Ultrasound Doppler System's Resolution Using Coherent Plane-Wave Compounding Technique
Abstract
Among modern ultrasound technologies for medical diagnostics, a special place is held by the technology of compounding plane waves with different propagation directions, which form synthesized images. In this work, based on the previously developed theory of Doppler response formation, the resolution of a system that uses plane wave compounding is investigated. In this case, small nonlinear components in the angle of inclination of the wave vectors of different plane waves were taken into account for the phase of the synthesized response and for the envelope of the radiation pulses. As a result of the study, it was found that the dimensions of the measuring volume in the longitudinal and transverse directions do not change. Taking into account small components leads to a slight change in the shape of the measuring volume, which ceases to be exactly spherical. This is explained by the fact that the resolution is determined not only by the interference of plane waves, but also by the area of their intersection at a certain point in space. The results obtained indicate that neglecting small inclination angles in the envelope is fully justified and allows simplifying the process of obtaining Doppler signal spectra in plane wave compounding technology.
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I. Trots, A. Nowicki, M. Lewandowski, and Y. Tasinkevych, Synthetic Aperture Method in Ultrasound Imaging, (IntechOpen, London, UK, 2011). http://dx.doi.org/10.5772/15986
M.H. Pedersen, K.L. Gammelmark, and J.A. Jensen, Ultrasound Med. Biol. 33(1), 37-47 (2007). https://doi.org/10.1016/j.ultrasmedbio.2006.07.041
J. Bercoff, G. Montaldo, T. Loupas, D. Savery, F. Meziere, M. Fink, and M. Tanter, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 58(1), 134 (2011). https://doi.org/10.1109/TUFFC.2011.1780
J. Provost, C. Papadacci, C. Demene, J. Gennisson, M. Tanter, and M. Pernot, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 62(8), 1467 (2015). https://doi.org/10.1109/TUFFC.2015.007032
J. Udesen, F. Gran, K.L. Hansen, J.A. Jensen, C. Thomsen and M.B. Nielsen, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 55(8), 1729 (2008). https://doi.org/10.1109/TUFFC.2008.858
B. Osmanski, M. Pernot, G. Montaldo, A. Bel, E. Messas, and M. Tanter, IEEE Trans. Med. Imag. 31(8), 1661 (2012). http://doi.org/10.1109/TMI.2012.2203316
C. Papadacci, M. Pernot, M. Couade, M. Fink and M. Tanter, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 61(2), 288 (2014). https://doi.org/10.1109/TUFFC.2014.6722614
G. Montaldo, M. Tanter, J. Bercoff, N. Benech, and M. Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 56(3), 489 (2009). https://doi.org/10.1109/TUFFC.2009.1067
J. Jensen, M.B. Stuart, and J.A. Jensen, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 63(11), 1922 (2016). https://doi.org/10.1109/TUFFC.2016.2591980
B. Denarieetal, IEEE Trans. Med. Imaging, 32(7), 1265 (2013). https://doi.org/10.1109/TMI.2013.2255310
R. Moshavegh, J. Jensen, C.A. Villagómez-Hoyos, M.B. Stuart, M.C. Hemmsenand, and J.A. Jensen, in: Proceedings of SPIE Medical Imaging, (SanDiego, California, United States, 2016), pp. 97900Z-97900Z-9. https://doi.org/10.1117/12.2216506
J.-l. Gennisson, et al., IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 62(6), 1059 (2015). https://doi.org/10.1109/TUFFC.2014.006936
J.A. Jensen, S.I. Nikolov, K.L. Gammelmarkand, and M.H. Pedersen, Ultrasonics, 44(1), e5 (2006). https://doi.org/10.1016/j.ultras.2006.07.017
M. Tanter, J. Bercoff, L. Sandrin, and M. Fink, IEEE Trans. Ultrason. Ferroelectr. Freq. Contr. 49(10), 1363 (2002). https://doi.org/10.1109/TUFFC.2002.1041078
J.Y. Lu, IEEE Trans. Ultrason., Ferroelec. Freq. Contr. 44(4), 839 (1997). https://doi.org/10.1109/58.655200
S. Ricci, L. Bassi and P. Tortoli, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 61(2), 314 (2014). https://doi.org/10.1109/TUFFC.2014.6722616
N. Oddershedeand J.A. Jensen, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 54(9), 1811 (2007). https://doi.org/10.1109/TUFFC.2007.465
Y. L, Li, D. Hyun, L. Abou-Elkacem, J. K. Willmann, J.J. Dahl, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 63(11), 1878 (2016), https://doi.org/10.1109/TUFFC.2016.2616112
Y.L. Li, J.J. Dahl, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 62(6), 1022 (2015). https://doi.org/10.1109/TUFFC.2014.006793
I. K. Ekroll, A. Swillens, P. Segers, T. Dahl, H. Torp and L. Lovstakken, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 60(4), 727 (2013). https://doi.org/10.1109/TUFFC.2013.2621
S. Salles, H. Liebgott, O. Basset, C. Cachard, D. Vray, and R. Lavarello, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 61, 1824–1834 (2014). https://doi.org/10.1109/TUFFC.2014.006543
C.-C. Shen, and and C.-L. Huang, Sensors, 24, 262 (2024). https://doi.org/10.3390/s24010262
J. Viti, H.J. Vos, N.D. Jong, F. Guidi, and P. Tortoli, “Contrast detection efficacy for plane vs. focused wave transmission,” in: 2014 IEEE International Ultrasonics Symposium, (Chicago, 2014), pp. 1750–1753.
