Quasi-linear sound propagation in the presence of cavitation bubbles for predicting HIFU biological lesions

It is now accepted that High Intensity Focused Ultrasound (HIFU) lesion formation is the result of a complex process that involves interaction between acoustical thermal effects and cavitation phenomena of micro-bubbles within biological tissue. In the present study, a sound propagation model that takes into account the cumulative effects of nonlinearity, diffraction and absorption in the presence of cavitation bubbles is analytically established. The model is based on a modified expression of the parabolic KZK equation where bubble dynamics is included. Then, this modified expression and the volume version of the Rayleigh-Plesset equation am written in the special case of quasi-linear wave motions. Finally, the equation system is solved by representing the source emanating from the focused transducer as a superposition of Gaussian beams. In this context, results are presented for the pressure field generated by the fundamental and second harmonics when the source is an axisymmetric transducer and the biological tissue is separated from the transducer by water. Good agreement is found between the pressure field calculations and measurements obtained with a needle hydrophone for the case of a water-only volume and a 3.0 MHz: transducer focused at 40 mm.