Ibrahim M. Hallaj

FDTD simulation of finite-amplitude pressure and temperature fields for biomedical ultrasound

Full wave simulations provide a valuable tool for studying the spatial and temporal nature of an acoustic field. One method for producing such simulations is the finite-difference time-domain (FDTD) method. This method uses discrete differences to approximate derivatives in the governing partial differential equations. We used the FDTD method to model the propagation of finite-amplitude sound in a homogeneous thermoviscous fluid. The calculated acoustic pressure field was then used to compute the transient temperature rise in the fluid; the heating results from absorption of acoustic energy by the fluid. As an example, the transient temperature field was calculated in biological tissue in response to a pulse of focused ultrasound. Enhanced heating of the tissue from finite-amplitude effects was observed. The excess heating was attributed to the nonlinear generation of higher-frequency harmonics which are absorbed more readily than the fundamental. The effect of nonlinear distortion on temperature rise in tissue was observed to range from negligible at 1 MPa source pressure to an 80% increase in temperature elevation at 10 MPa source pressure.

Simulations of the thermo-acoustic lens effect during focused ultrasound surgery

Laboratory measurements of soft tissue properties show a dependence of background propagation properties on temperature. For typical focused ultrasound surgery (FUS) applications, only the slow variations in tissue background parameters need to be accounted for when computing the outcome of a FUS sonication. The cumulative effect of slowly varying sound speed has been referred to in the literature as a thermal lens, or a thermo-acoustic lens because of its beam-distorting properties. An algorithm to solve the coupled acoustic-thermal problem is described, and numerical results are presented to illustrate the effects of dynamic sound-speed profiles in layered tissues undergoing FUS. The results of simulations in liver with and without a fat layer indicate that the thermal-acoustic interaction results in more complex dynamics in FUS than a simple model will predict. Both the size and the position of the lesions predicted from the simulations are affected by the thermo-acoustic lens effect. However, the overall effect from short sonications at high power from sharply focused single element sources (F-no. from 0.8 to 1.3) around 1 MHz similar to those used in clinical setups is found to be small.

The acoustic emissions from single-bubble sonoluminescence

Detailed measurements of the acoustic emissions from single-bubble sonoluminescence have been made utilizing both a small 200-μm aperture PVDF needle hydrophone, and a focused 10-MHz transducer. Signals obtained with the needle hydrophone show a fast (5.2 ns), probably bandlimited rise time and relatively large pulse amplitude (≈1.7 bar). Below the sonoluminescence threshold, the emissions are observable, but considerably smaller in amplitude (≈0.4 bar). Several signals are observed with the 10-MHz transducer and correspond to acoustic emissions from the bubble during the main collapse, as well as from the rebounds. Experiments reveal that the acoustic emissions occur at or near the minimum bubble radius. Calculations of the peak pressures and pulse widths are compared with experimental data.

Measurements of the acoustic emission from glowing bubbles

A single bubble trapped in an acoustic standing wave can be made to undergo highly nonlinear volume mode pulsations resulting in inertial cavitation—the expansive growth and violent collapse of bubbles. Under certain conditions the collapse results in light emission called sonoluminescence (SL). Though much has been studied regarding properties of the emitted light, little work has been done on the acoustic emission from such a bubble. Previous measurements [Cordry et al., J. Acoust. Soc. Am. 98, 2921(A) (1995)] using a needle hydrophone show only a general low‐level acoustic signature. In the present study, a broadband, nonfocused transducer is used to record the acoustic emission from single bubbles at various acoustic drive amplitudes in the SL and non‐SL producing regions. The typical acoustic signature includes a large amplitude pulse corresponding to the initial collapse followed by smaller amplitude pulses corresponding to the rebounds. The rebounding bubble essentially oscillates at its resonance ...

Modeling and simulating finite‐amplitude propagation through time‐varying inhomogeneous absorbing media

A model equation is derived for three‐dimensional wave propagation through an inhomogeneous, time‐varying medium. The model equation accounts for arbitrary inhomogeneities, finite‐amplitude distortion, and absorption. The effect of time dependence of the background medium parameters is included in the equation. An ordering scheme based on the characteristic time of the evolution of each parameter allows one to evaluate their relative importance. A two‐dimensional version of the wave equation is solved in the time‐domain using finite‐difference methods. Explicit, implicit, and operator splitting techniques were used in the solution to overcome numerical instabilities. Results from the code are compared to known solutions for some simple geometries in homogeneous and step indexed media. Various modeling and numerical schemes for treating the absorption on the computational domain interior and at the boundaries of the domain will be presented. [Work supported by ONR and DARPA.]

