Skip to main content

Elasticity Imaging

  • Conference paper
  • First Online:
Mathematical Sciences with Multidisciplinary Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 157))

  • 931 Accesses

Abstract

This chapter is devoted to summarize different approaches for the imaging technique of elastography: Quasi-Static, Harmonic and Transient elastography, Models for viscoelasticity. This promising technique is a good example of interdisciplinary mathematical research and applications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Adler, R.S., Barbosa, D.C., Cosgrove, D.O., Nassiri, D.K., Bamber, J.C., Hill, C.R.: Quantitative tissue motion analysis of digitized M-mode images: gestational differences of fetal lung. Ultrasound Med. Biol. 16, 561–569 (1990)

    Article  Google Scholar 

  2. Ammari, H., Garapon, P., Guadarrama Bustos, L., Kang, H.: Transient anomaly imaging by the acoustic radiation force. J. Differ. Equ. 249, 1579–1595 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  3. Ammari, H., Guadarrama Bustos, L., Kang, H., Lee, H.: Transient elasticity imaging and time reversal. Proc. R. Soc. Edinb. 141A, 1–20 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ammari, H., Bretin, E., Garnier, J., Jing, W., Kang, H., Wahab, A.: Localization, stability, and resolution of topological derivative based imaging functionals in elasticity. SIAM J. Imag. Sci. 6 (4), 2174–2212 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ammari, H., Bretin, E., Garnier, J., Wahab, A.: Time-reversal algorithms in viscoelastic media. Eur. J. Appl. Math. 24, 565–600 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ammari, H., Bretin, E., Garnier, J., Kang, H., Lee, H., Wahab, H.: Mathematical Methods in Elasticity Imaging. Princeton University Press, Princeton (2015)

    MATH  Google Scholar 

  7. Ammari, H., Bretin, E., Millien, P., Seppecher, L., Seo, J.-K.: Mathematical modeling in full-field optical coherence elastography. SIAM J. Appl. Math. 75 (3), 1015–1030 (2015) http://epubs.siam.org/doi/abs/10.1137/140970409

    Article  MathSciNet  MATH  Google Scholar 

  8. Ammari, H., Waters, A., Zhang, H.: Stability analysis for magnetic resonance elastography. J. Math. Anal. Appl. 430, 919–931 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Athanasiou, A., Tardivon, A., Tanter, M.I., SigalZafrani, B., Bercoff, J., Deffieux, T., Gennisson, J.L., Fink, M., Neuenschwander, S.: Breast lesions: quantitative elastography with supersonic shear imaging: preliminary results. Radiology 256, 297–303 (2010)

    Article  Google Scholar 

  10. Barbone, P.E., Bamber, J.C.: Quantitative elasticity imaging: what can and cannot be inferred from strain images. Phys. Med. Biol. 47, 2147–2164 (2002)

    Article  Google Scholar 

  11. Barbone, P.E., Gokhale, N.H.: Elastic modulus imaging: on the uniqueness and nonuniqueness of the elastography inverse problem in two dimensions. Inverse Probl. 20, 283–296 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Birnholz, J.C., Farrell, E.E.: Fetal lung development: compressibility as a measure of maturity. Radiology 157, 495–498 (1985)

    Article  Google Scholar 

  13. Bercoff, J., Tanter, M., Fink, M.: Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 396–409 (2004)

    Article  Google Scholar 

  14. Bercoff, J., Tanter, M., Muller, M., Fink, M.: The role of viscosity in the impulse diffraction field of elastic waves induced by the acoustic radiation force. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 51, 1523–1536 (2004)

    Article  Google Scholar 

  15. Bouchard, R.R., Hsu, S.J., Wolf, P.D., Trahey, G.E.: In vivo cardiac, acoustic-radiation-force-driven, shear wave velocimetry. Ultrason. Imaging 31, 201–213 (2009)

    Article  Google Scholar 

  16. Bretin, E., Guadarrama Bustos, L., Wahab, A.: On the Green function in visco-elastic media obeying a frequency power-law. Math. Methods Appl. Sci. 34, 819–838 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Castaneda, B., Hoyt, K., Westesson, K., An, L., Baxter, L., Joseph, J., Strang, J., Rubens, D., Parker, K.: Performance of three-dimensional sonoelastography in prostate cancer detection: a comparison between ex vivo and in vivo experiments. In: IEEE Ultrasonics Symposium, 20–23 September 2009, Rome, pp. 519–522

