Free Access
Math. Model. Nat. Phenom.
Volume 9, Number 6, 2014
Blood flows
Page(s) 98 - 116
Published online 31 July 2014
  1. F.E. Boas, D. Fleischmann. CT artifacts: causes and reduction techniques. Imaging in Medicine, 4 (2012), 229-240. [CrossRef] [Google Scholar]
  2. T. Bodnar, A. Sequeira, M. Prosi. On the shear-thinning effects of blood flow under various flow rates. Applied Mathematics and Computation, Elsevier, 217 (2011), 5055-5067. [CrossRef] [MathSciNet] [Google Scholar]
  3. J. Burkardt, M. Gunzburger, J. Peterson. Insensitivite Functionals, Inconsistent Gradients, Spurious Minima and Regularized Funcionals in Flow Optimization Problems. International Journal of Computational Fluid Dynamics, 16 (2002), 171-185. [CrossRef] [Google Scholar]
  4. J.R. Cebral, M.A. Castro, S. Appanaboyina, C.M. Putman, D. Millan, A.F. Frangi. Efficient pipeline for image-based patient-specific analysis of cerebral aneurism hemodynamics: technique and sensitivity. IEEE Transactions on Medical Imaging, 344 (2005), 457-467. [CrossRef] [Google Scholar]
  5. COMSOL Multiphysics, Users Guide, COMSOL 4.3, 2012. [Google Scholar]
  6. Optimization Module, Users Guide, COMSOL 4.3, 2012. [Google Scholar]
  7. M. D’ Elia, M. Perego, A. Veneziani. A Variational Data Assimilation Procedure for the Incompressible Navier-Stokes Equations in Hemodynamics. Journal of Scientific Computing, 53 (2011). [Google Scholar]
  8. M. D’ Elia, A. Veneziani. A Data Assimilation technique for including noisy measurements of the velocity field into Navier-Stokes simulations. Proceedings of V European Conference on Computational Fluid Dynamics, ECCOMAS, June (2010). [Google Scholar]
  9. J.C. De Los Reyes, K. Kunisch. A semi-smooth Newton method for control constrained boundary optimal control of the Navier-Stokes equations. Nonlinear Anal., 62 (2005), no. 7, 1289-1316. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.C. De Los Reyes, K. Kunisch. Optimal control of partial differential equations with affine control constraints. Control Cybernet., 38 (2009), no. 4, 1217-1249. [MathSciNet] [Google Scholar]
  11. J.C. De Los Reyes, Yousept, Irwin. Regularized state-constraint boundary Optimal control of the Navier-Stokes equations., J-Math. Anal. Appl., 356 (2009), no. 1, 257-279. [CrossRef] [MathSciNet] [Google Scholar]
  12. P. Deuflhard. A Modified Newton Method for the Solution of Ill-conditioned Systems of Nonlinear Equations with Application to Multiple Shooting. Numer. Math., 22 (1974), 289-315. [CrossRef] [MathSciNet] [Google Scholar]
  13. L. Formaggia, J.F. Gerbeau, F. Nobile, A. Quarteroni. Numerical treatment of defective boundary conditions for the Navier-Stokes equations. SIAM J. Numer. Anal., 40 (2002) 376-401. [CrossRef] [Google Scholar]
  14. A.M. Gambaruto, D.J. Doorly, T. Yamaguchi. Wall shear stress and near-wall convective transport: Comparisons with vascular remodelling in a peripheral graft anastomosis. Journal of Computational Physics, 229 (2010), no. 14, 5339-5356. [CrossRef] [Google Scholar]
  15. A. Garambuto, J. Janela, A. Moura and A. Sequeira. Sensitivity of hemodynamics in a patient specific cerebral aneurysm to vascular geometry and blood rheology. Mathematical Biosciences and Engineering, 8 (2011), no. 2, 409-423. [Google Scholar]
  16. A. Gambaruto, J. Janela, A. Moura, A. Sequeira. Shear-thinning effects of hemodynamics in patient-specific cerebral aneurysms. Mathematical Biosciences and Engineering, 10 (2013), no. 3, 649-665. [Google Scholar]
  17. A.M. Gambaruto, J. Peiro, D.J. Doorly, A.G. Radaelli. Reconstruction of shape and its effect on flow in arterial conduits. International Journal for Numerical Methods in Fluids, 57 (2008), no. 5, 495-517. [CrossRef] [Google Scholar]
  18. V. Girault, P.A. Raviart. Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Number 5 in Springer Series in Computational Mathematics. Springer-Verlag, Berlin, 1986. [Google Scholar]
  19. T. Guerra, J. Tiago, A. Sequeira. Optimal control in blood flow simulations. International Journal of Non-Linear Mechanics, Available online (2014), doi:10.1016/j.ijnonlinmec.2014.04.005. [Google Scholar]
