title: Uncertainty and variability in models of the cardiac action potential: Can we build trustworthy models?
abstract: Cardiac electrophysiology models have been developed for over 50years, and now include detailed descriptions of individual ion currents and sub-cellular calcium handling. It is commonly accepted that there are many uncertainties in these systems, with quantities such as ion channel kinetics or expression levels being difficult to measure or variable between samples. Until recently, the original approach of describing model parameters using single values has been retained, and consequently the majority of mathematical models in use today provide point predictions, with no associated uncertainty. In recent years, statistical techniques have been developed and applied in many scientific areas to capture uncertainties in the quantities that determine model behaviour, and to provide a distribution of predictions which accounts for this uncertainty. In this paper we discuss this concept, which is termed uncertainty quantification, and consider how it might be applied to cardiac electrophysiology models. We present two case studies in which probability distributions, instead of individual numbers, are inferred from data to describe quantities such as maximal current densities. Then we show how these probabilistic representations of model parameters enable probabilities to be placed on predicted behaviours. We demonstrate how changes in these probability distributions across data sets offer insight into which currents cause beat-to-beat variability in canine APs. We conclude with a discussion of the challenges that this approach entails, and how it provides opportunities to improve our understanding of electrophysiology.
authors.affiliation: Computational Biology, Dept. of Computer Science, University of Oxford, Oxford OX1 3QD, UK.
authors.forename: Ross H
authors.initials: RH
authors.lastname: Johnstone
authors.affiliation: Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield S1 4DP, UK.
authors.forename: Eugene T Y
authors.initials: ETY
authors.lastname: Chang
authors.affiliation: CNRS & CRIStAL, Université de Lille, 59651 Villeneuve d'Ascq, France.
authors.forename: Rémi
authors.initials: R
authors.lastname: Bardenet
authors.affiliation: Division of Heart & Lungs, Department of Medical Physiology, University Medical Center Utrecht, Utrecht, The Netherlands.
authors.forename: Teun P
authors.initials: TP
authors.lastname: de Boer
authors.affiliation: Computational Biology, Dept. of Computer Science, University of Oxford, Oxford OX1 3QD, UK.
authors.forename: David J
authors.initials: DJ
authors.lastname: Gavaghan
authors.affiliation: U.S. Food and Drug Administration, 10903 New Hampshire Avenue, Silver Spring, MD 20993, USA. Electronic address: pras.pathmanathan@fda.hhs.gov.
authors.forename: Pras
authors.initials: P
authors.lastname: Pathmanathan
authors.affiliation: Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield S1 4DP, UK. Electronic address: r.h.clayton@sheffield.ac.uk.
authors.forename: Richard H
authors.initials: RH
authors.lastname: Clayton
authors.affiliation: Computational Biology, Dept. of Computer Science, University of Oxford, Oxford OX1 3QD, UK. Electronic address: gary.mirams@cs.ox.ac.uk.
authors.forename: Gary R
authors.initials: GR
authors.lastname: Mirams
mesh_terms: D000200:Action Potentials; D000465:Algorithms; D000818:Animals; D004285:Dogs; D055724:Electrophysiological Phenomena; D006321:Heart / Q000502:physiology*; D007473:Ion Channels / Q000378:metabolism; D008564:Membrane Potentials; D008954:Models, Biological; D009206:Myocardium / Q000378:metabolism*
chemical_list: D007473:Ion Channels
keywords: Cardiac electrophysiology; Mathematical model; Probability; Uncertainty quantification