    Google Scholar 

  18. Catheline, S., Wu, F., Fink, M.: A solution to diffraction biases in sonoelasticity: the acoustic impulse technique. J. Acoust. Soc. Am. 105, 2941–2950 (1999)

    Article  Google Scholar 

  19. Catheline, S., Gennisson, J.-L., Delon, G., Sinkus, R., Fink, M., Abouelkaram, S., Culioli, J.: Measurement of viscoelastic properties of solid using transient elastography: an inverse problem approach. J. Acoust. Soc. Am. 116, 3734–3741 (2004)

    Article  Google Scholar 

  20. Chenevert, T.L., Skovoroda, A.R., O’Donnell, M., Emelianov, S.Y.: Elasticity reconstructive imaging by means of stimulated echo MRI. Magn. Reson. Med. 39, 482–490 (1998)

    Article  Google Scholar 

  21. Cox, M., Rogers, P.H.: Automated noninvasive motion measurement of auditory organs in fish using ultrasound. J. Vib. Acoust. Stress Reliab. Des. 109, 55–59 (1987)

    Article  Google Scholar 

  22. Deffieux, T., Montaldo, G., Tanter, M., Fink, M.: Shear wave spectroscopy for in vivo quantification of human soft tissues visco-elasticity. IEEE Trans. Med. Imaging 28, 313–322 (2009)

    Article  Google Scholar 

  23. Dickinson, R.J., Hill, C.R.: Measurement of soft tissue motion using correlation betweenA-scans. Ultrasound Med. Biol. 8, 263–271 (1982)

    Article  Google Scholar 

  24. Doyley, M.M.: Model-based elastography: survey of approaches to the inverse elasticity problem. Phys. Med. Biol. 57, R35–R37 (2012)

    Article  Google Scholar 

  25. Doyley, M.M., Meaney, P.M., Bamber, J.C.: Evaluation of an iterative reconstruction method for quantitative elastography. Phys. Med. Biol. 45, 1521–1540 (2000)

    Article  Google Scholar 

  26. Doyley, M.M., Van Houten, E.E., Weaver, J.B., Poplack, S., Duncan, L., Kennedy, F., Paulsen, K.D.: Shear modulus estimation using parallelized partial volumetric reconstruction. IEEE Trans. Med. Imaging 23, 1404–1416 (2004)

    Article  Google Scholar 

  27. Doyley, M.M., Srinivasan, S., Pendergrass, S.A., Wu, Z., Ophir, J.: Comparative evaluation of strain-based and model-based modulus elastography. Ultrasound Med. Biol. 31, 787–802 (2005)

    Article  Google Scholar 

  28. Doyley, M.M., Feng, Q., Weaver, J.B., Paulsen, K.D.: Performance analysis of steady-state harmonic elastography. Phys. Med. Biol. 52, 2657–2674 (2007)

    Article  Google Scholar 

  29. Doyley, M.M., Perreard, I., Patterson, A.J., Weaver, J.B., Paulsen, K.M.: The performance of steady-state harmonic magnetic resonance elastography when applied to viscoelastic materials. Med. Phys. 37 (8), 3970–3979 (2010)

    Article  Google Scholar 

  30. Fatemi, M., Greenleaf, J.F.: Ultrasound-stimulated vibro-acoustic spectrography. Science 280, 82–85 (1998)

    Article  Google Scholar 

  31. Fowlkes, J.B., Emelianov, S.Y., Pipe, J.G., Skovoroda, A.R., Carson, P.L., Adler, R.S., Sarvazyan, A.P.: Magnetic resonance imaging techniques for detection of elasticity variation. Med. Phys. 22, 1771–1778 (1995)

    Article  Google Scholar 

  32. Gao, L., Alam, S.K., Lerner, R.M., Parker, K.J.: Sonoelasticity imaging: theory and experimental verification. J. Acoust. Soc. Am. 97, 3875–3886 (1995)

    Article  Google Scholar 

  33. Gdoura, S., Guadarrama Bustos, L.: Transient wave imaging of anomalies: a numerical study. Contemp. Math. 548, 31–44 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  34. Greenleaf, J.F., Fatemi, M., Insana, M.: Selected methods for imaging elastic properties of biological tissues. Annu. Rev. Biomed. Eng. 5, 57–78 (2003)

    Article  Google Scholar 

  35. Harrigan, T.P., Konofagou, E.E.: Estimation of material elastic moduli in elastography: a local method, and an investigation of Poisson’s ratio sensitivity J. Biomech. 37 (8), 1215–1221 (2004)

