Applications of variational data assimilation in computational hemodynamics

Modeling, Simulation and Applications

Volumn 5, Issue , 2012, Pages 363-394

  D'Elia, Marta ^a   Mirabella, Lucia ^b   Passerini, Tiziano ^a   Perego, Mauro ^c   Piccinelli, Marina ^a   Vergara, Christian ^d   Veneziani, Alessandro ^a  

^a EMORY UNIVERSITY   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c FLORIDA STATE UNIVERSITY   (United States)

^d UNIVERSITY OF BERGAMO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84874364236     PISSN: 20375255     EISSN: 20375263     Source Type: Book Series    
DOI: 10.1007/978-88-470-1935-5_12     Document Type: Article

References (88)

1. Topol E.J. (ed.): Textbook of Cardiovascular Medicine. Lippincott-Raven Publisher, Philadelphia-New York, 1998.
2. Antiga L. et al.: Vascular modeling toolkit, website. www.vmtk.org.
3. Lions J.L.: Remarks on approximate controllability. Journal d'Analyse Mathématique 59(1): 103-116, 1992.
4. Brown L.G.: A survey of image registration techniques. ACM Computing Surveys (CSUR) 24(4): 325-376, 1992.
5. Vaillant M., Glaunes J.: Surface matching via currents. In Recent advances in parallel virtual machine and message passing interface: 11th European PVM/MPI Users' Group Meeting, Budapest, Hungary, September 19-22, 2004: proceedings, page 381. Springer-Verlag New York Inc, 2004.
6. Nocedal J., Wright S.: Numerical Optimization. Springer, apr 2000.
7. Lions J.L.: On the controllability of distributed systems. Proc Natl Acad Science 94: 4828-4835, 1997.
8. Welch G., Bishop G.: An introduction to the Kalman filter. University of North Carolina at Chapel Hill, Chapel Hill, NC, 1995.
9. Ward C.: Clinical significance of the bicuspid aortic valve. Heart 83(1): 81, 2000.
10. DeParis S. et al.: Lifev-library for finite elements, website. www.lifev.org.
11. Zitova B., Flusser J.: Image registration methods: a survey. Image and Vision Computing 21(11): 977-1000, 2003.
12. Gunzburger M.D.: Perspectives in flow control and optimization. Society for Industrial Mathematics, 2003.
13. Maintz J.B., Viergever M.A.: A survey of medical image registration. Medical Image Analysis 2(1): 1-36, 1998.
14. Hoffman J.I.E., Kaplan S.: The incidence of congenital heart disease. Journal of the American College of Cardiology 39(12): 1890, 2002.
15. Engl H.W., Hanke M., Neubauer A.: Regularization of inverse problems. Springer Netherlands, 1996.
16. Formaggia L., Quarteroni A., Veneziani A. (eds.): Cardiovascular Mathematics, vol. 1 of MM&S. Springer, Italy, 2009.
17. Lions J.L.: Are there connections between turbulence and controllability? In 9th INRIA International Conference, Antibes, 1990.
18. Robinson A.R., Lermusiaux P.F.J.: Overview of data assimilation. Technical Report 62, Harvard University, Cambridge, Massachusetts, aug 2000.
19. Bonesky T.: Morozov's discrepancy principle and Tikhonov-type functionals. Inverse Problems 25:015015, 2009.
20. Kaipio J., Somersalo E.: Statistical and Computational Inverse Problems. Springer, 2005.
21. Quarteroni A., Formaggia L., Veneziani A. (eds.): Complex Systems in Biomedicine. Springer, Italy, 2006.
22. Blum J., Le Dimet F.X., Navon I.M.: Data Assimilation for Geophysical Fluids, vol. XIV of Handbook of Numerical Analysis, chap. 9. Elsevier, 2005.
23. Barber C., Dobkin D., Hudhanpaa H.: The quickhull program for convex hulls. ACM Transactions on Mathematical Software 22: 469-483, 1996.
24. Antiga L., Steinman D.A., Peiró J.: From image data to computational domain. In: Formaggia L., Quarteroni A., Veneziani A. (eds.), Cardiovascular Mathematics, MM&S, chap. 4. Springer, Italy, 2009.
25. Gerbeau J.F., Fernandez M.: Algorithms for fluid-structure interaction problems. In: Formaggia L., Quarteroni A., Veneziani A. (eds.), Cardiovascular Mathematics, MM&S, chap. 9. Springer, Italy, 2009.
26. Lions J.L.: Optimal control of systems governed by partial differential equations. Springer-Verlag, 1971.
