Olga V. Bessonova

Shock-induced heating and millisecond boiling in gels and tissue due to high intensity focused ultrasound

Nonlinear propagation causes high-intensity ultrasound waves to distort and generate higher harmonics, which are more readily absorbed and converted to heat than the fundamental frequency. Although such nonlinear effects have been investigated previously and found to not significantly alter high-intensity focused ultrasound (HIFU) treatments, two results reported here change this paradigm. One is that at clinically relevant intensity levels, HIFU waves not only become distorted but form shock waves in tissue. The other is that the generated shock waves heat the tissue to boiling in much less time than predicted for undistorted or weakly distorted waves. In this study, a 2-MHz HIFU source operating at peak intensities up to 25,000 W/cm(2) was used to heat transparent tissue-mimicking phantoms and ex vivo bovine liver samples. Initiation of boiling was detected using high-speed photography, a 20-MHz passive cavitation detector and fluctuation of the drive voltage at the HIFU source. The time to boil obtained experimentally was used to quantify heating rates and was compared with calculations using weak shock theory and the shock amplitudes obtained from nonlinear modeling and measurements with a fiber optic hydrophone. As observed experimentally and predicted by calculations, shocked focal waveforms produced boiling in as little as 3 ms and the time to initiate boiling was sensitive to small changes in HIFU output. Nonlinear heating as a result of shock waves is therefore important to HIFU, and clinicians should be aware of the potential for very rapid boiling because it alters treatments.

FOCUSING OF HIGH POWER ULTRASOUND BEAMS AND LIMITING VALUES OF SHOCK WAVE PARAMETERS.

In this work, the influence of nonlinear and diffraction effects on amplification factors of focused ultrasound systems is investigated. The limiting values of acoustic field parameters obtained by focusing of high power ultrasound are studied. The Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation was used for the numerical modeling. Solutions for the nonlinear acoustic field were obtained at output levels corresponding to both pre- and post-shock formation conditions in the focal area of the beam in a weakly dissipative medium. Numerical solutions were compared with experimental data as well as with known analytic predictions.

A derating method for therapeutic applications of high intensity focused ultrasound

Current methods of determining high intensity focused ultrasound (HIFU) fields in tissue rely on extrapolation of measurements in water assuming linear wave propagation both in water and in tissue. Neglecting nonlinear propagation effects in the derating process can result in significant errors. A new method based on scaling the source amplitude is introduced to estimate focal parameters of nonlinear HIFU fields in tissue. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those simulated for propagation in water. Focal wave-forms, peak pressures, and intensities are calculated over a wide range of source outputs and linear focusing gains. Our modeling indicates, that for the high gain sources which are typically used in therapeutic medical applications, the focal field parameters derated with our method agree well with numerical simulation in tissue. The feasibility of the derating method is demonstrated experimentally in excised bovine liver tissue.

Modeling of nonlinear shock wave propagation and thermal effects in high‐intensity focused ultrasound fields.

Numerical simulations based on the Khokhlov–Zabolotskaya‐type equation are currently used to characterize therapeutic high‐intensity focused ultrasound fields in water and to predict bioeffects in tissue. Here results from three different algorithms that differ in calculating the nonlinear term in the equation are presented. Shock capturing schemes of Godunov type, exact implicit solution with further extrapolation of the waveform over a uniform temporal grid, and direct modeling in the frequency domain are tested. In the case of weak nonlinearity, all schemes give essentially the same solution. However, at high peak pressures around 50 MPa and strong shocks developed in the focal region, the predictions of acoustic variables and heat deposition become sensitive to the algorithm employed. The parameters of the schemes, such as number of harmonics or temporal samples and the inclusion of artificial absorption that provides consistent results, are discussed. It is shown that the spectral and Godunov‐type ap...

