A black-box decomposition approach for coupling heterogeneous components in hemodynamics simulations.

Area of Science:

• Computational Hemodynamics
• Mathematical Modeling
• Biomedical Engineering

Background:

• Accurate simulation of cardiovascular blood flow requires integrating models of varying dimensionalities (e.g., 3D, 1D, 0D).
• Strong iterative coupling of these dimensionally heterogeneous models presents significant computational challenges.
• Existing methods may lack generality or efficiency when combining different model types.

Purpose of the Study:

• To develop a generic and efficient black-box approach for strong iterative coupling of dimensionally heterogeneous flow models.
• To enable robust simulation of complex cardiovascular systems by integrating diverse vascular components.
• To introduce a multiple time-stepping strategy for optimizing simulations with varying component requirements.

Main Methods:

• A black-box methodology was employed to represent cardiovascular system components.
• Coupling equations were used to connect these black-box components.
• The Broyden algorithm was utilized for solving the coupled system of equations, alongside a multiple time-stepping strategy.

Main Results:

• The proposed approach successfully integrated 3D (vessels), 1D (arteries/peripheral vessels), and 0D (venous/cardiac/pulmonary circulation) models into a closed-loop cardiovascular system.
• Demonstrated robustness and suitability of the novel coupling algorithm through application examples.
• The method efficiently handles dimensionally heterogeneous models.

Conclusions:

• The developed generic black-box approach provides an efficient and robust solution for strong iterative coupling in computational hemodynamics.
• This methodology facilitates the creation of comprehensive, multi-scale cardiovascular models.
• The approach is suitable for complex simulations requiring the integration of diverse flow models.