Abstract
Measurements of electric potentials from neural activity have played a key role in neuroscience for almost a century, and simulations of neural activity is an important tool for understanding such measurements. Volume conductor (VC) theory is used to compute extracellular electric potentials stemming from neural activity, such as extracellular spikes, multi-unit activity (MUA), local field potentials (LFP), electrocorticography (ECoG), and electroencephalography (EEG). Further, VC theory is also used inversely to reconstruct neuronal current source distributions from recorded potentials through current source density methods. In this book chapter, we show how VC theory can be derived from a detailed electrodiffusive theory for ion concentration dynamics in the extracellular medium, and we show what assumptions must be introduced to get the VC theory on the simplified form that is commonly used by neuroscientists. Furthermore, we provide examples of how the theory is applied to compute spikes, LFP signals, and EEG signals generated by neurons and neuronal populations.
Torbjørn V. Ness and Geir Halnes authors have contributed equally to this work
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References
Almeida ACG, Texeira HZ, Duarte MA, Infantosi AFC (2004) Modeling extracellular space electrodiffusion during Leão’s spreading depression. IEEE Trans Biomed Eng 51(3):450–458
Bartels A, Goense J, Logothetis N (2012) Functional magnetic resonance imaging. In: Brette R, Destexhe A (eds) Handbook of neural activity measurement. Cambridge University, Cambridge, pp 92–135
Billeh YN, Cai B, Gratiy SL, Dai K, Iyer R, Gouwens NW, Abbasi-Asl R, Jia X, Siegle JH, Olsen SR, Koch C, Mihalas S, Arkhipov A (2020) Systematic integration of structural and functional data into multi-scale models of mouse primary visual cortex. Neuron 106(3):388–403. https://www.biorxiv.org/content/early/2019/06/06/662189
Buccino AP, Einevoll GT (2021) MEArec: a fast and customizable testbench simulator for ground-truth extracellular spiking activity. Neuroinformatics 19:185–204
Buccino AP, Kordovan M, Ness TV, Merkt B, Häfliger PD, Fyhn M, Cauwenberghs G, Rotter S, Einevoll GT (2018) Combining biophysical modeling and deep learning for multi-electrode array neuron localization and classification. J Neurophysiol 120:1212–1232. http://www.ncbi.nlm.nih.gov/pubmed/29847231. https://www.physiology.org/doi/10.1152/jn.00210.2018
Buccino AP, Kuchta M, Jæger KH, Ness TV, Berthet P, Mardal K.-A, Cauwenberghs G, Tveito A (2019) How does the presence of neural probes affect extracellular potentials? J Neural Eng 16(2):026030
Buzsáki G, Anastassiou Ca, Koch C (2012) The origin of extracellular fields and currents–EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6):407–20. http://www.ncbi.nlm.nih.gov/pubmed/22595786
Cartailler J, Kwon T, Yuste R, Holcman D (2018) Deconvolution of voltage sensor time series and electro-diffusion modeling reveal the role of spine geometry in controlling synaptic strength. Neuron 97(5):1126–1136
Chemla S, Chavane F (2012) Voltage-sensitive dye imaging. In: Brette R, Destexhe A. (Eds) Handbook of Neural Activity Measurement. Cambridge University, Cambridge, pp 92–135
Cohen MX (2017) Where Does EEG come from and what does it mean? Trends Neurosci 40(4):208–218. http://linkinghub.elsevier.com/retrieve/pii/S0166223617300243
Cserpán D, Meszéna D, Wittner L, Tóth K, Ulbert I, Somogyvári Z, Wójcik DK (2017) Revealing the distribution of transmembrane currents along the dendritic tree of a neuron from extracellular recordings. eLife 6:e29384
