Abstract
In computational neuroscience the transmission of electrical signals of neurons is normally simulated by means of point process neurons, which mainly reflect the scale in time, or the classical cable equation which additionally introduces one space dimension. Here we present a fully resolved electrical model based on Gauss’ law and the conservation of charges which considers all space dimensions and is capable to simulate the extracellular and intracellular potential. For these simulations three dimensional volume meshes are required and due to the inherent complexity of the neuronal structure, these 3D-reconstructions yield large data-sets and need efficient solving strategies. The UG4-simulation framework is a powerful software for the solution of partial differential equations on unstructured grids in one, two and three space dimensions and with its efficient, parallel solvers is well suited for this task. Computations of the 3D-cable equation on a simple geometry and on a three-dimensionally reconstructed neuron were performed on the Hazel Hen supercomputer, testing for weak scalability.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K. Xylouris, G. Wittum, A three-dimensional mathematical model for the signal propagation on a neuron’s membrane. Front. Comput. Neurosci. 9, 1–9 (2015)
A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952)
G. A. Ascoli, Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat. Rev. Neurosci. 7(4), 318–324 (2006)
Sebastian Reiter, Andreas Vogel, Ingo Heppner, Martin Rupp, Gabriel Wittum, A massively parallel geometric multigrid solver on hierarchically distributed grids. Comp. Vis. Sci. 16(4), 151–164 (2013)
T. Radman, R.L. Ramos, J.C. Brumberg, M. Bikson, Role of Cortical Cell Type and Morphology in Sub- and Suprathreshold Uniform Electric Field Stimulation. Brain Stimul. 2(4), 215–228 (2009)
K. Mörschel, M. Breit, G. Queisser, Generating neuron geometries for detailed three-dimensional simulations using anamorph. Neuroinformatics (2017)
A. Vogel, S. Reiter, M. Rupp, A. Nägel, G. Wittum, UG 4: A novel flexible software system for simulating PDE based models on high performance computers. Comp. Vis. Sci. 16(4), 165–179 (2013)
X.S. Li, An overview of superlu: Algorithms, implementation, and user interface. Toms (2005)
Acknowledgements
We thank the HLRS for the opportunity to use Hazel Hen and their kind support.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Huymayer, M., Lampe, M., Nägel, A., Wittum, G. (2021). First Steps Towards a Scaling Analysis of a Fully Resolved Electrical Neuron Model. In: Nagel, W.E., Kröner, D.H., Resch, M.M. (eds) High Performance Computing in Science and Engineering '19. Springer, Cham. https://doi.org/10.1007/978-3-030-66792-4_39
Download citation
DOI: https://doi.org/10.1007/978-3-030-66792-4_39
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-66791-7
Online ISBN: 978-3-030-66792-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)