Arterial Flow and Pulse Wave Propagation in one dimensional Arterial Networks with Statistically Distributed Model Parameters

Abstract

Parametric uncertainty in blood flow simulations of cardiovascular systems has received little attention, although methods for blood flow simulation has been subject of many studies. This work presents the implementation and assessment of a method for one dimensional flow and pressure wave simulations in arterial networks with statistically distributed model parameters. The pressure and flow waves in the arterial system are characterized by means of cross-sectionally averaged 1D governing equations for mass and momentum, discretized with a MacCormack scheme (explicit and second order in time and space). The stochastic model considered is a combination of a generalized polynomial chaos with a stochastic collocation method and joined with the one dimensional model. The implementation is validated with the simulation of a single arterial bifurcation, which has been published by others previously, with a somewhat different approach. The assessment is completed with a sensitivity analysis of the wave dynamics, in particular reflected waves, in the systemic arterial tree in the context of ageing. The numerical simulations showed that the impact of model uncertainty in different compartments of the arterial tree on systolic and diastolic pressure peaks can be determined with the elaborated method. In particular, the uncertainty in material parameters of the aortic arch showed a strong influence on the pressure wave forms.