Delgado Ruz I, Schultz SR (2014) Localising and classifying neurons from high density MEA recordings. J Neurosci Methods 233:115–128. https://doi.org/10.1016/j.jneumeth.2014.05.037
Denker M, Einevoll, GT, Franke F, Grün S, Hagen E, Kerr J, Nawrot M, Ness TV, Wójcik TWD (2012) Report from 1st INCF workshop on validation of analysis methods. Tech. rep, International Neuroinformatics Coordinating Facility (INCF)
Dubey A, Ray S (2019) Cortical Electrocorticogram (ECoG) is a local signal. J Neurosci 39(22):4299–4311
Einevoll GT, Pettersen KH, Devor A, Ulbert I, Halgren E, Dale, AM (2007) Laminar population analysis: estimating firing rates and evoked synaptic activity from multielectrode recordings in rat barrel cortex. J Neurophysiol 97(3):2174–90. http://www.ncbi.nlm.nih.gov/pubmed/17182911
Einevoll, GT, Kayser C, Logothetis N, Panzeri S (2013a) Modelling and analysis of local field potentials for studying the function of cortical circuits. Nat Rev Neurosci 14:770–785
Einevoll, GT, Lindén H, Tetzlaff T, Łeski S, Pettersen, KH (2013b) Local Field Potentials—Biophysical origin and analysis. In: Quiroga RQ, Panzeri S (Eds) Principles of Neural Coding. CRC Press, Boca Raton, pp 37–60, Ch3
Einevoll, GT, Destexhe A, Diesmann M, Grün S, Jirsa V, de Kamps M, Migliore M, Ness, TV, Plesser, HE, Schürmann F (2019) The Scientific Case for Brain Simulations. Neuron 102(4):735–744
Elbohouty M (2013) Electrical Conductivity of Brain Cortex Slices in Seizing and Non-seizing States. Ph.D. thesis, The University of Waikato, Waikato
Ellingsrud AJ, Solbrå A, Einevoll GT, Halnes G, Rognes ME (2020) Finite element simulation of ionic electrodiffusion in cellular geometries. Front Neuroinform 14:11. https://www.frontiersin.org/article/10.3389/fninf.2020.00011
Freeman WJ (1975) Mass action in the nervous system. Academic Press, New York
Frey U, Egert U, Heer F, Hafizovic S, Hierlemann A (2009) Microelectronic system for high-resolution mapping of extracellular electric fields applied to brain slices. Biosens. Bioelectron. 24(7):2191–2198. http://www.ncbi.nlm.nih.gov/pubmed/19157842
Gabriel S, Lau RW, Gabriel C (1996) The dielectric properties of biological tissues: II. Measurements in the frequency range 10 Hz to 20 GHz. Phys Med Biol 41(11):2251–2269. http://www.ncbi.nlm.nih.gov/pubmed/8938025
Gardner CL, Jones JR, Baer SM, Crook SM (2015) Drift-diffusion simulation of the ephaptic effect in the triad synapse of the retina. J Comput Neurosci 38(1):129–42. http://www.ncbi.nlm.nih.gov/pubmed/25260382
Gła̧bska H, Potworowski J, Łȩski S, Wójcik DK (2014) Independent components of neural activity carry information on individual populations. PLoS One 9(8):e105071. https://doi.org/10.1371/journal.pone.0105071
Gła̧bska HT, Norheim E, Devor A, Dale AM, Einevoll GT, Wójcik DK (2016) Generalized Laminar Population Analysis (gLPA) for Interpretation of Multielectrode Data from Cortex. Front Neuroinform 10:1
Gold C, Henze DA, Koch C (2007) Using extracellular action potential recordings to constrain compartmental models. J. Comput Neurosci 23(1):39–58. https://doi.org/10.1007/s10827-006-0018-2
Gonçalves PJ, Lueckmann JM, Deistler M, Nonnenmacher M, Öcal K, Bassetto G, Chintaluri C, Podlaski WF, Haddad SA, Vogels TP, Greenberg DS, Macke JH (2020) Training deep neural density estimators to identify mechanistic models of neural dynamics. eLife 9:e56261
Goto T, Hatanaka R, Ogawa T, Sumiyoshi A, Riera J, Kawashima R (2010) An evaluation of the conductivity profile in the somatosensory barrel cortex of Wistar rats. J Neurophysiol 104(6):3388–3412
Gratiy SL, Halnes G, Denman D, Hawrylycz MJ, Koch C, Einevoll, GT, Anastassiou CA (2017) From Maxwell’s equations to the theory of current-source density analysis. Eur J Neurosci 45(8):1013–1023
