01.03.2012
The numerical simulation of a non-linear parabolic equation (the KZK equation) can be favorably applied to the determination of extremely high pressure amplitudes of modern therapeutic ultrasound devices and complement the experimental hydrophone measurement technique.
The acoustic output characterization of medical ultrasound devices is important in terms of quality assurance and the safety of the patients. The measurements are usually performed in water using hydrophones to determine local pressure and intensity parameters. However, hydrophone measurements are difficult in the case of HIFU fields used, for instance, for tumor ablation. At the high intensity levels, the combined effects of nonlinearity and diffraction lead to the generation of higher harmonics in the wave spectrum and the formation of asymmetrically distorted waveforms with steep shock fronts. Direct measurements of such high amplitude waves thus require a hydrophone that is robust to mechanical damage, has a large bandwidth to capture the sharp shock fronts and a small diameter to accurately describe the small focal beam profiles. As an alternative to the hydrophone-based technique, numerical modeling can be used to predict ultrasound fields from medical devices.
The measurement possibilities of HIFU fields using particularly broadband membrane hydrophones developed at PTB have now been demonstrated. Waveforms with fundamental frequencies of about 1 MHz and 3.3 MHz were measured. The peak rarefactional and peak compressional pressures detected so far were 13 MPa and 56 MPa, respectively. For comparison, the nonlinear propagation of HIFU fields in water was described using the Khokhlov-Zabolotskaya-Kuznetsov (KZK) nonlinear parabolic equation. It was solved numerically with the boundary conditions given at the source for a focused beam with an initial harmonic waveform and uniform pressure distribution. The results of the nonlinear sound field modeling and the experimental results show good agreement (see Fig. 1). The numerical modeling performed has proven to be an effective method for the characterization of HIFU transducers. The experiments show both the favorable applicability of the hydrophones for HIFU field characterization in principle, as well as the technical limitations seen so far [1].
Figure 1: a) Dependences of peak compressional pcF and peak rarefactional prF pressure at focus on the pressure at the source. Red line shows the modeling results, blue points are the measured data with the membrane hydrophone. b) Waveform at the focus modeled (red line) and measured (blue line) for the pressure at the source p0 = 0.48 MPa.
References:
[1] Bessonova, O., Wilkens, V.: Numerical Modeling As An Effective Method For The Characterization Of High Intensity Focused Ultrasound Devices, submitted to J. Acoust. Soc. Am.
Contact person:
Olga Bessonova, Dept. 1.6, WG 1.62, E-Mail: Olga.Bessonova@ptb.de