title: Uncertainty Propagation in Nerve Impulses Through the Action Potential Mechanism.
abstract: We investigate the propagation of probabilistic uncertainty through the action potential mechanism in nerve cells. Using the Hodgkin-Huxley (H-H) model and Stochastic Collocation on Sparse Grids, we obtain an accurate probabilistic interpretation of the deterministic dynamics of the transmembrane potential and gating variables. Using Sobol indices, out of the 11 uncertain parameters in the H-H model, we unravel two main uncertainty sources, which account for more than 90 % of the fluctuations in neuronal responses, and have a direct biophysical interpretation. We discuss how this interesting feature of the H-H model allows one to reduce greatly the probabilistic degrees of freedom in uncertainty quantification analyses, saving CPU time in numerical simulations and opening possibilities for probabilistic generalisation of other deterministic models of great importance in physiology and mathematical neuroscience.
authors.affiliation: CWI, Amsterdam, Science Park 123, 1098 XG, Amsterdam, The Netherlands. atorresv@cwi.nl.|Department of Neurology and Neurosurgery, Brain Center Rudolf Magnus, University Medical Center Utrecht, Heidelberglaan 100, 3584 CX, Utrecht, The Netherlands. atorresv@cwi.nl.
authors.forename: Aldemar
authors.initials: A
authors.lastname: Torres Valderrama
authors.affiliation: CWI, Amsterdam, Science Park 123, 1098 XG, Amsterdam, The Netherlands. atorresv@cwi.nl.
authors.forename: Jeroen
authors.initials: J
authors.lastname: Witteveen
authors.affiliation: CWI, Amsterdam, Science Park 123, 1098 XG, Amsterdam, The Netherlands. atorresv@cwi.nl.
authors.forename: Maria
authors.initials: M
authors.lastname: Navarro
authors.affiliation: CWI, Amsterdam, Science Park 123, 1098 XG, Amsterdam, The Netherlands. atorresv@cwi.nl.
authors.forename: Joke
authors.initials: J
authors.lastname: Blom
keywords: Hodgkin–Huxley model; Neurodynamics; Neuronal Noise; Sparse grid quadrature; Uncertainty Quantification