Direct and inverse modeling of the cardiovascular and respiratory systems
Free access
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 http://dx.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]
  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]
  3. G. Allaire, Conception optimale de structures, vol. 58. Springer Verlag (2007).
  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. [CrossRef]
  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]
  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]
  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]
  8. R.P. Brent, Algorithms for Minimization Without Derivatives. Prentice-Hall, Englewood Cliffs, N.J. (1973).
  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]
  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]
  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]
  12. L. Dedè, Optimal flow control for Navier–Stokes equations: drag minimization. Int. J. Numer. Methods Fluids 55 (2007) 347–366. [CrossRef]
  13. S. Dempe, Foundations of bilevel programming. Kluwer Academic Publishers, Dordrecht, The Netherlands (2002).
  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]
  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]
  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]
  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.
  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]
  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]
  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]
  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]
  22. M.D. Gunzburger, Perspectives in Flow Control and Optimization. SIAM (2003).
  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]
  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]
  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. [CrossRef] [PubMed]
  26. J. Haslinger and R.A.E. Mäkinen, Introduction to shape optimization: theory, approximation, and computation. SIAM (2003).
  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]
  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]
  29. J.D. Humphrey, Review paper: Continuum biomechanics of soft biological tissues. Proc. R. Soc. A 459 (2003) 3–46. [CrossRef]
  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.
  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.
  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]
  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]
  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]
  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
  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. [CrossRef]
  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]
  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]
  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. [CrossRef]
  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]
  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]
  42. A. Manzoni, Reduced models for optimal control, shape optimization and inverse problems in haemodynamics, Ph.D. thesis, École Polytechnique Fédérale de Lausanne (2012).
  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. [CrossRef] [MathSciNet]
  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. [CrossRef] [MathSciNet]
  45. F. Migliavacca and G. Dubini, Computational modeling of vascular anastomoses. Biomech. Model. Mechanobiol. 3 (2005) 235–250. [CrossRef] [PubMed]
  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]
  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.
  48. J.S. Peterson, The reduced basis method for incompressible viscous flow calculations. SIAM J. Sci. Stat. Comput. 10 (1989) 777–786. [CrossRef]
  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]
  50. A. Qiao and Y. Liu, Medical application oriented blood flow simulation. Clinical Biomech. 23 (2008) S130–S136. [CrossRef]
  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]
  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. [CrossRef]
  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).
  54. S.S. Ravindran, Reduced-order adaptive controllers for fluid flows using POD. J. Sci. Comput. 15 (2000) 457–478. [CrossRef]
  55. A.M. Robertson, A. Sequeira and M.V. Kameneva, Hemorheology. Hemodynamical Flows (2008) 63–120.
  56. G. Rozza, On optimization, control and shape design of an arterial bypass. Int. J. Numer. Methods Fluids 47 (2005) 1411–1419. [CrossRef]
  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. [CrossRef] [MathSciNet]
  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]
  59. O. Stein, Bi-level strategies in semi-infinite programming. Kluwer Academic Publishers, Dordrecht, The Netherlands (2003).
  60. R. Temam, Navier-Stokes Equations. AMS Chelsea, Providence, Rhode Island (2001).
  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]
  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]
  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]

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