    Article  Google Scholar 

  36. Holen, J., Waag, R., Gramiak, R.: Representation of rapidly oscillating structures on Doppler display. Ultrasound Med. Biol. 11, 267–272 (1985)

    Article  Google Scholar 

  37. Hoyt, K., Parker, K.J., Rubens, D.J.: Real-time shear velocity imaging using sonoelastographic techniques Ultrasound Med. Biol. 33, 1086–1097 (2007)

    Google Scholar 

  38. Hoyt, K., Castaneda, B., Parker, K.J.: Two-dimensional sonoelastographic shear velocity imaging. Ultrasound Med. Biol. 34, 276–288 (2008)

    Article  Google Scholar 

  39. Huang, S.R., Lerner, R.M., Parker, K.J.: Time domain Doppler estimators of the amplitude of vibrating targets. J. Acoust. Soc. Am. 91, 965–974 (1992)

    Article  Google Scholar 

  40. Insana, M.F., Cook, L.T., Bigen, M., Chaturvede, P., Zhu, Y.: Maximum-likelihood approach to strain imaging using ultrasound. J. Acoust. Soc. Am. 107, 1421–1434 (2000)

    Article  Google Scholar 

  41. Jiang, J., Varghese, T., Brace, C.L., Madsen, E.L., Hall, T.J., Bharat, S., Hobson, M.A., Zagzebski, J. A., Lee Jr., F.T., Young’s modulus reconstruction for radio-frequency ablation electrode-induced displacement fields: a feasibility study. IEEE Trans. Med. Imaging 28, 1325–1334 (2009)

    Article  Google Scholar 

  42. Kallel, F., Bertrand, M.: Tissue elasticity reconstruction using linear perturbation method. IEEE Trans. Med. Imaging 15 (3), 299–313 (1996)

    Article  Google Scholar 

  43. Kallel, F., Ophir, J.: A least-squares strain estimator for elastography. Ultrason. Imaging 19, 195–208 (1997)

    Article  Google Scholar 

  44. Kallel, F., Ophir, J., Magee, K., Krouskop, T.: Elastographic imaging of low-contrast elastic modulus distributions in tissue. Ultrasound Med. Biol. 24, 409–425 (1998)

    Article  Google Scholar 

  45. Kennedy, B.F., Hillman, T.R., McLaughlin, R.A., Quirk, B.C., Sampson, D.D.: In vivo dynamic optical coherence elastography using a ring actuator. Opt. Express 17, 21762–21772 (2009)

    Article  Google Scholar 

  46. Kolipaka, A., Woodrum, D., Araoz, P.A., Ehman, R.L.: MR elastography of the in vivo abdominal aorta: a feasibility study for comparing aortic stiffness between hypertensives and normotensives. J. Magn. Reson. Imaging 35, 582–586 (2012)

    Article  Google Scholar 

  47. Konofagou, E., Dutta, P., Ophir, J., Cespedes, I.: Reduction of stress nonuniformities by apodization of compressor displacement in elastography. Ultrasound Med. Biol. 22, 1229–1236 (1996)

    Article  Google Scholar 

  48. Krouskop, T.A., Dougherty, D.R., Levinson, S.F.: A pulsed Doppler ultrasonic system for making noninvasive measurements of the mechanical properties of soft tissue. J. Rehabil. Res. Biol. 24, 1–8 (1987)

    Google Scholar 

  49. Kruse, S.A., Smith, J.A., Lawrence, A.J., Dresner, M.A., Manduca, A., Greenleaf, J.F., Ehman, R.L.: Tissue characterization using magnetic resonance elastography: preliminary results. Phys. Med. Biol. 45, 1579–1590 (2000)

    Article  Google Scholar 

  50. Kruse, S.A., Rose, G.H., Glaser, K.J., Manduca, A., Felmlee, J.P., Jack, C.R., Ehman, R.L.: Magnetic resonance elastography of the brain. Neuroimage 39, 231–237 (2008)

    Article  Google Scholar 

  51. Lerner, R.M., Parker, K.J.: Sonoelasticity in ultrasonic tissue characterization and echographic imaging. In: Proceedings of the European Communities Workshop, Nijmegen, 7th October 1987

    Google Scholar 

  52. Lerner, R.M., Parker, K.J., Holen, J., Gramiak, R., Waag, R.C.: Sono-elasticity: medical elasticity images derived from ultrasound signals in mechanically vibrated targets. Acoust. Imaging 16, 317–327 (1988)