Grodzinsky F (2011) Fields, Forces, and Flows in Biological Systems. Garland Science, Taylor and Francis Group, London
Hagen E, Dahmen D, Stavrinou ML, Lindén H, Tetzlaff T, Van Albada SJ, Grün S, Diesmann M, Einevoll GT (2016) Hybrid scheme for modeling local field potentials from point-neuron networks. Cerebral Cortex 26(12):4461–4496
Hagen E, Næss S, Ness TV, Einevoll GT (2018) Multimodal modeling of neural network activity: computing LFP, ECoG, EEG and MEG signals with LFPy 2.0. Front Neuroinform 12:92
Hagen E, Næss S, Ness TV, Einevoll GT (2019) LFPy—multimodal modeling of extracellular neuronal recordings in Python. In: Encyclopedia of Computational Neuroscience. Springer, New York, p 620286. https://doi.org/10.1007/978-1-4614-7320-6_100681-1
Haider B, Schulz, D. PA, Häusser M, Carandini M (2016) Millisecond coupling of local field potentials to synaptic currents in the awake visual cortex. Neuron 90:35–42
Halnes G, Østby I, Pettersen KH, Omholt SW, Einevoll GT (2013). Electrodiffusive model for astrocytic and neuronal ion concentration dynamics. PLoS Comput Biol 9(12):e1003386
Halnes G, Østby I, Pettersen KH, Omholt SW, Einevoll GT (2015) An electrodiffusive formalism for ion concentration dynamics in excitable cells and the extracellular space surrounding them. In: Advances in cognitive neurodynamics (IV). Springer, Netherlands, pp 353–360 http://link.springer.com/chapter/10.1007/978-94-017-9548-7_50
Halnes G, Mäki-Marttunen T, Keller D, Pettersen KH, Andreassen, OA, Einevoll GT (2016) Effect of ionic diffusion on extracellular potentials in neural tissue. PLoS Comput Biol 12(11):e1005193
Halnes G, Mäki-Marttunen T, Pettersen KH, Andreassen OA, Einevoll GT (2017) Ion diffusion may introduce spurious current sources in current-source density (CSD) analysis. J Neurophysiol 118(1):114–120. http://jn.physiology.org/lookup/doi/10.1152/jn.00976.2016
Hämäläinen M, Hari R, Ilmoniemi RJ, Knuutila J, Lounasmaa OV (1993) Magnetoencephalography—Theory, instrumentation, and applications to noninvasive studies of the working human brain. Rev Mod Phys 65(2):413
Haufe S, Huang Y, Parra LC (2015) A highly detailed FEM volume conductor model based on the ICBM152 average head template for EEG source imaging and TCS targeting. Conf Proc IEEE Eng Med Biol Soc 2015:5744–5747
Hay E, Hill S, Schürmann F, Markram H, Segev I (2011) Models of neocortical layer 5b pyramidal cells capturing a wide range of dendritic and perisomatic active properties. PLoS Comput Biol 7(7):1–18
Helmchen F (2012) Calcium imaging. In: Brette R, Destexhe A (eds) Handbook of neural activity measurement. Cambridge University, Cambridge, pp 92–135
Holcman D, Yuste R (2015) The new nanophysiology: regulation of ionic flow in neuronal subcompartments. Nat Rev Neurosci 16(11):685–692
Holsheimer J (1987) Electrical conductivity of the hippocampal CA1 layers and application to current-source-density analysis. Exp Brain Res 67(2):402–410
Holt G, Koch C (1999) Electrical interactions via the extracellular potential near cell bodies. J Comput Neurosci 6:169–184. http://link.springer.com/article/10.1023/A:1008832702585
Huang Y, Parra LC, Haufe S (2016) The New York Head–A precise standardized volume conductor model for EEG source localization and tES targeting. NeuroImage 140:150–162. https://doi.org/10.1016/j.neuroimage.2015.12.019
Ilmoniemi RJ, Sarvas J (2019) Brain Signals - Physics and Mathematics of MEG and EEG. MIT Press, Cambridge
Jackson JD (1998) Classical electrodynamics, 3rd edn. Wiley, New York
Joucla S, Yvert B (2012) Modeling extracellular electrical neural stimulation: from basic understanding to MEA-based applications. J Physiol Paris 106(3–4):146–58. http://www.ncbi.nlm.nih.gov/pubmed/22036892
