Uncertainty Quantification in a Patient-Specific One-Dimensional Arterial Network Model: EnKF-Based Inflow Estimator

Abstract

Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.

Sensitivity analysis and uncertainty quantification of 1‐D models of pulmonary hemodynamics in mice under control and hypertensive conditions

“…To address this problem, it is important to understand how the model sensitivity changes with network size and if it is possible to infer parameters given the available data. Several recent studies 6,15,20 have conducted sensitivity analyses and examined uncertainties in predictions for a range of cardiovascular models 17,28,44,65,79,80 . Two studies 25,44 have quantified how parameter influence changes with network size and complexity, and one study 17 has examined time-varying changes in model sensitivities.…”

MCMC methods for inference in a mathematical model of pulmonary circulation

“…To speed up the simulations, we will run this algorithm on an objective function emulated using Gaussian processes (Rasmussen & Williams, ). Another alternative to learn the unobserved parameters is by employing the Ensemble Kalman filter, following the idea in Arnold et al ().…”

Data-driven cardiovascular flow modelling: examples and opportunities

“…Parameters in zero-and one-dimensional blood flow models have been estimated based on clinical measurements using the ensemble Kalman filter [71,72] and the unscented Kalman filter [73], which are extensions formulated to deal with large state dimensions and nonlinear system dynamics, respectively. The ensemble Kalman filter has also been used to estimate the inlet flow waveform in patient-specific arterial network models [74]. Reduced-order unscented Kalman filter has been used in conjunction with fluid-structure interaction (FSI) simulations to estimate aortic aneurysm wall stiffness from wall displacement measurements [75].…”