Shape optimization in unsteady blood flow: A numerical study of non-Newtonian effects

This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newton...

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Bibliographic Details
Published in:Computer methods in biomechanics and biomedical engineering 2005-06, Vol.8 (3), p.201-212
Main Authors: Abraham, Feby, Behr, Marek, Heinkenschloss, Matthias
Format: Article
Language:English
Subjects:
Algorithms
Arterial graft geometry
Arteries - anatomy & histology
Arteries - physiology
Arteries - surgery
Biomedical Engineering
Blood Flow Velocity
Blood Vessel Prosthesis
Computer Simulation
Hemodynamics
Humans
Models, Cardiovascular
Navier-Stokes equations
Newtonian effects
Non-Newtonian fluid
Prosthesis Design
Pulsatile Flow - physiology
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Summary:This paper presents a numerical study of non-Newtonian effects on the solution of shape optimization problems involving unsteady pulsatile blood flow. We consider an idealized two dimensional arterial graft geometry. Our computations are based on the Navier-Stokes equations generalized to non-Newtonian fluid, with the modified Cross model employed to account for the shear-thinning behavior of blood. Using a gradient-based optimization algorithm, we compare the optimal shapes obtained using both the Newtonian and generalized Newtonian constitutive equations. Depending on the shear rate prevalent in the domain, substantial differences in the flow as well as in the computed optimal shape are observed when the Newtonian constitutive equation is replaced by the modified Cross model. By varying a geometric parameter in our test case, we investigate the influence of the shear rate on the solution.
ISSN:1025-5842
1476-8259
DOI:10.1080/10255840500309562