Koch C (1999) Biophysics of computation: information processing in single neurons., 1st edn. Oxford University, New York
Larson MG, Bengzon F (2013) The finite element method: theory, implementation, and applications, vol. 10. Springer, Berlin
Léonetti M, Dubois-Violette E (1998) Theory of electrodynamic instabilities in biological cells. Phys Rev Lett 81(9):1977–1980. https://doi.org/10.1103/PhysRevLett.81.1977
Léonetti M, Dubois-Violette E, Homblé F (2004) Pattern formation of stationary transcellular ionic currents in Fucus. Proc Natl Acad Sci USA 101(28):10243–10248. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=478558&tool=pmcentrez&rendertype=abstract
Łȩski S, Pettersen KH, Tunstall B, Einevoll GT, Gigg J, Wójcik DK (2011) Inverse current source density method in two dimensions: inferring neural activation from multielectrode recordings. Neuroinformatics 9(4):401–425. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3214268&tool=pmcentrez&rendertype=abstract
Łȩski S, Lindén H, Tetzlaff T, Pettersen KH, Einevoll GT (2013) Frequency dependence of signal power and spatial reach of the local field potential. PLoS Comput Biol 9(7):e1003137
Lindén H, Pettersen KH, Einevoll GT (2010) Intrinsic dendritic filtering gives low-pass power spectra of local field potentials. J Comput Neurosci 29(3):423–444. http://www.ncbi.nlm.nih.gov/pubmed/20502952
Lindén H, Tetzlaff T, Potjans TC, Pettersen KH, Grün S, Diesmann M, Einevoll GT (2011) Modeling the spatial reach of the LFP. Neuron 72(5):859–72. http://www.ncbi.nlm.nih.gov/pubmed/22153380
Lindén H, Hagen E, Łȩski S, Norheim ES, Pettersen KH, Einevoll GT (2014) LFPy: a tool for biophysical simulation of extracellular potentials generated by detailed model neurons. Front Neuroinform 7(41):1–15. http://journal.frontiersin.org/article/10.3389/fninf.2013.00041/abstract
Logg A, Mardal, K-A, Wells G (2012) Automated solution of differential equations by the finite element method: The FEniCS book, vol 84. Springer, Berlin
Logothetis NK, Kayser C, Oeltermann A (2007) In vivo measurement of cortical impedance spectrum in monkeys: implications for signal propagation. Neuron 55(5):809–823. http://www.ncbi.nlm.nih.gov/pubmed/17785187
López-Aguado L, Ibarz J, Herreras O (2001) Activity-dependent changes of tissue resistivity in the ca1 region in vivo are layer-specific: modulation of evoked potentials. Neuroscience 108(2):249–262
Lopreore CL, Bartol TM, Coggan JS, Keller DX, Sosinsky GE, Ellisman MH, Sejnowski TJ (2008) Computational modeling of three-dimensional electrodiffusion in biological systems: application to the node of Ranvier. Biophys J 95(6):2624–35. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2527256&tool=pmcentrez&rendertype=abstract
Lu B, Zhou YC, Huber, Ga, Bond SD, Holst MJ, McCammon JA (2007) Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution. J Chem Phys 127(13):135102. http://www.ncbi.nlm.nih.gov/pubmed/17919055
Luo J, Macias S, Ness TV, Einevoll GT, Zhang K, Moss CF (2018) Neural timing of stimulus events with microsecond precision. PLoS Biol 16(10):1–22
Markram H, Muller E, Ramaswamy S, Reimann MW, Abdellah M, Sanchez, CA, Ailamaki A, Alonso-Nanclares L, Antille N, Arsever S, et al (2015) Reconstruction and simulation of neocortical microcircuitry. Cell 163(2):456–492
Martínez-Cañada P, Ness TV, Einevoll GT, Fellin T, Panzeri S (2021) Computation of the electroencephalogram (EEG) from network models of point neurons. PLoS Comput Biol 17(4):e1008893
Martinsen ØG, Grimnes S (2008) Bioimpedance and bioelectricity basics, 2 edn. Academic Press, New York. http://www.amazon.com/Bioimpedance-Bioelectricity-Basics-Second-Edition/dp/0123740045
