Sub- and ultraharmonic (SUH) ultrasound contrast imaging is an alternative modality to the second harmonic imaging, since, in specific conditions it could produce high quality echographic images. This modality enables the contrast enhancement of echographic images by using SUH present in the contrast agent response but absent from the nonperfused tissue. For a better access to the components generated by the ultrasound contrast agents, nonlinear techniques based on Hammerstein model are preferred. As the major limitation of Hammerstein model is its capacity of modeling harmonic components only, in this work we propose two methods allowing to model SUH. These new methods use several Hammerstein models to identify contrast agent signals having SUH components and to separate these components from harmonic components. The application of the proposed methods for modeling simulated contrast agent signals shows their efficiency in modeling these signals and in separating SUH components. The achieved gain with respect to the standard Hammerstein model was 26.8？dB and 22.8？dB for the two proposed methods, respectively. 1. Introduction Introduction of contrast agents in ultrasound medical imaging has strongly improved the image contrast leading to a better medical diagnosis [1–3]. By adapting the transmitting ultrasound sequences composed of short wave trains to longer sinusoidal wave trains, it has been possible to enhance the harmonics detection witnessing of the presence of nonlinear explored media [3–5]. The most prominent example in echographic imaging is the second harmonic imaging (SHI) [3, 6] which consists to send a sinusoidal wave train of frequency and to receive the backscattered signal at twice the transmitted frequency, that is, (see Figure 1). Figure 1: Block diagram of second harmonic imaging. Although the second harmonic imaging possesses undoubted advantages compared to standard echographic imaging, contrast harmonic imaging, however, has image contrast limitations related to the presence of harmonic components of nonlinear nonperfused tissues [7]. This contrast reduction can be overcome by proposing no more contrast harmonic imaging but rather contrast subultraharmonic (SUH) imaging [8, 9]. Under certain conditions of incident frequency and pressure levels, this solution has been envisaged as a serious alternative [10, 11] since it has been shown that only contrast agent is capable of supplying SUH components sufficient to construct perfused tissue images with a strong contrast. Contrast SUH imaging consists to send a sinusoidal wave train of
References
[1]
F. Calliada, R. Campani, O. Bottinelli, A. Bozzini, and M. G. Sommaruga, “Ultrasound contrast agents: basic principles,” European Journal of Radiology, vol. 27, supplement 2, pp. S157–S160, 1998.
[2]
F. Forsberg, D. A. Merton, J. B. Liu, L. Needleman, and B. B. Goldberg, “Clinical applications of ultrasound contrast agents,” Ultrasonics, vol. 36, no. 1–5, pp. 695–701, 1998.
[3]
P. J. A. Frinking, A. Bouakaz, J. Kirkhorn, F. J. Ten Cate, and N. De Jong, “Ultrasound contrast imaging: current and new potential methods,” Ultrasound in Medicine and Biology, vol. 26, no. 6, pp. 965–975, 2000.
[4]
N. de Jong, M. Emmer, A. van Wamel, and M. Versluis, “Ultrasonic characterization of ultrasound contrast agents,” Medical and Biological Engineering and Computing, vol. 47, no. 8, pp. 861–873, 2009.
[5]
T. G. Leighton, The Acoustic Bubble, Academic Press, London, UK, 1994.
[6]
P. N. Burns, “Instrumentation for contrast echocardiography,” Echocardiography, vol. 19, no. 3, pp. 241–258, 2002.
[7]
M. A. Averkiou, “Tissue harmonic imaging,” in Proceedings of the IEEE Ultrasonics Symposium, vol. 2, pp. 1563–1572, October 2000.
[8]
P. M. Shankar, P. D. Krishna, and V. L. Newhouse, “Advantages of subharmonic over second harmonic backscatter for contrast-to-tissue echo enhancement,” Ultrasound in Medicine and Biology, vol. 24, no. 3, pp. 395–399, 1998.
[9]
R. Basude and M. A. Wheatley, “Generation of ultraharmonics in surfactant based ultrasound contrast agents: use and advantages,” Ultrasonics, vol. 39, no. 6, pp. 437–444, 2001.
[10]
F. Forsberg, W. T. Shi, and B. B. Goldberg, “Subharmonic imaging of contrast agents,” Ultrasonics, vol. 38, no. 1, pp. 93–98, 2000.
[11]
F. Forsberg, C. W. Piccoli, D. A. Merton, J. J. Palazzo, and A. L. Hall, “Breast lesions: imaging with contrast-enhanced subharmonic US: initial experience,” Radiology, vol. 244, no. 3, pp. 718–726, 2007.
[12]
O. M. Boaghe and S. A. Billings, “Subharmonic oscillation modeling and MISO Volterra series,” IEEE Transactions on Circuits and Systems I, vol. 50, no. 7, pp. 877–884, 2003.
[13]
C. Samakee and P. Phukpattaranont, “Application of MISO volterra series for modeling subharmonic of ultrasound contrast agent,” International Journal of Computer and Electrical Engineering, vol. 4, no. 4, pp. 445–451, 2012.
[14]
F. Sbeity, S. Ménigot, J. Charara, and J. M. Girault, “A general framework for modeling-sub and ultra-harmonics of ultrasound contrast agent signals with MISO volterra series,” Computational and Mathematical Methods in Medecine, vol. 2013, Article ID 934538, 2013.
[15]
A. Janczak, Identification of Nonlinear Systems Using Neural Networks and Polynomial Models, Springer, Berlin, Germany, 2005.
[16]
S. Boyd, L. O. Chua, and C. A. Desoer, “Analytical foundations of volterra series,” IMA Journal of Mathematical Control and Information, vol. 1, no. 3, pp. 243–282, 1984.
[17]
L. Hoff, Acoustic Characterization of Contrast Agents For Medical Ultrasound Imaging, Kluwer Academic, Boston, Mass, USA, 2001.
[18]
C. C. Church, “The effects of an elastic solid surface layer on the radial pulsations of gas bubbles,” Journal of the Acoustical Society of America, vol. 97, no. 3, pp. 1510–1521, 1995.