J. Bercoff, “Ultrafast ultrasound imaging,” in: Ultrasound Imaging-Medical applications, edited by I.V. Minin, and O.V. Minin, pp. 3-24, (2011). https://doi/org/10.5772/19729
C. Demené et al., "Spatiotemporal clutter filtering of ultrafast ultrasound data highly increases Doppler and fUltrasound sensitivity," IEEE transactions on medical imaging, vol. 34, no. 11, pp. 2271-2285, 2015.
S. Salles, F. Varray, Y. Bénane and O. Basset, 2016 IEEE International Ultrasonics Symposium (IUS), 2016, pp. 1-4, https://doi.org/10.1109/ULTSYM.2016.7728751
C. Zheng, Q. Zha, L. Zhang and H. Peng, IEEE Access 6, 495 (2018), https://doi.org/10.1109/ACCESS.2017.2768387
Y.M. Benane et al., 2017 IEEE International Ultrasonics Symposium (IUS), 2017, pp. 1-4, https://doi.org/10.1109/ULTSYM.2017.8091880
X. Yan, Y. Qi, Y. Wang, Y. Wang, Sensors 21, 394 (2021), https://doi.org/10.3390/s21020394
C. Golfetto, I. K. Ekroll, H. Torp, L. Løvstakken and J. Avdal, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 68(4), 1105 (2021), https://doi.org/10.1109/TUFFC.2020.3033719
C.-C. Shen, Y.-C. Chu, Sensors 21, 4856 (2021), https://doi.org/10.3390/s21144856
J. Baranger, B. Arnal, F. Perren, O. Baud, M. Tanter, and C. Demené, IEEE transactions on medical imaging, 37(7), 1574 (2018). https://doi.org/10.1109/TMI.2018.2789499
A. Daae, M. Wigen, M. Halvorsrød, L. Løvstakken, A. Støylen, S. Fadnes, Ultrasound i Medicine & Biology, 49(9), 1970 (2023), https://doi.org/10.1016/j.ultrasmedbio.2023.04.019
M. Hashemseresht, S. Afrakhteh, and H. Behnam, Biomedical Signal Processing and Control, 73, 103446 (2022). https://doi.org/10.1016/j.bspc.2021.103446
K. Miura, H. Shidara, T. Ishii, K. Ito, T. Aoki, Y. Saijo, and J. Ohmiya, Ultrasonics, 145, 107479 (2025). https://doi.org/10.1016/j.ultras.2024.107479
N. Chennakeshava, B. Luijten, O. Drori, M. Mischi, Y.C. Eldarand and R.J.G. van Sloun, “High ResolutionPlane Wave CompoundingThrough Deep Proximal Learning,” in: 2020 IEEE International UltrasonicsSymposium (IUS), (Las Vegas, USA, 2020), pp. 1-4, https://doi.org/10.1109/IUS46767.2020.9251399
J. Zhao, Y. Wang, X. Zeng, J. Yu, B.Y.S. Yiu, and A.C.H. Yu, Ferroelectrics, and Frequency Control, 62(8), 1440 (2015). https://doi.org/10.1109/tuffc.2014.006934
Y. Xu, B. Li, J. Luo, X. Liu, and D. Ta, AIP Advances, 14(6), 065001 (2024). https://doi.org/10.1063/5.0201371
I.K. Ekroll, M.M. Voormolen, O.K.-V. Standal, J.M. Rau, and L. Lovstakken, IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 62(9), 1634 (2015). https://doi.org/10.1109/TUFFC.2015.007010
J. Foiret, X. Cai, H. Bendjador, et.al., Sci. Rep. 12, 13386 (2022). https://doi.org/10.1038/s41598-022-16961-2
S. Afrakhteh, and H. Behnam, IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, 68(10), 3094 (2021). https://doi.org/10.1109/tuffc.2021.3087504
R. Paridar, and B.M. Asl, Ultrasonics, 135, 107136 (2023). https://doi.org/10.1016/j.ultras.2023.107136
E.A. Barannik, Ultrasonics, 39(2), 311 (2001). https://doi.org/10.1016/S0041-624X(01)00059-2
I.V. Skresanova, and E.A. Barannik, Ultrasonics, 52(5), 676 (2012). https://doi.org/10.1016/j.ultras.2012.01.014
I.V. Sheina, O.B. Kiselov, and E.A. Barannik, East Eur. J. Phys. (4), 5 (2020), https://doi.org/10.26565/2312-4334-2020-4-01
I.V. Sheina, and E.A. Barannik, East European Journal ofPhysics, (1), 116-122. https://doi.org/10.26565/2312-4334-2022-1-16
E.A. Barannik, and O.S. Matchenko, East Eur. J. Phys. 3(2) 61 (2016). https://doi.org/10.26565/2312-4334-2016-2-08. (in Russian)
E.A. Barannik, and M.O. Hrytsenko, East Eur. J. Phys. (1), 476 (2024). https://doi.org/10.26565/2312-4334-2024-1-52
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