Journal of Mathematical Imaging and Vision

, Volume 52, Issue 3, pp 369–384 | Cite as

Texture Generation for Photoacoustic Elastography

  • Thomas Glatz
  • Otmar Scherzer
  • Thomas Widlak


Elastographic imaging is a widely used technique which can in principle be implemented on top of every imaging modality. In elastography, the specimen is exposed to a force causing local displacements, and imaging is performed before and during the displacement experiment. The computed mechanical displacements can either directly be used for clinical diagnosis or deliver a basis for the deduction of material parameters. Photoacoustic imaging is an emerging image modality, which exhibits functional and morphological contrast. However, opposed to ultrasound imaging, for instance, it is considered a modality which is not suited for elastography, because it does not reveal speckle patterns. However, this is somehow counterintuitive, because photoacoustic imaging makes available the whole frequency spectrum as opposed to single frequency standard ultrasound imaging. In this work, we show that in fact artificial speckle patterns can be introduced by using only a band-limited part of the measurement data. We also show that after introduction of artificial speckle patterns, deformation estimation can be implemented more reliably in photoacoustic imaging.


Elastography Photoacoustic imaging Texture 



We thank Joyce McLaughlin, Paul Beard, and Ben Cox for helpful discussions and express our gratitude to the referees for their stimulating remarks. We acknowledge support from the Austrian Science Fund (FWF) in Projects S10505-N20 and P26687-N25.


