Abstract
The study of intense waves in soft biological tissues is necessary both for diagnostics and therapeutic aims. Tissue represents an inherited medium with frequency-dependent dissipative properties, in which waves are described by nonlinear integro-differential equations. The equations for such waves are well known. Their group analysis has been performed, and a number of exact solutions have been found. However, statistical problems for nonlinear waves in tissues have hardly been studied. As well, for medical applications, both intense noise waves and waves with fluctuating parameters can be used. In addition, statistical solutions are simpler in structure than regular solutions; they are useful for understanding the physics of processes. Below a general approach is described for solving nonlinear statistical problems applied to the considered mathematical models of biological tissues. We have calculated the dependences of the intensities of the narrowband noise harmonics on distance. For wideband noise, we have calculated the dependence of the spectral integral intensity on distance. In all cases, wave attenuation is determined both by the specific dissipative properties of the tissue and the nonlinearity of the medium.
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References
O. V. Rudenko and S. N. Gurbatov, Acoust. Phys. 58, 243 (2012).
N. H. Ibragimov, S. V. Meleshko, and O. V. Rudenko, J. Phys. A: Math. Theor. 44, 315201 (2011).
O. V. Rudenko, Sov. Phys. Usp. 29, 620 (1986).
O. V. Rudenko and S. I. Soluyan, Theoretical Foundations of Nonlinear Acoustics (Plenim, New York, 1977).
Physical Principles of Medical Ultrasonics Ed. by C. R. Hill, J. C. Bamber, and G. R. ter Haar, 2nd ed. (Wiley, Chichester, 2004).
S. N. Gurbatov, A. N. Malakhov, and A. I. Saichev, Nonlinear Random Waves and Turbulence in Nondispersive Media: Waves, Rays, Particles Manchester Univ., Manchester, 1991).
S. N. Gurbatov, A. I. Saichev, and I. G. Yakushkin, Sov. Phys. Usp. 26, 857 (1983).
S. N. Gurbatov and O. V. Rudenko, in Nonlinear Acoustics Ed. by M. F. Hamilton and D. T. Blackstock, (Academic, New York, 1998).
S. N. Gurbatov, O. V. Rudenko, and A. I. Saichev, Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics (Springer-Verlag, Berlin, 2011).
S. N. Gurbatov and A. I. Saichev, Chaos 3, 333 (1993).
U. Frisch, Turbulence: The Legacy of A. N. Kolmogorov (Cambridge Univ., Cambridge, 1995).
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Original Russian Text © O.V. Rudenko, S.N. Gurbatov, I.Yu. Demin, 2013, published in Akusticheskii Zhurnal, 2013, Vol. 59, No. 5, pp. 630–635.
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Rudenko, O.V., Gurbatov, S.N. & Demin, I.Y. Nonlinear noise waves in soft biological tissues. Acoust. Phys. 59, 584–589 (2013). https://doi.org/10.1134/S1063771013050126
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DOI: https://doi.org/10.1134/S1063771013050126