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Model reduction techniques for fast blood flow simulation in parametrized geometries.

Andrea Manzoni1, Alfio Quarteroni, Gianluigi Rozza

  • 1CMCS - Modelling and Scientific Computing, MATHICSE - Mathematics Institute of Computational Science and Engineering, EPFL - Ecole Polytechnique Fédérale de Lausanne, Station 8, CH-1015 Lausanne, Switzerland. andrea.manzoni@epfl.ch.

International Journal for Numerical Methods in Biomedical Engineering
|November 4, 2014
PubMed
Summary

This study introduces a novel model reduction method for fast, real-time blood flow simulations in arterial vessels. The technique uses shape parametrization and the reduced basis method for patient-specific analysis and risk assessment.

Keywords:
Navier-Stokes equationsgeometrical and computational reductionhaemodynamicsmodel reductionradial basis functionsreal-time simulationreduced basis methods

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Area of Science:

  • Computational fluid dynamics
  • Biomedical engineering
  • Mathematical modeling

Background:

  • Accurate blood flow simulation is crucial for understanding cardiovascular diseases.
  • Existing methods can be computationally expensive, limiting real-time applications.
  • Patient-specific arterial geometries present a challenge for traditional simulation techniques.

Purpose of the Study:

  • To develop a model reduction technique for real-time blood flow simulations.
  • To enable analysis of parametrized arterial vessel geometries.
  • To facilitate patient-specific simulations and pathological risk assessment.

Main Methods:

  • Combining low-dimensional shape parametrization of the computational domain.
  • Employing the reduced basis method to solve parametrized flow equations.
  • Utilizing radial basis functions for geometry description and parameter identification for patient-specific reconstruction.

Main Results:

  • Demonstrated real-time blood flow simulations on reconstructed parametrized geometries.
  • Focused on a family of parametrized carotid artery bifurcations using Navier-Stokes equations.
  • Measured outputs like viscous energy dissipation and vorticity for potential pathological risk correlation.

Conclusions:

  • The proposed model reduction technique enables efficient, real-time blood flow simulations.
  • The approach is applicable to various flow problems involving geometry variations.
  • This method supports shape sensitivity analysis, parametric exploration, and shape design in vascular modeling.