Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography

Journal of Computational Physics

Volumn 283, Issue , 2015, Pages 271-298

  Corrado, Cesare ^a,b   Gerbeau, Jean Frédéric ^a,b   Moireau, Philippe ^c  

^a INRIA   (France)

^b SORBONNE UNIVERSITÉ   (France)

^c INRIA SACLAY   (France)

Author keywords

Data assimilation; Electro mechanics; Electrocardiogram; Identification; Proper orthogonal decomposition; Reduced order unscented kalman filter

Indexed keywords

BANDPASS FILTERS; BIOMEDICAL SIGNAL PROCESSING; DATA REDUCTION; ELECTROPHYSIOLOGY; INVERSE PROBLEMS; KALMAN FILTERS; MEDICAL IMAGING; PRINCIPAL COMPONENT ANALYSIS;

DATA ASSIMILATION; ELECTRICAL STATE; ELECTRO-MECHANICS; IDENTIFICATION; ORTHOGONAL DECOMPOSITION; PROPER ORTHOGONAL; PROPER ORTHOGONAL DECOMPOSITION; REDUCED ORDER; REDUCED-ORDER UNSCENTED KALMAN FILTER; UNSCENTED KALMAN FILTER;

ELECTROCARDIOGRAMS;

EID: 84918797810     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2014.11.041     Document Type: Article

References (65)

