Full-wave modeling of therapeutic ultrasound: nonlinear ultrasound propagation in ideal fluids

The number of applications of high-intense, focused ultrasound for therapeutic purposes is growing. Besides established applications like lithotripsy, new applications like ultrasound in orthopedics or for the treatment of tumors arise. Therefore, new devices have to be developed which provide pressure waveforms and distributions in the focal zone specifically for the application. In this paper, a nonlinear full-wave simulation model is presented which predicts the therapeutically important characteristics of the generated ultrasound field for a given transducer and initial pressure signal. A nonlinear acoustic approximation in conservation form of the original hydrodynamic equations for ideal fluids rather than a wave equation provides the base for the nonlinear model. The equations are implemented with an explicit high-order finite-difference time-domain algorithm. The necessary coefficients are derived according to the dispersion relation preserving method. Simulation results are presented for two different therapeutic transducers: a self-focusing piezoelectric and one with reflector focusing. The computational results are validated by comparison with analytical solutions and measurements. An agreement of about 10% is observed between the simulation and experimental results.