Propagating uncertainties in large-scale hemodynamics models via network uncertainty quantification and reduced-order modeling

Numerical simulations of the cardiovascular system are affected by uncertainties arising from a substantial lack of data related to the boundary conditions and the physical parameters of the mathematical models. Quantifying the impact of this uncertainty on the numerical results along the circulatory network is challenged by the complexity of both the morphology of the domain and the local dynamics. In this paper, we propose to integrate (i) the Transverse Enriched Pipe Element Methods (TEPEM) as a reduced-order model for effectively computing the 3D local hemodynamics; and (ii) a combination of uncertainty quantification via Polynomial Chaos Expansion and classical relaxation methods – called network uncertainty quantification (NetUQ) – for effectively propagating random variables that encode uncertainties throughout the networks. The results demonstrate the computational effectiveness of computing the propagation of uncertainties in networks with nontrivial topology, including portions of the cerebral and the coronary systems.