1. Auroux D., Blum J. Back and forth nudging algorithm for data assimilation problems. C. R. Math. 2005, 340(12):873-878.
2. Barr R.C., Ramsey M., Spach M.S. Relating epicardial to body surface potential distributions by means of transfer coefficients based on geometry measurements. IEEE Trans. Biomed. Eng. 1977, 1:1-11.
3. Baumeister J., Scondo W. Adaptive methods for parameter identification. Optimization in Mathematical Physics 1987, 87-116. Lang, Frankfurt am Main.
4. Bensoussan A. Filtrage optimal des systèmes linéaires 1971, Dunod.
5. Bertoglio C., Chapelle D., Fernández M.A., Gerbeau J.-F., Moireau P. State observers of a vascular fluid-structure interaction model through measurements in the solid. Comput. Methods Appl. Mech. Eng. 2011, 256(2013):149-168.
6. Bertoglio C., Moireau P., Gerbeau J.-F. Sequential parameter estimation for fluid-structure problems. Application to hemodynamics. Comput. Methods Appl. Mech. Eng. 2012, 28(4):434-455.
7. Bestel J., Clément F., Sorine M. A biomechanical model of muscle contraction. Lectures Notes in Computer Science 2001, vol. 2208. Springer-Verlag.
8. Blum J., Le Dimet F.-X., Navon I.M. Data assimilation for geophysical fluids. Handbook of Numerical Analysis: Computational Methods for the Atmosphere and the Oceans 2008, Elsevier. R. Temam, J. Tribbia (Eds.).
9. Bonnabel S., Mirrahimi M., Rouchon P. Observer-based Hamiltonian identification for quantum systems. Automatica 2009, 45(5):1144-1155.
10. Boulakia M., Cazeau S., Fernández M.A., Gerbeau J.-F., Zemzemi N. Mathematical modeling of electrocardiograms: a numerical study. Ann. Biomed. Eng. 2010, 38(3):1071-1097.
11. Boulakia M., Schenone El., Gerbeau J.-F. Reduced-order modeling for cardiac electrophysiology. Application to parameter identification. Int. J. Numer. Methods Biomed. Eng. 2012, 28(6-7):727-744.
12. Burger M., Mardal K.-A., Nielsen B.F. Stability analysis of the inverse transmembrane potential problem in electrocardiography. Inverse Problems 2010, 26(10).
13. Burnes John E., Taccardi Bruno, Rudy Yoram A noninvasive imaging modality for cardiac arrhythmias. Circulation 2000, 102(17):2152-2158.
14. Chabiniok R., Moireau P., Lesault P.-F., Rahmouni A., Deux J.-F., Chapelle D. Estimation of tissue contractility from cardiac cine-MRI using a biomechanical heart model. Biomech. Model. Mechanobiol. 2012, 11(5):609-630.
15. Chapelle D., Cîndea N., de Buhan M., Moireau P. Exponential convergence of an observer based on partial field measurements for the wave equation. Math. Probl. Eng. 2012, 1-12. 581053.
16. Chapelle D., Gariah A., Moireau P., Sainte-Marie J. A Galerkin strategy with proper orthogonal decomposition for parameter-dependent problems - analysis, assessments and applications to parameter estimation. ESAIM Math. Model. Numer. Anal. 2013, 47(6):1821-1843.
17. Chapelle D., Le Tallec P., Moireau P., Sorine M. An energy-preserving muscle tissue model: formulation and compatible discretizations. Int. J. Multiscale Comput. Eng. 2012, 10(2):189-211.
18. Clements J., Nenonen J., Li P.K.J., Horacek B.M. Activation dynamics in anisotropic cardiac tissue via decoupling. Ann. Biomed. Eng. 2004, 32(7):984-990.
19. Colli Franzone P., Savaré G. Degenerate evolution systems modeling the cardiac electric field at micro- and macroscopic level. Evolution equations, semigroups and functional analysis. Prog. Nonlinear Differ. Equ. Appl. 2002, 1(50):49-78.
20. D'Elia M., Mirabella L., Passerini T., Perego M., Piccinelli M., Vergara C., Veneziani A. Applications of variational data assimilation in computational hemodynamics. MS&A - Modeling, Simulation and Applications 2012, vol. 5:363-394. Springer, Milan. D. Ambrosi, A. Quarteroni, G. Rozza (Eds.).
21. Eldar M., Ohad D.G., Goldberger J.J., Rotstein Z., Hsu S., Swanson D.K., Greenspon A.J. Transcutaneous multielectrode basket catheter for endocardial mapping and ablation of ventricular tachycardia in the pig. Circulation 1997, 96(7):2430-2437.
22. Evensen G. Data Assimilation: The Ensemble Kalman Filter 2009, Springer.
23. Fleming W.H. Deterministic nonlinear filtering. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 1998, 25(3-4):435-454. 1997.
24. Greensite F., Huiskamp G. An improved method for estimating epicardial potentials from the body surface. IEEE Trans. Biomed. Eng. 1998, 45(1):98-104.
25. Gulrajani R.M., Roberge F.A., Savard P. Moving dipole inverse ECG and EEG solutions. IEEE Trans. Biomed. Eng. 1984, 12:903-910.
26. Hoke J.E., Anthes R.A. The initialization of numerical models by a dynamic-initialization technique (fluid flow models for wind forecasting). Mon. Weather Rev. 1976, 104:1551-1556.
27. Huxley A.F. Muscle structure and theories of contraction. Progress in Biophysics and Biological Chemistry, vol. 7 1957, 255-318. Pergamon Press.
28. Julier S.J. Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations. Proceedings of the 2002 American Control Conference, vol. 2 2002, 887-892.
29. Julier S.J., Uhlmann J.K. A new extension of the Kalman filter to nonlinear systems. Proc. of AeroSense: The 11th Int. Symp. on Aerospace/Defence Sensing, Simulation and Controls 1997.
30. Kalman R., Bucy R. New results in linear filtering and prediction theory. J. Basic Eng. 1961, 83:95-108.
31. Krishnamurthy A., Villongco C.T., Chuang J., Frank L.R., Nigam V., Belezzuoli E., Stark P., Krummen D.E., Narayan S., Omens J.H., McCulloch A.D., Kerckhoffs R.C.P. Patient-specific models of cardiac biomechanics. J. Comput. Phys. 2013, 244:4-21.
32. Kunisch K., Volkwein S. Galerkin proper orthogonal decomposition methods for parabolic problems. Numer. Math. 2001, 90(1):117-148.
33. Le Dimet F.-X., Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A 2010, 38(2):97-110.
