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Novel Ultrasound Imaging Applications

  • Chapter
Acoustic Metamaterials

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 166))

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Abstract

Routine applications of ultrasound imaging combine array technology and beamforming (BF) algorithms for image formation. Although BF is very robust, it discards a significant proportion of the information encoded in ultrasonic signals. Therefore, BF can reconstruct some of the geometrical features of an object but with limited resolution due to the diffraction limit. Inverse scattering theory offers an alternative approach to BF imaging that has the potential to break the diffraction limit and extract quantitative information about the mechanical properties of the object. High-resolution, quantitative imaging is central to modern diagnostic technology to achieve cost-effective detection through high sensitivity and limited false positive rate. This chapter lays out a framework encompassing theoretical and experimental results, and in which inverse scattering and modern array technology can be combined together to achieve super-resolution, quantitative imaging.

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Notes

  1. 1.

    This is a convenient way of describing both the continuous and discrete cases. For instance, |v(r)〉 can refer to a continuous function of space, v(r), or a vector field, v, whose entries correspond to the values of v(r) at the nodes of a discrete representation of space. Similarly, an operator becomes a matrix such as the multistatic matrix representing T ∞. Note that 〈v(r)| is the transpose conjugate of the vector |v(r)〉 [2].

  2. 2.

    In practice BF is performed in the time domain according to the procedure illustrated in Fig. 5.7. This is equivalent to integrating (5.24) over the frequency bandwidth of the input signal and including the negative frequencies.

  3. 3.

    Consider, for instance, the spherical wave expansion of a plane wave [39].

  4. 4.

    For a phantom diameter of 120 mm and λ=2 mm the sampling criterion given in (5.34) requires 377 sensors while the array has 256 only.

References

  1. Abbott, J.G., Thurstone, F.L.: Acoustic speckle: Theory and experimental analysis. Ultrason. Imag. 1, 303–324 (1979)

    Article  CAS  Google Scholar 

  2. Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists. Academic Press, London (2001)

    Google Scholar 

  3. Baggeroer, A.B.: Sonar arrays and array processing. In: Thompson, D.O., Chimenti, D.E. (eds.) Rev. Prog. Quant. NDE, vol. 760, pp. 3–24 (2005)

    Google Scholar 

  4. Born, M., Wolf, E.: Principles of Optics. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  5. Bucci, O.M., Insernia, T.: Electromagnetic inverse scattering: Retrievable information and measurement strategies. Radio Sci. 32, 2123–2137 (1997)

    Article  Google Scholar 

  6. Chaumet, P., Belkebir, K., Sentenac, A.: Experimental microwave imaging of three-dimensional targets with different inversion procedures. J. Appl. Phys. 106, 034901 (2009)

    Article  Google Scholar 

  7. Chen, F.C., Chew, W.C.: Experimental verification of super resolution in nonlinear inverse scattering. Appl. Phys. Lett. 72, 3080–3082 (1998)

    Article  CAS  Google Scholar 

  8. Colton, D., Coyle, J., Monk, P.: Recent developments in inverse acoustic scattering theory. SIAM Rev. 42, 369–414 (2000)

    Article  Google Scholar 

  9. Colton, D., Kress, R.: Inverse Acoustic and Electromagnetic Scattering Theory, vol. 93. Springer, Berlin (1992)

    Google Scholar 

  10. Colton, D., Kress, R.: Eigenvalues of the far field operator for the Helmholtz equation in an absorbing medium. SIAM J. Appl. Math. 55, 1724–1735

    Google Scholar 

  11. Courjon, D.: Near-field Microscopy and Near-field Optics. Imperial College Press, London (2003)

    Book  Google Scholar 

  12. Cox, I.J., Sheppard, C.J.R.: Information capacity and resolution in an optical system. J. Opt. Soc. Am. A 3, 1152–1158 (1986)

    Article  Google Scholar 

  13. Drinkwater, B., Wilcox, P.: Ultrasonic arrays for non-destructive evaluation: A review. NDT E Int. 39, 525–541 (2006)

    Article  CAS  Google Scholar 

  14. Driscoll, J.R., Healy, D.M.: Computing Fourier transforms and convolutions on the 2-sphere. Adv. Appl. Math. 15, 202–250 (1994)

    Article  Google Scholar 

  15. Duric, N., Poulo, L.P., et al.: Detection of breast cancer with ultrasound tomography: first results with the computed ultrasound risk evaluation (CURE) prototype. Med. Phys. 34, 773–785 (2007)

    Article  Google Scholar 

  16. Goodman, J.W.: Introduction to Fourier Optics. McGraw-Hill, New York (1996)

    Google Scholar 

  17. Huang, S., Ingber, D.E.: Cell Tension, Matrix Mechanics and Cancer Development. Cancer Cell 8, 175–176 (2005)

    Article  CAS  Google Scholar 

  18. Jackson, W.D.: Classical Electrodynamics. Wiley, New York (1999)

    Google Scholar 

  19. Kak, A.C., Slaney, M.: Principles of Computerized Tomographic Reconstruction. IEEE Press, New York (1998)

    Google Scholar 

  20. Kirsch, A.: Characterization of the shape of a scattering obstacle using the spectral data of the far field operator. Inverse Probl. 14, 1489–1512 (1998)

    Article  Google Scholar 

  21. Kirsch, A.: The MUSIC algorithm and the factorization method in inverse scattering theory for inhomogeneous media. Inverse Probl. 18, 1025–1040 (2002)

