Abstract
This study introduces a proof-of-concept methodology for evaluating pressure-dependent non-linear acoustic properties of liver tissue. The proposed non-linearity index (NLI) is derived from echo amplitudes obtained at two substantially different acoustic pressures. Unlike previous harmonic-based approaches, the method relies solely on the fundamental frequency band, allowing clinical implementation without additional system modifications. The image acquired for the lower pressure is then amplified to correct for the pressure difference between the beams. Next, the NLI is estimated as a ratio of local amplitudes of the amplified low-pressure image (ALPI) to the high-pressure image (HPI). In the case of nonlinear media some energy of the wave is transferred from the pulse fundamental frequency to higher harmonics, which affects mainly the HPI. With the harmonics being filtered out from the signal, the HPI amplitude becomes lower than the ALPI amplitude. As a result, the NLI becomes higher than 1 and increases with the non-linearity of the imaged tissue. The hydrophone measurements were compared to the simulation (k-Wave) of the ultrasonic field in water and vegetable oil. Next, we performed NLI imaging of healthy and fatty livers using SonixTouch (Ultrasonix) systems and two acoustic pressures of 390 kPa and 1590 kPa. Preliminary studies – imaging healthy and fatty livers using SonixTouch (Ultrasonix) systems were performed on the 4 livers of the authors of the article showed that for ‘healthy’ livers the NLI was below 1.1, while in one of the authors with previously diagnosed steatosis falling between score 1 and 2, the NLI locally exceeded 1.3.
These results show that the obtained NLI values increase with the degree of steatosis, which agrees with theoretical expectations based on tissue B/A coefficients. The work emphasizes methodological feasibility and physical consistency rather than clinical validation, given the limited number of volunteers and ethical restrictions on patient recruitment.
Keywords:
ultrasound imaging, abdominal ultrasound, non-linear propagationReferences
- Adler L., Hiedemann E. (1962), Determination of the nonlinearity parameter B/A for water and m-Xylene, Journal of the Acoustical Society of America, 34(4): 410–412, https://doi.org/10.1121/1.1918142
- Akiyama I. (2000), Reflection mode measurement of nonlinearity parameter B/A, AIP Conference Proceedings, 524(1): 321–324, https://doi.org/10.1063/1.1309232
- Averkiou M.A. (2001), Tissue harmonic ultrasonic imaging, Comptes Rendus de l’Academie des Sciences – Series IV – Physics, 2(8): 1139–1151, https://doi.org/10.1016/S1296-2147(01)01259-8
- Averkiou M.A., Roundhill D.R., Powers J.E. (1997), A new imaging technique based on the nonlinear properties of tissues, [in:] 1997 IEEE Ultrasonics Symposium Proceedings. An International Symposium (Cat. No.97CH36118), 2: 1561–1566, https://doi.org/10.1109/ULTSYM.1997.663294
- Beye R.T. (1973), Nonlinear acoustics, American Journal of Physics, 41(9): 1060–1067, https://doi.org/10.1119/1.1987473
- Bohte A.E., van Werven J.R., Bipat S., Stoker J. (2011), The diagnostic accuracy of US, CT, MRI and 1H-MRS for the evaluation of hepatic steatosis compared with liver biopsy: A meta-analysis, European Radiology, 21: 87–97, https://doi.org/10.1007/s00330-010-1905-5
- Byra M. et al. (2018), Transfer learning with deep convolutional neural network for liver steatosis assessment in ultrasound images, International Journal of Computer Assisted Radiology and Surgery, 13(12): 1895–1903, https://doi.org/10.1007/s11548-018-1843-2
- Byra M., Wojcik J., Nowicki A. (2017), Ultrasound nonlinearity parameter assessment using plane wave imaging, [in:] 2017 IEEE International Ultrasonics Symposium (IUS), pp. 1511–1516, https://doi.org/10.1109/ULTSYM.2017.8092733
- Coila A., Oelze M.L. (2020), Effects of acoustic nonlinearity on pulse-echo attenuation coefficient estimation from tissue-mimicking phantoms, The Journal of the Acoustical Society of America, 148(2): 805–814, https://doi.org/10.1121/10.0001690
