Recovering vector displacement estimates in quasistatic elastography using sparse relaxation of the momentum equation

References

• Gao L, Parker K, Lerner R, et al. Imaging of the elastic properties of tissue -- a review. Ultrasound Med. Biol. 1996;22:959–977.
   PubMed Web of Science ®Google Scholar
• Ophir J, Alam S, Garra B, et al. Elastography: ultrasonic estimation and imaging of the elastic properties of tissues. Proc. Inst. Mech. Eng. Part H: J. Eng. Med. 1999;213:203–233.
   PubMed Web of Science ®Google Scholar
• Parker KJ, Taylor LS, Gracewski S, et al. A unified view of imaging the elastic properties of tissue. J. Acoust. Soc. Am. 2005;117:2705–2712.
   PubMed Web of Science ®Google Scholar
• Greenleaf JF, Fatemi M, Insana M. Selected methods for imaging elastic properties of biological tissues. Annu. Rev. Biomed. Eng. 2003;5:57–78.
   PubMed Web of Science ®Google Scholar
• Parker KJ, Doyley M, Rubens D. Imaging the elastic properties of tissue: the 20 year perspective. Phys. Med. Biol. 2011;56:R1–R29.
   PubMed Web of Science ®Google Scholar
• Doyley M. Model-based elastography: a survey of approaches to the inverse elasticity problem. Phys. Med. Biol. 2012;57:R35–R73.
   PubMed Web of Science ®Google Scholar
• Szabo TL. Diagnostic ultrasound imaging: inside out. Kidlington: Elsevier Academic Press; 2004.
   Google Scholar
• Barbone PE, Oberai AA. A review of the mathematical and computational foundations of biomechanical imaging. In: Suvranu D, Farshid G, Mohammad M,editors. Computational modeling in biomechanics. Dordrecht: Springer; 2010. p. 375–408.
   Google Scholar
• Dord J, Goenezen S, Oberai A, et al. Validation of quantitative linear and nonlinear compression elastography. In: Nenadic IZ, Urban MW, Greenleaf JF, editors. Ultrasound elastography for biomedical applications and medicine. Elsevier; 2016.
   Google Scholar
• Goenezen S, Dord J, Sink Z, et al. Linear and nonlinear elastic modulus imaging: An application to breast cancer diagnosis. IEEE Trans. Med. Imaging. 2012;31:1628–1637.
   PubMed Web of Science ®Google Scholar
• Richards M, Barbone P, Oberai A. Quantitative three-dimensional elasticity imaging from quasi-sta tic deformation: a phantom study. Phys. Med. Biol. 2009;54:757–779.
   PubMed Web of Science ®Google Scholar
• Albocher U, Oberai A, Barbone P, et al. Adjoint-weighted equation for inverse problems of incompressible plane-stress elasticity. Comput. Methods Appl. Mech. Eng. 2009;198:2412–2420.
   Web of Science ®Google Scholar
• Barbone P, Rivas C, Harari I, et al. Adjoint-weighted variational formulation for the direct solution of inverse problems of general linear elasticity with full interior data. Int. J. Numer. Methods Eng. 2010;81:1713–1736.
   Web of Science ®Google Scholar
• Albocher U, Barbone P, Richards M, et al. Approaches to accommodate noisy data in the direct solution of inverse problems in incompressible plane strain elasticity. Inverse Probl. Sci. Eng. 2014;22:1307–1328.
   PubMed Web of Science ®Google Scholar
• Konofagou E, Ophir J. A new elastographic method for estimation and imaging of lateral displacements, lateral strains, corrected axial strains and poissons ratios in tissues. Ultrasound Med. Biol. 1998;24:1183–1199.
   PubMed Web of Science ®Google Scholar
• Geiman BJ, Bohs LN, Anderson ME, et al. A novel interpolation strategy for estimating subsample speckle motion. Phys. Med. Biol. 2000;45:1541–1552.
   PubMed Web of Science ®Google Scholar
• Konofagou EE, Ophir J. Precision estimation and imaging of normal and shear components of the 3d strain tensor in elastography. Phys. Med. Biol. 2000;45:1553–1563.
   PubMed Web of Science ®Google Scholar
• Chen X, Zohdy M, Emelianov S, et al. Lateral speckle tracking using synthetic lateral phase. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2004;51:540–550.
   PubMed Web of Science ®Google Scholar
• Ebbini E. Phase-coupled two-dimensional speckle tracking algorithm. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2006;53:972–990.
   PubMed Web of Science ®Google Scholar
• Brusseau E, Kybic J, Deprez J-F, et al. 2-D locally regularized tissue strain estimation from radio-frequency ultrasound images: theoretical developments and results on experimental data. IEEE Trans. Med. Imaging. 2008;27:145–160.
   PubMed Web of Science ®Google Scholar
• Deprez J-F, Brusseau E, Schmitt C, et al. 3D estimation of soft biological tissue deformation from radio-frequency ultrasound volume acquisitions. Med. Image Anal. 2009;13:116–127.
   PubMed Web of Science ®Google Scholar
• Kim S, Aglyamov SR, Park S, et al. An autocorrelation-based method for improvement of sub-pixel displacement estimation in ultrasound strain imaging. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2011;58:838–843.
