Projection-based reduced order modelling for unsteady parametrized optimal control problems in 3D cardiovascular...

Area of Science:

• Computational fluid dynamics
• Biomedical engineering
• Mathematical modeling

Background:

• Accurate patient-specific cardiovascular (CV) hemodynamic modeling is challenged by complex vascular geometries and high computational costs.
• Current methods struggle to integrate clinical data like 4D MRI for realistic flow simulations.
• Optimizing outflow boundary conditions is crucial for reliable CV hemodynamic computations.

Purpose of the Study:

• To develop and present a projection-based reduced order modeling (ROM) framework for unsteady, parametrized optimal control problems (OCP(μ)s) in CV applications.
• To control outflow boundary conditions for optimizing CV hemodynamics and minimizing discrepancies in flow velocity profiles.
• To enable efficient and accurate simulations of patient-specific CV flows.

Main Methods:

• Utilized a projection-based reduction technique with an offline-online paradigm for computational efficiency.
• Employed the Galerkin finite element method to compute high-fidelity solutions in the offline phase.
• Implemented a nested-proper orthogonal decomposition (nested-POD) for temporal and parametric-space compression.

Main Results:

• Demonstrated the framework's efficacy on idealized and patient-specific vascular models (coronary artery bypass graft).
• Achieved consistent speed-up compared to high-fidelity simulation strategies.
• Provided insights into flow characteristics and factors influencing atherosclerosis risk.

Conclusions:

• The projection-based ROM framework offers an efficient and accurate method for simulating parametrized CV flows.
• Enables real-time, patient-specific modeling for personalized medical interventions.
• Improves predictions of disease progression in vascular regions.