H. Ashikaga, S. R. Mickelsen, D. B. Ennis, I. Rodriguez, P. Kellman et al., Electromechanical analysis of infarct border zone in chronic myocardial infarction, AJP: Heart and Circulatory Physiology, vol.289, issue.3, pp.1099-1105, 2005.
DOI : 10.1152/ajpheart.00423.2005

K. F. Augenstein, B. R. Cowan, I. J. Legrice, P. M. Nielsen, and A. A. Young, Method and Apparatus for Soft Tissue Material Parameter Estimation Using Tissue Tagged Magnetic Resonance Imaging, Journal of Biomechanical Engineering, vol.127, issue.1, pp.148-157, 2005.
DOI : 10.1115/1.1835360

L. Axel, A. Montillo, and D. Kim, Tagged magnetic resonance imaging of the heart: a survey, Medical Image Analysis, vol.9, issue.4, pp.376-393, 2005.
DOI : 10.1016/j.media.2005.01.003

J. Baerentzen and H. Aanaes, Signed Distance Computation Using the Angle Weighted Pseudonormal, IEEE Transactions on Visualization and Computer Graphics, vol.11, issue.3, pp.243-253, 2005.
DOI : 10.1109/TVCG.2005.49

K. J. Bathe, Finite Element Procedures, 1996.

J. Bestel, F. Clément, and M. Sorine, A Biomechanical Model of Muscle Contraction, In Lectures Notes in Computer Science, vol.2208, 2001.
DOI : 10.1007/3-540-45468-3_143

J. Blum, F. Dimet, and I. M. Navon, Data assimilation for geophysical fluids. Computational Methods for the Atmosphere and the Oceans, pp.385-441, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00391892

E. Bogatyrenko and U. Hanebeck, Simultaneous state and parameter estimation for physicsbased tracking of heart surface motion, Multisensor Fusion and Integration for Intelligent Systems (MFI), 2010 IEEE Conference on, pp.109-114, 2010.

M. D. Cerqueira, N. J. Weissman, and V. Dilsizian, Standardized Myocardial Segmentation and Nomenclature for Tomographic Imaging of the Heart, Journal of Cardiovascular Magnetic Resonance, vol.4, issue.2, pp.539-542, 2002.
DOI : 10.1081/JCMR-120003946

R. Chabiniok, D. Chapelle, P. F. Lesault, A. Rahmouni, and J. F. Deux, Validation of a biomechanical heart model using animal data with acute myocardial infarction, CI2BM09 -MICCAI Workshop on Cardiovascular Interventional Imaging and Biophysical Modelling, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00418373

D. Chapelle, M. A. Fernàndez, J. Gerbeau, P. Moireau, J. Sainte-marie et al., Numerical Simulation of the Electromechanical Activity of the Heart, Proceedings of Functional Imaging and Modeling of the Heart, pp.357-365, 2009.
DOI : 10.1016/j.compstruc.2006.05.003
URL : https://hal.archives-ouvertes.fr/inria-00542779

D. Chapelle, P. Le-tallec, P. Moireau, and M. Sorine, ENERGY-PRESERVING MUSCLE TISSUE MODEL: FORMULATION AND COMPATIBLE DISCRETIZATIONS, International Journal for Multiscale Computational Engineering, vol.10, issue.2, 2010.
DOI : 10.1615/IntJMultCompEng.2011002360
URL : https://hal.archives-ouvertes.fr/hal-00678772

P. G. Ciarlet and G. Geymonat, Sur les lois de comportement enélasticitéenélasticité non linéaire, pp.423-426, 1982.

K. D. Costa, J. W. Holmes, and A. D. Mcculloch, Modelling cardiac mechanical properties in three dimensions, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.359, issue.1783, pp.1233-50, 2001.
DOI : 10.1098/rsta.2001.0828

O. Ecabert and N. Smith, euHeart: integrated cardiace care using patient-specific cardiovascular modeling, SPIE Newsroom, 2008.
DOI : 10.1117/2.1200804.1126

P. J. Frey and P. L. George, Mesh Generation, 2008.
DOI : 10.1002/9780470611166
URL : https://hal.archives-ouvertes.fr/inria-00073738

S. Göktepe, S. Acharya, J. Wong, and E. Kuhl, Computational modeling of passive myocardium, International Journal for Numerical Methods in Biomedical Engineering, vol.37, issue.1, pp.1-12, 2011.
DOI : 10.1002/cnm.1402

G. A. Holzapfel and R. W. Ogden, Constitutive modelling of passive myocardium: a structurally based framework for material characterization, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.192, issue.Pt 2, pp.3445-3475, 2009.
DOI : 10.1016/0021-9290(87)90279-X

