Joshua E. Soneson

A User‐Friendly Software Package for HIFU Simulation

A freely‐distributed, MATLAB (The Mathworks, Inc., Natick, MA)‐based software package for simulating axisymmetric high‐intensity focused ultrasound (HIFU) beams and their heating effects is discussed. The package (HIFU_Simulator) consists of a propagation module which solves the Khokhlov‐Zabolotskaya‐Kuznetsov (KZK) equation and a heating module which solves Pennes’ bioheat transfer (BHT) equation. The pressure, intensity, heating rate, temperature, and thermal dose fields are computed, plotted, the output is released to the MATLAB workspace for further user analysis or postprocessing.

Gaussian representation of high-intensity focused ultrasound beams

A method for fast numerical simulation of high-intensity focused ultrasound beams is derived. The method is based on the frequency-domain representation of the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, and assumes for each harmonic a Gaussian transverse pressure distribution at all distances from the transducer face. The beamwidths of the harmonics are constrained to vary inversely with the square root of the harmonic number, and as such this method may be viewed as an extension of a quasilinear approximation. The technique is capable of determining pressure or intensity fields of moderately nonlinear high-intensity focused ultrasound beams in water or biological tissue, usually requiring less than a minute of computer time on a modern workstation. Moreover, this method is particularly well suited to high-gain simulations since, unlike traditional finite-difference methods, it is not subject to resolution limitations in the transverse direction. Results are shown to be in reasonable agreement with numerical solutions of the full KZK equation in both tissue and water for moderately nonlinear beams.

A parametric study of error in the parabolic approximation of focused axisymmetric ultrasound beams

The parabolic approximation results in a tractible model for studying ultrasound beams, but the limits of validity of the approximation are often presented only qualitatively. In this work the most common model for axisymmetric ultrasound beam propagation, the Kuznetsov-Zabolotskaya-Khokhlov equation, is directly compared with the more general Westervelt equation with regard to diffractive and absorptive effects in continuous wave beams. The parametric study compares the solutions of the two models as a function of source frequency and focusing geometry using peak focal pressure, the axial location at which that peak occurs, and the loss due to absorption as metrics.

Temperature modes for nonlinear Gaussian beams

In assessing the influence of nonlinear acoustic propagation on thermal bioeffects, approximate methods for quickly estimating the temperature rise as operational parameters are varied can be very useful. This paper provides a formula for the transient temperature rise associated with nonlinear propagation of Gaussian beams. The pressure amplitudes for the Gaussian modes can be obtained rapidly using a method previously published for simulating nonlinear propagation of Gaussian beams. The temperature-mode series shows that the nth temperature mode generated by nonlinear propagation, when normalized by the fundamental, is weaker than the nth heat-rate mode (also normalized by the fundamental in the heat-rate series) by a factor of log(n)/n, where n is the mode number. Predictions of temperature rise and thermal dose were found to be in close agreement with full, finite-difference calculations of the pressure fields, temperature rise, and thermal dose. Applications to non-Gaussian beams were made by fitting the main lobe of the significant modes to Gaussian functions.

Comparison between experimental and computational methods for the acoustic and thermal characterization of therapeutic ultrasound fields

For high intensity therapeutic ultrasound (HITU) devices, pre-clinical testing can include measurement of power, pressure/intensity and temperature distribution, acoustic and thermal simulations, and assessment of targeting accuracy and treatment monitoring. Relevant International Electrotechnical Commission documents recently have been published. However, technical challenges remain because of the often focused, large amplitude pressure fields encountered. Measurement and modeling issues include using hydrophones and radiation force balances at HITU power levels, validation of simulation models, and tissue-mimicking material (TMM) development for temperature measurements. To better understand these issues, a comparison study was undertaken between simulations and measurements of the HITU acoustic field distribution in water and TMM and temperature rise in TMM. For the specific conditions of this study, the following results were obtained. In water, the simulated values for p+ and p- were 3% lower and 10% higher, respectively, than those measured by hydrophone. In TMM, the simulated values for p+ and p- were 2% and 10% higher than those measured by hydrophone, respectively. The simulated spatial-peak temporal-average intensity values in water and TMM were greater than those obtained by hydrophone by 3%. Simulated and measured end-of-sonication temperatures agreed to within their respective uncertainties (coefficients of variation of approximately 20% and 10%, respectively).

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...

Extending the Utility of the Parabolic Approximation in Medical Ultrasound Using Wide-Angle Diffraction Modeling

Wide-angle parabolic models are commonly used in geophysics and underwater acoustics but have seen little application in medical ultrasound. Here, a wide-angle model for continuous-wave high-intensity ultrasound beams is derived, which approximates the diffraction process more accurately than the commonly used Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation without increasing implementation complexity or computing time. A method for preventing the high spatial frequencies often present in source boundary conditions from corrupting the solution is presented. Simulations of shallowly focused axisymmetric beams using both the wide-angle and standard parabolic models are compared to assess the accuracy with which they model diffraction effects. The wide-angle model proposed here offers improved focusing accuracy and less error throughout the computational domain than the standard parabolic model, offering a facile method for extending the utility of existing KZK codes.

Comparison between computational and experimental methods for the characterization of therapeutic ultrasound fields

Analytical modeling of medical ultrasound fields has been developed by the FDA to aid in pre-clinical characterization of therapeutic ultrasound devices. In order to assess this publicly available software, called the HIFU Simulator, acoustic and thermal measurements of power, pressure/intensity and temperature distribution have been performed for comparison. Measurement and modeling issues include using hydrophones and radiation force balances at therapeutic power levels, validation of simulation models, and tissue-mimicking material (TMM) development for temperature measurements. To better understand these issues, a comparison study was undertaken between simulations and measurements of the HITU acoustic field distribution in water and TMM, and temperature rise in TMM. For the specific conditions of this study, the following results were obtained. In water, the simulated values for p + and p- were 3% lower and 10% higher, respectively, than those measured by hydrophone. In TMM, the simulated values for ...

Effects of dose‐dependent absorption on heating and lesion formation

A mathematical model for studying the effects of dose‐dependent tissue absorption on high intensity focused ultrasound (HIFU) treatments is presented and a numerical solution method is discussed. An example HIFU system is considered and comparisons are made between including and neglecting dynamic absorption. Simulations show that neglecting dynamic absorption can result in highly underpredicted focal temperature, hotspot size, and lesion volume.

Thermal analysis of ultrasound-powered miniaturized implants: A tissue-phantom study

Neurological implants that harvest ultrasound power have the potential to provide long-term stimulation without complications associated with battery power. An important safety question associated with long-term operation of the implant involves the heat generated by the interaction of the device with the ultrasound field. A study was performed in which the temperature rise generated by this interaction was measured. Informed by temperature data from thermocouples outside the ultrasound beam, a mathematical inverse method was used to determine the volume heat source generated by ultrasound absorption within the implant as well as the surface heat source generated within the viscous boundary layer on the surface of the implant. For the test implant used, it was determined that most of the heat was generated in the boundary layer, giving a maximum temperature rise ∼5 times that for absorption in an equivalent volume of soft tissue. This result illustrates that thermal safety guidelines based solely on ultrasound absorption of tissue alone are not sufficient. The method presented represents an alternative approach for quantifying ultrasound thermal effects in the presence of implants. The analysis shows a steady temperature rise of about 0.2 °C for every 100 mW/cm2 for the presented test implant.