Focused Ultrasonic Power Measurement Based On The Axial Vibration Velocity Of The Focal Point

Focused ultrasound is a new technique for non-invasive therapy,of which the acoustic power(AP)is an important dosage parameter related to the therapeutic efficacy for biological tissues.Consequently,the accurate measurement of the AP in focused ultrasound shows a great significance in biomedical engineering.In the actual focused ultrasound treatment,the propagation of the ultrasound induced particle vibration in the medium can be measured by laser vibrometer to describe the sound field.However,for the focused transducer,the focal axial vibration velocity(FAVV)is greatly increased by constructive interference(in-phase superimposition),whereas the vibration components in the radial directions at the focal point are reduced to zero by destructive interference.In conventional measurements,the AP is often calculated by the surface integral of the acoustic intensity over the scanned region with a drop of 6 dB to the FAVV.Therefore,the calculation of the AP using only the FAVV is insufficient without taking the lost vibration energy in the radial directions into account.By considering the radial vibration velocity,a new method of AP measurement for focused ultrasound using FAW is proposed.In this paper,based on the princple of linear and nonlinear acoustic radiation,the formulae of FAW for Low-intensity focused ultrasound(LIFU)and High-intensity focused ultrasound(HIFU)are theoretically deduced,and a simplified inversion algorithm of AP estimation is proposed with the measurement of FAVV.Firstly,the LIFU model is established to simulate the vibration velocities for different transducers with various suriace vibration velocities using the finite element method,the relationship between the AP and FAVV is analyzed.It is shown that the FAVV increases linearly with the surface vibration velocity and the AP is proportional to the square of the FAVV with a fixed power gain determined by the physical properties of transducers.By keeping a constant of the FAW,a higher AP can be generated by using a transducer with a longer focal length or a smaller radius.In addition,the proposed AP measurement method is verified by experimental measurement of the FAW and surface vibration velocity for two transducers with different physical parameters.The favorable results suggest that FAW can be used as a valuable parameter for non-contact AP measurement.Furthermore,based on the nonlinear parabolic KZK equation,the formula of FAW for HIFU is derived and the HIFU field is calculated by using the finite difference method in frequency domain(FDFD).With the simulations of FAVV for different harmonics with various APs in HIFU field,the ratios of harmonics to FAVV(fundamental)are obtained and analyzed.The results are further proved by the simulations that,with the increase of the excitation acoustic pressure,the nonlinearity of the focal region is enhanced and higher order harmonics should be calculated to guarantee the accuracy of AP measurement.In addition,based on the-40dB ratio of harmonic to FAVV,the harmonic order of the nonlinear acoustic velocity is achieved based on the measured FAVV Based on the established algorithm of accurate AP calculation,the APs of HIFU fields with different excitations are simulated with corresponding harmonic orders and demonstrated by experimental measurement using a laser vibro me ter.The good agreements of the theoretical,numerical and experimental results show that the FAVV can be used as a valuable parameter for non-contact AP measurement for the LIFU and HIFU fields,and might provide a new strategy for accurate power control for focused ultrasound in biomedical engineering.