Bayesian Windkessel calibration using optimized zero-dimensional surrogate models.

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Uncertainty quantification

Background:

• Bayesian boundary condition (BC) calibration quantifies uncertainties in cardiovascular fluid dynamics simulations.
• Estimating posterior distributions for all BC parameters in 3D simulations is computationally infeasible.

Purpose of the Study:

• To develop an efficient method for identifying Windkessel parameter posteriors in cardiovascular fluid dynamics.
• To reduce the computational demand of Bayesian Windkessel calibration.

Main Methods:

• A single 3D simulation is used to create a highly accurate 0D surrogate model.
• Sequential Monte Carlo (SMC) is performed on the 0D surrogate to derive the high-dimensional Windkessel BC posterior distribution.
• Optimizing 0D models *a priori* to match 3D data significantly reduced approximation error.

Main Results:

• Optimized 0D models achieved nearly one order of magnitude lower median approximation error across 72 vascular models.
• The 0D models demonstrated good generalization to various boundary conditions.
• SMC successfully evaluated the high-dimensional Windkessel parameter posterior, validated against a 3D posterior.

Conclusions:

• The proposed method significantly enhances the efficiency and accessibility of Bayesian Windkessel calibration in cardiovascular fluid dynamics.
• Minimal computational demand and open-source implementation facilitate wider adoption.
• This approach aids in quantifying uncertainties in complex physiological simulations.