    Article  Google Scholar 

  53. Levinson, S.F., Shinagawa, M., Sato, T.: Sonoelastic determination of human skeletal muscle elasticity. J. Biomech. 28, 11445–11454 (1995)

    Article  Google Scholar 

  54. Liang, X., Adie, S.G., Renu, J.R., Boppart, S.A.: Dynamic spectral-domain optical coherence elastography for tissue characterization. Opt. Express 18, 14183–14190 (2010)

    Article  Google Scholar 

  55. Manduca, A., Dutt, V., Borup, D.T., Muthupillai, R., Greenleaf, J.F., Ehman, R.L.: An inverse approach to the calculation of elasticity maps for magnetic resonance elastography. Proc. SPIE 3338, 426–436 (1998)

    Article  Google Scholar 

  56. Manduca, A., Oliphant, T.E., Dresner, M.A., Mahowald, J.L., Kruse, S.A., Amromin, E., Felmlee, J.P., Greenleaf, J.F., Ehman, R.L.: Magnetic resonance elastography: non-invasive mapping of tissue elasticity. Med. Image. Anal. 5, 237–254 (2001)

    Article  Google Scholar 

  57. McLaughlin, J.R., Yoon, J.R.: Unique identifiability of elastic parameters from time-dependent interior displacement measurement. Inverse Probl. 20, 25–45 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  58. Muller, M., Gennisson, J.L., Deffieux, T., Tanter, M., Fink, M.: Quantitative viscoelasticity mapping of human liver using supersonic shear imaging: preliminary in vivo feasability study. Ultrasound Med. Biol. 35, 219–229 (2009)

    Article  Google Scholar 

  59. Muthupillai, R., Lomas, D.J., Rossman, P.J., Greenleaf, J.F., Manduca, A., Ehman, R.L.: Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 269, 1854–1857 (1995)

    Article  Google Scholar 

  60. Nederveen, A.J., Avril, S., Speelman, L.: MRI strain imaging of the carotid artery: present limitations and future challenges. J. Biomech. 47, 824–833 (2014)

    Article  Google Scholar 

  61. Nightingale, K.R., Soo, M.S., Nightingale, R., Trahey, G.: Acoustic radiation force impulse imaging: in vivo demonstration of clinical feasibility. Ultrasound Med. Biol. 28, 227–235 (2002)

    Article  Google Scholar 

  62. Nightingale, K.R., Zhai, L., Dahl, J.J., Frinkley, K.D., Palmeri, M.L.: Shear wave velocity estimation using acoustic radiation force impulsive excitation in liver in vivo. In: Proceedings of IEEE Ultrasonic Symposium, Vancouver, pp. 1156–1160 (2006)

    Google Scholar 

  63. Oberai, A.A., Gokhale, N.H., Feijoo, G.R.: Solution of inverse problems in elasticity imaging using the adjoint method. Inverse Probl. 19, 297–313 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  64. Ophir, J., Cespedes, I., Ponnekanti, H., Yazdi, Y., Li, X.: Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason. Imaging 13, 111–134 (1991)

    Article  Google Scholar 

  65. Palmeri, P.L., Wang, M.H., Dahl, J.J., Frinkley, K.D., Nightingale, K.R.: Quantifying hepatic shear modulus in vivo using acoustic radiation force. Ultrasound Med. Biol. 34, 546–558 (2008)

    Article  Google Scholar 

  66. Park, E., Maniatty, A.M.: Shear modulus reconstruction in dynamic elastography: time harmonic case. Phys. Med. Biol. 51, 3697–3721 (2006)

    Article  Google Scholar 

  67. Parker, K.J., Lerner, R.M.: Sonoelasticity of organs: shear waves ring a bell. J. Ultrasound Med. 11, 387–392 (1992)

    Google Scholar 

  68. Parker, K.J., Doyley, M.M., Rubens, D.J.: Imaging the elastic properties of tissue: the 20 year perspective. Phys. Med. Biol. 56, R1–R29 (2011)

    Article  Google Scholar 

  69. Pellot-Barakat, C., Mai, J.J., Kargel, C., Hermen, A., Trummer, B., Insana, M.F.: Accelerating ultrasonic strain reconstructions by introducing mechanical constraints. Proc. SPIE 4684, 323–333 (2002)

    Article  Google Scholar 

  70. Petrov, A.Y., Sellier, M., Docherty, P.D., Chase, J.G.: Parametric-based brain Magnetic Resonance Elastography using a Rayleigh damping material model. Comput. Methods Programs Biomed. 116 (3), 328–339 (2014)

