Efficient Uncertainty Quantification in a Multiscale Model of Pulmonary Arterial and Venous Hemodynamics

Computational hemodynamics models are becoming increasingly useful in the management and prognosis of complex, multiscale pathologies, including those attributed to the development of pulmonary vascular disease. However, diseases like pulmonary hypertension are heterogeneous, and affect both the proximal arteries and veins as well as the microcirculation. Simulation tools and the data used for model calibration are also inherently uncertain, requiring a full analysis of the sensitivity and uncertainty attributed to model inputs and outputs. Thus, this study quantifies model sensitivity and output uncertainty in a multiscale, pulse-wave propagation model of pulmonary hemodynamics. Our pulmonary circuit model consists of fifteen proximal arteries and twelve proximal veins, connected by a two-sided, structured tree model of the distal vasculature. We use polynomial chaos expansions to expedite the sensitivity and uncertainty quantification analyses and provide results for both the proximal and distal vasculature. Our analyses provide uncertainty in blood pressure, flow, and wave propagation phenomenon, as well as wall shear stress and cyclic stretch, both of which are important stimuli for endothelial cell mechanotransduction. We conclude that, while nearly all the parameters in our system have some influence on model predictions, the parameters describing the density of the microvascular beds have the largest effects on all simulated quantities in both the proximal and distal circulation.Comment: 10 Figures, 2 table

Parameter Inference in the Pulmonary Circulation of Mice

This study focuses on parameter inference in a pulmonary blood cir- culation model for mice. It utilises a fluid dynamics network model that takes selected parameter values and aims to mimic features of the pulmonary haemody- namics under normal physiological and pathological conditions. This is of medical relevance as it allows monitoring of the progression of pulmonary hypertension. Constraint nonlinear optimization is successfully used to learn the parameter values

MCMC with Delayed Acceptance using a Surrogate Model with an Application to Cardiovascular Fluid Dynamics

Parameter estimation and uncertainty quantification in physiological modelling is a vital step towards personalised medicine. Current state-of-the-art in this research area performs parameter optimisation, with very limited uncertainty quantification. This paper demonstrates the advantage of novel sampling methods, applied on a complex biological PDE system of the pulmonary circulation. The aim is to find an efficient and accurate method for the inference and uncertainty quantification of unknown parameters, relevant for disease diagnosis (pulmonary hypertension) from limited and noisy blood pressure data. The data likelihood is expensive to evaluate as it requires solving numerically a system of PDEs. Therefore, having a model that best trades off accuracy and computational efficiency is of uppermost importance. In this study, we employ fast Bayesian methods, namely MCMC algorithms coupled with emulation using Gaussian Processes, to achieve a computational speed-up. We compare the Delayed Rejection Adaptive Metropolis algorithm in a History Matching framework to the delayed acceptance Adaptive Metropolis algorithm. The first algorithm draws samples from the approximate posterior distribution, while the latter is guaranteed to generate samples from the exact posterior distribution asymptotically. In this paper we propose and derive the n-steps ahead delayed acceptance Metropolis-Hastings algorithm, which is a generalisation of the classical 1-step ahead delayed acceptance Metropolis-Hastings. We show the superiority of the n-steps ahead algorithm over the 1-step ahead method

Inference in Cardiovascular Modelling Subject to Medical Interventions

Pulmonary hypertension (PH), i.e., high blood pressure in the lungs, is a serious medical condition that can damage the right ventricle of the heart and ultimately lead to heart failure. Standard diagnostic procedures are based on right-heart catheterization, which is an invasive technique that can potentially have serious side effects. Recent methodological advancements in fluid dynamics modelling of the pulmonary blood circulation system promise to mathematically predict the blood pressure based on non-invasive measurements of the blood flow. Thus, subsequent to PH diagnostication, further investigations would no longer require catheterization. However, in order for these alternative techniques to be applicable in the clinic, accurate model calibration and parameter estimation are paramount. Medical interventions taken to combat high blood pressure (as predicted from the mathematical model) alter the underlying cardiovascular physiology, thus interfering with the parameter estimation procedure. In the present study, we have carried out a series of cardiovascular simulations to assess the reliability of cardiovascular physiological parameter estimation in the presence of medical interventions. Our principal result is that if the closed-loop effect of medical interventions is accounted for, the model calibration provides accurate parameter estimates. This finding has important implications for the applicability of cardio-physiological modelling in the clinical practice

Influence of image segmentation on one-dimensional fluid dynamics predictions in the mouse pulmonary arteries

Computational fluid dynamics (CFD) models are emerging as tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation has made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension (PH), which requires a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation can easily propagate to CFD model predictions, making uncertainty quantification crucial for subject-specific models. This study quantifies the variability of one-dimensional (1D) CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of an image of an excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii, and network connectivity for each segmented pulmonary network. We quantify uncertainty in geometric features by constructing probability densities for vessel radius and length, and then sample from these distributions and propagate uncertainties of haemodynamic predictions using a 1D CFD model. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length

Assessing model mismatch and model selection in a Bayesian uncertainty quantification analysis of a fluid-dynamics model of pulmonary blood circulation

This study uses Bayesian inference to quantify the uncertainty of model parameters and haemodynamic predictions in a one-dimensional pulmonary circulation model based on an integration of mouse haemodynamic and micro-computed tomography imaging data. We emphasize an often neglected, though important source of uncertainty: in the mathematical model form due to the discrepancy between the model and the reality, and in the measurements due to the wrong noise model (jointly called ‘model mismatch’). We demonstrate that minimizing the mean squared error between the measured and the predicted data (the conventional method) in the presence of model mismatch leads to biased and overly confident parameter estimates and haemodynamic predictions. We show that our proposed method allowing for model mismatch, which we represent with Gaussian processes, corrects the bias. Additionally, we compare a linear and a nonlinear wall model, as well as models with different vessel stiffness relations. We use formal model selection analysis based on the Watanabe Akaike information criterion to select the model that best predicts the pulmonary haemodynamics. Results show that the nonlinear pressure–area relationship with stiffness dependent on the unstressed radius predicts best the data measured in a control mouse