title: Efficient calculation of the quasi-static electrical potential on a tetrahedral mesh and its implementation in STEPS.
abstract: We describe a novel method for calculating the quasi-static electrical potential on tetrahedral meshes, which we call E-Field. The E-Field method is implemented in STEPS, which performs stochastic spatial reaction-diffusion computations in tetrahedral-based cellular geometry reconstructions. This provides a level of integration between electrical excitability and spatial molecular dynamics in realistic cellular morphology not previously achievable. Deterministic solutions are also possible. By performing the Rallpack tests we demonstrate the accuracy of the E-Field method. Efficient node ordering is an important practical consideration, and we find that a breadth-first search provides the best solutions, although principal axis ordering suffices for some geometries. We discuss potential applications and possible future directions, and predict that the E-Field implementation in STEPS will play an important role in the future of multiscale neural simulations.
authors.affiliation: Computational Neuroscience Unit, Okinawa Institute of Science and Technology Onna-son, Japan ; Theoretical Neurobiology, University of Antwerp Antwerp, Belgium.
authors.forename: Iain
authors.initials: I
authors.lastname: Hepburn
authors.forename: Robert
authors.initials: R
authors.lastname: Cannon
authors.forename: Erik
authors.initials: E
authors.lastname: De Schutter
keywords: 3D electrical potential; complex morphology; efficient node ordering; membrane potential; multiscale simulation; spatial stochastic simulation; tetrahedral meshes