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

Surabhi Rathore1, Pasquale C Africa1, Francesco Ballarin2

  • 1mathLab, Mathematics Area, SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste, 34136, Italy.

Computer Methods and Programs in Biomedicine
|May 29, 2025
PubMed
Summary

This study introduces a projection-based reduced order modeling (ROM) framework to optimize cardiovascular (CV) hemodynamics by controlling outflow boundary conditions. The novel approach significantly speeds up simulations for patient-specific vascular models.

Keywords:
Cardiovascular flowsGalerkin finite element methodLagrange multiplierNested-proper orthogonal decompositionOptimal controlParametrized partial differential equations

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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.