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Adjoint shape optimization of blood flow applications under uncertainties
Citation Link: https://doi.org/10.15480/882.15270
Publikationstyp
Doctoral Thesis
Date Issued
2025
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2025-01-23
Institute
TORE-DOI
Citation
Technische Universität Hamburg: (2025)
Peer Reviewed
true
This thesis aims to advance traditional gradient-based shape optimization techniques by incorporating blood-specific features. The work can be broadly classified into four main categories, (a) computational blood flow modeling, (b) parameter-free shape optimization, (c) the continuous adjoint method and (d) robust shape optimization.
As regards (a), this work presents key aspects related to the computational fluid dynamics (CFD) or fluid-structure interaction (FSI) simulations employed for the solution of the blood flow problem (primal problem). The underlying primal problem is enhanced to account for blood damage (hemolysis) by the numerical solution of an additional partial differential equation (PDE). The minimization of hemolysis is one of the main objectives of interest in this work. In order to account for the shear-thinning behavior of blood, several non-Newtonian viscosity models are also employed. The numerical solution of the primal problem is verified against analytical solutions and literature-reported results when deemed necessary.
The shape optimization problem is formulated based on a parameter-free approach. To this end, the identification of the shape gradient or at least, a suitable descent direction, based on the shape sensitivity is addressed. Several methods that compute the descent direction based on the solution of one (or two) additional PDE(s) are presented. Auxiliary aspects related to the optimization problem are also discussed in the context of (b).
The thesis presents the novel derivation of continuous adjoint equation systems dual to the blood-specific problems. Specifically, contributions to (c) relate to the development of the continuous adjoint to the steady-state Navier-Stokes equations for an incompressible fluid with hemolysis modeling and with non-Newtonian viscosity properties. The accuracy of the novel systems in estimating the shape sensitivity is assessed against second-order accurate finite difference (FD) studies.
On the topic of (d), this work focuses on the necessary uncertainty quantification techniques able to drive a robust shape optimization procedure. The problem is considered uncertain by means of the employed parameters or the boundary conditions thus rendering the objective functional a statistical quantity. The optimization targets the minimization of the statistical moments of the objective functional through the use of methods based on sampling or the method of moments.
The biomedical applications studied in this thesis refer to an idealized medical device and an idealized bypass-graft.
As regards (a), this work presents key aspects related to the computational fluid dynamics (CFD) or fluid-structure interaction (FSI) simulations employed for the solution of the blood flow problem (primal problem). The underlying primal problem is enhanced to account for blood damage (hemolysis) by the numerical solution of an additional partial differential equation (PDE). The minimization of hemolysis is one of the main objectives of interest in this work. In order to account for the shear-thinning behavior of blood, several non-Newtonian viscosity models are also employed. The numerical solution of the primal problem is verified against analytical solutions and literature-reported results when deemed necessary.
The shape optimization problem is formulated based on a parameter-free approach. To this end, the identification of the shape gradient or at least, a suitable descent direction, based on the shape sensitivity is addressed. Several methods that compute the descent direction based on the solution of one (or two) additional PDE(s) are presented. Auxiliary aspects related to the optimization problem are also discussed in the context of (b).
The thesis presents the novel derivation of continuous adjoint equation systems dual to the blood-specific problems. Specifically, contributions to (c) relate to the development of the continuous adjoint to the steady-state Navier-Stokes equations for an incompressible fluid with hemolysis modeling and with non-Newtonian viscosity properties. The accuracy of the novel systems in estimating the shape sensitivity is assessed against second-order accurate finite difference (FD) studies.
On the topic of (d), this work focuses on the necessary uncertainty quantification techniques able to drive a robust shape optimization procedure. The problem is considered uncertain by means of the employed parameters or the boundary conditions thus rendering the objective functional a statistical quantity. The optimization targets the minimization of the statistical moments of the objective functional through the use of methods based on sampling or the method of moments.
The biomedical applications studied in this thesis refer to an idealized medical device and an idealized bypass-graft.
Subjects
Shape optimization
Adjoint optimization
Robust optimization
Fluid-structure interaction
Non-Newtonian fluid
Hemolysis
DDC Class
620.1: Engineering Mechanics and Materials Science
515: Analysis
519: Applied Mathematics, Probabilities
610: Medicine, Health
Funding Organisations
More Funding Information
Project No. LFF-GK11
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Bletsos_Georgios_Adjoint_shape_optimization_of_blood_flow_applications_under_uncertainties.pdf
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