title: A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications.
abstract: As we shift from population-based medicine towards a more precise patient-specific regime guided by predictions of verified and well-established cardiovascular models, an urgent question arises: how sensitive are the model predictions to errors and uncertainties in the model inputs? To make our models suitable for clinical decision-making, precise knowledge of prediction reliability is of paramount importance. Efficient and practical methods for uncertainty quantification (UQ) and sensitivity analysis (SA) are therefore essential. In this work, we explain the concepts of global UQ and global, variance-based SA along with two often-used methods that are applicable to any model without requiring model implementation changes: Monte Carlo (MC) and polynomial chaos (PC). Furthermore, we propose a guide for UQ and SA according to a six-step procedure and demonstrate it for two clinically relevant cardiovascular models: model-based estimation of the fractional flow reserve (FFR) and model-based estimation of the total arterial compliance (CT ). Both MC and PC produce identical results and may be used interchangeably to identify most significant model inputs with respect to uncertainty in model predictions of FFR and CT . However, PC is more cost-efficient as it requires an order of magnitude fewer model evaluations than MC. Additionally, we demonstrate that targeted reduction of uncertainty in the most significant model inputs reduces the uncertainty in the model predictions efficiently. In conclusion, this article offers a practical guide to UQ and SA to help move the clinical application of mathematical models forward. Copyright © 2015 John Wiley & Sons, Ltd.
authors.affiliation: Division of Biomechanics, Department of Structural Engineering, NTNU, Trondheim, Norway.
authors.forename: Vinzenz Gregor
authors.initials: VG
authors.lastname: Eck
authors.affiliation: Department of Biomedical Engineering, School for Mental Health and Neuroscience, Maastricht University, Maastricht, The Netherlands.
authors.forename: Wouter Paulus
authors.identifier: 0000-0002-2899-9181
authors.initials: WP
authors.lastname: Donders
authors.affiliation: Division of Biomechanics, Department of Structural Engineering, NTNU, Trondheim, Norway.
authors.forename: Jacob
authors.initials: J
authors.lastname: Sturdy
authors.affiliation: Center for Biomedical Computing, Simula Research Laboratory, Lysaker, Norway.|Department of Mathematics, University of Oslo, Oslo, Norway.
authors.forename: Jonathan
authors.initials: J
authors.lastname: Feinberg
authors.affiliation: Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands.
authors.forename: Tammo
authors.initials: T
authors.lastname: Delhaas
authors.affiliation: Division of Biomechanics, Department of Structural Engineering, NTNU, Trondheim, Norway.|Center for Biomedical Computing, Simula Research Laboratory, Lysaker, Norway.
authors.forename: Leif Rune
authors.initials: LR
authors.lastname: Hellevik
authors.affiliation: Department of Biomedical Engineering, CARIM School for Cardiovascular Diseases, Maastricht University, Maastricht, The Netherlands.
authors.forename: Wouter
authors.initials: W
authors.lastname: Huberts
mesh_terms: D000465:Algorithms; D006801:Humans; D008955:Models, Cardiovascular; D009010:Monte Carlo Method; D015203:Reproducibility of Results
keywords: Monte Carlo; arterial compliance; cardiovascular modeling; fractional flow reserve; polynomial chaos; sensitivity analysis; uncertainty quantification