  1. 1.
    Adams, R.A., Fournier, J.J.F.: Sobolev Spaces. Pure and Applied MathematicsGoogle Scholar
  2. 2.
    Agranovsky, M., Berenstein, C., Kuchment, P.: Approximation by spherical waves in \({L}^p\)-spaces. J. Geom. Anal. 6(3), 365–383 (1996)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Aigner, F., Pallwein, L., Schocke, M., Lebovici, A., Junker, D., Schäfer, G., Pedross, F., Horninger, W., Jaschke, W., Hallpern, E.J., Frauscher, F.: Comparison of real-time sonoelastography with T2-weighted endorectal magnetic resonance imaging for prostate cancer detection. J. Ultrasound Med. 30, 643–649 (2011)Google Scholar
  4. 4.
    Arridge, S., Scherzer, O.: Imaging from coupled physics. Inverse Probl. 28(8), 080201 (2012)CrossRefGoogle Scholar
  5. 5.
    Beard, P.: Biomedical photoacoustic imaging. Interface. Focus 1, 602–631 (2011)Google Scholar
  6. 6.
    Biswas, R., Patel, P., Park, D.W., Cichonski, T.J., Richards, M.S., Rubin, J.M., Hamilton, J., Weitzel, W.F.: Venous elastography: validation of a novel high-resolution ultrasound method for measuring vein compliance using finite element analysis. Sem. Dial. 23(1), 105–109 (2010)CrossRefGoogle Scholar
  7. 7.
    Bohs, L.N., Geiman, B.J., Anderson, M.E., Gebhart, S.C., Trahey, G.E.: Speckle tracking for multi-dimensional flow estimation. Ultrasons 38, 369–375 (2000)CrossRefGoogle Scholar
  8. 8.
    Bruhn, A., Schnoerr, C., Weickert, J.: Lucas/Canade meets Horn/Schunck: Combining local and global optic flow methods. Int. J. Comput. Vision 61(3), 211–231 (2005)CrossRefGoogle Scholar
  9. 9.
    Doyley, M.M.: Model-based elastography: a survey of approaches to the inverse elasticity problem. Phys. Med. Biol. 57, R35–R73 (2012)CrossRefGoogle Scholar
  10. 10.
    Dular, P., Geuzaine, C., Henrotte, F., Legros, W.: A general environment for the treatment of discrete problems and its application to the finite element method. IEEE Trans. Magn. 34(5), 3395–3398 (1998)CrossRefGoogle Scholar
  11. 11.
    Elbau, P., Scherzer, O., Schulze, R.: Reconstruction formulas for photoacoustic sectional imaging. Inverse Probl. 28(4), 045004 (2012). Funded by the Austrian Science Fund (FWF) within the FSP S105 - “Photoacoustic Imaging”CrossRefMathSciNetGoogle Scholar
  12. 12.
    Emelianov, S.Y., Aglyamov, S.R., Shah, J.: S Sethuraman, W. G. Scott, R. Schmitt, M. Motamedi, A. Karpiouk, and A. Oraevsky. Combined ultrasound, optoacoustic and elasticity imaging. Proc. SPIE 5320, 101–12 (2004)CrossRefGoogle Scholar
  13. 13.
    Evans, L.C.: Partial Differential Equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (1998)Google Scholar
  14. 14.
    Fawcett, J.A.: Inversion of \(n\)-dimensional spherical averages. SIAM J. Appl. Math. 45(2), 336–341 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  15. 15.
    Finch, D., Haltmeier, M., Rakesh, : Inversion of spherical means and the wave equation in even dimensions. SIAM J. Appl. Math. 68(2), 392–412 (2007)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Finch, D., Rakesh, : Trace identities for solutions of the wave equation with initial data supported in a ball. Math. Methods Appl. Sci. 28, 1897–1917 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Fu, Y.B., Chui, C.K., Teo, C.L., Kobayashi, E.: Motion tracking and strain map computation from quasi-static magnetic resonance elastography. In: Fichtinger, B., Martel, A., Peters, T. (eds.) Medical Image Computing and Computer-Assisted Intervention MICCAI 2011, Volume 6891 of Lecture Notes in Computer Science, pp. 428–435. Springer, (2011)Google Scholar
  18. 18.
    Geuzaine, C., Remacle, J.-F.: Gmsh: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Numer. Meth. in Engineering 79(11), 1309–1331 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Haltmeier, M.: A mollification approach for inverting the spherical mean Radon transform. SIAM J. Appl. Math. 71(5), 1637–1652 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Haltmeier, M., Scherzer, O., Zangerl, G.: Influence of detector bandwidth and detector size to the resolution of photoacoustic tomagraphy. In: Breitenecker, F., Troch, I. (eds) Argesim Report no. 35: Proceedings Mathmod 09 Vienna. pages 1736–1744 (2009)Google Scholar
  21. 21.
    Haltmeier, M., Zangerl, G.: Spatial resolution in photoacoustic tomography: effects of detector size and detector bandwidth. Inverse Probl. 26(12), 125002 (2010)CrossRefMathSciNetGoogle Scholar
  22. 22.
    Helgason, S.: Integral Geometry and Radon Transform. Springer, New York, NY (2011)CrossRefGoogle Scholar
  23. 23.
    Horn, B.K.P., Schunck, B.G.: Determining optical flow. Artificial Intelligence 17, 185–203 (1981)CrossRefGoogle Scholar
  24. 24.
    Ledesma-Carbayo, M.J., Kybic, J., Desco, M., Santos, A., Sühling, M., Hunziker, P., Unser, M.: Spatio-temporal nonrigid registration for ultrasound cardiac motion estimation. IEEE Trans. Med. Imag. 24(9), 1113–1126 (2005)CrossRefGoogle Scholar
  25. 25.
    Kuchment, P., Kunyansky, L.: Mathematics of thermoacoustic tomography. European J. Appl. Math. 19, 191–224 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Lecompte, D., Smits, A., Bussuyt, S., Sol, H., Vantomme, H., Van Hemelrijck, D., Habraken, A.M.: Quality assessment of speckle patterns for digital image correlation. Opt. Laser Eng. 44(11), 1132–1145 (2006)CrossRefGoogle Scholar
  27. 27.
    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)CrossRefGoogle Scholar
  28. 28.
    Li, C., Wang, L.V.: Photoacoustic tomography and sensing in biomedicine. Phys. Med. Biol. 54, R59–R97 (2009)CrossRefGoogle Scholar
  29. 29.
    Li, L., Wang, L.V.: Speckle in photoacoustic tomography. Proc. SPIE 6095, 60860Y (2006)CrossRefGoogle Scholar
