Gaussian process emulators for 1D vascular models

One-dimensional numerical models of the arterial vasculature are capable of simulating the physics of pulse wave transmission and reflection. These models are computationally efficient and represents and ideal choice with great translational opportunities in healthcare. However, the use of these models in a patient-specific scenario is hampered by the difficulty in measuring the model inputs (parameters, boundary conditions, and initial conditions) in the clinical setting. As a result, most of the model inputs are noisy or missing, and the inputs uncertainty is transmitted to the model outputs. A fundamental step in the model development consists in performing a sensitivity and uncertainty analysis aimed at understanding how variations on the inputs affect the output variability, with the final aim of instruct the measurement process. A typical sensitivity analysis conducted by means of \break Monte Carlo sampling is computationally expensive due to the large number of runs required. A novel approach aimed at reducing the computational time consists in using a statistical emulator capable of mimicking mean and variance behaviours of the 1D deterministic model. In this study, emulators built through Gaussian process method are used to predict outcomes of a 1D finite-volume solver for networks of elastic vessels. The 1D model is discussed and validated showing good agreement with published results. The emulator approach for sensitivity analysis is validated against Monte Carlo sampling and a 99.9% reduction in computational time is obtained. This methodology is further applied in the context of cerebral vasospasm where the sensitivity analysis results are used to identify new biomechanical metrics for this pathology. The novel biomarkers are effective at detecting the cerebral vasospasm better than the currently used one. In particular, the progression of the disease is characterised from an early onset even when the vasospasm is occurring at some distance away from the measurement location.