Research of the nonlinear interaction of an acoustic wave with biological tissues for the purposes of acoustic elastography

The purpose of the research is investigation of the parameters of nonlinear interaction of low-frequency acoustic radiation with biological tissues to improve the accuracy of determining structural changes in organs and tissues by elastography.
Methods. Improving the accuracy of determining the degree and nature of structural changes in human organs and tissues is an urgent task today. The use of nonlinear effects of the interaction of powerful low-frequency acoustic radiation with biological tissues will allow obtaining new information characteristics, as well as improving the accuracy of differentiation of various degrees of structural changes in tissues and organs at the initial stages of diseases. In the framework of this work, the relationship between the viscoelastic and nonlinear characteristics of biological media and the processes of propagation of elastic transverse waves in them is considered. The physical foundations of the processes of formation and propagation of harmonic components of a transverse acoustic wave, as well as the change in its ratio N to the fundamental frequency wave, are also considered.
Results. The results of mathematical modeling of the processes of changing the correlation between the amplitude of the fundamental frequency wave and the third harmonic formed in the medium due to the nonlinearity of the interaction of acoustic radiation with biological tissues are obtained. The results were the graphs of the dependence of the change in N with distance for liver tissues at various stages of fibrosis and fatty hepatosis.
Conclusion. The obtained dependences allow us to conclude that the use of nonlinear effects of the interaction of low-frequency acoustic radiation with biological tissues will improve the quality of diagnostics of structural changes in organs and tissues in the early stages of diseases, when standard linear methods are less informative.

1. Belyaeva A.V., Belyaeva O.A., Rozinov V.M. Diagnostic potential of ultrasonic elastography in patients with surgical diseases and injuries. Rossiiskii vestnik detskoi khirurgii, anesteziologii i reanimatologii = Russian Bulletin of Pediatric Surgery, Anesthesiology and Intensive Care. 2023;3(3):373–384. (In Russ.) https://doi.org/10.17816/psaic1523

2. Kulebina E.A., Surkov A.N., Usoltseva O.V. Noninvasive diagnosis of liver fibrosis: possibilities of instrumental techniques at the present stage. RMZh. Meditsinskoe obozrenie = Russian Medical Inquiry. Medical Review. 2020;4(5):297–301. (In Russ.)

3. Diomidova V.N., Razbinina E.A., Valeeva O.N., Vasilyeva L.N. The effectiveness of shear wave elastography in assessing liver damage in patients with postcovoid syndrome. Acta Medica Eurasica. 2022;(3):99–113. (In Russ.)

4. Diomidova V.N., Valeeva O.V., Vasilyeva L.N., Razbirina E.A. Informative value of transient and two-dimensional shear wave elastography.in assessing liver stiffness in post-covoid and cardiohepatic syndrome. Acta Medica Eurasica. 2023;(4):31–43. (In Russ.)

5. Zhirkov I.I., Gordienko A.V., Pavlovich I.M., Yakovlev V.V., Serdyukov D.Y. The possibilities of transient and two-dimensional shift-wave elastography in the diagnosis of fibrosis in chronic diffuse liver diseases of non-viral etiology. Eksperimental'naya i klinicheskaya gastroenterologiya = Experimental and Clinical Gastroenterology. 2020;(7):86–91. (In Russ.) https://doi.org/10.31146/1682-8658-ecg-179-7-86-91

6. Omar Isam Darwish, Ahmed M. Gha-rib, Sami Jeljeli, Nader S. Metwalli, Jenna Feeley, Yaron Rotman, Rebecca J. Brown, Ronald Ouwerkerk, David E. Kleiner, Daniel Stäb, Peter Speier, Ralph Sinkus, Radhouene Neji. Single Breath-Hold 3-Dimensional Magnetic Resonance Elastography Depicts Liver Fibrosis and Inflammation in Obese Patients. Invest Radiol. 2023;(58):413–419. https://doi.org/10.1097/RLI.0000000000000952

7. Kravchuk D.A., Chernov N.N., Mikhralieva A.I. Analytical modeling of breast elastography. Izvestiya Yugo-Zapadnogo gosudarstvennogo universiteta. Seriya: Upravlenie, vychislitel'naya tekhnika, informatika. Meditsinskoe priborostroenie = Proceedings of the Southwest State University. Series: Control, Computer Engineering, Information Science. Medical Instruments Engineering. 2024;14(1):104–113. (In Russ.) EDN SHBQKL. https://doi.org/10.21869/2223-1536-2024-14-1-104-113

8. Kraeva T.V., Demina A.S., Noskova L.R., Shakirova G.H. Elastography in ultrasound diagnostics and the possibilities of its use in diseases. Using the example of data from the department of ultrasound diagnostics of the BU «District Clinical Hospital». Zdravookhranenie Yugry: opyt i innovatsii = Healthcare of Ugra: Experience and Innovations. 2023;(1):9–18. (In Russ.)

