Archives of Acoustics, 43, 3, pp. 425–435, 2018
10.24425/123914

Modeling Breast Ultrasound on the Applicability of Commonly Made Approximations

Ulas TASKIN
Delft University of Technology
Netherlands

Neslihan OZMEN
Philips Healthcare
Netherlands

Hartmut GEMMEKE
Karlsruhe Institute of Technology
Germany

Koen W.A. van Dongen
Delft University of Technology
Netherlands

To design breast ultrasound scanning systems or to test new imaging methods, various computer models are used to simulate the acoustic wave field propagation through a breast. The computer models vary in complexity depending on the applied approximations. The objective of this paper is to investigate how the applied approximations affect the resulting wave field. In particular, we investigate the importance of taking three-dimensional (3-D) spatial variations in the compressibility, volume density of mass, and attenuation into account. In addition, we compare four 3-D solution methods: a full-wave method, a Born approximation method, a parabolic approximation method, and a ray-based method. Results show that, for frequencies below 1 MHz, the amplitude of the fields scattering off the compressibility or density contrasts are at least 24 dB higher than the amplitude of the fields scattering off the attenuation contrasts. The results also show that considering only speed of sound as a contrast is a valid approximation. In addition, it is shown that the pressure field modeled with the full-wave method is more accurate than the fields modeled using the other three methods. Finally, the accuracy of the full-wave method is location independent whereas the accuracy of the other methods strongly depends on the point of observation.
Keywords: breast ultrasound; forward modeling; full-wave method
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Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

Alles E.J., van Dongen K.W.A. (2011), Perfectly matched layers for frequency-domain integral equation acoustic scattering problems, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 58, 5, 1077–1086.

Bakker J.F., Paulides M.M., Obdeijn I., van Rhoon G.C., van Dongen K.W.A. (2009), An ultrasound cylindrical phased-array for deep heating in the breast: theoretical design using heterogeneous models, Physics in Medicine & Biology, 54, 3201–3215.

Bird R.E.,Wallace T.W., Yankaskas B.C. (1992), Analysis of cancers missed at screening mammography, Radiology, 184, 3, 613–617.

Cobbold R.S.C. (2007), Foundations of biomedical ultrasound, Oxford University Press, New York.

Dagrau F., R´enier M., Marchiano R., Coulouvrat F. (2011), Acoustic shock wave propagation in a heterogeneous medium: a numerical simulation beyond the parabolic approximation, Journal of the Acoustical Society of America, 130, 1, 20–32.

d’Astous F., Foster F. (1986), Frequency dependence of ultrasound attenuation and backscatter in breast tissue, Ultrasound in Medicine and Biology, 12, 10, 795–808.

Demi L., van Dongen K.W.A., Verweij M.D. (2011), A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation, Journal of the Acoustical Society of America, 129, 3, 1221–1230.

Duck F.A. (2013), Physical properties of tissues: a comprehensive reference book, Academic Press.

Duric N. et al. (2007), Detection of breast cancer with ultrasound tomography: First results with the computerized ultrasound risk evaluation (C.U.R.E.), Medical Physics, 34, 2, 773–785.

Fletcher R. (1976), Conjugate gradient methods for indefinite systems, [in:] Numerical analysis, pp. 73–89, Springer.

Fokkema J.T., van den Berg P.M. (1993), Seismic Applications of Acoustic Reciprocity, Elsevier, Amsterdam.

Gisolf A., Verschuur D.J. (2010), The principles of quantitative acoustical imaging, EAGE Publications, The Netherlands.

Goss S., Johnston R., Dunn F. (1980), Compilation of empirical ultrasonic properties of mammalian tissues. II, Journal of the Acoustical Society of America, 68, 1, 93–108.

Hardin R., Tappert F. (1973), Applications of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations, Siam Review, 15, 423.

Herman G.C., van den Berg P.M. (1982), A leastsquare iterative technique for solving time-domain scattering problems, Journal of the Acoustical Society of America, 72, 6, 1947–1953.

Hesse M.C., Schmitz G. (2012), Comparison of linear and nonlinear unidirectional imaging approaches in ultrasound breast imaging, Ultrasonics Symposium (IUS), 2012 IEEE International, pp. 1295–1298. IEEE.

Huijssen J., Verweij M.D., de Jong N. (2008), Green’s function method for modeling nonlinear threedimensional pulsed acoustic fields in diagnostic ultrasound including tissue-like attenuation, Ultrasonics Symposium (IUS), 2008 IEEE International, pp. 375– 378.

Jirik R. et al. (2012), Sound-speed image reconstruction in sparse-aperture 3-d ultrasound transmission tomography, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 59, 2, ??–??.

Kak A.C., Slaney M. (1988), Principles of computerized tomographic imaging, Vol. 33, SIAM.

Kleinman R.E., van den Berg P. M. (1991), Iterative methods for solving integral equations, Radio Science, 26, 1, 175–181.

Ozmen N., Dapp R., Zapf M., Gemmeke H., Ruiter N.V., van Dongen K.W.A. (2015), Comparing different ultrasound imaging methods for breast cancer detection, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 62, 4, 637–646.

Ozmen-Eryilmaz N., Demi L., Alles E.J., Verweij M.D., van Dongen K.W.A. (2011), Modeling acoustic wave field propagation in 3D breast models, Ultrasonics Symposium (IUS), 2011 IEEE International, pp. 1700–1703.

Ruiter N.V., Schwarzenberg G.F., Zapf M., Liu R., Stotzka R., Gemmeke H. (2006), 3D ultrasound computer tomography: Results with a clinical breast phantom, Ultrasonics Symposium (IUS), 2006 IEEE.

Siegel R.L et al. (2017), Colorectal cancer statistics, CA: A Cancer Journal for Clinicians, 67, 3, 177–193.

Simonetti F., Huang L., Duric N., Rama O. (2007), Imaging beyond the Born approximation: An experimental investigation with an ultrasonic ring array, Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 76, 3, 036601–036610.

Skudrzyk E. (2012), The foundations of acoustics: basic mathematics and basic acoustics, Springer Science & Business Media.

Sohrab B., Farzan G., Ashkan B., Amin J. (2006), Ultrasound thermotherapy of breast: theoretical design of transducer and numerical simulation of procedure, Japanese Journal of Applied Physics, 45, 3R, 1856.

Stoffa P., Fokkema J.T., de Luna Freire R., Kessinger W. (1990), Split-step Fourier migration, Geophysics, 55, 4, 410–421.

Szabo T.L. (1995), Causal theories and data for acoustic attenuation obeying a frequency power law, Journal of the Acoustical Society of America, 97, 1, 14–24.

Szabo T.L. (2004), Diagnostic ultrasound imaging: inside out, Academic Press.

van Dongen K.W.A., Brennan C., Wright W.M. (2007), Reduced forward operator for electromagnetic wave scattering problems, IET Science, Measurement & Technology, 1, 1, 57–62.

van Dongen K.W.A., Wright W.M.D. (2006), A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging, Journal of the Acoustical Society of America, 120, 4, 2086–2095.

Wiskin J., Borup D.T., Johnson S.A., Berggren M. (2012), Non-linear inverse scattering: High resolution quantitative breast tissue tomography, Journal of the Acoustical Society of America, 131, 5, 3802– 3813.

Zwamborn P., van den Berg P.M. (1992), The three-dimensional weak form of the conjugate gradient FFT method for solving scattering problems, IEEE Transactions on Microwave Theory and Techniques, 40, 9, 1757–1766.




DOI: 10.24425/123914