    Article  Google Scholar 

  22. Kolb, T.M., Lichy, J., Newhouse, J.H.: Comparison of the performance of screening mammography, physical examination, and breast us and evaluation of factors that influence them: an analysis of 27,825 patient evaluation. Radiology 225, 165–175 (2002)

    Article  Google Scholar 

  23. Lavarello, R.J., Oelze, M.L.: Density imaging using inverse scattering. J. Acoust. Soc. Am. 125, 793–802 (2009)

    Article  Google Scholar 

  24. Lin, F.C., Fiddy, A.: The Born-Rytov controversy: I. Comparing analytical and approximate expressions for the one-dimensional deterministic case. J. Opt. Soc. Am. A 9, 1102–1110 (1992)

    Article  Google Scholar 

  25. Lukosz, W.: Optical systems with resolving powers exceeding the classical limit. J. Opt. Soc. Am. 56, 932–941 (1966)

    Article  Google Scholar 

  26. Marengo, E.A., Gruber, F.K., Simonetti, F.: Time-reversal music imaging of extended targets. IEEE Trans. Image Process. 16, 1967–1984 (2007)

    Article  Google Scholar 

  27. Morse, P.M., Ingard, K.U.: Theoretical Acoustics. McGraw-Hill, New York (1968)

    Google Scholar 

  28. Pratt, G.R.: Seismic waveform inversion in the frequency domain, part 1: Theory and verification in a physical scale model. Geophysics 64, 888–901 (1999)

    Article  Google Scholar 

  29. Sentenac, A., Guerin, C.A., Chaumet, P.C., et al.: Influence of multiple scattering on the resolution of an imaging system: A Cramer-Rao analysis. Opt. Express 15, 1340–1347 (2007)

    Article  Google Scholar 

  30. Shemer, A., Mendlovic, D., Zalevsky, Z., et al.: Superresolving optical system with time multiplexing and computer encoding. Appl. Opt. 38, 7245–7251 (1999)

    Article  CAS  Google Scholar 

  31. Simonetti, F.: Localization of point-like scatterers in solids with subwavelength resolution. Appl. Phys. Lett. 89, 094105 (2006)

    Article  Google Scholar 

  32. Simonetti, F.: Multiple scattering: The key to unravel the subwavelength world from the far-field pattern of a scattered wave. Phys. Rev. E 73, 036619 (2006)

    Article  CAS  Google Scholar 

  33. Simonetti, F., Huang, L.: From beamforming to diffraction tomography. J. Appl. Phys. 103, 103110 (2008)

    Article  Google Scholar 

  34. Simonetti, F., Huang, L., Duric, N.: On the sampling of the far-field operator with a circular ring array. J. Appl. Phys. 101, 083103 (2007)

    Article  Google Scholar 

  35. Simonetti, F., Huang, L., Duric, N., Rama, O.: Imaging beyond the Born approximation: An experimental investigation with an ultrasonic ring array. Phys. Rev. E 76, 036601 (2007)

    Article  CAS  Google Scholar 

  36. Simonetti, F.: Illustration of the role of multiple scattering in subwavelength imaging from far-field measurements. J. Opt. Soc. Am. A 25, 292–303 (2008)

    Article  CAS  Google Scholar 

  37. Simonetti, F., Huang, L., Duric, N.: A multiscale approach to diffraction tomography of complex three-dimensional objects. Appl. Phys. Lett. 95, 067904 (2009)

    Article  Google Scholar 

  38. Simonetti, F., Huang, L., Duric, N., Littrup, P.: Diffraction and coherence in breast ultrasound tomography: A study with a toroidal array. Med. Phys. 36, 2955–2965 (2009)

    Article  CAS  Google Scholar 

  39. Stratton, J.A.: Electromagnetic Theory. McGraw-Hill, New York (1941)

    Google Scholar 

  40. Waag, R.C., Fedewa, R.J.: A ring transducer system for medical ultrasound research. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 53, 1707–1718 (2006)

    Article  Google Scholar 

  41. Waterman, P.C.: New formulation of acoustic scattering. J. Acoust. Soc. Am. 45, 1417–1429 (1968)

    Article  Google Scholar 

  42. Wells, P.N.T.: Ultrasonic imaging of the human body. Rep. Prog. Phys. 62, 671–722 (1999)

    Article  Google Scholar 

  43. Zweig, M.H., Campbell, G.: Receiver-operating characteristics (ROC) plots: A fundamental evaluation tool in clinical medicine. Clin. Chem. 39, 561–577 (1993)

    CAS  Google Scholar 

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Acknowledgements

The author is grateful to the UK Engineering and Physical Sciences Research Council (EPSRC) for supporting this work under grant EP/F00947X/1.

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Authors and Affiliations

  1. College of Engineering and Applied Science, School of Aerospace Systems, University of Cincinnati, 726 Rhodes Hall, P. O. Box 210070, Cincinnati, OH, 45221, USA

    Francesco Simonetti

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  1. Francesco Simonetti
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Correspondence to Francesco Simonetti .

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Editors and Affiliations

  1. Department of Mathematics, Imperial College, South Kensington Campus, London, SW7 2BZ, United Kingdom

    Richard V. Craster

  2. Institut Fresnel CNRS, Rue du Coteau 71, Marseille, 13770, France

    Sébastien Guenneau

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Simonetti, F. (2013). Novel Ultrasound Imaging Applications. In: Craster, R., Guenneau, S. (eds) Acoustic Metamaterials. Springer Series in Materials Science, vol 166. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4813-2_5

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