Issue
ESAIM: M2AN
Volume 47, Number 4, July-August 2013
Direct and inverse modeling of the cardiovascular and respiratory systems
Page(s) 1107 - 1131
DOI https://doi.org/10.1051/m2an/2012059
Published online 17 June 2013
  1. V. Agoshkov, A. Quarteroni and G. Rozza, A mathematical approach in the design of arterial bypass using unsteady Stokes equations. J. Sci. Comput. 28 (2006) 139–165. [CrossRef] [MathSciNet] [Google Scholar]
  2. V. Agoshkov, A. Quarteroni and G. Rozza, Shape design in aorto-coronaric bypass anastomoses using perturbation theory. SIAM J. Numer. Anal. 44 (2006) 367–384. [CrossRef] [MathSciNet] [Google Scholar]
  3. G. Allaire, Conception optimale de structures, vol. 58. Springer Verlag (2007). [Google Scholar]
  4. D. Amsallem, J. Cortial, K. Carlberg and C. Farhat, A method for interpolating on manifolds structural dynamics reduced-order models. Int. J. Numer. Methods Eng. 80 (2009) 1241–1258. [Google Scholar]
  5. H. Antil, M. Heinkenschloss, R.H.W. Hoppe and D.C. Sorensen, Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables. Comput. Vis. Sci. 13 (2010) 249–264. [CrossRef] [MathSciNet] [Google Scholar]
  6. M. Berggren, Numerical solution of a flow-control problem: Vorticity reduction by dynamic boundary action. SIAM J. Sci. Comput. 19 (1998) 829. [CrossRef] [MathSciNet] [Google Scholar]
  7. M. Bergmann and L. Cordier, Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models. J. Comput. Phys. 227 (2008) 7813–7840. [CrossRef] [MathSciNet] [Google Scholar]
  8. R.P. Brent, Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs, N.J. (1973). [Google Scholar]
  9. E. Burman and M.A. Fernández, Continuous interior penalty finite element method for the time-dependent Navier–Stokes equations: space discretization and convergence. Numer. Math. 107 (2007) 39–77. [CrossRef] [MathSciNet] [Google Scholar]
  10. K. Carlberg and C. Farhat, A low-cost, goal-oriented compact proper orthogonal decomposition basis for model reduction of static systems. Int. J. Numer. Methods Eng. 86 (2011) 381–402. [CrossRef] [Google Scholar]
  11. T. F. Coleman and Y. Li, An interior trust region approach for nonlinear minimization subject to bounds. SIAM J. Optim. 6 (1996) 418–445. [CrossRef] [MathSciNet] [Google Scholar]
  12. L. Dedè, Optimal flow control for Navier–Stokes equations: drag minimization. Int. J. Numer. Methods Fluids 55 (2007) 347–366. [Google Scholar]
  13. S. Dempe, Foundations of bilevel programming. Kluwer Academic Publishers, Dordrecht, The Netherlands (2002). [Google Scholar]
  14. S. Deparis, Reduced basis error bound computation of parameter-dependent Navier-Stokes equations by the natural norm approach. SIAM J. Numer. Anal. 46 (2008) 2039–2067. [CrossRef] [MathSciNet] [Google Scholar]
  15. S. Deparis and G. Rozza, Reduced basis method for multi-parameter-dependent steady Navier-Stokes equations: Applications to natural convection in a cavity. J. Comput. Phys. 228 (2009) 4359–4378. [CrossRef] [MathSciNet] [Google Scholar]
  16. H. Do, A.A. Owida, W. Yang and Y.S. Morsi, Numerical simulation of the haemodynamics in end-to-side anastomoses. Int. J. Numer. Methods Fluids 67 (2011) 638–650. [CrossRef] [Google Scholar]
  17. O. Dur, S.T. Coskun, K.O. Coskun, D. Frakes, L.B. Kara and K. Pekkan, Computer-aided patient-specific coronary artery graft design improvements using CFD coupled shape optimizer. Cardiovasc. Eng. Tech. (2011) 1–13. [Google Scholar]
  18. Z. El Zahab, E. Divo and A. Kassab, Minimisation of the wall shear stress gradients in bypass grafts anastomoses using meshless CFD and genetic algorithms optimisation. Comput. Methods Biomech. Biomed. Eng. 13 (2010) 35–47. [CrossRef] [Google Scholar]
  19. C.R. Ethier, S. Prakash, D.A. Steinman, R.L. Leask, G.G. Couch and M. Ojha, Steady flow separation patterns in a 45 degree junction. J. Fluid Mech. 411 (2000) 1–38. [CrossRef] [Google Scholar]
  20. C.R. Ethier, D.A. Steinman, X. Zhang, S.R. Karpik and M. Ojha, Flow waveform effects on end-to-side anastomotic flow patterns. J. Biomech. 31 (1998) 609–617. [CrossRef] [PubMed] [Google Scholar]