27. Walters R.W., Huyse L.: Uncertainty analysis for fluid mechanics with applications, 2002.
28. Fischer B., Modersitzki J.: Ill-posed medicine: an introduction to image registration. Inverse Problems 24: 034008, 2008.
29. Lions J.L.: Exact Controllability for distributed systems. Some trends and some problems. Applied and Industrial Mathematics: Venice-1, 1989, p. 59, 1991.
30. Perktold K.: On numerical simulation of three-dimensional physiological flow problems. Technical report, Ber. Math.-Stat. Sekt. Forschungsges. Joanneum 280, 1-32, 1987.
31. Taylor C.A., Draney M.T., Ku J.P., Parker D., Steele B.N., Wang K., Zarins C.K.: Predictive medicine: Computational techniques in therapeutic decision-making. Computer Aided Surgery 4(5): 231-247, 1999.
32. Taylor C.A., Draney M.T.: Experimental and Computational Methods in Cardiovascular Fluid Mechanics. Ann. Rev. Fluid. Mech. 36: 197-231, 2004.
33. Grinberg L., Anor T., Cheever E., Marsden. J.P., Karniadakis G.E.: Simulation of the human intracranial arterial tree. Phil. Trans. R. Soc. A 367: 2371-2386, 2009.
34. Heys J.J., Manteuffel T.A., McCormick S.F., Milano M., Westerdale J., Belohlavek M.: Weighted least-squares finite elements based on particle imaging velocimetry data. Journal of Computational Physics 229(1): 107-118, 2010.
35. Ide K., Courtier P., Ghil M., Lorenc A.C.: Unified notation for data assimilation: Operational, sequential and variational. Journal of Meteorological Society of Japan 75(Special): 181-189, 1997.
36. Chapelle D., Moireau P.: Robust filter for joint state parameters estimation in distributed mechanical system. Discrete and Continous Dynamical Systems 23(1-2): 65-84, 2009.
37. Moireau P., Chapelle D.: Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems. ESAIM: Control, Optimisation and Calculus of Variations, 2010.
38. Moireau P., Chapelle D., Le Tallec P.: Joint state and parameter estimation for distributed mechanical systems. Computer Methods in Applied Mechanics and Engineering 197(6-8): 659-677, 2008.
39. Moireau P., Chapelle D., Le Tallec P.: Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging. Inverse Problems 25: 035010, 2009.
40. Sermesant M., Moireau P., Camara O., Sainte-Marie J., Andriantsimiavona R., Cimrman R., Hill D.L.G., Chapelle D., Razavi R.: Cardiac function estimation from MRI using a heart model and data assimilation: advances and difficulties. Functional Imaging and Modeling of the Heart, pp. 325-337, 2005.
41. Funamoto K., Suzuki Y., Hayase T., Kosugi T., Isoda H.: Numerical validation of mrmeasurement-integrated simulation of blood flow in a cerebral aneurysm. Ann. Biomed. Eng. 37(6): 1105-1116, 2009.
42. Glowinski R., Li C.H., Lions J.L.: A numerical approach to the exact boundary controllability of the wave equation (I) Dirichlet controls: Description of the numerical methods. Japan Journal of Industrial and Applied Mathematics 7(1):1-76, 1990.
43. Glowinski R., Lions J.L.: Exact and approximate controllability for distributed parameter systems. Acta Numerica 3: 269-378, 1994.
44. Zuazua E.: Controllability of partial differential equations and its semi-discrete approximations. Dynamical Systems 8(2): 469-513, 2002.
45. Ervin V.J.; Lee H.: Numerical approximation of a quasi-Newtonian Stokes flow problem with defective boundary conditions. SIAM J. Numer. Anal. 45(5): 2120-2140, 2007.
46. Formaggia L., Veneziani A., Vergara C.: A new approach to numerical solution of defective boundary value problems in incompressible fluid dynamics. SIAM Journal on Numerical Analysis 46(6): 2769-2794, 2008.
47. Formaggia L., Veneziani A., Vergara C.: Flow rate boundary problems for an incompressible fluid in deformable domains: formulations and solution methods. Computer Methods in Applied Mechanics and Engineering 199(9-12): 677-688, 2010.
48. Darema F.: Dynamic data driven applications systems (dddas)-a transformative paradigm. In ICCS (3), p. 5, 2008.