  20. M. Gunzburger. Adjoint Equation-Based Methods for Control Problems in Incompressible, Viscous Flows. Flow, Turbulence and Combustion, 65 (2000), no. 3, 249-272. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Gunzburger, L.S. Hou, T.P. Svobodny. Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls. RAIRO - Modélisation mathémathique et analyse numérique, 25 (1991), no. 6, 711-748. [Google Scholar]
  22. P. Gill, W. Murray, M.A. Saunders. SNOPT: An SQP Algoritm for Large-Scale Constrained Optimization. Society for Industrial and Applied Mathematics, SIAM REVIEW, 47 (2005) no. I, 99-131. [Google Scholar]
  23. B.M. Johnston, P.R. Johnston, S. Corney, D. Kilpatrick. Non-Newtonian blood flow in human right coronary arteries: transient simulations. Journal of Biomechanics, 39 (2006), no. 6, 1116-1128. [CrossRef] [PubMed] [Google Scholar]
  24. M. Kroon, G.A. Holzapfel. Estimation of the distributions of anisotropic, elastic properties and wall stresses of saccular cerebral aneurysms by inverse analysis. Proc. R. Soc. A, 464 (2008), 807-825. [CrossRef] [Google Scholar]
  25. K.L. Lee, D.J. Doorly, D.N. Firmin. Numerical simulations of phase contrast velocity mapping of complex flows in an anatomically realistic bypass graft geometry. Medical Physics, 7 (2006), 2621-2631. [CrossRef] [Google Scholar]
  26. J.G. Myers, J.A. Moore, M. Ojha, K.W. Johnston, C.R. Ethier. Factors Influencing Blood Flow Patterns in the Human Right Coronary Artery. Annals of Biomedical Engineering, 29 (2001), no. 2, 109-120. [CrossRef] [PubMed] [Google Scholar]
  27. R.W. Ogden, G. Saccomandi, I. Sgura. Fitting hyperelastic models to experimental data. Computational Mechanics, 34 (2004), no. 6, 484-502. [CrossRef] [Google Scholar]
  28. E. Pusey, R.B. Lufkin, R.K. Brown, M.A. Solomon, D.D. Stark, R.W. Tarr, W.N. Hanafee. Magnetic resonance imaging artifacts: mechanism and clinical significance. Radiographics, 6 (1986), no. 5, 891-911. [CrossRef] [PubMed] [Google Scholar]
  29. A. Quarteroni, L. Formaggia. Mathematical Modelling and Numerical Simulation of the Cardiovascular System, Modelling of living Systems. Handbook of Numerical Analysis Series. Elsevier, Amsterdam, 2002. [Google Scholar]
  30. S. Ramalho, A. Moura, A.M. Gambaruto, A. Sequeira. Sensitivity to outflow boundary conditions and level of geometry description for a cerebral aneurysm. International Journal for Numerical Methods in Biomedical Engineering, 28 (2012), no. 6-7, 697-713. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  31. A.M. Robertson, A. Sequeira, M.V. Kameneva. Hemorheology. Hemodynamical Flows. Modeling, Analysis and Simulation. Oberwolfach Seminars. Birkhauser Verlag, Basel, 37 (2008), 63-120. [Google Scholar]
  32. O. Schenk, K. Gärtner, W. Fichtner, A. Stricker. PARDISO: A High-Performance Serial and Parallel Sparse Linear Solver in Semiconductor Device Simulation, Journal of Future Generation Computers Systems, 18 (2001), 69-78. [CrossRef] [Google Scholar]
  33. T. Silva, A. Sequeira, R. Santos, J. Tiago. Mathematical Modeling of Atherosclerotic Plaque Formation Coupled with a Non-Newtonian Model of Blood Flow. Conference Papers in Mathematics, vol. 2013, Article ID 405914, 2013. doi:10.1155/2013/405914. [Google Scholar]
  34. N.P. Smith, A.J. Pullan, P.J. Hunter. An anatomically based model of coronary blood flow and myocardial mechanics. SIAM J. Appl. Math., 62 (2002), 990-1018. [CrossRef] [Google Scholar]
  35. P. Tricerri. Mathematical and Numerical Modeling of Healthy and Unhealthy Cerebral Arterial Tissue. École Polytechnique Fédérale de Lausanne. Ph.D. thesis, 2014. [Google Scholar]
  36. Y. Wei, S. Cotin, J. Dequidt, C. Duriez, J. Allard, E. Kerrien. A (Near) Real-Time Simulation Method of Aneurysm Coil Embolization, INTECH, 2012. [Google Scholar]
  37. C. Westbrook, C.K. Roth, J. Talbot. MRI in Practice. Wiley-Blackwell, 2011. [Google Scholar]

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