A Bayesian approach to blood rheological uncertainties in aortic hemodynamics

• Published in: International journal for numerical methods in biomedical engineering 2023-04, Vol.39 (4), p.e3576-n/a
• Main Authors: Ranftl, Sascha, Müller, Thomas Stephan, Windberger, Ursula, Brenn, Günter, von der Linden, Wolfgang
• Format: Article
• Language: English
• Subjects: Aorta; aortic hemodynamics; Bayes Theorem; Bayesian analysis; Bayesian probability theory; Blood; Blood Flow Velocity; blood rheology; Boundary conditions; computational fluid dynamics; Computer applications; Computer Simulation; Computing costs; Fluid flow; Hemodynamics; Humans; Mathematical models; Models, Cardiovascular; non‐Newtonian fluids; Probability theory; Reynolds number; Rheological properties; Rheology; Shear stress; Simulation; Stress, Mechanical; Uncertainty; uncertainty quantification; Wall shear stresses
• ISSN: 2040-7939; 2040-7947
• DOI: 10.1002/cnm.3576

Computational hemodynamics has received increasing attention recently. Patient‐specific simulations require questionable model assumptions, for example, for geometry, boundary conditions, and material parameters. Consequently, the credibility of these simulations is much doubted, and rightly so. Yet, the matter may be addressed by a rigorous uncertainty quantification. In this contribution, we investigated the impact of blood rheological models on wall shear stress uncertainties in aortic hemodynamics obtained in numerical simulations. Based on shear‐rheometric experiments, we compare the non‐Newtonian Carreau model to a simple Newtonian model and a Reynolds number‐equivalent Newtonian model. Bayesian Probability Theory treats uncertainties consistently and allows to include elusive assumptions such as the comparability of flow regimes. We overcome the prohibitively high computational cost for the simulation with a surrogate model, and account for the uncertainties of the surrogate model itself, too. We have two main findings: (1) The Newtonian models mostly underestimate the uncertainties as compared to the non‐Newtonian model. (2) The wall shear stresses of specific persons cannot be distinguished due to largely overlapping uncertainty bands, implying that a more precise determination of person‐specific blood rheological properties is necessary for person‐specific simulations. While we refrain from a general recommendation for one rheological model, we have quantified the error of the uncertainty quantification associated with these modeling choices. With a Bayesian approach, experimental uncertainties of blood rheological parameters have been quantified (contours of joint posterior, left hand side). The uncertainties are then propagated to aortic wall shear stresses (right hand side). The results demonstrate that Newtonian models (simple: black, Reynolds‐equivalent: blue) can underestimate the uncertainty (shaded area) as compared to the non‐Newtonian Carreau model (red). The results further suggest that a more precise shear‐rheometry could be advantageous for personalized simulations.