title: Uncertainty quantification in virtual surgery hemodynamics predictions for single ventricle palliation.
abstract: The adoption of simulation tools to predict surgical outcomes is increasingly leading to questions about the variability of these predictions in the presence of uncertainty associated with the input clinical data. In the present study, we propose a methodology for full propagation of uncertainty from clinical data to model results that, unlike deterministic simulation, enables estimation of the confidence associated with model predictions. We illustrate this problem in a virtual stage II single ventricle palliation surgery example. First, probability density functions (PDFs) of right pulmonary artery (PA) flow split ratio and average pulmonary pressure are determined from clinical measurements, complemented by literature data. Starting from a zero-dimensional semi-empirical approximation, Bayesian parameter estimation is used to find the distributions of boundary conditions that produce the expected PA flow split and average pressure PDFs as pre-operative model results. To reduce computational cost, this inverse problem is solved using a Kriging approximant. Second, uncertainties in the boundary conditions are propagated to simulation predictions. Sparse grid stochastic collocation is employed to statistically characterize model predictions of post-operative hemodynamics in models with and without PA stenosis. The results quantify the statistical variability in virtual surgery predictions, allowing for placement of confidence intervals on simulation outputs.
authors.affiliation: Mechanical and Aerospace Engineering Department, University of California at San Diego, San Diego, CA, U.S.A.
authors.forename: D E
authors.initials: DE
authors.lastname: Schiavazzi
authors.affiliation: INRIA Paris-Rocquencourt and Sorbonne Universités UPMC Paris 6, Paris, France.
authors.forename: G
authors.initials: G
authors.lastname: Arbia
authors.affiliation: Great Ormond Street Hospital for Children and UCL Institute of Cardiovascular Science, London, U.K.
authors.forename: C
authors.initials: C
authors.lastname: Baker
authors.affiliation: Department of Pediatrics Medical University of South Carolina, Charleston, SC, U.S.A.
authors.forename: A M
authors.initials: AM
authors.lastname: Hlavacek
authors.affiliation: Great Ormond Street Hospital for Children and UCL Institute of Cardiovascular Science, London, U.K.
authors.forename: T Y
authors.initials: TY
authors.lastname: Hsia
authors.affiliation: Mechanical and Aerospace Engineering Department, University of California at San Diego, San Diego, CA, U.S.A.
authors.forename: A L
authors.initials: AL
authors.lastname: Marsden
authors.affiliation: INRIA Paris-Rocquencourt and Sorbonne Universités UPMC Paris 6, Paris, France.
authors.forename: I E
authors.identifier: http://orcid.org/0000-0001-9754-4386
authors.initials: IE
authors.lastname: Vignon-Clementel
authors.affiliation: Mechanical and Aerospace Engineering Department, University of California at San Diego, San Diego, CA, U.S.A.
mesh_terms: D001499:Bayes Theorem; D001783:Blood Flow Velocity; D013504:Cardiovascular Surgical Procedures; D003198:Computer Simulation; D006352:Heart Ventricles / Q000601:surgery*; D006439:Hemodynamics; D006801:Humans; D008955:Models, Cardiovascular; D011312:Pressure; D011651:Pulmonary Artery / Q000601:surgery; D013314:Stress, Mechanical; D035501:Uncertainty; D014584:User-Computer Interface
keywords: Fontan palliation surgery; inverse Bayesian parameter estimation; single ventricle congenital heart disease; sparse grids; uncertainty quantification; virtual surgery