- Coila A., Romero A., Oelze M.L., Lavarello R. (2025), Nonlinearity parameter estimation method from fundamental band signal depletion in pulse-echo using a dual-energy model, The Journal of the Acoustical Society of America, 157(3): 1969–1980, https://doi.org/10.1121/10.0036215
- Dasarathy S., Dasarathy J., Khiyami A., Joseph R., Lopez R., McCullough A.J. (2009), Validity of real time ultrasound in the diagnosis of hepatic steatosis: A prospective study, Journal of Hepatology, 51(6): 1061–1067, https://doi.org/10.1016/j.jhep.2009.09.001
- Dong F., Madsen E.L., MacDonald M.C., Zagzebski J.A. (1999), Nonlinearity parameter for tissue-mimicking materials, Ultrasound in Medicine & Biology, 25(5): 831–838, https://doi.org/10.1016/s0301-5629(99)00016-2
- Duck F.A. (2002), Nonlinear acoustics in diagnostic ultrasound, Ultrasound in Medicine & Biology, 28(1): 1–18, https://doi.org/10.1016/s0301-5629(01)00463-x
- Errabolu R.V., Sehgal C.M., Bahn R.C., Greenleaf J.F. (1988), Measurement of ultrasonic nonlinear parameter in excised fat tissues, Ultrasound in Medicine & Biology, 14(2): 137–146, https://doi.org/10.1016/0301-5629(88)90181-0
- Estes C. et al. (2018), Modeling NAFLD disease burden in China, France, Germany, Italy, Japan, Spain, United Kingdom, and United States for the period 2016–2030, Journal of Hepatology, 69(4): 896–904, https://doi.org/10.1016/j.jhep.2018.05.036
- Everbach E.C., Apfel R.E. (1995), An interferometric technique for B/A measurement, The Journal of the Acoustical Society of America, 98(6): 3428–3438, https://doi.org/10.1121/1.413794
- Ferraioli G., Kumar V., Ozturk A., Nam K., de Korte Ch.L., Barr R.G. (2022), US attenuation for liver fat quantification: An AIUM-RSNA QIBA pulse-echo quantitative ultrasound initiative, Radiology, 302(3): 495–506, https://doi.org/10.1148/radiol.210736
- Fujii Y., Taniguchi N., Akiyam I., Tsao J., Itoh K. (2004), A new system for in vivo assessment of the degree of nonlinear generation using the second harmonic component in echo signals, Ultrasound in Medicine & Biology, 30(11): 1511–1516, https://doi.org/10.1016/j.ultrasmedbio.2004.08.016
- Gong X., Zhang D., Liu J., Wang H., Yan Y., Xu X. (2004), Study of acoustic nonlinearity parameter imaging methods in reflection mode for biological tissues, The Journal of the Acoustical Society of America, 116(3): 1819–1825, https://doi.org/10.1121/1.1781709
- Gong X.F., Liu X.Z., Zhang D. (1993), Influences of tissue composition and structural features of biological media on the ultrasonic nonlinearity parameter, Chinese Journal of Acoustics, 12(3): 265–270.
- Hernaez R. et al. (2011), Diagnostic accuracy and reliability of ultrasonography for the detection of fatty liver: A meta-analysis, Hepatology, 54(3): 1082–1090, https://doi.org/10.1002/hep.24452
- Hsu P.-K. et al. (2021), Attenuation imaging with ultrasound as a novel evaluation method for liver steatosis, Journal of Clinical Medicine, 10(5): 965, https://doi.org/10.3390/jcm10050965
- Hunter C. et al. (2016), An ultrasonic caliper device for measuring acoustic nonlinearity, Physics Procedia, 87: 93–98, https://doi.org/10.1016/j.phpro.2016.12.015
- Jesper D. et al. (2020), Ultrasound-based attenuation imaging for the non-invasive quantification of liver fat – A pilot study on feasibility and inter-observer variability, IEEE Journal of Translational Engineering in Health and Medicine, 8: 1800409, https://doi.org/10.1109/JTEHM.2020.3001488
- Law W.K., Frizzell L.A., Dunn F. (1985), Determination of the nonlinearity parameter B/A of biological media, Ultrasound in Medicine & Biology, 11(2): 307–318, https://doi.org/10.1016/0301-5629(85)90130-9
- Lu Z., Daridon J.L., Lagourette B., Ye S. (1998), A phase-comparison method for measurement of the acoustic nonlinearity parameter B/A, Measurement Science and Technology, 9: 1699–1705, https://doi.org/10.1088/0957-0233/9/10/009
- Madigosky W.M., Rosenbaum I., Lucas R. (1981), Sound velocities and B/A in fluorocarbon fluids and in several low density solids, The Journal of the Acoustical Society of America, 69(6): 1639–1643, https://doi.org/10.1121/1.385941
- Nikoonahad M., Liu D.C. (1989), Pulse-echo B/A measurement using variable amplitude excitation, [in:] Proceedings of the 1989 IEEE Ultrasonics Symposium, pp. 1047–1051.