    Article  Google Scholar 

  71. Plewes, D.B., Betty, I., Urchuk, S.U., Soutar, I.: Visualizing tissue compliance with MR imaging. J. Magn. Reson. Imaging 5, 733–738 ( 1995)

    Article  Google Scholar 

  72. Ponnekanti, H., Ophir, J., Cespedes, I.: Ultrasonic-imaging of the stress-distribution in elastic media due to an external compressor. Ultrasound Med. Biol. 20, 27–33 (1994)

    Article  Google Scholar 

  73. Raghavan, K.R., Yagle, A.E.: Forward and inverse problems in elasticity imaging of soft-tissues. IEEE Trans. Nucl. Sci. 41, 1639–1648 (1994)

    Article  Google Scholar 

  74. Richards, M.S., Barbone, P.E., Oberai, A.A.: Quantitative three-dimensional elasticity imaging from quasi-static deformation: a phantom study. Phys. Med. Biol. 54, 757–779 (2009)

    Article  Google Scholar 

  75. Sarvazyan, A.P., Rudenko, O.V., Swanson, S.D., Fowlkes, J.B., Emelianov, S.Y.: Shear wave elasticity imaging—a new ultrasonic technology of medical diagnostic. Ultrasound Med. Biol. 20, 1419–1436 (1998)

    Article  Google Scholar 

  76. Sarvazyan, A.P., Urban, M.W., Greenleaf, J.F.: Acoustic waves in medical imaging and diagnostics. Ultrasound Med. Biol. 39 (7), 1133–1146 (2013)

    Article  Google Scholar 

  77. Schmitt, J.M.: OCT elastography: imaging microscopic deformation and strain of tissue. Opt. Express 3, 199–211 (1998)

    Article  Google Scholar 

  78. Shiina, T.: Ultrasound elastography: development of novel technologies and standardization. Jpn. J. Appl. Phys. 53, 07KA02 (2014)

    Google Scholar 

  79. Shiina, T., Nitta, N., Ueno, E., Bamber, J.C.: Real time elasticity imaging using the combined autocorrelation method. J. Med. Ultrason. 29, 119–128 (2002)

    Article  Google Scholar 

  80. Sinkus, R., Lorenzen, J., Schrader, D., Lorenzen, M., Dargatz, M., Holz, D.: High-resolution tensor MR elastography for breast tumor detection. Phys. Med. Biol. 45, 1649–1664 (2000)

    Article  Google Scholar 

  81. Sinkus, R., Tanter, M., Xydeas, T., Catheline, S., Bercoff, J., Fink, M.: Viscoelastic shear properties of in vivo breast lesions measured by MR elastography. Magn. Reson. Imaging 23, 159–165 (2005)

    Article  Google Scholar 

  82. Skovoroda, A.R., Emelianov, S.Y., Lubinski, M.A., Sarvazyan, A.P., O’Donnell, M.: Theoretical analysis and verification of ultrasound displacement and strain imaging. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 41, 302–313 (1994)

    Article  Google Scholar 

  83. Skovoroda, A.R., Emelianov, S.Y., O’Donnell, M.: Tissue elasticity reconstruction based on ultrasonic displacement and strain images. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 42, 747–765 (1995)

    Article  Google Scholar 

  84. Sumi, C.: Spatially variant regularization for tissue strain measurement and shear modulus reconstruction. J. Med. Ultrason. 34, 125–131 (2007)

    Article  Google Scholar 

  85. Sumi, C.: Displacement vector measurement using instantaneous ultrasound signal phase-multidimensional autocorrelation and Doppler methods. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 55, 24–43 (2008)

    Article  Google Scholar 

  86. Sumi, C., Suzuki, A., Nakayama, K.: Phantom experiment on estimation of shear modulus distribution in softtissue from ultrasonic measurement of displacement vector field. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 78, 1655–1664 (1995)

    Google Scholar 

  87. Szabo, T.L., Wu, J.: A model for longitudinal and shear wave propagation in viscoelastic media. J. Acous. Soc. Am. 107, 2437–2446 (2000)

    Article  Google Scholar 

  88. Tanter, M., Bercoff, J., Athanasiou, A., Deffieux, T., Gennisson, J.L., Montaldo, G., Muller, M., Tardivon, A., Fink, M.: Quantitative assessment of breast lesion viscoelasticity: initial clinical results using supersonic shear imaging. Ultrasound Med. Biol. 34, 1373–1386 (2008)

