S. N. Gurbatov

Noise Signal Propagation in Soft Biological Tissues

Mathematical models are formulated that discribe linear and nonlinear wave propagation in biological tissues. The basis of the method is evolutionary integro-differential equations with a kernel that takes into account the specific properties of tissue. An equation is obtained for the correlation function of acoustic noise in a medium with memory. The procedure for calculating the correlation function by the given type of kernel and noise spectrum at the entrance to the medium is described. It is shown that in different tissue, there is a difference in the laws of decrease in full intensity of a wideband signal with distance. It is demonstrated that the nonlinear equation in the limiting cases of “short-” and “long-term” memory reduces to equations that have been well studied in statistical nonlinear acoustics.

Acoustic analysis of the composition of human blood serum

New acoustic methods of determining total protein, protein fractions, and lipid components of the human blood serum are presented. Acoustic methods are based on high-precision measurements of velocity and temperature dependences and frequency and temperature dependences of ultrasound absorption. Acoustic characteristics of the blood serum were measured using the method of a fixed length interferometer in acoustic cells ∼80 mcl in volume in the temperature range from 15 to 40°C and the 4–9 MHz frequency range with the acoustic analyzer developed by BIOM company. An error in measuring ultrasound velocity in the blood serum was 3 × 10−5; that of absorption, 2 × 10−2. The developed acoustic methods were clinically tested and recommended for application at clinical diagnostic laboratories with RF treatment-and-prophylactics establishments.

Inverse problem of nonlinear acoustics: Synthesizing intense signals to intensify the thermal and radiation action of ultrasound

Inverse problems of nonlinear acoustics have important applied significance. On the one hand, they are necessary for nonlinear diagnostics of media, materials, manufactured articles, building units, and biological and geological structures. On the other hand, they are needed for creating devices that ensure optimal action of acoustic radiation on a target. However, despite the many promising applications, this direction remains underdeveloped, especially for strongly distorted high-intensity waves containing shock fronts. An example of such an inverse problem is synthesis of the spatiotemporal structure of a field in a radiating system that ensures the highest possible energy density in the focal region. This problem is also related to the urgent problems of localizing wave energy and the theory of strongly nonlinear waves. Below we analyze some quite general and simple inverse nonlinear problems.

Absorption of intense regular and noise waves in relaxing media

An integro-differential equation is written down that contains terms responsible for nonlinear absorption, visco-heat-conducting dissipation, and relaxation processes in a medium. A general integral expression is obtained for calculating energy losses of the wave with arbitrary characteristics—intensity, profile (frequency spectrum), and kernel describing the internal dynamics of the medium. It is shown that for weak waves, the general integral leads to well-known results of a linear approximation. Profiles of stationary solutions are constructed both for an exponential relaxation kernel and for other types of kernels. Energy losses at the front of week shock waves are calculated. General integral formulas are obtained for energy losses of intense noise, which are determined by the form of the kernel, the structure of the noise correlation function, and the mean square of the derivative of realization of a random process.

On exact solutions to the Kolmogorov-Feller equation

The integrodifferential Kolmogorov–Feller equation describing the stochastic dynamics of a system subjected to a regular “force” and a random external disturbance in the form of short pulses with random “amplitudes” and occurrence times is considered. The equation is written in differential form. A method for finding the regular force from a given stationary probability distribution is described. The method is illustrated by examples.

Parametric generation of low-frequency sound in the propagation of high-intensity modulated noise

With the use of the one-dimensional Burgers equation, the evolution of a high-intensity noise with periodically modulated intensity is analyzed. The nonlinearity is shown to lead to partial suppression of the amplitude modulation and to the generation of a regular low-frequency component. The probability distributions and the power spectra of the field are studied.

Statistical Problems for the Generalized Burgers Equation: High-Intensity Noise in Waveguide Systems

A one-dimensional equation is presented that generalizes the Burgers equation known in the theory of waves and in turbulence models. It describes the nonlinear evolution of waves in pipes of variable cross section filled with a dissipative medium, as well as in ray tubes, if the approximation of geometric acoustics of an inhomogeneous medium is used. The generalized equation is reduced to the common Burgers equation with a dissipative parameter—the “Reynolds–Goldberg number,” depending on the coordinate. The method for solving statistical problems corresponding to specified characteristics of a noise signal at the input of the system is described. Integral expressions for exact solutions are given for the correlation function and the noise intensity spectrum experiencing nonlinear distortions during propagation in a waveguide. For waves in a dissipative medium, an approximate method of calculating statistical characteristics is given, consisting in finding an auxiliary correlation function and the subsequent nonlinear functional transformation. Solutions have a complicated form, so physical analysis of phenomena requires the numerical methods. For some correlation functions of stationary noise with initial Gaussian statistics and some waveguide systems, it is possible to obtain simple results.

Using a High-Quality Thermostated Acoustic Interferometer to Study Changes in the Structure of Human Serum Proteins

An acoustic interferometric technique for determining the protein in blood serum is presented. This acoustic approach is based on high-precision measurements of the temperature dependences of the velocity, frequency, and absorption of ultrasound. The acoustic characteristics of blood serum are measured by a constant-length interferometer in acoustic wells with volumes of around 80 μL in the temperature range of 28–40°C and the frequency range of 1.4–14 MHz.

Bispectral analysis in inverse nonlinear acoustics problems

Using the spectral solution to the evolutionary Burgers equation, we have numerically simulated the propagation of intense random acoustic waves in a nondisperse medium. We have solved the problem of reconstructing the initial signal spectrum using the measured spectral and bispectral characteristics of the received signal on short tracks.

The use of the Verasonics ultrasound system to measure shear wave velocities in CIRS phantoms

The shear wave velocity is measured in calibrated polymeric CIRS phantoms containing various spheres of two diameters located at different depths. The measurements are performed at the Verasonics ultrasound system using the method of the shear wave elasticity imaging.