49. Erdemir A., Guess T., Halloran J., Tadepalli S.C., Morrison T.M.: Recommendations for reporting finite element analysis studies in biomechanics. http://www.imagwiki.nibib.nih.gov/mediawiki/index.php?title=Reporting in FEA, 2010.
50. Robicsek F., Thubrikar M.J., Cook J.W., Fowler B.: The congenitally bicuspid aortic valve: how does it function? Why does it fail? The Annals of Thoracic Surgery 77(1): 177-185, 2004.
51. Gurvitz M., Chang R.K., Drant S., Allada V.: Frequency of aortic root dilation in children with a bicuspid aortic valve. The American Journal of Cardiology 94(10): 1337-1340, 2004.
52. den Reijer P.M., Sallee D., van der Velden P., Zaaijer E., Parks W.J., Ramamurthy S., Robbie T., Donati G. Lamphier C., Beekman R., and Brummer M.: Hemodynamic predictors of aortic dilatation in bicuspid aortic valve by velocity-encoded cardiovascular magnetic resonance. Journal of Cardiovascular Magnetic Resonance 12(1): 4, 2010.
53. Viscardi F., Vergara C., Antiga L., Merelli S., Veneziani A., Puppini G., Faggian G., Mazzucco A., Luciani G.B.: Comparative Finite Element Model Analysis of Ascending Aortic Flow in Bicuspid and Tricuspid Aortic Valve. Artificial Organs 34(12): 1114-1120, 2010.
54. Dwight R.P.: Bayesian inference for data assimilation using Least-Squares Finite Element methods. In IOP Conference Series: Materials Science and Engineering, vol. 10, p. 012224. IOP Publishing, 2010.
55. D'Elia M., Veneziani A.: Methods for assimilating blood velocity measures in hemodynamics simulations: Preliminary results. Procedia Computer Science 1(1): 1231-1239, 2010. ICCS 2010.
56. Quarteroni A., Valli A.: Numerical Approximation of Partial Differential Equations. Springer, 1994.
57. Hansen P.C.: Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion. Society for Industrial Mathematics, 1998.
58. D'Elia M., Perego M., Veneziani A.: A variational data assimilation procedure for the incompressible Navier-Stokes equations in hemodynamics. Technical Report TR-2010-19, Department of Mathematics & CS, Emory University, 2010.
59. Nobile F., Tempone R.: Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients. International Journal for Numerical Methods in Engineering 80: 979-1006, 2009.
60. Oden J.T., Babuska I., Nobile F., Feng Y., Tempone R.: Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty. Computer Methods in Applied Mechanics and Engineering 194(2-5): 195-204, 2005. Selected papers from the 11th Conference on The Mathematics of Finite Elements and Applications.
61. Elman H.C., Miller C.W., Phipps E.T., Tuminaro R.S.: Assessment Of Collocation And Galerkin Approaches To Linear Diffusion Equations With Random Data. International Journal for Uncertainty Quantification 1(1), 2011.
62. Bertero M., Piana M.: Inverse problems in biomedical imaging: modeling and methods of solution. In: Quarteroni A., Formaggia L., Veneziani A. (eds.), Complex Systems in Biomedicine, chap. 1, pp. 1-33. Springer, 2006.
63. Sforza D.M., Lohner R., Putman C., Cebral J.R.: Hemodynamic analysis of intracranial aneurysms with moving parent arteries: Basilar tip aneurysms. International Journal for Numerical Methods in Biomedical Engineering, 2010.
64. Holzapfel G.A., Gasser T.C., Ogden R.W.: A new constitutive framework for arterial wall mechanics and a comparative study of material models. Journal of Elasticity 61(1): 1-48, 2000.
65. Wulandana R., Robertson A.M.: An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomechanics and Modeling in Mechanobiology 4(4): 235-248, 2005.
66. Causin P., Gerbeau J.F., Nobile F.: Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Computer Methods in Applied Mechanics and Engineering 194(42-44): 4506-4527, 2005.
67. Gerardo-Giorda L., Nobile F., Vergara C.: Analysis and optimization of robin-robin partitioned procedures in fluid-structure interaction problems. SIAM J. Num. Anal. 48(6): 2091-2116, 2010.
