Dependence of non-linear ultrasound beam propagation on boundary conditions

Abstract

The dependence of the non-linear propagation of the axially symmetrical (2D) ultrasound beam on boundary condition parameters, such as an acoustic source geometry, initial pulse characteristics as well as linear and non-linear properties of the tested medium has been investigated and analyzed. The results of those investigations are presented in this paper. 2D acoustic sources with diameters of Æ = 10, 15, 20, 30 mm, plane and focused (with focal distance of F = 80 mm) have been considered. The 8-cycle and 4-cycle radiated initial pulse with carrier frequencies equal to f ₀ = 1, 2, 3, 4 MHz and pressure amplitudes p₀ = 0.1, 0.2, 0.3, 0.4 MPa have been investigated. The influence of the tested medium density, acoustic velocity, weak-signal attenuation coefficient and its frequency-dependence index, as well as acoustic non-linearity parameter on the field harmonic distributions in space and time have been studied. The analysis was carried out on the basis of numerical simulations of the spatial harmonic distributions of 2D ultrasonic beam propagating in water (reference medium) and in two-layer structures: water – standard liquid and water–soft tissue. The time-efficient software (2D numerical solver), which allows description of nonlinear ultrasonic fields radiated by circularly symmetrical sources in multi-layer attenuating media for given boundary conditions, was used as a tool to predict the behavior of the beams. The boundary condition parameters were the input data of the solver. The numerical solver, proposed by the second author, provides the numerical solution in frequency-domain to the non-linear wave equation for finite amplitude sound beams. That equation accounts for the effects of diffraction, non-linearity and thermo-viscous absorption on the propagation of sound beams in the frequency-dependent attenuating medium. The analysis of the investigated numerical simulations for various boundary conditions made it possible to note that in the case of strongly attenuating liquids or biological tissues the medium weak-signal attenuation coefficient and its frequency-dependence index have the dominant influence on the field harmonic distributions with respect to the medium non-linearity parameter.