In this talk I will present a Bayesian approach to quantify the uncertainty of model parameters and hemodynamic predictions in a one-dimensional fluid-dynamics model of the pulmonary system by integrating mouse imaging data and hemodynamic data. The long-term aim is to devise a calibrated patient-specific model. I emphasize an often neglected, though the important source of uncertainty: uncertainty in the mathematical model form, caused by the discrepancy between the model and the reality. I will 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 hemodynamic predictions. The proposed method in this study, based on Gaussian Processes allow for model mismatch and correct the bias. Additionally, I investigate several vessel stiffness relations, as well as a linear and a non-linear wall model, and use formal model selection analysis based on the Watanabe Akaike Information Criterion (WAIC) to select the model that best predicts pulmonary hemodynamics. Results indicate that predicting vessel deformation using a non-linear pressure-area relationship with stiffness dependent on the unstressed radius is best supported by the control mouse data.
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