  30. 30.
    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, 237–354 (2001)CrossRefGoogle Scholar
  31. 31.
    Modersitzki, J.: Numerical Methods for Image Registration. Oxford University Press, New York (2003)CrossRefGoogle Scholar
  32. 32.
    Morozov, V.A.: Methods for Solving Incorrectly Posed Problems. Springer, New York, Berlin, Heidelberg (1984)CrossRefGoogle Scholar
  33. 33.
    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)CrossRefGoogle Scholar
  34. 34.
    Nahas, A., Bauer, M., Roux, S., Boccara, A.C.: 3D static elastography at the micrometer scale using Full Field OCT. Biomed. Opt. Express 4(10), 2138–2149 (2013)CrossRefGoogle Scholar
  35. 35.
    Nilsson, S.: Application of Fast Backprojection Techniques for Some Inverse Problems of Integral Geometry. PhD thesis, Linköping University, Dept. of Mathematics (1997)Google Scholar
  36. 36.
    Norton, S.J.: Reconstruction of a two-dimensional reflecting medium over a circular domain: Exact solution. J. Acoust. Soc. Amer. 67(4), 1266–1273 (1980)CrossRefzbMATHMathSciNetGoogle Scholar
  37. 37.
    Norton, S.J., Linzer, M.: Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solutions for plane, cylindrical and spherical apertures. IEEE Trans. Biomed. Eng. 28(2), 202–220 (1981)CrossRefGoogle Scholar
  38. 38.
    Nuster, R., Slezak, P., Paltauf, G.: Imaging of blood vessels with CCD-camera based three-dimensional photoacoustic tomography. Proc. SPIE 8943, 894357 (2014)CrossRefGoogle Scholar
  39. 39.
    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)CrossRefGoogle Scholar
  40. 40.
    Palamodov, V.P.: Reconstructive Integral Geometry, volume 98 of Monographs in Mathematics. Birkhäuser Verlag, Basel (2004)CrossRefGoogle Scholar
  41. 41.
    Pan, X., Gao, J., Tao, S., Liu, K., Bai, J., Luo, J.: A two-step optical flow method for strain estimation in elastography: simulation and phantom study. Ultrasons 54, 990–996 (2014)CrossRefGoogle Scholar
  42. 42.
    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)CrossRefGoogle Scholar
  43. 43.
    Prasad, P.R., Bhattacharya, S.: Improvements in speckle tracking algorithms for vibrational analysis using optical coherence tomography. J. Biomed. Opt. 18(4), 18 (2014)Google Scholar
  44. 44.
    Prince, J.L., McVeigh, E.R.: Motion estimation from tagged MR image sequences. IEEE Trans. Med. Imag. 11(2), 238–249 (1992)CrossRefGoogle Scholar
  45. 45.
    Ramm, A.G.: Inversion of the backscattering data and a problem of integral geometry. Phys. Lett. A 113, 172–176 (1985)CrossRefMathSciNetGoogle Scholar
  46. 46.
    Revell, J., Mirmehdi, M., McNally, D.: Computer vision elastography: speckle adaptive motion estimation for elastography using ultrasound sequences. IEEE Trans. Med. Imag. 24(6), 755–766 (2005)CrossRefGoogle Scholar
  47. 47.
    Scherzer, O., Grasmair, M., Grossauer, H., Haltmeier, M., Lenzen, F.: Variational methods in imaging, volume 167 of Applied Mathematical Sciences. Springer, New York (2009)Google Scholar
  48. 48.
    Schmitt, J.M.: OCT elastography: imaging microscopic deformation and strain of tissue. Opt. Express 3(6), 199–211 (1998)CrossRefGoogle Scholar
  49. 49.
    Segal, L.A.: Mathematics Applied to Continuum Mechanics. MacMillan Publishing, London (1977)Google Scholar
  50. 50.
    Solmon, D.C.: Asymptotic formulas for the dual Radon transform and applications. Math. Z. 195(3), 321–343 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  51. 51.
    Sun, C., Standish, B., Yang, V.X.D.: Optical coherence elastography, current status and future applications. J. Biomed. Opt. 16(4), 043001 (2011)CrossRefGoogle Scholar
  52. 52.
    Treeby, B.E., Cox, B.T.: K-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wace fields. J. Biomed. Opt. 15, 021314 (2010)CrossRefGoogle Scholar
  53. 53.
    Wang, H.J., Changchien, C.S., Hung, C.H., Eng, E.L., Tung, W.C., Kee, K.M., Chen, C.H., Hu, T.H., Lee, C.M., Lu, S.N.: Fibroscan and ultrasonography in the prediction of hepatic fibrosis in patients with chronic viral hepatitis. J. Gastroenterol. 44, 439–436 (2009)CrossRefGoogle Scholar
  54. 54.
    Washington, C.W., Miga, M.I.: Modality independent elastography (MIE): a new approach to elasticity imaging. IEEE Trans. Med. Imag. 23(9), 1117–1128 (2004)CrossRefGoogle Scholar
  55. 55.
    Wejcinski, S., Farrokh, A., Weber, S., Thomas, A., Fischer, T., Slowinski, T., Schmidt, W., Degenhardt, F.: Multicenter study of ultrasound real-time tissue elastography in 779 cases for the assessment of breast lesions: improved diagnostic performance by combining the BI-RADS\(^{\textregistered }\)-US classification system with sonoelastography. Ultraschall Med. 31, 484–491 (2010)CrossRefGoogle Scholar
  56. 56.
    Woodrum, D.A., Romano, A.J., Lerman, A., Pandya, U.H., Brosh, D., Rossman, P.J., Lerman, L.O., Ehman, R.L.: Vascular wall elasticity measurement by magnetic resonance imaging. Magn. Reson. Med. 56, 593–600 (2006)CrossRefGoogle Scholar
  57. 57.
    Zakaria, T., Qin, Z., Maurice, R.L.: Optical flow-based B-mode elastography: application in the hypertensitive rat carotid. IEEE Trans. Med. Imag. 29(2), 570–578 (2010)CrossRefGoogle Scholar
  58. 58.
    Zhou, P., Goodson, K.E.: Subpixel displacement and deformation gradient measurement using digital image/speckle correlation (DISC). Opt. Eng. 40(8), 1613–1620 (2001)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Computational Science CenterUniversity of ViennaViennaAustria
  2. 2.Radon Institute of Computational and Applied MathematicsAustrian Academy of SciencesLinzAustria

Personalised recommendations