Mazzoni A, Lindén H, Cuntz H, Lansner A, Panzeri S, Einevoll GT (2015) Computing the Local Field Potential (LFP) from integrate-and-fire network models. PLoS Comput Biol 11(12):e1004584
McIntyre CC, Grill WM (2001) Finite element analysis of the current-density and electric field generated by metal microelectrodes. Ann Biomed Eng 29(3):227–235
Mechler F, Victor JD (2012) Dipole characterization of single neurons from their extracellular action potentials. J Comput Neurosci 32(1):73–100. http://www.ncbi.nlm.nih.gov/pubmed/21667156
Miceli S, Ness TV, Einevoll GT, Schubert D (2017) Impedance spectrum in cortical tissue: Implications for propagation of LPF signals on the microscopic level. eNeuro 4(1). https://www.eneuro.org/content/4/1/ENEURO.0291-16.2016
Mitzdorf U (1985) Current source-density method and application in cat cerebral cortex: investigation of evoked potentials and EEG phenomena. Physiol Rev 65(1):37–100
Moffitt M, McIntyre CC 2005 Model-based analysis of cortical recording with silicon microelectrodes. Clin Neurophysiol 116(9):2240–2250. http://www.ncbi.nlm.nih.gov/pubmed/16055377
Mori Y (2009) From three-dimensional electrophysiology to the cable model: an asymptotic study. arXiv preprint arXiv:0901.3914, 1–39. http://arxiv.org/abs/0901.3914
Mori Y, Peskin C (2009) A numerical method for cellular electrophysiology based on the electrodiffusion equations with internal boundary conditions at membranes. Commun Appl Math Comput Sci 4(1):85–134. http://msp.org/camcos/2009/4-1/p04.xhtml
Mori Y, Fishman GI, Peskin CS (2008) Ephaptic conduction in a cardiac strand model with 3D electrodiffusion. PNAS 105(17):6463–6468. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2359793&tool=pmcentrez&rendertype=abstract
Mori Y, Liu C, Eisenberg RS (2011) A model of electrodiffusion and osmotic water flow and its energetic structure. arXiv preprint arXiv:1101.5193
Moulin C, Glière A, Barbier D, Joucla S, Yvert B, Mailley P, Guillemaud R (2008) A new 3-D finite-element model based on thin-film approximation for microelectrode array recording of extracellular action potential. IEEE Trans Biomed Eng 55(2 Pt 1): 683–692. http://www.ncbi.nlm.nih.gov/pubmed/18270005
Nanninga P (2008) A computational neuron model based on Poisson-Nernst-Planck theory. ANZIAM J 50:46–59. http://journal.austms.org.au/ojs/index.php/anziamj/article/view/1390
Nelson MJ, Pouget P (2010) Do electrode properties create a problem in interpreting local field potential recordings? J Neurophysiol 103(5):2315–2317. http://www.ncbi.nlm.nih.gov/pubmed/20220081
Ness TV, Chintaluri C, Potworowski J, Łȩski S, Gła̧bska H, Wójcik DK, Einevoll GT (2015) Modelling and analysis of electrical potentials recorded in microelectrode arrays (MEAs). Neuroinformatics 13(4):403–426. http://link.springer.com/10.1007/s12021-015-9265-6
Ness TV, Remme, M. WH, Einevoll GT (2016) Active subthreshold dendritic conductances shape the local field potential. J Physiol 594(13):3809–3825
Ness TV, Remme, MWH, Einevoll GT (2018) h-Type membrane current shapes the local field potential from populations of pyramidal neurons. J Neurosci 38(26):6011–6024. http://www.jneurosci.org/lookup/doi/10.1523/JNEUROSCI.3278-17.2018
NeuroEnsemble (2017) Elephant—electrophysiology analysis toolkit. https://github.com/NeuralEnsemble/elephant
Nicholson C, Freeman JA (1975) Theory of current source-density analysis and determination of conductivity tensor for anuran cerebellum. J Neurophysiol 38(2):356–368
Nicholson C, Syková E (1998) Extracellular space structure revealed by diffusion analysis. Trends Neurosci 21(5):207–215. http://www.ncbi.nlm.nih.gov/pubmed/9610885
