A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications. (26th November 2015)

• Record Type: Journal Article
• Authors: Eck, Vinzenz Gregor; Donders, Wouter Paulus; Sturdy, Jacob; Feinberg, Jonathan; Delhaas, Tammo; Hellevik, Leif Rune; Huberts, Wouter
• Is Part Of: International journal for numerical methods in biomedical engineering. Volume 32:Number 8(2016:Aug.)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2015-11-26
• Subjects: uncertainty quantification -- sensitivity analysis -- cardiovascular modeling -- Monte Carlo -- polynomial chaos -- fractional flow reserve -- arterial compliance; Biomedical engineering -- Periodicals; Imaging systems in medicine -- Periodicals; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 610.28
• DOI: 10.1002/cnm.2755
• Languages: English
• ISSNs: 2040-7939

Abstract

Summary: 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 ( C T ). 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 C T . 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. Abstract : Uncertainty quantification (UQ) and sensitivity analysis (SA) are critical for the clinical application of mathematical models. We review the best practices for UQ and SA and present a practical guide that can help move models towards clinical application. We demonstrate the practical guide in two examples using both the Monte Carlo method and the polynomial chaos method.