Elasticity imaging of biological soft tissue using a combined finite element and non-linear optimization method

References

• Srinivasan S, Krouskop T, Ophir J. A quantitative comparison of modulus images obtained using nanoindentation with strain elastograms. Ultrasound Med. Biol. 2004;30:899–918.10.1016/j.ultrasmedbio.2004.05.005
   PubMed Web of Science ®Google Scholar
• Richards MS, Barbone PE, Oberai AA. Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study. Phys. Med. Biol. 2009;54:757–779.10.1088/0031-9155/54/3/019
   PubMed Web of Science ®Google Scholar
• Skovoroda AR, Lubinski LA, Emelianov SY, O’Donnell M. Reconstructive elasticity imaging for large deformations. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1999;46:523–535.10.1109/58.764839
   PubMed Web of Science ®Google Scholar
• Khaled W, Reichling S, Bruhns OT, Ermert H. Ultrasonic strain imaging and reconstructive elastography for biological tissue. Ultrasonics. 2006;44:e199–e202.10.1016/j.ultras.2006.06.007
   PubMed Web of Science ®Google Scholar
• Chikayoshi Sumi K, Nakayama K. A robust numerical solution to reconstruct a globally relative shear modulus distribution from strain measurements. IEEE Trans. Med. Imaging. 1998;17:419–428.10.1109/42.712131
   PubMed Web of Science ®Google Scholar
• Sumi C. Shear modulus reconstruction by ultrasonically measured strain ratio. J. Med. Ultrason. 2007;34:171–188.10.1007/s10396-007-0151-1
   PubMed Web of Science ®Google Scholar
• Sette MM, Goethals P, D’hooge J, Van Brussel H, Vander Sloten J. Algorithms for ultrasound elastography: a survey. Comput. Methods Biomech. Biomed. Eng. 2011;14:283–292.10.1080/10255841003766837
   PubMed Web of Science ®Google Scholar
• Latorre-Ossa H, Gennisson JL, Brosses EE, Tanter M. Quantitative imaging of nonlinear shear modulus by combining static elastography and shear wave elastography. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2012;59:833–839.
   PubMed Web of Science ®Google Scholar
• Sack I, Bernarding J, Braun J. Analysis of wave patterns in MR elastography of skeletal muscle using coupled harmonic oscillator simulations. Magn. Reson. Imaging. 2002;20:95–104.10.1016/S0730-725X(02)00474-5
   PubMed Web of Science ®Google Scholar
• Hamhaber U, Sack I, Papazoglou S, Rump J, Klatt D, Braun J. Three-dimensional analysis of shear wave propagation observed by in vivo magnetic resonance elastography of the brain. Acta Biomater. 2007;3:127–137.10.1016/j.actbio.2006.08.007
   PubMed Web of Science ®Google Scholar
• Kruse SA, Rose GH, Glaser KJ, Manduca A, Felmlee JP Jr, Jack CR, Ehman RL. Magnetic resonance elastography of the brain. NeuroImage. 2008;39:231–237.10.1016/j.neuroimage.2007.08.030
   PubMed Web of Science ®Google Scholar
• Manduca A, Oliphant TE, Dresner MA, Mahowald JL, Kruse SA, Amromin E, Felmlee JP, Greenleaf JF, Ehman RL. Magnetic resonance elastography: Non-invasive mapping of tissue elasticity. Med. Image Anal. 2001;5:237–254.10.1016/S1361-8415(00)00039-6
   PubMed Web of Science ®Google Scholar
• Steele DD, Chenevert TL, Skovoroda AR, Emelianov SY. Three-dimensional static displacement, stimulated echo NMR elasticity imaging. Phys. Med. Biol. 2000;45:1633–1648.10.1088/0031-9155/45/6/316
   PubMed Web of Science ®Google Scholar
• Plewes DB, Bishop J, Samani A, Sciarretta J. Visualization and quantification of breast cancer biomechanical properties with magnetic resonance Elastography. Phys. Med. Biol. 2000;45:1591–1610.10.1088/0031-9155/45/6/314
   PubMed Web of Science ®Google Scholar
• Barbone PE, Gokhale NH. Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions. Inverse Probl. 2004;20:283–296.10.1088/0266-5611/20/1/017
   Web of Science ®Google Scholar
• Barbone PE, Oberai AA. Elastic modulus imaging: some exact solutions of the compressible elastography inverse problem. Phys. Med. Biol. 2007;52:1577–1593.10.1088/0031-9155/52/6/003
   PubMed Web of Science ®Google Scholar
• Gokhale NH, Barbone PE, Oberai AA. Solution of the nonlinear elasticity imaging inverse problem: the compressible case. Inverse Prob. 2008;24:1–26.
