and removal of toxic byproducts through diffusion processes and the cerebral blood flow. A comprehensive mathematical model of brain metabolism should account not only for the biochemical processes and the interaction of neurons and astrocytes, but also the diffusion of metabolites. In the present article, we present a computational methodology based on a multidomain model of the brain tissue and a homogenization argument for the diffusion processes. In our spatially distributed compartment model, communication between compartments occur both through local transport fluxes, as is the case within local astrocyte-neuron complexes, and through diffusion of some substances in some of the compartments. The model assumes that diffusion takes place in the extracellular space (ECS) and in the astrocyte compartment. In the astrocyte compartment, the diffusion across the syncytium network is implemented as a function of gap junction strength. The diffusion process is implemented numerically by means of a finite element method (FEM) based spatial discretization, and robust stiff solvers are used to time integrate the resulting large system. Computed experiments show the effects of ECS tortuosity, gap junction strength and spatial anisotropy in the astrocyte network on the brain energy metabolism.
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Affiliation(s)
- Gideon Idumah
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, USA
| | - Erkki Somersalo
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, USA
| | - Daniela Calvetti
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, USA.
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4
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Mukherjee S, Mirzaee M, Tithof J. Quantifying the relationship between spreading depolarization and perivascular cerebrospinal fluid flow. Sci Rep 2023; 13:12405. [PMID: 37524734 PMCID: PMC10390554 DOI: 10.1038/s41598-023-38938-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2023] [Accepted: 07/17/2023] [Indexed: 08/02/2023] Open
Abstract
Recent studies have linked spreading depolarization (SD, an electro-chemical wave in the brain following stroke, migraine, traumatic brain injury, and more) with increase in cerebrospinal fluid (CSF) flow through the perivascular spaces (PVSs, annular channels lining the brain vasculature). We develop a novel computational model that couples SD and CSF flow. We first use high order numerical simulations to solve a system of physiologically realistic reaction-diffusion equations which govern the spatiotemporal dynamics of ions in the extracellular and intracellular spaces of the brain cortex during SD. We then couple the SD wave with a 1D CSF flow model that captures the change in cross-sectional area, pressure, and volume flow rate through the PVSs. The coupling is modelled using an empirical relationship between the excess potassium ion concentration in the extracellular space following SD and the vessel radius. We find that the CSF volumetric flow rate depends intricately on the length and width of the PVS, as well as the vessel radius and the angle of incidence of the SD wave. We derive analytical expressions for pressure and volumetric flow rates of CSF through the PVS for a given SD wave and quantify CSF flow variations when two SD waves collide. Our numerical approach is very general and could be extended in the future to obtain novel, quantitative insights into how CSF flow in the brain couples with slow waves, functional hyperemia, seizures, or externally applied neural stimulations.
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Affiliation(s)
- Saikat Mukherjee
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA.
- Department of Mechanical Engineering, Iowa State University, Ames, IA, 50011, USA.
| | - Mahsa Mirzaee
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA
| | - Jeffrey Tithof
- Department of Mechanical Engineering, University of Minnesota, Minneapolis, MN, 55455, USA
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5
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Interneuronal dynamics facilitate the initiation of spike block in cortical microcircuits. J Comput Neurosci 2022; 50:275-298. [PMID: 35441302 DOI: 10.1007/s10827-022-00815-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/28/2021] [Revised: 02/09/2022] [Accepted: 03/09/2022] [Indexed: 10/18/2022]
Abstract
Pyramidal cell spike block is a common occurrence in migraine with aura and epileptic seizures. In both cases, pyramidal cells experience hyperexcitation with rapidly increasing firing rates, major changes in electrochemistry, and ultimately spike block that temporarily terminates neuronal activity. In cortical spreading depression (CSD), spike block propagates as a slowly traveling wave of inactivity through cortical pyramidal cells, which is thought to precede migraine attacks with aura. In seizures, highly synchronized cortical activity can be interspersed with, or terminated by, spike block. While the identifying characteristic of CSD and seizures is the pyramidal cell hyperexcitation, it is currently unknown how the dynamics of the cortical microcircuits and inhibitory interneurons affect the initiation of hyperexcitation and subsequent spike block.We tested the contribution of cortical inhibitory interneurons to the initiation of spike block using a cortical microcircuit model that takes into account changes in ion concentrations that result from neuronal firing. Our results show that interneuronal inhibition provides a wider dynamic range to the circuit and generally improves stability against spike block. Despite these beneficial effects, strong interneuronal firing contributed to rapidly changing extracellular ion concentrations, which facilitated hyperexcitation and led to spike block first in the interneuron and then in the pyramidal cell. In all cases, a loss of interneuronal firing triggered pyramidal cell spike block. However, preventing interneuronal spike block was insufficient to rescue the pyramidal cell from spike block. Our data thus demonstrate that while the role of interneurons in cortical microcircuits is complex, they are critical to the initiation of pyramidal cell spike block. We discuss the implications that localized effects on cortical interneurons have beyond the isolated microcircuit and their contribution to CSD and epileptic seizures.