  21. S. Giordana, S.J. Sherwin, J. Peiró, D.J. Doorly, J.S. Crane, K.E. Lee, N.J.W. Cheshire and C.G. Caro, Local and global geometric influence on steady flow in distal anastomoses of peripheral bypass grafts. J. Biomech. Eng. 127 (2005) 1087. [CrossRef] [PubMed] [Google Scholar]
  22. M.D. Gunzburger, Perspectives in Flow Control and Optimization. SIAM (2003). [Google Scholar]
  23. M.D. Gunzburger, L. Hou and T.P. Svobodny, Boundary velocity control of incompressible flow with an application to viscous drag reduction. SIAM J. Control Optim. 30 (1992) 167. [CrossRef] [MathSciNet] [Google Scholar]
  24. M.D. Gunzburger, H. Kim and S. Manservisi, On a shape control problem for the stationary Navier-Stokes equations. ESAIM: M2AN 34 (2000) 1233–1258. [CrossRef] [EDP Sciences] [Google Scholar]
  25. H. Haruguchi and S. Teraoka, Intimal hyperplasia and hemodynamic factors in arterial bypass and arteriovenous grafts: a review. J. Artif. Organs 6 (2003) 227–235. [Google Scholar]
  26. J. Haslinger and R.A.E. Mäkinen, Introduction to shape optimization: theory, approximation, and computation. SIAM (2003). [Google Scholar]
  27. R. Herzog and F. Schmidt, Weak lower semi-continuity of the optimal value function and applications to worst-case robust optimal control problems. Optim. 61 (2012) 685–697. [CrossRef] [Google Scholar]
  28. M. Hintermüller, K. Kunisch, Y. Spasov and S. Volkwein, Dynamical systems-based optimal control of incompressible fluids. Int. J. Numer. Methods Fluids 46 (2004) 345–359. [CrossRef] [Google Scholar]
  29. J.D. Humphrey, Review paper: Continuum biomechanics of soft biological tissues. Proc. R. Soc. A 459 (2003) 3–46. [CrossRef] [Google Scholar]
  30. M. Jiang, R. Machiraju and D. Thompson, Detection and visualization of vortices, in The Visualization Handbook, edited by C.D. Hansen and C.R. Johnson (2005) 295–309. [Google Scholar]
  31. H. Kasumba and K. Kunisch, Shape design optimization for viscous flows in a channel with a bump and an obstacle, in Proc. 15th Int. Conf. Methods Models Automation Robotics, Miedzyzdroje, Poland (2010) 284–289. [Google Scholar]
  32. R.S. Keynton, M.M. Evancho, R.L. Sims, N.V. Rodway, A. Gobin and S.E. Rittgers, Intimal hyperplasia and wall shear in arterial bypass graft distal anastomoses: an in vivo model study. J. Biomech. Eng. 123 (2001) 464. [CrossRef] [PubMed] [Google Scholar]
  33. D.N. Ku, D.P. Giddens, C.K. Zarins and S. Glagov, Pulsatile flow and atherosclerosis in the human carotid bifurcation. positive correlation between plaque location and low oscillating shear stress. Arterioscler. Thromb. Vasc. Biol. 5 (1985) 293–302. [CrossRef] [Google Scholar]
  34. K. Kunisch and B. Vexler, Optimal vortex reduction for instationary flows based on translation invariant cost functionals. SIAM J. Control Optim. 46 (2007) 1368–1397. [CrossRef] [MathSciNet] [Google Scholar]
  35. T. Lassila, A. Manzoni, A. Quarteroni and G. Rozza, A reduced computational and geometrical framework for inverse problems in haemodynamics (2011). Technical report MATHICSE 12.2011: Available on http://mathicse.epfl.ch/files/content/sites/mathicse/files/Mathicse [Google Scholar]
  36. T. Lassila and G. Rozza, Parametric free-form shape design with PDE models and reduced basis method. Comput. Methods Appl. Mechods Eng. 199 (2010) 1583–1592. [Google Scholar]
  37. M. Lei, J. Archie and C. Kleinstreuer, Computational design of a bypass graft that minimizes wall shear stress gradients in the region of the distal anastomosis. J. Vasc. Surg. 25 (1997) 637–646. [CrossRef] [PubMed] [Google Scholar]
  38. A. Leuprecht, K. Perktold, M. Prosi, T. Berk, W. Trubel and H. Schima, Numerical study of hemodynamics and wall mechanics in distal end-to-side anastomoses of bypass grafts. J. Biomech. 35 (2002) 225–236. [CrossRef] [PubMed] [Google Scholar]
  39. F. Loth, P.F. Fischer and H.S. Bassiouny. Blood flow in end-to-side anastomoses. Annu. Rev. Fluid Mech. 40 (200) 367–393. [Google Scholar]
  40. F. Loth, S.A. Jones, D.P. Giddens, H.S. Bassiouny, S. Glagov and C.K. Zarins. Measurements of velocity and wall shear stress inside a PTFE vascular graft model under steady flow conditions. J. Biomech. Eng. 119 (1997) 187. [CrossRef] [PubMed] [Google Scholar]