I. Hoteit, D. T. Pham, and J. Blum, A simplified reduced order Kalman filtering and application to altimetric data assimilation in Tropical Pacific, Journal of Marine Systems, vol.36, issue.1-2, pp.101-127, 2002.
DOI : 10.1016/S0924-7963(02)00129-X

Z. H. Hu, D. Metaxas, and L. Axel, In vivo strain and stress estimation of the heart left and right ventricles from MRI images, Medical Image Analysis, vol.7, issue.4, pp.435-444, 2003.
DOI : 10.1016/S1361-8415(03)00032-X

J. D. Humphrey, Cardiovascular Solid Mechanics: Cells, Tissues, and Organs, Applied Mechanics Reviews, vol.55, issue.5, 2002.
DOI : 10.1115/1.1497492

P. Hunter, A vision and strategy for the virtual physiological human in 2010 and beyond, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.366, issue.1920, pp.2595-2614, 2010.
DOI : 10.1098/rsta.2010.0048

A. F. Huxley, Muscle structure and theories of contraction, Progress in Biophysics and Biological Chemistry, pp.255-318, 1957.

A. Imperiale, R. Chabiniok, P. Moireau, and D. Chapelle, Constitutive Parameter Estimation Methodology Using Tagged-MRI Data, Proceedings of Functional Imaging and Modeling of the Heart, 2011.
DOI : 10.1109/42.414605

S. J. Julier, J. K. Uhlmann, and H. F. Durrant-whyte, A new approach for filtering nonlinear systems, Proceedings of 1995 American Control Conference, ACC'95, pp.1628-1632, 1995.
DOI : 10.1109/ACC.1995.529783

R. Kalman, A New Approach to Linear Filtering and Prediction Problems, Journal of Basic Engineering, vol.82, issue.1, pp.35-45, 1960.
DOI : 10.1115/1.3662552

R. J. Kim, D. S. Fieno, T. D. Parrish, K. Harris, E. Chen et al., Relationship of MRI Delayed Contrast Enhancement to Irreversible Injury, Infarct Age, and Contractile Function, Circulation, vol.100, issue.19, pp.1992-2002, 1999.
DOI : 10.1161/01.CIR.100.19.1992

P. and L. Tallec, Numerical methods for nonlinear three-dimensional elasticity, Handbook of Numerical Analysis, 1994.
DOI : 10.1016/S1570-8659(05)80018-3

H. Liu and P. Shi, Maximum a posteriori strategy for the simultaneous motion and material property estimation of the heart, IEEE Transactions on Biomedical Engineering, vol.56, issue.2, pp.378-389, 2009.

T. Mansi, J. Peyrat, M. Sermesant, H. Delingette, J. Blanc et al., Physically-Constrained Diffeomorphic Demons for the Estimation of 3D Myocardium Strain from Cine-MRI, Proceedings of Functional Imaging and Modeling of the Heart, pp.201-210, 2009.
DOI : 10.1148/radiology.214.2.r00fe17453
URL : https://hal.archives-ouvertes.fr/inria-00616138

P. Moireau and D. Chapelle, Reduced-order Unscented Kalman Filtering with application to parameter identification in large-dimensional systems, ESAIM: COCV, 2010.
URL : https://hal.archives-ouvertes.fr/inria-00550104

P. Moireau, D. Chapelle, and P. L. Tallec, Joint state and parameter estimation for distributed mechanical systems, Computer Methods in Applied Mechanics and Engineering, vol.197, issue.6-8, pp.6-8659, 2008.
DOI : 10.1016/j.cma.2007.08.021
URL : https://hal.archives-ouvertes.fr/hal-00175623

P. Moireau, D. Chapelle, and P. L. Tallec, Filtering for distributed mechanical systems using position measurements: perspectives in medical imaging, Inverse Problems, vol.25, issue.3, 2009.
DOI : 10.1088/0266-5611/25/3/035010
URL : https://hal.archives-ouvertes.fr/hal-00358914

P. Moireau, X. Nan, M. Astorino, C. A. Figueroa, D. Chapelle et al., External tissue support and fluid???structure simulation in blood flows, Biomechanics and Modeling in Mechanobiology, vol.31, issue.3, 2011.
DOI : 10.1007/s10237-011-0289-z
URL : https://hal.archives-ouvertes.fr/hal-00701801

M. P. Nash and P. J. Hunter, Computational mechanics of the heart ? from tissue structure to ventricular function, Journal of Elasticity, vol.61, issue.1/3, pp.113-141, 2000.
DOI : 10.1023/A:1011084330767

