title: Application of an Adaptive Polynomial Chaos Expansion on Computationally Expensive Three-Dimensional Cardiovascular Models for Uncertainty Quantification and Sensitivity Analysis.
abstract: When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, "An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis," Probab. Eng. Mech., 25(2), pp. 183-197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model's quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70-80% and 50-90% for the AAA and AVF model, respectively.
authors.affiliation: Department of Biomedical Engineering, School for Cardiovascular Diseases (CARIM), Maastricht University, Universiteitssingel 50, Maastricht 6229 ER, The Netherlands e-mail: s.quicken@maastrichtuniversity.nl.
authors.forename: Sjeng
authors.initials: S
authors.lastname: Quicken
authors.affiliation: Department of Biomedical Engineering, School for Mental Health and Neuroscience (MHENS), Maastricht University, Universiteitssingel 50, Maastricht 6229 ER, The Netherlands e-mail: w.donders@maastrichtuniversity.nl.
authors.forename: Wouter P
authors.initials: WP
authors.lastname: Donders
authors.affiliation: Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands e-mail: e.m.j.v.disseldorp@tue.nl.
authors.forename: Emiel M J
authors.initials: EM
authors.lastname: van Disseldorp
authors.affiliation: Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands e-mail: k.gashi@tue.nl.
authors.forename: Kujtim
authors.initials: K
authors.lastname: Gashi
authors.affiliation: Department of Vascular Surgery, Maastricht University Medical Center, P.O. Box 5800, Maastricht 6202 AZ, The Netherlands e-mail: barend.mees@mumc.nl.
authors.forename: Barend M E
authors.initials: BM
authors.lastname: Mees
authors.affiliation: Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands e-mail: f.n.v.d.vosse@tue.nl.
authors.forename: Frans N
authors.initials: FN
authors.lastname: van de Vosse
authors.affiliation: Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, Eindhoven 5600 MB, The Netherlands e-mail: r.lopata@tue.nl.
authors.forename: Richard G P
authors.initials: RG
authors.lastname: Lopata
authors.affiliation: Department of Biomedical Engineering, School for Cardiovascular Diseases (CARIM), Maastricht University, Universiteitssingel 50, Maastricht 6229 ER, The Netherlands e-mail: tammo.delhaas@maastrichtuniversity.nl.
authors.forename: Tammo
authors.initials: T
authors.lastname: Delhaas
authors.affiliation: Department of Biomedical Engineering, School for Cardiovascular Diseases (CARIM), Maastricht University, Universiteitssingel 50, Maastricht 6229 ER, The Netherlands e-mail: wouter.huberts@maastrichtuniversity.nl.
authors.forename: Wouter
authors.initials: W
authors.lastname: Huberts
mesh_terms: D000465:Algorithms; D001012:Aorta, Abdominal / Q000503:physiopathology*; D017544:Aortic Aneurysm, Abdominal / Q000503:physiopathology*; D001783:Blood Flow Velocity; D001794:Blood Pressure; D003198:Computer Simulation; D055119:Elastic Modulus; D006801:Humans; D008955:Models, Cardiovascular; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D066230:Patient-Specific Modeling; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D033081:Shear Strength