Abstract
Mathematical modeling of neurons is an essential tool to investigate neuronal activity alongside with experimental approaches. However, the conventional modeling framework to simulate neuronal dynamics and extracellular potentials makes several assumptions that might need to be revisited for some applications. In this chapter we apply the EMI model to investigate the ephaptic effect and the effect of the extracellular probes on the measured potential. Finally, we introduce reduced EMI models, which provide a more computationally efficient framework for simulating neurons with complex morphologies.
Chapter PDF
Similar content being viewed by others
References
Anastassiou CA, Perin R, Markram H, Koch C (2011) Ephaptic coupling of cortical neurons. Nature Neuroscience 14(2):217
Ascoli GA, Donohue DE, Halavi M (2007) Neuromorpho.org: a central resource for neuronal morphologies. Journal of Neuroscience 27(35):9247–9251
Buccino AP, Kuchta M, Jæger KH, Ness TV, Berthet P, Mardal KA, Cauwenberghs G, Tveito A (2019) How does the presence of neural probes affect extracellular potentials? Journal of Neural Engineering 16(2):026030
Cerroni D, Laurino F, Zunino P (2019) Mathematical analysis, finite element approximation and numerical solvers for the interaction of 3d reservoirs with 1d wells. GEM-International Journal on Geomathematics 10(1):4
D’Angelo C, Quarteroni A (2008) On the coupling of 1d and 3d diffusion-reaction equations: application to tissue perfusion problems. Mathematical Models and Methods in Applied Sciences 18(08):1481–1504
Einevoll GT, Kayser C, Logothetis NK, Panzeri S (2013) Modelling and analysis of local field potentials for studying the function of cortical circuits. Nature Reviews Neuroscience 14(11):770–785
Geuzaine C, Remacle JF (2009) Gmsh: A 3-d finite element mesh generator with built-in preand post-processing facilities. International Journal for Numerical Methods in Engineering 79(11):1309–1331
Gouwens NW, Berg J, Feng D, Sorensen SA, Zeng H, Hawrylycz MJ, Koch C, Arkhipov A (2018) Systematic generation of biophysically detailed models for diverse cortical neuron types. Nature Communications 9(1):710
Holt GR, Koch C (1999) Electrical interactions via the extracellular potential near cell bodies. Journal of Computational Neuroscience 6(2):169–184
Jæger KH, Tveito A (2020) Derivation of a cell-based mathematical model of excitable cells. In: Tveito A, Mardal KA, Rognes ME (eds) Modeling excitable tissue - The EMI framework, Simula Springer Notes in Computing, SpringerNature
Jun JJ, Steinmetz NA, Siegle JH, Denman DJ, Bauza M, Barbarits B, Lee AK, Anastassiou CA, Andrei A, Aydın Ç, et al. (2017) Fully integrated silicon probes for high-density recording of neural activity. Nature 551(7679):232–236
Kuchta M, Mardal KA (2020) Iterative solvers for cell-based EMI models. In: Tveito A, Mardal KA, Rognes ME (eds) Modeling excitable tissue - The EMI framework, Simula Springer Notes in Computing, SpringerNature
Kuchta M, Laurino F, Mardal KA, Zunino P (2020) Analysis and approximation of mixeddimensional pdes on 3d-1d domains coupled with lagrange multipliers. arXiv preprint arXiv:200402722
Kuchta M, Mardal KA, Rognes ME (2020) Solving the EMI equations using finite element methods. In: Tveito A, Mardal KA, Rognes ME (eds) Modeling excitable tissue - The EMI framework, Simula Springer Notes in Computing, SpringerNature
Laurino F, Zunino P (2019) Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction. ESAIM: M2AN 53(6):2047–2080
Markram H, et al. (2015) Reconstruction and simulation of neocortical microcircuitry. Cell 163(2):456–492
Mörschel K, Breit M, Queisser G (2017) Generating neuron geometries for detailed threedimensional simulations using AnaMorph. Neuroinformatics 15(3):247–269
Ramaswamy S, et al. (2015) The neocortical microcircuit collaboration portal: a resource for rat somatosensory cortex. Frontiers in Neural Circuits 9
Sterratt D, Graham B, Gillies A,Willshaw D (2011) Principles of computational modelling in neuroscience. Cambridge University Press
Tveito A, Jæger KH, Kuchta M, Mardal KA, Rognes ME (2017) A cell-based framework for numerical modeling of electrical conduction in cardiac tissue. Frontiers in Physics 5:48
Tveito A, Jæger KH, Lines GT, Paszkowski Ł, Sundnes J, Edwards AG, M¯aki-Marttunen T, Halnes G, Einevoll GT (2017) An evaluation of the accuracy of classical models for computing the membrane potential and extracellular potential for neurons. Frontiers in Computational Neuroscience 11:27
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2021 The Author(s)
About this chapter
Cite this chapter
Buccino, A.P., Kuchta, M., Schreiner, J., Mardal, KA. (2021). Improving Neural Simulations with the EMI Model. In: Tveito, A., Mardal, KA., Rognes, M.E. (eds) Modeling Excitable Tissue. Simula SpringerBriefs on Computing(), vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-61157-6_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-61157-6_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-61156-9
Online ISBN: 978-3-030-61157-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)