    Article  Google Scholar 

  89. Taylor, L.S., Porter, B.C., Rubens, D.J., Parker, K.J.: Three-dimensional sonoelastography: principles and practices. Phys. Med. Biol. 45, 1477–1494 (2000)

    Article  Google Scholar 

  90. Timoshenko, S.P., Goodier, J.N.: Theory of Elasticity. McGraw-Hill, New York (1970)

    MATH  Google Scholar 

  91. Tristam, M., Barbosa, D.C., Crosgrove, D.O., Nassire, D.K., Bamber, J.C., Hill, C.R.: Ultrasonic study of in vivo kinetic characteristics of human tissue. Ultrasound Med. Biol. 12, 927–937 (1986)

    Article  Google Scholar 

  92. Van Houten, E.E.W., Paulsen, K.D., Miga, M.I., Kennedy, F.E., Weaver, J.B.: An overlapping subzone technique for MR-based elastic property reconstruction. Mag. Reson. Med. 42, 779–786 (1999)

    Article  Google Scholar 

  93. Van Houten, E.E.W., Miga, M.I., Weaver, J.B., Kennedy, F.E., Paulsen, K.D.: Three-dimensional subzone-based reconstruction algorithm for MR elastography. Magn. Reson. Med. 45, 827–837 (2001)

    Article  Google Scholar 

  94. Van Houten, E.E.W., Doyley, M.M., Kennedy, F.E., Weaver, J.B., Paulsen, K.D.: Initial in vivo experience with steady-state subzone-based MR elastography of the human breast. J. Magn. Reson. Imaging 17, 72–85 (2003)

    Article  Google Scholar 

  95. Varghese, T., Ophir, J.: A theoretical framework for performance characterization of elastography: the strain filter. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 44, 164–172 (1997)

    Article  Google Scholar 

  96. Vogel, C.: Computational Methods for Inverse Problems. SIAM, Philadelphia (2002)

    Book  MATH  Google Scholar 

  97. Weaver, J.B., Van Houten, E.E.W., Miga, M.I., Kennedy, F.E., Paulsen, K.D., Magnetic resonance elastography using 3D gradient echo measurements of steady-state motion. Med. Phys. 28, 1620–1628 (2001)

    Article  Google Scholar 

  98. Wilson, L.S., Robinson, D.E.: Ultrasonic measurement of small displacements and deformation tissue. Ultrason. Imaging 4, 71–82 (1982)

    Article  Google Scholar 

  99. Wu, Z., Taylor, L.S., Rubens, D.J., Parker, K.J.: Sonoelastographic imaging of interference patterns for estimation of the shear velocity of homogenous materials. Phys. Med. Biol. 49, 911–922 (2004)

    Article  Google Scholar 

  100. Wu, Z., Hoyt, K., Rubens, D.J., Parker, K.J.: Sonoelastographic imaging of interference patterns for estimation of shear velocity distribution in biomaterials. J. Acoust. Soc. Am. 120, 535–545 (2006)

    Article  Google Scholar 

  101. Yamakoshi, Y., Sato, J., Sato, T.: Ultrasonic-imaging of internal vibration of soft-tissue under force vibration. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 37, 45–57 (1990)

    Article  Google Scholar 

  102. Zhai, L., Madden, J., Mouraviev, V., Polascik, T., Nightingale, K.: Correlation between SWEI and ARFI image findings in ex vivo human prostates. In: IEEE Ultrasonics Symposium, Rome, pp. 523–526 (2009)

    Google Scholar 

  103. Zhang, Y., Hall, L.O., Goldgof, D.B., Sarkar, S.: A constrained genetic approach for computing material property of elastic objects. IEEE Trans. Evol. Comput. 10, 341–357 (2006)

    Article  Google Scholar 

  104. Zhang, M., Castaneda, B., Wu, Z., Nigwekar, P., Joseph, J.V., Rubens, D.J., Parker, K.J.: Congruence of imaging estimators and mechanical measurements of viscoelastic properties of soft tissues. Ultrasound Med. Biol. 33, 1617–1631 (2007)

    Article  Google Scholar 

  105. Zhu, Y., Chaturvedi, P., Insana, M.F.: Strain imaging with a deformable mesh. Ultrason. Imaging 20, 127–146 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Lilí Guadarrama .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Guadarrama, L. (2016). Elasticity Imaging. In: Toni, B. (eds) Mathematical Sciences with Multidisciplinary Applications. Springer Proceedings in Mathematics & Statistics, vol 157. Springer, Cham. https://doi.org/10.1007/978-3-319-31323-8_10

Download citation

Publish with us

Policies and ethics