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A reduced computational and geometrical framework for inverse problems in hemodynamics.

Toni Lassila1, Andrea Manzoni, Alfio Quarteroni

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

International Journal for Numerical Methods in Biomedical Engineering
|June 27, 2013
PubMed
Summary

This study reduces computational costs for cardiovascular inverse problems using domain parametrization and reduced-basis approximations. These methods enable efficient hemodynamic modeling for atherosclerosis risk and bypass graft design.

Keywords:
fluid-structure interactionhemodynamicsinverse problemsmodel reductionparametrized Navier-Stokes equationsreduced-basis methodsshape optimization

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Area of Science:

  • Cardiovascular mathematics
  • Computational fluid dynamics
  • Biomedical engineering

Background:

  • Solving inverse problems in cardiovascular mathematics is computationally intensive.
  • Existing methods for simulating blood flow (e.g., finite element methods for Navier-Stokes equations) are often too slow for complex inverse problems.
  • Hemodynamics modeling is crucial for understanding cardiovascular diseases and designing medical interventions.

Purpose of the Study:

  • To reduce the computational expense of solving inverse problems in cardiovascular mathematics.
  • To develop efficient methods for hemodynamic modeling in cardiovascular applications.
  • To enable robust quantification of uncertainty in inverse problems.

Main Methods:

  • Applied a domain parametrization technique to simplify geometrical and computational complexities of the forward problem.
  • Replaced computationally expensive finite element solutions of incompressible Navier-Stokes equations with reduced-basis approximations.
  • Addressed inverse problems in both deterministic (least-squares) and statistical (Bayesian framework) senses.

Main Results:

  • Significantly reduced the computational cost of simulating the forward problem in hemodynamics.
  • Successfully applied the methods to two inverse problems: quantifying atherosclerosis risk in stenosed arteries and robust shape design for femoral bypass grafts.
  • Enabled identification of arterial wall material parameters and robust design under flow uncertainty using pressure measurements.

Conclusions:

  • The proposed domain parametrization and reduced-basis approximation techniques offer a computationally efficient approach for cardiovascular inverse problems.
  • These methods facilitate more accessible and robust hemodynamic modeling for clinical applications and medical device design.
  • The study demonstrates the utility of these techniques for both risk quantification and design optimization in cardiovascular contexts.