- Nowicki A., Tasinkiewicz J., Karwat P., Trots I., Zołek N., Tymkiewicz R. (2024), Ultrasound imaging of nonlinear media response using a pressure-dependent nonlinearity index, Archives of Acoustics, 49(4): 557–563, https://doi.org/10.24425/aoa.2024.148814
- Nowicki A., Wojcik J., Secomski W. (2007), Harmonic imaging using multitone nonlinear coding, Ultrasound in Medicine & Biology, 33(7): 1112–1122, https://doi.org/10.1016/j.ultrasmedbio.2007.02.001
- Ogino Y., Wakui N., Nagai H., Igarashi Y. (2021), The ultrasound-guided attenuation parameter is useful in quantification of hepatic steatosis in non-alcoholic fatty liver disease, JGH Open, 5: 947–952, https://doi.org/10.1002/jgh3.12615
- Panfilova A., van Sloun R.J.G., Wijkstra H., Sapozhnikov O.A., Mischi M. (2021), A review on B/A measurement methods with a clinical perspective, The Journal of the Acoustical Society of America, 149(4): 2200–2237, https://doi.org/10.1121/10.0003627
- Parker K.J., Asztely M.S., Lerner R.M., Schenkh E.A., Waag R.C. (1988), In-vivo measurements of ultrasound attenuation in normal or diseased liver, Ultrasound in Medicine & Biology, 14(2): 127–136, https://doi.org/10.1016/0301-5629(88)90180-9
- Saadeh S. et al. (2002), The utility of radiological imaging in nonalcoholic fatty liver disease, Gastroenterology, 123(3): 745–50, https://doi.org/10.1053/gast.2002.35354
- Sarvazyan A.P., Chalikian T.V., Dunn F. (1990), Acoustic nonlinearity parameter B/A of aqueous solutions of some amino acids and proteins, The Journal of the Acoustical Society of America, 88(3): 1555–1561, https://doi.org/10.1121/1.400314
- Sehgal C.M., Brown G.M., Bahn R.C., Greenleaf J.F. (1986), Measurement and use of acoustic nonlinearity and sound speed to estimate composition of excised livers, Ultrasound in Medicine & Biology, 12(11): 865–874, https://doi.org/10.1016/0301-5629(86)90004-9
- Simpson D.H., Chien T.C., Burns P.N. (1999), Pulse inversion Doppler: A new method for detecting nonlinear echoes from microbubble contrast agents, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control, 46(2): 372–382, https://doi.org/10.1109/58.753026
- Tada T. et al. (2019), Usefulness of attenuation imaging with an ultrasound scanner for the evaluation of hepatic steatosis, Ultrasound in Medicine & Biology, 45(10): 2679–2687, https://doi.org/10.1016/j.ultrasmedbio.2019.05.033
- Takahashi S. (1995), Measurement of acoustic nonlinearity parameter by observation waveforms, Japanese Journal of Applied Physics, 34: 2790–2792, https://doi.org/10.1143/JJAP.34.2790
- Treeby B.E., Cox B.T. (2010), k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave-fields, Journal of Biomedical Optics, 15(2): 021314, https://doi.org/10.1117/1.3360308
- van Wijk M.C., Thijssen J.M. (2002), Performance testing of medical ultrasound equipment: Fundamental vs. harmonic mode, Ultrasonics, 40(1–8): 585–591, https://doi.org/10.1016/s0041-624x(02)00177-4
- Varray F., Cachard C., Tortoli P., Basset O. (2010), Nonlinear radio frequency image simulation for harmonic imaging: CREANUIS, [in:] 2010 IEEE International Ultrasonics Symposium, pp. 2179–2182, https://doi.org/10.1109/ULTSYM.2010.5935538
- Varray F., Chenot J., Basset O., Tortoli P., Melodelima D., Cachard C. (2011), Nonlinear parameter imaging to characterize HIFU ablation: Preliminary in vitro results in porcine liver, [in:] Proceedings of the 2011 IEEE International Ultrasonics Symposium, pp. 1361–1363, https://doi.org/10.1109/ULTSYM.2011.0336
- Wallace K., Lloyd C., Holland M., Miller J.G. (2007), Finite amplitude measurements of the nonlinear parameter B/A for liquid mixtures spanning a range relevant to tissue harmonic mode, Ultrasound in Medicine & Biology, 33(4): 620–629, https://doi.org/10.1016/j.ultrasmedbio.2006.10.008
- Yoo J. et al. (2020), Reproducibility of ultrasound attenuation imaging for the noninvasive evaluation of hepatic steatosis, Ultrasonography, 39(2): 121–129, https://doi.org/10.14366/usg.19034
- Younossi Z.M., Diehl A.M., Ong J.P. (2002), Nonalcoholic fatty liver disease: An agenda for clinical research, Hepatology, 35(4): 746–752, https://doi.org/10.1053/jhep.2002.32483
- Younossi Z.M., Koenig A.B., Abdelatif D., Fazel Y., Henry L., Wymer M. (2016), Global epidemiology of nonalcoholic fatty liver disease: Meta-analytic assessment of prevalence, incidence, and outcomes, Hepatology, 64(1): 73–84, https://doi.org/10.1002/hep.28431
- Zhang D., Gong X. (1999), Experimental investigation of the acoustic nonlinearity parameter tomography for excised pathological biological tissues, Ultrasound in Medicine & Biology, 25(4): 593–599, https://doi.org/10.1016/s0301-5629(98)00185-9
- Zhang J., Dunn F. (1991), A small volume thermodynamic system for B/A measurement, The Journal of the Acoustical Society of America, 89(1): 73–79, https://doi.org/10.1121/1.400370
- Zhe Z., Gong C., Dong Z. (2014), Molecular structure dependence of acoustic nonlinearity parameter B/A for silicone oils, Chinese Physics B, 23(5): 054302, https://doi.org/10.1088/1674-1056/23/5/054302
- Zhu Z., Roos M., Cobb W.N., Jensen K. (1983), Determination of the acoustic nonlinearity parameter B/A from phase measurements, The Journal of the Acoustical Society of America, 74(5): 1518–1521, https://doi.org/10.1121/1.390154