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Ellingsrud AJ, Dukefoss DB, Enger R, Halnes G, Pettersen K, Rognes ME. Validating a Computational Framework for Ionic Electrodiffusion with Cortical Spreading Depression as a Case Study. eNeuro 2022; 9:ENEURO.0408-21.2022. [PMID: 35365505 PMCID: PMC9045477 DOI: 10.1523/eneuro.0408-21.2022] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2021] [Revised: 02/21/2022] [Accepted: 03/12/2022] [Indexed: 11/21/2022] Open
Abstract
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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Affiliation(s)
- Ada J Ellingsrud
- Department for Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo 0164, Norway
| | - Didrik B Dukefoss
- Letten Centre, Division of Anatomy, Department of Molecular Medicine, Institute of Basic Medical Sciences, University of Oslo, Oslo 0317, Norway
| | - Rune Enger
- Letten Centre, Division of Anatomy, Department of Molecular Medicine, Institute of Basic Medical Sciences, University of Oslo, Oslo 0317, Norway
| | - Geir Halnes
- CINPLA, Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo 0316, Norway
- Institute of Physics, Faculty of Science and Technology, Norwegian University of Life Sciences, Ås 1432, Norway
| | - Klas Pettersen
- NORA, Faculty of Mathematics and Natural Sciences, University of Oslo, Oslo 0316, Norway
| | - Marie E Rognes
- Department for Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo 0164, Norway
- Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Bergen, Bergen 5020, Norway
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Computing Extracellular Electric Potentials from Neuronal Simulations. ADVANCES IN EXPERIMENTAL MEDICINE AND BIOLOGY 2022; 1359:179-199. [DOI: 10.1007/978-3-030-89439-9_8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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8
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Ellingsrud AJ, Boullé N, Farrell PE, Rognes ME. Accurate numerical simulation of electrodiffusion and water movement in brain tissue. MATHEMATICAL MEDICINE AND BIOLOGY-A JOURNAL OF THE IMA 2021; 38:516-551. [PMID: 34791309 DOI: 10.1093/imammb/dqab016] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2021] [Revised: 08/09/2021] [Accepted: 10/19/2021] [Indexed: 12/19/2022]
Abstract
Mathematical modelling of ionic electrodiffusion and water movement is emerging as a powerful avenue of investigation to provide a new physiological insight into brain homeostasis. However, in order to provide solid answers and resolve controversies, the accuracy of the predictions is essential. Ionic electrodiffusion models typically comprise non-trivial systems of non-linear and highly coupled partial and ordinary differential equations that govern phenomena on disparate time scales. Here, we study numerical challenges related to approximating these systems. We consider a homogenized model for electrodiffusion and osmosis in brain tissue and present and evaluate different associated finite element-based splitting schemes in terms of their numerical properties, including accuracy, convergence and computational efficiency for both idealized scenarios and for the physiologically relevant setting of cortical spreading depression (CSD). We find that the schemes display optimal convergence rates in space for problems with smooth manufactured solutions. However, the physiological CSD setting is challenging: we find that the accurate computation of CSD wave characteristics (wave speed and wave width) requires a very fine spatial and fine temporal resolution.