Bandwidth Limitations in Characterization of High Intensity Focused Ultrasound Fields in the Presence of Shocks

Nonlinear propagation effects result in the formation of weak shocks in high intensity focused ultrasound (HIFU) fields. When shocks are present, the wave spectrum consists of hundreds of harmonics. In practice, shock waves are modeled using a finite number of harmonics and measured with hydrophones that have limited bandwidths. The goal of this work was to determine how many harmonics are necessary to model or measure peak pressures, intensity, and heat deposition rates of the HIFU fields. Numerical solutions of the Khokhlov‐Zabolotskaya‐Kuznetzov‐type (KZK) nonlinear parabolic equation were obtained using two independent algorithms, compared, and analyzed for nonlinear propagation in water, in gel phantom, and in tissue. Measurements were performed in the focus of the HIFU field in the same media using fiber optic probe hydrophones of various bandwidths. Experimental data were compared to the simulation results.

Spatial Structure of High Intensity Focused Ultrasound Beams of Various Geometry

The influence of nonlinear and diffraction effects on distortion of the spatial structure of peak positive and negative pressures in focused acoustic beams was studied for a weakly dissipative propagation medium. The problem was solved numerically based on the Khokhlov-Zabolotskaya-Kuznetsov equation for beams with uniform and Gaussian distributions of the harmonic signal amplitude at the source.

Nonlinear derating method for high intensity focused ultrasound (HIFU) fields

In this work, a new derating method to extrapolate nonlinear ultrasound fields in water to biological tissue is proposed and tested for therapeutic medical systems. Focal values of acoustic field parameters in absorptive tissue are obtained from a numerical solution to a KZK-type equation and are compared to those derated, using the proposed method, from the results of simulations in water. It is validated in modeling that for high gain sources, which are typically used for therapeutic medical applications, the focal field parameters in tissue can be obtained from the results obtained in water. The feasibility of the derating method is also demonstrated experimentally in water and excised bovine liver tissue using a 2 MHz HIFU source of 44 mm aperture and focal length.

A method of HIFU field characterization in water and deration to tissue

Acoustic characterization of nonlinear HIFU fields is important for both the accurate prediction of ultrasound induced bioeffects and the development of regulatory standards for clinical HIFU devices. In this work a new characterization method is proposed and tested in water, tissue phantoms, and ex‐vivo tissues. The method is based on the combined use of measurements and modeling. Experiments were performed with a 2 MHz transducer of 4.2 cm aperture and 4.5 cm focal length. Low amplitude measurements in water were used to establish boundary conditions for modeling based on the KZK‐type equation. High amplitude focal waveforms then were simulated and measured with a fiber optic probe hydrophone in water, within tissue phantom, or adjacent to excised tissue. It was shown that at high amplitudes, the simulations of shock waveforms were more accurate than the measurements. The focal waveforms obtained in water were found to be in a good agreement with those produced in tissue with higher source pressure scal...

Full‐diffraction and parabolic axisymmetric numerical models to characterize nonlinear ultrasound fields of two‐dimensional therapeutic arrays.

Numerical modeling has been shown to be an effective tool to characterize nonlinear pressure fields for single‐element HIFU transducers, but it has not yet been applied for the much more complex three‐dimensional (3‐D) fields generated by therapeutic phased arrays. In this work, two approaches are presented to simulate nonlinear effects in the field of a 256‐element focused array. A new full‐diffraction approach includes rigorous 3‐D simulations of the nonlinear wave equation with a boundary condition given at the elements of the array. A second simpler approach is based on the KZK model and a focused piston source as the boundary condition. The effective aperture and initial pressure of the piston source are set by matching linear simulations of the two models in the focal region. It is shown that as output power is increased, agreement in the focal waveforms of the two simulations, even when shocks were present, is maintained up to very high power outputs of the array. These results demonstrate the feas...

Spatial distributions of acoustic parameters in nonlinear focused beams of various geometry

In this work, numerical simulations are performed and spatial distributions of specific parameters of nonlinear focused ultrasound beams of various geometry are compared. The numerical algorithm is based on the solution of the Khokhlov‐Zabolotskaya (KZ) equation. Focused acoustic beams of periodic waves with an initially uniform amplitude distribution, typical for medical therapeutic transducers, and with Gaussian amplitude shading are considered. Numerical solutions are obtained and analyzed for nonlinear acoustic field in various regimes of linear, quasilinear, and nonlinear propagation when shock fronts are developed in the waveform close to the focus and while propagating to the focus of the beam.