68. Torii R., Keegan J., Wood N.B., Dowsey A.W., Hughes A.D., Yang G.Z., Firmin D.N., Thom S.A.M.G., Xu X.Y.: MR Image-Based Geometric and Hemodynamic Investigation of the Right Coronary Artery with Dynamic Vessel Motion. Annals of Biomedical Engineering 8: 1-15, 2010.
69. Piccinelli M., Mirabella L., Passerini T., Haber E., Veneziani A.: 4d Image-Based CFD Simulation of a Compliant Blood Vessel. Technical Report TR-2010-27, Department of Mathematics & CS, Emory University, www.mathcs.emory.edu, 2010.
70. Hughes T.J.R., Liu W.K., Zimmermann T.K.: Lagrangian-Eulerian finite element formulation for incompressible viscous flows. Computer Methods in Applied Mechanics and Engineering 29(3): 329-349, 1981.
71. Audette M.A., Ferrie F.P., Peters T.M.: An algorithmic overview of surface registration techniques for medical imaging. Medical Image Analysis 4(3): 201-217, 2000.
72. Perperidis D., Mohiaddin R.H., Rueckert D.: Spatio-temporal free-form registration of cardiac MR image sequences. Medical Image Analysis 9(5): 441-456, 2005.
73. Mollemans W., Schutyser F., Van Cleynenbreugel J., Suetens P.: Tetrahedral mass spring model for fast soft tissue deformation. In: Surgery Simulation and Soft Tissue Modeling, pp. 1002-1003, 2003.
74. Ku D.N., Giddens D.P., Zarins C.K., Glagov S.: Pulsatile flow and atherosclerosis in the human carotid bifurcation. positive correlation between plaque location and low oscillating shear stress. Arterioscler. Thromb. Vasc. Biol. 5(3): 293-302, 1985.
75. Consolini M., Passerini T., Veneziani A., Taylor R.W.: Angiotensin II and Shear Stress in the Development and Localization of Abdominal Aortic Aneurysms. in preparation, 2011.
76. Titaud O., Vidard A., Souopgui I., Le Dimet F.X.: Assimilation of image sequences in numerical models. Tellus A 62(1): 30-47, 2010.
77. Giuliani E.R., Gersh B.J., McGoon M.D., Hayes D.L., Schaff H.V.: Mayor Clinic Practice of Cardiolgy. Mosby Publisher, St. Louis, 1996.
78. Manduca A., Muthupillai R., Rossman P. J., Greenleaf J. F.: Visualization of tissue elasticity by magnetic resonance elastography. Lecture Notes in Computer Science 1131: 63, 1996.
79. Barbone P.E., Oberai A.A.: Elastic modulus imaging: some exact solutions of the compressible elastography inverse problem. Physics in Medicine and Biology 52(6): 1577, 2007.
80. Oberai A.A., Gokhale N.H., Goenezen S., Barbone P.E., Hall T.J., Sommer A.M., Jiang J.: Linear and nonlinear elasticity imaging of soft tissue in vivo: demonstration of feasibility. Physics in Medicine and Biology 54(5): 1191, 2009.
81. Gokhale N.H., Barbone P.E., Oberai A.A.: Solution of the nonlinear elasticity imaging inverse problem: the compressible case. Inverse Problems 24(4): 045010, 2008.
82. Nobile F., Vergara C.: An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions. SIAM J. Sc. Comp. 30(2): 731-763, 2008.
83. Perego M., Veneziani A., Vergara C.: A variational approach for estimating the compliance of the cardiovascular tissue: An inverse fluid-structure interaction problem. Technical Report TR-2010-18, Department of Mathematics &CS, Emory University, www.mathcs.emory.edu, 2010. to appear in SIAM J. Sc. Comp.
84. Perktold K., Hilbert D.: Numerical simulation of pulsatile flow in a carotid bifurcation model. Journal of Biomedical Engineering 8(3): 193-199, 1986.
85. Rindt C.C.M., Vosse F.N., Steenhoven A.A., Janssen J.D., Reneman R.S.: A numerical and experimental analysis of the flow field in a two-dimensional model of the human carotid artery bifurcation. Journal of Biomechanics 20(5): 499-509, 1987.
86. Xiu D., Karniadakis G.E.: Modeling uncertainty in flow simulations via generalized polynomial chaos. Journal of Computational Physics 187(1): 137-167, 2003.
87. Xiu D., Lucor D., Su C.H., Karniadakis G.E.: Stochastic modeling of flow-structure interactions using generalized polynomial chaos. Journal of Fluids Engineering 124: 51, 2002.
88. Xiu D., Karniadakis G.E.: Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos. Computer Methods in Applied Mechanics and Engineering 191(43): 4927-4948, 2002.