Effect of Acoustic Nonlinearity on Heating of Biological Tissue 469

Abstract

mates of the role of acoustic nonlinearity in the effi-ciency of thermal action of ultrasound upon a tissue. ACOUSTIC FIELD The propagation of an intense focused acoustic wave in a tissue is described in the parabolic approxi-mation by the nonlinear evolution equation of the Khokhlov–Zabolotskaya–Kuznetsov type [8] (1) where p is the acoustic pressure in the beam; z is the coordinate along the beam axis; c 0 = 1614 m/s is the propagation velocity of longitudinal acoustic waves in the tissue; ρ 0 = 1214 kg/m 3 is the equilibrium density; ε = 4.78 is the nonlinearity factor of the tissue [7]; τ = t – z / c 0 is the time in the moving coordinate system; and ∆ ⊥ is the Laplacian with respect to the transverse coor-dinates, which, in the case of an axisymmetric beam considered here, has the form ∆ ⊥ = ∂ 2 / ∂ r 2 + 1/ r ∂ / ∂ r . The linear operator L abs describes the absorption of a wave in compliance with the power law characteristic of bio-logical tissues: (2) where the power index η is close to unity, α is the absorption coefficient at a frequency f , and α 0 is the absorption coefficient at the selected frequency f 0 [2]. For a tissue of liver type, the values of the parameters η and α 0 at the selected radiation frequency 1.7 MHz are equal to η = 1.266 and α 0 = 8.42 m –1 [7], respectively. Equation (1) takes into account the nonlinear, dissipa-tive, and diffraction effects. In the case of a focused piston radiator under study, we have (3)