34. Liu Z., Liu C., He B. Noninvasive reconstruction of three-dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density. IEEE Trans. Med. Imag. 2006, 25(10):1307-1318.
35. Luenberger D.G. An introduction to observers. IEEE Trans. Autom. Control 1971, 16:596-602.
36. Marchesseau S., Delingette H., Sermesant M., Cabrera-Lozoya R., Tobon-Gomez C., Moireau P., Figueras R.M., Ventura I., Lekadir K., Hernandez A., Garreau M., Donal E., Leclercq C., Duckett S.G., Rhode K., Rinaldi C.A., Frangi A.F., Razavi R., Chapelle D., Ayache N. Personalization of a cardiac electromechanical model using reduced order unscented Kalman filtering from regional volumes. Med. Image Anal. 2013, 17(7):816-829.
37. Messinger-Rapport B.J., Rudy Y. Regularization of the inverse problem of electrocardiology: a model study. Math. Biosci. 1988, 89:79-118.
38. Messnarz B., Seger M., Modre R., Fischer G., Hanser F., Tilg B. A comparison of noninvasive reconstruction of epicardial versus transmembrane potentials in consideration of the null space. IEEE Trans. Biomed. Eng. 2004, 51(9):1609-1618.
39. Mirvis D.M., Keller F.W., Ideker R.E., Cox J.W., Dowdie R.F., Zettergren D.G. Detection and localization of multiple epicardial electrical generators by a two-dipole ranging technique. Circ. Res. 1977, 41(4):551-557.
40. Mitchell C.C., Schaeffer D.G. A two-current model for the dynamics of cardiac membrane. Bull. Math. Biol. 2003, 65:767-793.
41. Moireau P., Bertoglio C., Xiao N., Figueroa C.A., Taylor C.A., Chapelle D., Gerbeau J.-F. Sequential identification of boundary support parameters in a fluid-structure vascular model using patient image data. Biomech. Model. Mechanobiol. 2013, 12(3):475-496.
42. 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 March 2011, 17(2):380-405.
43. Moireau P., Chapelle D., Le Tallec P. Joint state and parameter estimation for distributed mechanical systems. Comput. Methods Appl. Mech. Eng. 2008, 197:659-677.
44. Moireau P., Chapelle D., Le Tallec P. Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging. Inverse Problems 2009, 25(3):035010. 25 pp.
45. Nielsen B.F., Cai X., Lysaker M. On the possibility for computing the transmembrane potential in the heart with a one shot method: an inverse problem. Math. Biosci. 2007, 210(2):523-553.
46. Nielsen B.F., Lysaker M., Tveito A. On the use of the resting potential and level set methods for identifying ischemic heart disease: an inverse problem. J. Comput. Phys. 2007, 220(2):772-790.
47. Nielsen B.F., Lysaker O.M., Tarrou C., Sundnes J., Cai X., Mardal K.-A. On the use of the bidomain equations for computing the transmembrane potential throughout the heart wall: an inverse problem. Computers in Cardiology 2006, 797-800. 0276-6574. A. Murray (Ed.).
48. Oster H.S., Rudy Y. The use of temporal information in the regularization of the inverse problem of electrocardiography. IEEE Trans. Biomed. Eng. 1992, 39(1):65-75.
49. Perego M., Veneziani A., Vergara C. A variational approach for estimating the compliance of the cardiovascular tissue: an inverse fluid-structure interaction problem. SIAM J. Sci. Comput. 2011, 33(3):1181-1211.
50. Potse M., Dubé B., Richer J., Vinet A., Gulrajani R.M. A comparison of monodomain and bidomain reaction-diffusion models for action potential propagation in the human heart. IEEE Trans. Biomed. Eng. 2006, 53(12):2425-2435.
51. Pullan A.J., Buist M.L., Cheng L.K. Mathematically Modelling the Electrical Activity of the Heart. From Cell to Body Surface and Back Again 2005, World Scientific.
52. Ramanathan C., Ghanem R.J., Jia P., Ryu K., Rudy Y. Noninvasive electrocardiographic imaging for cardiac electrophysiology and arrhythmia. Nat. Med. 2004, 10:422-428.
53. Rathinam M., Petzold L.R. A new look at proper orthogonal decomposition. SIAM J. Numer. Anal. 2004, 41(5):1893-1925.
54. Rincon A.L., Bendahmane M., Ainseba B. Computing the electrical activity of the heart with a dynamic inverse monodomain operator. Engineering in Medicine and Biology Society (EMBC) 2013, 3797-3800. IEEE.
55. Rutz A.K., Ryf S., Plein S., Boesiger P., Kozerke S. Accelerated whole-heart 3D CSPAMM for myocardial motion quantification. Magn. Reson. Med. 2008, 755-763.
56. Sachse F.B. Computational Cardiology: Modeling of Anatomy, Electrophysiology, and Mechanics 2004, Springer-Verlag.
57. ∞, and Nonlinear Approaches 2006, Wiley-Interscience.
58. Stauffer D.R., Seaman N.L. Use of four-dimensional data assimilation in a limited-area mesoscale model. Part I: experiments with synoptic-scale data. Mon. Weather Rev. 1990, 118(6):1250-1277.
59. Sundnes J., Lines G.T., Cai X., Nielsen B.F., Mardal K.-A., Tveito A. Computing the Electrical Activity in the Heart 2006, Springer-Verlag.
60. Tung L. A bi-domain model for describing ischemic myocardial D-C potentials 1978, PhD thesis, MIT.
61. Wang D., Kirby R.M., Johnson C.R. Finite-element-based discretization and regularization strategies for 3-d inverse electrocardiography. IEEE Trans. Biomed. Eng. 2011, 58(6):1827-1838.
62. Wang D., Kirby R.M., MacLeod R.S., Johnson C.R. Inverse electrocardiographic source localization of ischemia: an optimization framework and finite element solution. J. Comput. Phys. 2013, 250:403-424.
63. Xi J., Lamata P., Lee J., Moireau P., Chapelle D., Smith N. Myocardial transversely isotropic material parameter estimation from in-silico measurements based on a reduced-order unscented Kalman filter. J. Mech. Behav. Biomed. Mater. October 2011, 4(7):1090-1102.
64. Xu C.Z., Deguenon J., Sallet G. Infinite dimensional observers for vibrating systems. Proceedings of 45th IEEE Conference on Decision and Control 2006, 3979-3983.
65. Zhang Q. Adaptive observer for multiple-input-multiple-output (MIMO) linear time-varying systems. IEEE Trans. Autom. Control 2002, 47(3):525-529. 10.1109/9.989154.