9. Park S.Y., Kang B.J. Combination of shear-wave elastography with ultrasonography for detection of breast cancer and reduction of unnecessary biopsies: a systematic review and meta-analysis. Ultrasonography. 2021;(40):318–332.

10. Pimanov S.I., Kaportseva V.S., Mikhailova N.A., Vergasova E.V. Disturbing factors in ultrasound elastography of the liver. Part 1. General provisions and methodological errors. Vestnik Vitebskogo gosudarstvennogo meditsinskogo universiteta = Bulletin of Vitebsk State Medical University. 2023;22(1):9–18. (In Russ.)

11. Zhirkov I.I., Gordienko A.V., Pavlovich I.M., Chumak B.A., Yakovlev V.V. Diagnosis of liver fibrosis: emphasis on elastography. Eksperimental'naya i klinicheskaya gastroenterologiya = Experimental and Clinical Gastroenterology. 2021;(194):72–82. (In Russ.)

12. Kravchuk D.A., Chernov N.N., Perestelkov S.A., Mikhralieva A.I. Experimental studies of the acoustic field of transverse waves in the model of biological tissue. Radioelektronika. Nanosistemy. Informatsionnye tekhnologii = Radioelectronics. Nanosystems. Information Technology. 2024;16(3):381–386. (In Russ.) EDN HJAPTZ. https://doi.org/10.17725/rensit.2024.16.381

13. Shkuratnik V.L., Nikolenko P.V., Anufrenkova P.S. On the features of ultrasonic measurements in coal samples using transverse elastic waves. Gornyi informatsionno-analiticheskii byulleten' (nauchno-tekhnicheskii zhurnal) = Mining Information and Analytical Bulletin (Scientific and Technical Journal). 2020;(4):117–126. (In Russ.)

14. Bratsun D.A., Krasnyakov I.V., Bratsun A.D. Biomechanical models of living tissue. Rossiiskii zhurnal biomekhaniki = Russian Journal of Biomechanics. 2023;(4):50–71. (In Russ.) https://doi.org/10.15593/RZhBiomeh/2023.4.04

15. Kruglov V.M., Bakushev S.V., Shein A.I., Erofeev V. T., Al Dulaimi Salman Dawud Salman, Tomilov A.A. Dependencies between stresses and deformations in a nonlinearly deformable body. Part 1. Basic principles and relations of mechanics of a deformable solid. Ekspert: teoriya i praktika = Expert: Theory and Practice. 2023;(4):154–163. (In Russ.)

16. Shamaev A.S., Shumilova V.V. Averaging the equations of motion of a medium consisting of an elastic material and an incompressible Kelvin-voigt fluid. Ufimskii matematicheskii zhurnal = Ufa Mathematical Journal. 2024;(1):99–110. (In Russ.)

17. Astapov Y., Markin A., Sokolova M., Khristich D. Concretization of nonlinear constitutional relations by results of uniaxial compression and indentation experiments. Journal of Physics: Conference Series. 2021;(1902):012002.

18. Chernov N.N., Varenikova A.Yu., Laguta M.V. Using a relatively nonlinear parameter to create ultrasound imaging systems for biological systems. Modelirovanie, optimizatsiya i informatsionnye tekhnologii = Modeling, Optimization, and Information Technology. 2022;10(1):1–12. (In Russ.)

19. Staddon M.F., Murrell M.P., Banerjee S. Interplay between substrate rigidity and tissue fluidity regulates cell monolayer spreading. Soft Matter. 2022;18:7877–7886. https://doi.org/10.1039/D2SM00757F

20. Nefedov N.N., Rudenko O.V. On the motion, strengthening and destruction of fronts in Burgers type equations with quadratic and modular nonlinearity. Doklady rossiiskoi akademii nauk. Matematika, informatika, protsessy upravleniya = Reports of the Russian Academy of Sciences. Mathematics, Computer Science, Management Processes. 2020;493:26–31. (In Russ.)