Simulation-based Inference for Cardiovascular Models

This paper was accepted at the workshop Machine Learning and the Physical Sciences at NeurIPS 2023.

Over the past decades, hemodynamics simulators have steadily evolved and have become tools of choice for studying cardiovascular systems in-silico. This comes naturally at the cost of increasing complexity since state-of-the-art models are non-linear partial differential equations depending on many parameters. While such tools are routinely used to simulate hemodynamics given physiological parameters, solving the related inverse problems — mapping waveforms to physiological parameters — has received comparably less attention. Motivated by advances in simulation-based inference (SBI), we reconsider the inverse problems specified by whole-body hemodynamics as statistical inferences. In opposition to traditional analyses, SBI provides a multi-dimensional representation of uncertainty for individual measurements, as encoded by posterior distributions. We perform an uncertainty analysis in-silico on a focused set of physiological parameters of clinical interest and compare several measurement modalities. Beyond the corroboration of known facts, such as the feasibility of estimating heart rate, our study highlights the potential of estimating new physiological parameters from standard-of-care measurements. Furthermore, SBI reveals practically relevant facts missed by alternative sensitivity analyses, such as the existence of sub-populations for which parameter estimation exhibits distinct uncertainty regimes. Finally, we study the gap between in-vivo and in-silico with the MIMIC-III waveform database and critically discuss how cardiovascular simulations can inform real-world data analysis.