Statistical emulation and uncertainty quantification in cardiovascular disease modelling

Pulmonary hypertension, 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 modeling of the pulmonary blood circulation system promise to mathematically predict the blood pressure based on non-invasive measurements of the blood flow, which would no longer require catheterization. However, in order for these alternative techniques to be applicable in the clinic, patient-specific model calibration and parameter estimation are needed, and the computational costs of repeated forward simulations as part of an iterative numerical optimization or sampling scheme constitute a serious bottleneck for their practical use as real time digital twins in the clinic. Emulation is a common tool for overcoming this issue, yet an extensive investigation into the benefits, trade-offs, and limitations is warranted. In part 1 of my talk, I will give an overview of alternative "classical" emulation strategies for hemodynamics models of the pulmonary circulation, based on Gaussian processes and polynomial chaos expansions. Starting from a reduction of the parameter space of the models via global sensitivity analysis, the alternative emulation strategies are compared in both forward emulation on test data, as well as in their ability to infer the critical biophysical parameters in the inverse problem. The second part of my talk will discuss the application of physics-informed machine learning to develop improved emulators with an inductive bias based on directly integrating prior knowledge about physical laws and boundary conditions into the statistical model. The resulting performance improvement is quantified in terms of accuracy and efficiency.