Coupled thermal‐acoustic simulation results with temperature‐dependent tissue parameters for therapeutic ultrasound

Recently the authors used direct simulations of the transient acoustic pressure field to calculate heat energy deposition and, thus, temperature fields in two‐dimensional tissue like media [J. Acoust. Soc. Am. 102, 3172(A) (1997)]. It is known that acoustic‐induced temperature rises will alter the properties of the medium in hyperthermia situations. In this presentation the simulations are extended to simultaneously solve the wave propagation and tissue heating problems so that the effect of temperature‐dependent tissue parameters can be accounted for directly. In other words, there is a continuous feedback of temperature on the sound propagation parameters, which in turn affects the thermal energy deposition. The simulations are second order accurate in time, fourth order in space full wave calculations using the finite‐difference time‐domain technique, and allow for finite‐amplitude wave propagation in an inhomogeneous, thermoviscous fluid. The model allows for spatially and temporally varying sound spe...

Two‐dimensional nonlinear propagation of pulsed ultrasound through a tissue‐like material

During a lithotripsy operation or ultrasound surgery, high‐intensity acoustic waves propagate through tissue. Damage and thermal dose delivered to the target site and to tissue neighboring the target site is of significant interest in such operations. Results of a study of the propagation of intense ultrasonic pulses through a tissuelike material are presented. Two‐dimensional simulations showing the effects of nonlinearity in inhomogeneous absorbing materials are used to calculate the acoustic pressure field, from which input is obtained for a bioheat equation calculation. Results show the mean and peak acoustic pressures within a target volume as a function of time, and the thermal dose delivered to a target volume due to a pulsed source in the range of frequencies used for ultrasound surgery. The degradation of the focusing ability of an ultrasonic array in nonlinear inhomogeneous media is illustrated, and conclusions regarding therapeutic ultrasound are made. [Work supported by ONR and DARPA.]

Path‐integrated Goldberg number as a predictor of enhanced heating from finite‐amplitude therapeutic ultrasound sources

Several theoretical and experimental studies have demonstrated that the higher‐frequency harmonics generated by finite‐amplitude propagation from therapeutic ultrasound sources result in enhanced heating of tissue. However, published results vary in their assessments of the significance of the nonlinearity on tissue heating. The variations in the results are due to the use of different sources and propagation paths. It would be useful to have an easily computed estimator of finite‐amplitude effects for therapeutic ultrasound sources. The present study describes a dimensionless quantity, which takes the propagation path into account, to estimate the excess temperature rise due to nonlinearity. The dimensionless parameter is based on the Goldberg number which is a measure of the importance of nonlinear effects to absorption effects. The relationship between the enhanced heating of tissue and the path‐integrated Goldberg number for water‐tissue paths is presented for typical therapeutic devices. [Work sponso...

Time reversal array focal zone predictions using simulations in the time domain

The use of finite‐difference time‐domain (FDTD) computer simulations for wave equation calculations has deep roots in the electromagnetic pulse propagation literature, where many of the modern techniques were developed. Results are presented from high‐resolution simulations of the linear acoustic wave equation in inhomogeneous media with absorbing boundary conditions. The results address the focusing behavior of sparse ultrasonic arrays under various propagation conditions. Focal spot attributes and size are investigated in the presence of inhomogeneities, time‐varying media, and multiple scatterers. Comparison with known benchmarks, such as the diffraction limit, show that useful results can be obtained using FDTD calculations in medical applications, for example, where the frequencies and scales allow full‐sized simulations in major organs. [Work supported by the Office of Naval Research.]

Acoustic time reversal in nonlinear wave propagation

The application of acoustic time reversal in nonlinear underwater propagation is investigated theoretically and numerically. An acoustic wave equation containing thermal and viscous absorption as well as finite‐amplitude terms is presented. The behavior of such a system under time reversal is discussed. Theoretical results and numerical examples are presented, showing when and why the propagation is time reversible, and when the equation is no longer time invariant. [IMH and SGK’s work is supported by the Office of Naval Research.]