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Affiliation(s)
| | - Nicolas Boullé
- Mathematical Institute, University of Oxford, Oxford, UK
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9
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Sætra MJ, Einevoll GT, Halnes G. An electrodiffusive neuron-extracellular-glia model for exploring the genesis of slow potentials in the brain. PLoS Comput Biol 2021; 17:e1008143. [PMID: 34270543 PMCID: PMC8318289 DOI: 10.1371/journal.pcbi.1008143] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2020] [Revised: 07/28/2021] [Accepted: 06/28/2021] [Indexed: 11/29/2022] Open
Abstract
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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Affiliation(s)
- Marte J. Sætra
- Department of Numerical Analysis and Scientific Computing, Simula Research Laboratory, Oslo, Norway
| | - Gaute T. Einevoll
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, University of Oslo, Oslo, Norway
- Department of Physics, Norwegian University of Life Sciences, Ås, Norway
| | - Geir Halnes
- Centre for Integrative Neuroplasticity, University of Oslo, Oslo, Norway
- Department of Physics, Norwegian University of Life Sciences, Ås, Norway
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10
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Zhu Y, Xu S, Eisenberg RS, Huang H. A tridomain model for potassium clearance in optic nerve of Necturus. Biophys J 2021; 120:3008-3027. [PMID: 34214534 DOI: 10.1016/j.bpj.2021.06.020] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2020] [Revised: 03/28/2021] [Accepted: 06/14/2021] [Indexed: 12/20/2022] Open
Abstract
Complex fluids flow in complex ways in complex structures. Transport of water and various organic and inorganic molecules in the central nervous system are important in a wide range of biological and medical processes. However, the exact driving mechanisms are often not known. In this work, we investigate flows induced by action potentials in an optic nerve as a prototype of the central nervous system. Different from traditional fluid dynamics problems, flows in biological tissues such as the central nervous system are coupled with ion transport. They are driven by osmosis created by concentration gradient of ionic solutions, which in turn influence the transport of ions. Our mathematical model is based on the known structural and biophysical properties of the experimental system used by the Harvard group Orkand et al. Asymptotic analysis and numerical computation show the significant role of water in convective ion transport. The full model (including water) and the electrodiffusion model (excluding water) are compared in detail to reveal an interesting interplay between water and ion transport. In the full model, convection due to water flow dominates inside the glial domain. This water flow in the glia contributes significantly to the spatial buffering of potassium in the extracellular space. Convection in the extracellular domain does not contribute significantly to spatial buffering. Electrodiffusion is the dominant mechanism for flows confined to the extracellular domain.
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Affiliation(s)
- Yi Zhu
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
| | - Shixin Xu
- Zu Chongzhi Center for Mathematics and Computational Sciences, Division of Natural and Applied Sciences, Duke Kunshan University, Kunshan, China.
| | - Robert S Eisenberg
- Department of Applied Mathematics, Illinois Institute of Technology, Chicago, Illinois; Department of Physiology & Biophysics, Rush University, Chicago, Illinois
| | - Huaxiong Huang
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada; Research Centre for Mathematics, Advanced Institute of Natural Sciences, Beijing Normal University (Zhuhai), Zhuhai, China; Division of Science and Technology, BNU-HKBU United International College, Zhuhai, China.
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11
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Masvidal-Codina E, Smith TM, Rathore D, Gao Y, Illa X, Prats-Alfonso E, Corro ED, Calia AB, Rius G, Martin-Fernandez I, Guger C, Reitner P, Villa R, Garrido JA, Guimerà-Brunet A, Wykes RC. Characterization of optogenetically-induced cortical spreading depression in awake mice using graphene micro-transistor arrays. J Neural Eng 2021; 18. [PMID: 33690187 DOI: 10.1088/1741-2552/abecf3] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 03/09/2021] [Indexed: 11/11/2022]
Abstract
Objective.The development of experimental methodology utilizing graphene micro-transistor arrays to facilitate and advance translational research into cortical spreading depression (CSD) in the awake brain.Approach.CSDs were reliably induced in awake nontransgenic mice using optogenetic methods. High-fidelity DC-coupled electrophysiological mapping of propagating CSDs was obtained using flexible arrays of graphene soultion-gated field-effect transistors (gSGFETs).Main results.Viral vectors targetted channelrhopsin expression in neurons of the motor cortex resulting in a transduction volume ⩾1 mm3. 5-10 s of continous blue light stimulation induced CSD that propagated across the cortex at a velocity of 3.0 ± 0.1 mm min-1. Graphene micro-transistor arrays enabled high-density mapping of infraslow activity correlated with neuronal activity suppression across multiple frequency bands during both CSD initiation and propagation. Localized differences in the CSD waveform could be detected and categorized into distinct clusters demonstrating the spatial resolution advantages of DC-coupled recordings. We exploited the reliable and repeatable induction of CSDs using this preparation to perform proof-of-principle pharmacological interrogation studies using NMDA antagonists. MK801 (3 mg kg-1) suppressed CSD induction and propagation, an effect mirrored, albeit transiently, by ketamine (15 mg kg-1), thus demonstrating this models' applicability as a preclinical drug screening platform. Finally, we report that CSDs could be detected through the skull using graphene micro-transistors, highlighting additional advantages and future applications of this technology.Significance.CSD is thought to contribute to the pathophysiology of several neurological diseases. CSD research will benefit from technological advances that permit high density electrophysiological mapping of the CSD waveform and propagation across the cortex. We report anin vivoassay that permits minimally invasive optogenetic induction, combined with multichannel DC-coupled recordings enabled by gSGFETs in the awake brain. Adoption of this technological approach could facilitate and transform preclinical investigations of CSD in disease relevant models.
