Solution of the nonlinear elasticity imaging inverse problem: The incompressible case

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 13-16, 2011, Pages 1406-1420

  Goenezen, Sevan ^a   Barbone, Paul ^b   Oberai, Assad A ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

^b Boston University   (United States)

Author keywords

Adjoint equations; Inverse problem; Ladyzenskaya Babuska Brezzi condition; Mixed finite element formulation; Nonlinear elasticity imaging; Stabilization

Indexed keywords

ADJOINT EQUATIONS; BABUSKA-BREZZI CONDITION; COMPRESSIBLE HYPERELASTIC MATERIALS; DEFORMATION FIELD; DEVIATORIC STRESS TENSOR; EFFICIENT ALGORITHM; FORWARD PROBLEM; GRADIENT BASED; INVERSE ELASTICITY PROBLEMS; LADYZENSKAYA-BABUSKA-BREZZI CONDITION; MATERIAL PARAMETER; MIXED FINITE ELEMENT FORMULATION; NEARLY INCOMPRESSIBLE; NON-LINEAR PARAMETERS; NONLINEAR ELASTICITY; NOVEL STRATEGIES; QUASI-NEWTON; QUASI-STATIC DEFORMATION; SLOW DEFORMATION; STRAIN ENERGY DENSITY FUNCTIONS; STRAIN LEVELS; STRESS-STRAIN BEHAVIORS; SYSTEM OF EQUATIONS;

ALGORITHMS; DEFORMATION; ELASTICITY; EXPONENTIAL FUNCTIONS; INCOMPRESSIBLE FLOW; INVERSE PROBLEMS; SPATIAL DISTRIBUTION; STABILIZATION; STRAIN ENERGY;

NONLINEAR EQUATIONS;

EID: 78751642836     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.12.018     Document Type: Article

References (28)

1. Gao L., Parker K.J., Lerner R.M., Levinson S.F. Imaging of the elastic properties of tissue - A review. Ultrasound in Medicine and Biology 1996, 22:959-977.
2. Parker K.J., Gao L., Lerner R.M., Levinson S.F. Techniques for elastic imaging: a review. IEEE Engineering in Medicine and Biology Magazine 1996, 15:52-59.
3. Ophir J., Alam S.K., Garra B., Kallel F., Konofagou E., Krouskop T., Varghese T. Elastography: ultrasonic estimation and imaging of the elastic properties of tissues. Proceedings of the Institution of Mechanical Engineers Part H-Journal of Engineering in Medicine 1999, 213:203-233.
4. Greenleaf J.F., Fatemi M., Insana M. Selected methods for imaging elastic properties of biological tissues. Annual Review of Biomedical Engineering 2003, 5:57-78.
5. Parker K.J., Taylor L.S., Gracewski S., Rubens D.J. A unified view of imaging the elastic properties of tissue. Journal of the Acoustical Society of America 2005, 117:2705-2712.
6. P. Wellman, R.H. Howe, E. Dalton, K.A. Kern, Breast Tissue Stiffness in Compression is Correlated to Histological Diagnosis, Technical Report, Harvard BioRobotics Laboratory, Division of Engineering and Applied Sciences, Harvard University, 1999.
7. Samani A., Plewes D. A method to measure the hyperelastic parameters of ex vivo breast tissue samples. Physics in Medicine and Biology 2004, 49:4395-4405.
8. 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 2009, 54:1191-1207.
9. Paszek M.J., Zahir N., Johnson K.R., Lakins J.N., Rozenberg G.I., Gefen A., Reinhart-King C.A., Margulies S.S., Dembo M., Boettiger D., Hammer D.A., Weaver V.M. Tensional homeostasis and the malignant phenotype. Cancer Cell 2005, 8:241-254.
10. Falzon G., Pearson S., Murison R. Analysis of collagen fibre shape changes in breast cancer. Physics in Medicine and Biology 2008, 53:6641-6652.
11. O'Hagan J.J., Samani A. Measurement of the hyperelastic properties of 44 pathological ex vivo breast tissue samples. Physics in Medicine and Biology 2009, 54:2557-2569.
12. Gokhale N.H., Barbone P.E., Oberai A.A. Solution of the nonlinear elasticity imaging inverse problem: the compressible case. Inverse Problems 2008, 24.
13. Veronda D.R., Westmann R.A. Mechanical characterization of skin-finite deformations. Journal of Biomechanics 1970, 3:111-122. IN9, 123-124.
14. Babuska I. The finite element method with Lagrangian multipliers. Numerische Mathematik 1973, 20:179-192.
15. Brezzi F. Existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. Revue Francaise D Automatique Informatique Recherche Operationnelle 1974, 8:129-151.
16. Klaas O., Maniatty A., Shephard M.S. A stabilized mixed finite element method for finite, elasticity.: formulation for linear displacement and pressure interpolation. Computer Methods in Applied Mechanics and Engineering 1999, 180:65-79.
17. Maniatty A.M., Liu Y., Klaas O., Shephard M.S. Higher order stabilized finite element method for hyperelastic finite deformation. Computer Methods in Applied Mechanics and Engineering 2002, 191:1491-1503.
18. Blatz P.J., Chu B.M., Wayland H. On the mechanical behavior of elastic animal tissue. Journal of Rheology 1969, 13:83-102.
19. Hughes T.J.R. The Finite Element Method-linear Static and Dynamic Finite Element Analysis 2000, Dover Publications, Mineola, New York, USA.
20. Simo J.C., Hughes T.J.R. On the variational foundations of assumed strain methods. Journal of Applied Mechanics-Transactions of the ASME 1986, 53:51-54.
21. Hughes T.J.R., Franca L.P., Balestra M. A new finite element formulation for computational fluid dynamics: V. circumventing the Babuska-Brezzi condition: a stable Petrov-Galerkin formulation of the stokes problem accommodating equal-order interpolations. Computer Methods in Applied Mechanics and Engineering 1986, 59:85-99.
22. Krouskop T.A., Wheeler T.M., Kallel F., Garra B.S., Hall T. Elastic moduli of breast and prostate tissues under compression. Ultrasonic Imaging 1998, 20:260-274.
23. Humphrey J.D. Mechanics of the arterial wall: review and directions. Critical Reviews in Biomedical Engineering 1995, 23:1-162.
24. Byrd R.H., Lu P., Nocedal J., Zhu C.Y. A limited memory algorithm for bound constrained optimization. SIAM Journal on Scientific Computing 1995, 16:1190-1208.
25. C.R. Vogel, Computational methods for inverse problems, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 2002.
26. Oberai A.A., Gokhale N.H., Doyley M.M., Bamber J.C. Evaluation of the adjoint equation based algorithm for elasticity imaging. Physics in Medicine and Biology 2004, 49:2955-2974.
27. Natterer F., Wubbeling F. A propagation-backpropagation method for ultrasound tomography. Inverse Problems 1995, 11.
28. Dorn O., Bertete-Aguirre H., Berryman J.G., Papanicolaou G.C. A nonlinear inversion method for 3D electromagnetic imaging using adjoint fields. Inverse Problems 1999, 15.