   PubMed Web of Science ®Google Scholar
• Rivaz H, Boctor EM, Choti MA, et al. Real-time regularized ultrasound elastography. IEEE Trans. Med. Imaging. 2011;30:928–945.
   PubMed Web of Science ®Google Scholar
• Mailloux GE, Bleau A, Bertrand M, et al. Computer analysis of heart motion from two-dimensional echocardiograms. IEEE Trans. Biomed. Eng. 1987;BME-34:356–364.
   Web of Science ®Google Scholar
• Basarab A, Liebgott H, Morestin F, et al. A method for vector displacement estimation with ultrasound imaging and its application for thyroid nodular disease. Med. Image Anal. 2008;12:259–274.
   PubMed Web of Science ®Google Scholar
• Tanter M, Bercoff J, Sandrin L, et al. Ultrafast compound imaging for 2-d motion vector estimation: application to transient elastography. IEEE Trans Ultrason. Ferroelectr. Freq. Control. 2002;49:1363–1374.
   PubMed Web of Science ®Google Scholar
• Techavipoo U, Chen Q, Varghese T, et al. Estimation of displacement vectors and strain tensors in elastography using angular insonifications. IEEE Trans. Med. Imaging. 2004;23:1479–1489.
   PubMed Web of Science ®Google Scholar
• Rao M, Chen Q, Shi H, et al. Normal and shear strain estimation using beam steering on linear-array transducers. Ultrasound Med. Biol. 2007;33:57–66.
   PubMed Web of Science ®Google Scholar
• Hansen H, Lopata R, Idzenga T, et al. Full 2d displacement vector and strain tensor estimation for superficial tissue using beam-steered ultrasound imaging. Phys. Med. Biol. 2010;55:3201–3218.
   PubMed Web of Science ®Google Scholar
• Xu H, Varghese T. Normal and shear strain imaging using 2d deformation tracking on beam steered linear array datasets. Med. Phys. 2013;40:012902. 13 p.
   PubMed Web of Science ®Google Scholar
• Abeysekera JM, Zahiri Azar R, Goksel O, et al. Analysis of 2-d motion tracking in ultrasound with dual transducers. Ultrasonics. 2012;52:156–168.
   PubMed Web of Science ®Google Scholar
• Korukonda S, Doyley MM. Estimating axial and lateral strain using a synthetic aperture elastographic imaging system. Ultrasound Med. Biol. 2011;37:1893–1908.
   PubMed Web of Science ®Google Scholar
• Korukonda S, Doyley MM. Visualizing the radial and circumferential strain distribution within vessel phantoms using synthetic-aperture ultrasound elastography. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2012;59:1639–1653.
   PubMed Web of Science ®Google Scholar
• Jensen JA, Munk P. A new method for estimation of velocity vectors. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1998;45:837–851.
   PubMed Web of Science ®Google Scholar
• Liebgott H, Wilhjehm J, Jensen JA, et al. Psf dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2007;54:746–756.
   PubMed Web of Science ®Google Scholar
• Lubinski M, Emelianov S, Raghavan K, et al. Lateral displacement estimation using tissue incompressibility. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1996;43:247–256.
   Web of Science ®Google Scholar
• Skovoroda AR, Lubinski MA, Emelianov SY, et al. Nonlinear estimation of the lateral displacement using tissue incompressibility. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 1998;45:491–503.
   PubMed Web of Science ®Google Scholar
• O’Donnell M, Chen X, Kaluzynski K, et al. Strain magnitude estimation based on adaptive incompressibility processing. In: 2001 IEEE Ultrasonics Symposium. Vol. 2; Atlanta, GA: IEEE; 2001. p. 1643–1646.
   Google Scholar
• Hu Z, Zhang H, Yuan J, et al. An H∞ strategy for strain estimation in ultrasound elastography using biomechanical modeling constraint. PloS One. 2013;8:1–15.
   Google Scholar
• Atkin RJ, Fox N. An introduction to the theory of elasticity. Mineola, NY: Dover Publications; 2005.
   Google Scholar
• Hughes TJR. The finite element method: linear static and dynamic finite element analysis. Dover Publications; 2000.
   Google Scholar
• Babaniyi O. Direct elastic modulus reconstruction via sparse relaxation of physical constraints [Master’s thesis]. Boston, MA: Boston University; 2012.
   Google Scholar
• Honein T. On heterogenization in elasticity [PhD dissertation]. Stanford, CA: Stanford University; 1990.
   Google Scholar
• Vogel CR. Computational methods for inverse problems. Vol. 10. Philadelphia: SIAM; 2002.
   Google Scholar
• Pavan T, Madsen E, Frank G, et al. Nonlinear elastic behavior of phantom materials for elastography. Phys. Med. Biol. 2010;55:2679–2692.
   PubMed Web of Science ®Google Scholar
• Jiang J, Hall T. A fast hybrid algorithm combining regularized motion tracking and predictive search for reducing the occurrence of large displacement errors. IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 2011;58:730–736.
   PubMed Web of Science ®Google Scholar