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Affiliation(s)
- Eduard Masvidal-Codina
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Madrid 28029, Spain
| | - Trevor M Smith
- Department of Clinical and Experimental Epilepsy, Queen Square Institute of Neurology, University College London, London WC1N 3BG, United Kingdom
| | - Daman Rathore
- Department of Clinical and Experimental Epilepsy, Queen Square Institute of Neurology, University College London, London WC1N 3BG, United Kingdom
| | - Yunan Gao
- Department of Clinical and Experimental Epilepsy, Queen Square Institute of Neurology, University College London, London WC1N 3BG, United Kingdom
| | - Xavi Illa
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Madrid 28029, Spain
| | - Elisabet Prats-Alfonso
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Madrid 28029, Spain
| | - Elena Del Corro
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, Bellaterra, Barcelona 08193, Spain
| | - Andrea Bonaccini Calia
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, Bellaterra, Barcelona 08193, Spain
| | - Gemma Rius
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain
| | - Iñigo Martin-Fernandez
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain.,Universitat Autònoma de Barcelona, Bellaterra 08193, Spain
| | - Christoph Guger
- g.tec medical engineering GmbH, Guger Technologies OG, 8020 Graz, Austria
| | - Patrick Reitner
- g.tec medical engineering GmbH, Guger Technologies OG, 8020 Graz, Austria
| | - Rosa Villa
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Madrid 28029, Spain
| | - Jose A Garrido
- Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and The Barcelona Institute of Science and Technology (BIST), Campus UAB, Bellaterra, Barcelona 08193, Spain.,ICREA, Barcelona 08010, Spain
| | - Anton Guimerà-Brunet
- Institut de Microelectrònica de Barcelona, IMB-CNM (CSIC), Esfera UAB, Bellaterra 08193, Spain.,Centro de Investigación Biomédica en Red en Bioingeniería, Biomateriales y Nanomedicina (CIBER-BBN), Madrid 28029, Spain
| | - Rob C Wykes
- Department of Clinical and Experimental Epilepsy, Queen Square Institute of Neurology, University College London, London WC1N 3BG, United Kingdom.,Nanomedicine Lab, Faculty of Biology Medicine and Geoffrey Jefferson Brain Research Centre, University of Manchester, Manchester M13 9PT, United Kingdom
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12
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An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms. PLoS Comput Biol 2020; 16:e1007661. [PMID: 32348299 PMCID: PMC7213750 DOI: 10.1371/journal.pcbi.1007661] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/15/2020] [Revised: 05/11/2020] [Accepted: 04/07/2020] [Indexed: 02/05/2023] Open
Abstract
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. Neurons generate their electrical signals by letting ions pass through their membranes. Despite this fact, most models of neurons apply the simplifying assumption that ion concentrations remain effectively constant during neural activity. This assumption is often quite good, as neurons contain a set of homeostatic mechanisms that make sure that ion concentrations vary quite little under normal circumstances. However, under some conditions, these mechanisms can fail, and ion concentrations can vary quite dramatically. Standard models are thus not able to simulate such conditions. Here, we present what to our knowledge is the first multicompartmental neuron model that accounts for ion concentration variations in a way that ensures complete and consistent ion concentration and charge conservation. In this work, we use the model to explore under which activity conditions the ion concentration variations become important for predicting the neurodynamics. We expect the model to be of great value for the field of neuroscience, as it can be used to simulate a range of pathological conditions, such as spreading depression or epilepsy, which are associated with large changes in extracellular ion concentrations.
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