The Necessary Modeling Detail for Neuronal Signaling: Poisson--Nernst--Planck and Cable Equation Models in One and Three Dimensions

DOI10.1137/20M1344226zbMath1465.92013OpenAlexW3153155560MaRDI QIDQ4986542

Gillian Queisser, Markus Breit

Publication date: 27 April 2021

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1344226

zbMATH Keywords

cable equationPoisson-Nernst-PlanckPDE modelingneuronal signalingion dynamicselectrical signaling

Mathematics Subject Classification ID

Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Biophysics (92C05) Cell biology (92C37)

Uses Software

• Unnamed Item
• UG4
• libGrid
• libAlgebra
• libDiscretization
• pcl

Cites Work

• Unnamed Item
• What is required for neuronal calcium waves? A numerical parameter study
• A massively parallel geometric multigrid solver on hierarchically distributed grids
• \textit{UG} 4: a novel flexible software system for simulating PDE based models on high performance computers
• Analysis of the Poisson-Nernst-Planck equation in a ball for modeling the voltage-current relation in neurobiological microdomains
• An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Neuronal Calcium Wave Propagation Varies with Changes in Endoplasmic Reticulum Parameters: A Computer Model

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