X. Papademetris, A. J. Sinusas, D. P. Dione, R. T. Constable, and J. S. Duncan, Estimation of 3-D left ventricular deformation from medical images using biomechanical models, IEEE Transactions on Medical Imaging, vol.21, issue.7, pp.786-800, 2002.
DOI : 10.1109/TMI.2002.801163

J. Peters, O. Ecabert, C. Meyer, R. Kneser, and J. Weese, Optimizing boundary detection via Simulated Search with applications to multi-modal heart segmentation, Medical Image Analysis, vol.14, issue.1, pp.70-84, 2010.
DOI : 10.1016/j.media.2009.10.004

D. T. Pham, Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems, Monthly Weather Review, vol.129, issue.5, pp.1194-1207, 2001.
DOI : 10.1175/1520-0493(2001)129<1194:SMFSDA>2.0.CO;2
URL : https://hal.archives-ouvertes.fr/inria-00073082

K. Raghavan and A. Yagle, Forward and inverse problems in elasticity imaging of soft tissues, IEEE Transactions on Nuclear Science, vol.41, issue.4, pp.1639-1648, 1994.
DOI : 10.1109/23.322961

R. S. Rivlin and J. L. Ericksen, Stress-deformation relations for isotropic materials, J. Rational Mech. Anal, vol.4, pp.323-425, 1955.

F. B. Sachse, R. Frech, C. D. Werner, and O. Dössel, A model based approach to assignment of myocardial fibre orientation, Computers in Cardiology 1999. Vol.26 (Cat. No.99CH37004), pp.145-148, 1999.
DOI : 10.1109/CIC.1999.825927

J. Sainte-marie, D. Chapelle, R. Cimrman, and M. Sorine, Modeling and estimation of the cardiac electromechanical activity, Computers & Structures, vol.84, issue.28, pp.1743-1759, 2006.
DOI : 10.1016/j.compstruc.2006.05.003
URL : https://hal.archives-ouvertes.fr/hal-00839206

J. Schaerer, C. Casta, J. Pousin, and P. Clarysse, A dynamic elastic model for segmentation and tracking of the heart in MR image sequences, Medical Image Analysis, vol.14, issue.6, pp.738-749, 2010.
DOI : 10.1016/j.media.2010.05.009
URL : https://hal.archives-ouvertes.fr/hal-00877519

M. Sermesant, F. Billet, R. Chabiniok, T. Mansi, P. Chinchapatnam et al., Personalised Electromechanical Model of the Heart for the Prediction of the Acute Effects of Cardiac Resynchronisation Therapy, Proceedings of Functional Imaging and Modeling of the Heart, pp.239-248, 2009.
DOI : 10.1016/j.media.2006.04.002
URL : https://hal.archives-ouvertes.fr/inria-00616177

M. Sermesant, P. Moireau, O. Camara, J. Sainte-marie, R. Andriantsimiavona et al., Cardiac function estimation from MRI using a heart model and data assimilation: Advances and difficulties, Medical Image Analysis, vol.10, issue.4, pp.642-656, 2006.
DOI : 10.1016/j.media.2006.04.002
URL : https://hal.archives-ouvertes.fr/inria-00614997

D. Simon, Optimal State Estimation: Kalman, H ? , and Nonlinear Approaches, 2006.
DOI : 10.1002/0470045345

J. Sundnes, G. T. Lines, X. Cai, B. F. Nielsen, K. Mardal et al., Computing the Electrical Activity in the Heart, 2006.

N. Toussaint, T. Mansi, H. Delingette, N. Ayache, and M. Sermesant, An integrated platform for dynamic cardiac simulation and image processing: Application to personalised tetralogy of Fallot simulation, Proc. Eurographics Workshop on Visual Computing for Biomedicine (VCBM), 2008.
URL : https://hal.archives-ouvertes.fr/inria-00616120

N. Toussaint, J. C. Souplet, and P. Fillard, MedINRIA: Medical image navigation and research tool by INRIA, Proc. of MICCAI'07 Workshop on Interaction in medical image analysis and visualization, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00616047

L. Wang, H. Zhang, K. C. Wong, and P. Shi, A reduced-rank square root filtering framework for noninvasive functional imaging of volumetric cardiac electrical activity, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.533-536, 2009.
DOI : 10.1109/ICASSP.2009.4959638

J. Xi, P. Lamata, J. Lee, P. Moireau, D. Chapelle et al., Myocardial transversely isotropic material parameter estimation from in-silico measurements based on reducedorder unscented Kalman filter, J. of the Mechanical Behavior of Biomedical Materials, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00654545

Q. Zhang, Adaptive observer for MIMO linear time varying systems, IEEE Transactions on Automatic Control, vol.3, pp.525-529, 2002.
URL : https://hal.archives-ouvertes.fr/inria-00072520