   Web of Science ®Google Scholar
• Goenezen S, Barbone P, Oberai AA. Solution of the nonlinear elasticity imaging inverse problem: the incompressible case. Comput. Methods Appl. Mech. Eng. 2011;200:1406–1420.10.1016/j.cma.2010.12.018
   PubMed Web of Science ®Google Scholar
• Mcgrath DM, Foltz WD, Al-Mayah A, Niu CJ, Brock KK. Quasi-static magnetic resonance elastography at 7 T to measure the effect of pathology before and after fixation on tissue biomechanical properties. Magn. Reson. Med. 2012;68:152–165.10.1002/mrm.23223
   PubMed Web of Science ®Google Scholar
• Moulton M, Creswell L, Actis R, Myers K, Vannier M, Szabo B, Pasque M. An inverse approach to determining myocardial material properties. J. Biomech. 1995;28:935–948.10.1016/0021-9290(94)00144-S
   PubMed Web of Science ®Google Scholar
• Kauer M, Vuskovic V, Dual J, Szekely G, Bajka M. Inverse finite element characterization of soft tissues. Med. Image Anal. 2002;6:275–287.10.1016/S1361-8415(02)00085-3
   PubMed Web of Science ®Google Scholar
• Kim J, Ahn B, De S, Srinivasan MA. An efficient soft tissue characterization algorithm from in vivo indentation experiments for medical simulation. Int. J. Med. Rob. Comput. Assist. Surg. 2008;4:277–285.10.1002/rcs.v4:3
   PubMed Web of Science ®Google Scholar
• Erdemir A, Viveiros ML, Ulbrecht JS, Cavanagh PR. An inverse finite-element model of heel-pad indentation. J. Biomech. 2006;39:1279–1286.10.1016/j.jbiomech.2005.03.007
   PubMed Web of Science ®Google Scholar
• Liu KF, VanLandingham MR, Ovaert TC. Mechanical characterization of soft viscoelastic gels via indentation and optimization-based inverse finite element analysis. J. Mech. Behav. Biomed. Mater. 2009;2:355–363.10.1016/j.jmbbm.2008.12.001
   PubMed Web of Science ®Google Scholar
• Schnur DS, Zabaras N. An inverse method for determining elastic material properties and a material interface. Int. J. Numer. Methods Eng. 1992;33:2039–2057.10.1002/(ISSN)1097-0207
   Web of Science ®Google Scholar
• Guo ZY, You SH, Wan XP, Bicanic N. A FEM-based direct method for material reconstruction inverse problem in soft tissue elastography. Comput. Struct. 2008;88:1459–1468.
   Web of Science ®Google Scholar
• Zhu YN, Hall TJ, Jiang JF. A finite-element approach for Young’s modulus reconstruction. IEEE Trans. Med. Imaging. 2003;22:890–900.
   PubMed Web of Science ®Google Scholar
• Chui CK, Kobayashi E, Chen X, Hisada T, Sakuma I. Combined compression and elongation experiments and non-linear modelling of liver tissue for surgical simulation. Med. Biol. Eng. Comput. 2004;42:787–798.10.1007/BF02345212
   PubMed Web of Science ®Google Scholar
• Chui CK, Kobayashi E, Chen X, Hisada T, Sakuma I. Transversely isotropic properties of porcine liver tissue: experiments and constitutive modelling. Med. Biol. Eng. Comput. 2007;45:99–106.10.1007/s11517-006-0137-y
   PubMed Web of Science ®Google Scholar
• Nava A, Mazza E, Furrer M, Villiger P, Reinhart WH. In vivo mechanical characterization of human liver. Med. Image Anal. 2008;12:203–216.10.1016/j.media.2007.10.001
   PubMed Web of Science ®Google Scholar
• Liu GR, Quek SS. The finite element method: A practical course. Oxford: Butterworth Heinemann; 2003.
   Google Scholar
• Engl HW. Regularization methods for the stable solution of inverse problems. Surv. Math. Ind. 1993;3:71–143.
   Google Scholar
• Hanke M, Raus T. A general heuristic for choosing the regularization parameter in ill-posed problems. SIAM J. Sci. Comput. 1996;17:956–972.10.1137/0917062
   Web of Science ®Google Scholar
• Fu YB, Chui CK, Teo CL, Kobayashi E. Motion tracking and strain map computation for quasi-static magnetic resonance elastography. LNCS MICCAI. 2011;6891:428–435.
   Google Scholar
• Bensamoun SF, Ringleb SI, Littrell L, Chen QS, Brennan M, Ehman RL, An KN. Determination of thigh muscle stiffness using magnetic resonance elastography. J. Magn. Reson. Imaging. 2006;23:242–247.10.1002/(ISSN)1522-2586
   PubMed Web of Science ®Google Scholar
• Pathmanathan P, Gavaghan D, Whiteley J. A comparison of numerical methods used for finite element modelling of soft tissue deformation. J. Strain Anal. Eng. Des. 2009;44:391–406.10.1243/03093247JSA482
   Web of Science ®Google Scholar