Niederer S (2013) Regulation of ion gradients across myocardial ischemic border zones: a biophysical modelling analysis. PloS One 8(4):e60323
Nunez PL, Srinivasan R (2006) Electric Fields of the Brain. Oxford University, New York
Næss S, Chintaluri C, Ness TV, Dale AM, Einevoll GT, Wójcik DK (2017) Corrected Four-Sphere Head Model for EEG Signals. Front Hum Neurosci 11(October):1–7. http://journal.frontiersin.org/article/10.3389/fnhum.2017.00490/full
Næss S, Halnes G, Hagen E, Hagler DJ, Dale AM, Einevoll, GT, Ness TV (2021) Biophysically detailed forward modeling of the neural origin of EEG and MEG signals. NeuroImage 225(117467):2020.07.01.181875. https://doi.org/10.1016/j.neuroimage.2020.117467
Obien, MEJ, Hierlemann A, Frey U (2019) Accurate signal-source localization in brain slices by means of high-density microelectrode arrays. Sci Rep 9(1):1–19
O’Connell R, Mori Y (2016) Effects of glia in a triphasic continuum model of cortical spreading depression. Bull Math Biol 78(10):1943–1967. https://doi.org/10.1007/s11538-016-0206-9
Pesaran B, Vinck M, Einevoll GT, Sirota A, Fries P, Siegel M, Truccolo W, Schroeder CE, Srinivasan R (2018) Investigating large-scale brain dynamics using field potential recordings: analysis and interpretation. Nat Neurosci 21:903–919. https://doi.org/10.1038/s41593-018-0171-8
Pettersen KH, Einevoll GT (2008) Amplitude variability and extracellular low-pass filtering of neuronal spikes. Biophys J 94(3):784–802. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=2186261&tool=pmcentrez&rendertype=abstract
Pettersen KH, Devor A, Ulbert I, Dale AM, Einevoll GT (2006) Current-source density estimation based on inversion of electrostatic forward solution: effects of finite extent of neuronal activity and conductivity discontinuities. J Neurosci methods 154(1–2):116–33. http://www.ncbi.nlm.nih.gov/pubmed/16436298
Pettersen KH, Hagen E, Einevoll GT (2008) Estimation of population firing rates and current source densities from laminar electrode recordings. J Comput Neurosci 24(3):291–313. http://www.ncbi.nlm.nih.gov/pubmed/17926125
Pettersen KH, Lindén H, Dale AM, Einevoll GT (2012) Extracellular spikes and CSD. In: Brette R, Destexhe A (eds) Handbook of neural activity measurement. Cambridge University, Cambridge, pp 92–135
Pettersen KH, Lindén H, Tetzlaff T, Einevoll GT (2014) Power laws from linear neuronal cable theory: power spectral densities of the soma potential, soma membrane current and single-neuron contribution to the EEG. PLoS Comput Biol 10(11):e1003928. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=4230751&tool=pmcentrez&rendertype=abstract
Pfurtscheller G, Cooper R (1975) Frequency dependence of the transmission of the EEG from cortex to scalp. Electroencephalogr Clin Neurophysiol 38(1):93–96
Pods J (2017) A comparison of computational models for the extracellular potential of neurons. J Integr Neurosci 16(1):19–32
Pods J, Schönke J, Bastian P (2013) Electrodiffusion models of neurons and extracellular space using the Poisson-Nernst-Planck equations–numerical simulation of the intra- and extracellular potential for an axon model. Biophys J 105(1):242–254. http://www.pubmedcentral.nih.gov/articlerender.fcgi?artid=3703912&tool=pmcentrez&rendertype=abstract
Potworowski J, Jakuczun W, Leski S, Wójcik D (2012) Kernel current source density method. Neural Comput 24(2):541–75. http://www.ncbi.nlm.nih.gov/pubmed/22091662
Ranck JB (1963) Specific impedance of rabbit cerebral cortex. Exp Neurol 7(2):144–152
Ranta R, Le Cam S, Tyvaert L, Louis-Dorr V (2017) Assessing human brain impedance using simultaneous surface and intracerebral recordings. Neuroscience 343:411–422
