This study uses a one dimensional fluid dynamics arterial network model to infer changes in hemodynamic quantities associated with pulmonary hypertension in mice. Data for this study include blood flow and pressure measurements from the main pulmonary artery for 7 control mice with normal pulmonary function and 5 hypertensive mice with hypoxia induced pulmonary hypertension. Arterial dimensions for a 21 vessel network are extracted from micro-CT images of lungs from a representative control and hypertensive mouse. Each vessel is represented by its length and radius. Fluid dynamic computations are done assuming that the flow is Newtonian, viscous, laminar, and has no swirl. The system of equations is closed by a constitutive equation relating pressure and area, using a linear model derived from stress-strain deformation in the circumferential direction assuming that the arterial walls are thin, and also an empirical nonlinear model. For each dataset, an inflow waveform is extracted from the data, and nominal parameters specifying the outflow boundary conditions are computed from mean values and characteristic time scales extracted from the data. The model is calibrated for each mouse by estimating parameters that minimize the least squares error between measured and computed waveforms. Optimized parameters are compared across the control and the hypertensive groups to characterize vascular remodeling with disease. Results show that pulmonary hypertension is associated with stiffer and less compliant proximal and distal vasculature with augmented wave reflections, and that elastic nonlinearities are insignificant in the hypertensive animal. arXiv:1712.01699v2 [physics.flu-dyn] 17 May 2018 disease progression (Castelain et al., 2001;Hunter et al., 2011). In particular, the proximal arterial stiffness is an excellent predictor of mortality in patients with pulmonary arterial hypertension (Gan et al., 2007). Quantifying relative distributions of proximal and distal arterial stiffness (or compliance) and wave reflections in elevating the mPAP and PVR is vital for understanding disease mechanisms.In this study, we setup and calibrate a mathematical model predicting wave propagation in the pulmonary vasculature in C57BL6/J male mice with normal pulmonary function (control group (CTL), n = 7) and in mice with hypoxia-induced pulmonary hypertension (hypertensive group (HPH), n = 5) (Tabima et al., 2012;Vanderpool et al., 2011). The novelty of this study is the integration of high fidelity morphometric and hemodynamic data from multiple mice with a one dimensional (1D) model of large pulmonary arteries coupled with a zero dimensional (0D) model of the vascular beds. This is achieved by incorporating available data at each stage of the modeling including network extraction, parameter estimation and model validation. The outcome is used to infer disease progression by quantifying relative changes in PVR, proximal and distal arterial stiffness, compliance, and amplitudes of wave reflections, across the two groups (CTL and HPH)...

This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics under normal physiological and pathological conditions. This is of medical interest as it enables tracking the progression of pulmonary hypertension. We show how we make the fluids model tractable by reducing the parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive Metropolis algorithm, coupled with constraint non-linear optimization, is successfully used to learn the parameter values and quantify the uncertainty in the parameter estimates.To accommodate for different magnitudes of the parameter values, we introduce an improved parameter scaling technique in the Delayed Rejection Adaptive Metropolis algorithm. Formal convergence diagnostics are employed to check for convergence of the Markov chains. Additionally, we perform model selection using different information criteria, including Watanabe Akaike Information Criteria.

Pulmonary hypertension (PH), defined as an elevated mean blood pressure in the main pulmonary artery (MPA) at rest, is associated with vascular remodeling of both large and small arteries. PH has several sub-types that are all linked to high mortality rates. In this study, we use a one-dimensional (1D) fluid dynamics model driven by in-vivo measurements of MPA flow to understand how model parameters and network size influence MPA pressure predictions in the presence of PH. We compare model predictions to in-vivo MPA pressure measurements from a control and a hypertensive mouse and analyze model predictions in three networks of increasing complexity, extracted from micro-CT images. We introduce global scaling factors for boundary condition parameters and perform local and global sensitivity analysis to calculate parameter influence on model predictions of MPA pressure, and correlation analysis to determine a subset of identifiable parameters. These are inferred using frequentist optimization and Bayesian inference via the Delayed Rejection Adaptive Metropolis (DRAM) algorithm. Frequentist and Bayesian uncertainty is computed for model parameters and MPA pressure predictions. Results show that model predictions of MPA pressure are most sensitive to distal vascular resistance, and that parameter influence changes with increasing network complexity. Our outcomes suggest that PH leads to increased vascular stiffness and decreased peripheral compliance, congruent with clinical observations.

Computational fluid dynamics (CFD) models are emerging tools for assisting in diagnostic assessment of cardiovascular disease. Recent advances in image segmentation have made subject-specific modelling of the cardiovascular system a feasible task, which is particularly important in the case of pulmonary hypertension, requiring a combination of invasive and non-invasive procedures for diagnosis. Uncertainty in image segmentation propagates to CFD model predictions, making the quantification of segmentation-induced uncertainty crucial for subject-specific models. This study quantifies the variability of one-dimensional CFD predictions by propagating the uncertainty of network geometry and connectivity to blood pressure and flow predictions. We analyse multiple segmentations of a single, excised mouse lung using different pre-segmentation parameters. A custom algorithm extracts vessel length, vessel radii and network connectivity for each segmented pulmonary network. Probability density functions are computed for vessel radius and length and then sampled to propagate uncertainties to haemodynamic predictions in a fixed network. In addition, we compute the uncertainty of model predictions to changes in network size and connectivity. Results show that variation in network connectivity is a larger contributor to haemodynamic uncertainty than vessel radius and length.