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

References

• Abraham F Stabilized finite element solution of optimal control problems in computational fluid dynamics Ph.D. thesis Department of Mechanical Engineering and Materials Science, Rice University 2004
   Google Scholar
• Abraham , F , Behr , M and Heinkenschloss , M . 2004 . The effect of stabilization in finite element methods for the optimal boundary control of the Oseen equations . Finite Elem. Anal. Des. , 41 : 229 – 251 .
   Google Scholar
• Antaki , JF , Ghattas , O , Burgreen , GW and He , B . 1995 . Computational flow optimization of rotary blood pump components . Artif. Organs , 19 : 608 – 615 .
   PubMedGoogle Scholar
• Arora , D , Behr , M and Pasquali , M . 2004 . A tensor-based measure for estimating blood damage . Artif. Organs , 28 : 1002 – 1015 .
   PubMed Web of Science ®Google Scholar
• Behr , M and Arora , D . 2003 . Shear-slip mesh update method: Implementation and applications . Comput. Methods Biomech. Biomed. Eng. , 6 : 113 – 123 .
   PubMedGoogle Scholar
• Burgreen , GW , Antaki , JF , Wu , ZJ and Holmes , AJ . 2001 . Computational fluid dynamics as a development tool for rotary blood pumps . Artif. Organs , 25 : 336 – 340 .
   PubMedGoogle Scholar
• Dennis JE Schnabel RB Numerical Methods for Nonlinear Equations and Unconstrained Optimization Philadelphia SIAM 1996
   Google Scholar
• Gijsen , FJH , van de Vosse , FN and Janssen , JD . 1999 . The influence of the non-Newtonian properties of blood on the flow in large arteries: Steady flow in a carotid bifurcation model . J. Biomech. , 32 : 601 – 608 .
   PubMed Web of Science ®Google Scholar
• Girault V Raviart PA Finite Element Methods for the Navier-Stokes Equations New York Springer-Verlag 1986
   Google Scholar
• Grad Y Einav S Spectral and instantaneous flow characteristics of vascular junctions using continuous dpiv 9th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, Portugal 1998
   Google Scholar
• Grigioni , M , Daniele , C , Morbiducci , U , D'Avenio , G , Di Benedetto , G , Del Gaudio , C and Barbaro , V . 2002 . Computational model of the fluid dynamics of a cannula inserted in a vessel: Incidence of the presence of side holes in blood flow . J. Biomech. , 35 : 1599 – 1612 .
   PubMedGoogle Scholar
• Gunzburger MD Finite Element Methods for Incompressible Viscous Flows: A Guide to Theory, Practice and Algorithms Boston Academic Press 1989
   Google Scholar
• Gunzburger MD Perspectives in Flow Control and Optimization Philadelphia SIAM 2003
   Google Scholar
• Guo , L , Steinman , D , Moon , B , Wan , W and Millsap , R . 2001 . Effect of distal graft anastomosis site on retrograde perfusion and flow patterns of native coronary vasculature . Ann. Thorac. Surg. , 72 : 782 – 787 .
   PubMedGoogle Scholar
• Haslinger J Neittaanmäki P Finite Element Approximation for Optimal Shape, Material, and Topology Design 2nd ed. Chichester, NY John Wiley & Sons 1996
   Google Scholar
• He B Ghattas O Antaki JF Computational strategies for shape optimization of Navier-Stokes flows Technical Report CMU-CML-97-102 Pittsburgh, FL Computational Mechanics Lab, Department of Civil and Environmental Engineering, Carnegie Mellon University 1997
   Google Scholar
• Hughes , TJR , Franca , LP and Hulbert , GM . 1989 . A new finite element formulation for computational fluid dynamics: VIII. The Galerkin/least-squares method for advective-diffusive equations . Comput. Methods Appl. Mech. Eng. , 73 : 173 – 189 .