Reimann MW, Anastassiou CA, Perin R, Hill SL, Markram H, Koch, C (2013) A biophysically detailed model of neocortical local field potentials predicts the critical role of active membrane currents. Neuron 79(2):375–390. http://linkinghub.elsevier.com/retrieve/pii/S0896627313004431
Savtchenko LP, Poo MM, Rusakov DA (2017) Electrodiffusion phenomena in neuroscience: a neglected companion. https://doi.org/10.1038/nrn.2017.101
Schomburg EW, Anastassiou CA, Buzsaki G, Koch C (2012) The spiking component of oscillatory extracellular potentials in the rat hippocampus. J Neurosci 32(34):11798–11811. http://www.jneurosci.org/cgi/doi/10.1523/JNEUROSCI.0656-12.2012
Skaar, J-EW, Stasik AJ, Hagen E, Ness TV, Einevoll GT (2020). Estimation of neural network model parameters from local field potentials (LFPs). PLoS Comput Biol 16(3):e1007725
Solbrå A, Bergersen AW, van den Brink J, Malthe-Sørenssen A, Einevoll GT, Halnes G (2018) A Kirchhoff-Nernst-Planck framework for modeling large scale extracellular electrodiffusion surrounding morphologically detailed neurons. PLoS Comput Biol 14(10):1–26
Srinivasan R, Nunez PL, Silberstein RB (1998) Spatial filtering and neocortical dynamics: estimates of EEG coherence. IEEE Trans Biomed Eng 45(7):814–826
Sterratt D, Graham B, Gillies A, Willshaw D (2011) Principles of computational modelling in neuroscience. Cambridge University, Cambridge
Suzuki M, Larkum ME (2017) Dendritic calcium spikes are clearly detectable at the cortical surface. Nature Commun. 8(276):1–10. https://doi.org/10.1038/s41467-017-00282-4
Sætra MJ, Einevoll GT, Halnes G (2020) An electrodiffusive, ion conserving Pinsky-Rinzel model with homeostatic mechanisms. PLoS Comput Biol 16(4):1–36. https://doi.org/10.1371/journal.pcbi.1007661
Teleńczuk B, Dehghani N, Le Van Quyen M, Cash SS, Halgren E, Hatsopoulos NG, Destexhe A (2017) Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex. Sci Rep 7:40211
Tracey B, Williams M (2011) Computationally efficient bioelectric field modeling and effects of frequency-dependent tissue capacitance. J Neural Eng 8(3):036017
Tuttle A, Diaz JR, Mori Y (2019) A computational study on the role of glutamate and NMDA receptors on cortical spreading depression using a multidomain electrodiffusion model. PLoS Comput Biol 15(12):e1007455
Wagner T, Eden U, Rushmore J, Russo CJ, Dipietro L, Fregni F, Simon S, Rotman S, Pitskel NB, Ramos-Estebanez C, Pascual-Leone A, Grodzinsky AJ, Zahn M, Valero-Cabré A (2014) Impact of brain tissue filtering on neurostimulation fields: a modeling study. NeuroImage 85(3):1048–1057. http://www.ncbi.nlm.nih.gov/pubmed/23850466
Zangiabadi N, Ladino LD, Sina F, Orozco-Hernández JP, Carter A, Téllez-Zenteno JF (2019). Deep brain stimulation and drug-resistant epilepsy: a review of the literature. Front Neurol 10:601
Acknowledgements
This research has received funding from the European Union Horizon 2020 Framework Programme for Research and Innovation under Specific Grant Agreement No. 785907 and No. 945539 [Human Brain Project (HBP) SGA2 and SGA3], and the Research Council of Norway (Notur, nn4661k; DigiBrain, no. 248828; INCF National Node, no. 269774).
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Ness, T.V., Halnes, G., Næss, S., Pettersen, K.H., Einevoll, G.T. (2022). Computing Extracellular Electric Potentials from Neuronal Simulations. In: Giugliano, M., Negrello, M., Linaro, D. (eds) Computational Modelling of the Brain. Advances in Experimental Medicine and Biology(), vol 1359. Springer, Cham. https://doi.org/10.1007/978-3-030-89439-9_8
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