AUTHOR=Hepburn Iain , Cannon Robert , De Schutter Erik TITLE=Efficient calculation of the quasi-static electrical potential on a tetrahedral mesh and its implementation in STEPS JOURNAL=Frontiers in Computational Neuroscience VOLUME=7 YEAR=2013 URL=https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2013.00129 DOI=10.3389/fncom.2013.00129 ISSN=1662-5188 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.