A Bayesian approach to blood rheological uncertainties in aortic hemodynamics

Sascha Ranftl*, Thomas Stephan Müller, Ursula Windberger, Günter Brenn, Wolfgang von der Linden

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article numbere3576
JournalInternational Journal for Numerical Methods in Biomedical Engineering
Publication statusE-pub ahead of print - 2022


  • aortic hemodynamics
  • Bayesian probability theory
  • blood rheology
  • computational fluid dynamics
  • non-Newtonian fluids
  • uncertainty quantification

ASJC Scopus subject areas

  • Software
  • Biomedical Engineering
  • Modelling and Simulation
  • Molecular Biology
  • Computational Theory and Mathematics
  • Applied Mathematics


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