  41. F. Loth, S.A. Jones, C.K. Zarins, D.P. Giddens, R.F. Nassar, S. Glagov and H.S. Bassiouny, Relative contribution of wall shear stress and injury in experimental intimal thickening at PTFE end-to-side arterial anastomoses. J. Biomech. Eng. 124 (2002) 44. [CrossRef] [PubMed] [Google Scholar]
  42. A. Manzoni, Reduced models for optimal control, shape optimization and inverse problems in haemodynamics, Ph.D. thesis, École Polytechnique Fédérale de Lausanne (2012). [Google Scholar]
  43. A. Manzoni, A. Quarteroni and G. Rozza, Shape optimization for viscous flows by reduced basis methods and free-form deformation, Internat. J. Numer. Methods Fluids 70 (2012) 646–670. [Google Scholar]
  44. A. Manzoni, A. Quarteroni and G. Rozza, Model reduction techniques for fast blood flow simulation in parametrized geometries. Int. J. Numer. Methods Biomed. Eng. 28 (2012) 604–625. [Google Scholar]
  45. F. Migliavacca and G. Dubini, Computational modeling of vascular anastomoses. Biomech. Model. Mechanobiol. 3 (2005) 235–250. [Google Scholar]
  46. I.B. Oliveira and A.T. Patera, Reduced-basis techniques for rapid reliable optimization of systems described by affinely parametrized coercive elliptic partial differential equations. Optim. Eng. 8 (2008) 43–65. [CrossRef] [Google Scholar]
  47. A.A. Owida, H. Do and Y.S. Morsi, Numerical analysis of coronary artery bypass grafts: An over view. Comput. Methods Programs Biomed. (2012). DOI: 10.1016/j.cmpb.2011.12.005. [Google Scholar]
  48. J.S. Peterson, The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10 (1989) 777–786. [CrossRef] [Google Scholar]
  49. M. Probst, M. Lülfesmann, M. Nicolai, H.M. Bücker, M. Behr and C.H. Bischof. Sensitivity of optimal shapes of artificial grafts with respect to flow parameters. Comput. Methods Appl. Mech. Eng. 199 (2010) 997–1005. [CrossRef] [Google Scholar]
  50. A. Qiao and Y. Liu, Medical application oriented blood flow simulation. Clinical Biomech. 23 (2008) S130–S136. [CrossRef] [Google Scholar]
  51. A. Quarteroni and G. Rozza, Optimal control and shape optimization of aorto-coronaric bypass anastomoses. Math. Models Methods Appl. Sci. 13 (2003) 1801–1823. [CrossRef] [MathSciNet] [Google Scholar]
  52. A. Quarteroni and G. Rozza, Numerical solution of parametrized Navier-Stokes equations by reduced basis methods. Numer. Methods Part. Differ. Equ. 23 (2007) 923–948. [Google Scholar]
  53. A. Quarteroni, G. Rozza and A. Manzoni. Certified reduced basis approximation for parametrized partial differential equations in industrial applications. J. Math. Ind. 1 (2011). [Google Scholar]
  54. S.S. Ravindran, Reduced-order adaptive controllers for fluid flows using POD. J. Sci. Comput. 15 (2000) 457–478. [CrossRef] [Google Scholar]
  55. A.M. Robertson, A. Sequeira and M.V. Kameneva, Hemorheology. Hemodynamical Flows (2008) 63–120. [Google Scholar]
  56. G. Rozza, On optimization, control and shape design of an arterial bypass. Int. J. Numer. Methods Fluids 47 (2005) 1411–1419. [CrossRef] [Google Scholar]
  57. G. Rozza, D.B.P. Huynh and A.T. Patera, Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Arch. Comput. Methods Eng. 15 (2008) 229–275. [Google Scholar]
  58. S. Sankaran and A.L. Marsden, The impact of uncertainty on shape optimization of idealized bypass graft models in unsteady flow. Phys. Fluids 22 (2010) 121902. [CrossRef] [Google Scholar]
  59. O. Stein, Bi-level strategies in semi-infinite programming. Kluwer Academic Publishers, Dordrecht, The Netherlands (2003). [Google Scholar]
  60. R. Temam, Navier-Stokes Equations. AMS Chelsea, Providence, Rhode Island (2001). [Google Scholar]
  61. K. Veroy and A.T. Patera, Certified real-time solution of the parametrized steady incompressible Navier-Stokes equations: rigorous reduced-basis a posteriori error bounds. Int. J. Numer. Methods Fluids 47 (2005) 773–788. [CrossRef] [MathSciNet] [Google Scholar]
  62. G. Weickum, M.S. Eldred and K. Maute, A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization. Struct. Multidisc. Optim. 38 (2009) 599–611. [CrossRef] [Google Scholar]
  63. D. Zeng, Z. Ding, M.H. Friedman and C.R. Ethier, Effects of cardiac motion on right coronary artery hemodynamics. Ann. Biomed. Eng. 31 (2003) 420–429. [CrossRef] [PubMed] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you