   Web of Science ®Google Scholar
• Jansen , K , Collis , SS , Whiting , C and Shakib , F . 1999 . A better consistency for low-order stabilized finite element methods . Comput. Methods Appl. Mech. Eng. , 174 : 153 – 170 .
   Web of Science ®Google Scholar
• Johnston , B , Johnston , PR , Corney , S and Kilpatrick , D . 2004 . Non-Newtonian blood flow in human right coronary arteries: Steady state simulations . J. Biomech. , 37 : 709 – 720 .
   PubMed Web of Science ®Google Scholar
• Kelley CT Iterative Methods for Linear and Nonlinear Equations Philadelphia SIAM 1995
   Google Scholar
• Leuprecht , A and Perktold , K . 2001 . Computer simulation of non-newtonian effects on blood flow in large arteries . Comput. Methods Biomech. Biomed. Eng. , 4 : 149 – 163 .
   PubMedGoogle Scholar
• Longest , PW and Kleinstreurer , C . 2003 . Particle-haemodynamics modeling of the distal end-to-side femoral bypass: Effects of graft caliber and graft-end cut . Med. Eng. Phys. , 25 : 843 – 858 .
   PubMedGoogle Scholar
• Mohammadi B Pironneau O Applied Shape Optimization for Fluids Oxford Oxford University Press 2001
   Google Scholar
• Neofytou , P and Drikakis , D . 2003 . Non-Newtonian flow instability in a channel with a sudden expansion . J. Non-Newtonian Fluid Mech. , 111 : 127 – 150 .
   Google Scholar
• Nocedal J Wright SJ Numerical Optimization Berlin/Heidelberg/New York Springer Verlag 1999
   Google Scholar
• Perktold , K , Peter , RO , Resch , M and Langs , G . 1991 . Pulsatile non-Newtonian flow in three-dimensional carotid bifurcation models: A numerical study of flow phenomena under different bifurcation angles . J. Biomed. Eng. , 13 : 507 – 515 .
   PubMedGoogle Scholar
• Quarteroni , A and Rozza , G . 2003 . Optimal control and shape optimization in aorto-coronaric bypass anastomoses . Math. Models Methods Appl. Sci. (M3AS) , 13 : 1801 – 1823 .
   Web of Science ®Google Scholar
• Quarteroni , A , Tuveri , M and Veneziani , A . 2000 . Computational vascular fluid dynamics: Problems, models and methods . Comput. Visualization Sci. , 2 : 163 – 197 .
   Google Scholar
• Shakib F Finite element analysis of the compressible Euler and Navier-Stokes equations Ph.D. thesis Department of Mechanical Engineering, Stanford University 1988
   Google Scholar
• Spellucci P DONLP2 users guide Technical report, Fachbereich Mathematik, Technische Universität Darmstadt, 1998 http://www.mathematik.tu-darmstadt.de
   Google Scholar
• Stanley L Stewart D Design sensitivity analysis Frontiers in Applied Mathematics Philadelphia, PA Society for Industrial and Applied Mathematics (SIAM) 2002
   Google Scholar
• Taylor CA Finite element modeling of blood flow: Relevance to atherosclerosis Computational Fluid–Structure Interaction in the Cardiovascular System, Advances in Fluid Mechanics, Vol. 2—Fluid Structure Interaction, Intra and Extracorporeal Cardiovascular Fluid Dynamics Verdonck P Perktold K Southampton, Boston, MA WIT Press 2000 249 289
   Google Scholar
• Tezduyar , TE , Behr , M and Liou , J . 1992 . A new strategy for finite element computations involving moving boundaries and interfaces—the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary tests . Comput. Methods Appl. Mech. Eng. , 94 : 339 – 351 .
   Web of Science ®Google Scholar
• Yeleswarapu KK Evaluation of continuum models for characterizing the constitutive behavior of blood Ph.D. thesis Department of Mechanical Engineering, University of Pittsburgh 1996
   Google Scholar