Finite element simulation of nonlinear wave propagation in thermoviscous fluids including dissipation

The nonlinear ultrasound needle pulse

Recent work has established an analytical formulation of broadband fields which extend in the axial direction and converge to a narrow concentrated line. Those unique (needle) fields have their origins in an angular spectrum configuration in which the forward propagating wavenumber of the field ( kz ) is constant across any z plane for all of the propagated frequencies. A 3 MHz-based, finite amplitude distorted simulation of such a field is considered here in a water path scenario relevant to medical imaging. That nonlinear simulation had its focal features compared to those of a comparable Gaussian beam. The results suggest that the unique convergence of the needle pulse to a narrow but extended axial line in linear propagation is also inherited by higher harmonics in nonlinear propagation. Furthermore, the linear needle field's relatively short duration focal pulses, and the asymptotic declines of its radial profiles, also hold for the associated higher harmonics. Comparisons with the Gaussian field highlight some unique and potentially productive features of needle fields.

Thermoacoustic Lensing in Ultrasound Imaging of Nonechogenic Tissue During High-intensity Focused Ultrasound Exposure

We develop a ray-tracing theory to describe the effects of thermoacoustic lensing during high-intensity focused ultrasound (HIFU) on ultrasound images of reflectors lying distal to the HIFU focal region and discuss the application of thermal lensing effects to dose monitoring in HIFU therapy. By analyzing the effects of thermal and geometric delays of acoustic rays passing through a region of tissue undergoing localized heating, we show how the shape of a reflector distal to the heated region can be predicted and present experimental measurements in good agreement with the model. We also apply the model in reverse to estimate the thermal profile of a heated region based on a measured change in the shape of a distal reflector during HIFU delivery. As an example, we apply this technique to the measurements of thermal diffusion in porcine fat. An interesting aspect of the technique is that it can be applied to measure temperature in nonechogenic tissues as long as there is an observable reflector in the ultrasound images that is located distal to the region of localized heating.

A pumpless microfluidic device driven by surface tension for pancreatic islet analysis

We present a novel pumpless microfluidic array driven by surface tension for studying the physiology of pancreatic islets of Langerhans. Efficient fluid flow in the array is achieved by surface tension-generated pressure as a result of inlet and outlet size differences. Flow properties are characterized in numerical simulation and further confirmed by experimental measurements. Using this device, we perform a set of biological assays, which include real-time fluorescent imaging and insulin secretion kinetics for both mouse and human islets. Our results demonstrate that this system not only drastically simplifies previously published experimental protocols for islet study by eliminating the need for external pumps/tubing and reducing the volume of solution consumption, but it also achieves a higher analytical spatiotemporal resolution due to efficient flow exchanges and the extremely small volume of solutions required. Overall, the microfluidic platform presented can be used as a potential powerful tool for understanding islet physiology, antidiabetic drug development, and islet transplantation.

Simulation of nonlinear propagation of biomedical ultrasound using pzflex and the Khokhlov-Zabolotskaya-Kuznetsov Texas code

Nonlinear acoustics plays an important role in both diagnostic and therapeutic applications of biomedical ultrasound and a number of research and commercial software packages are available. In this manuscript, predictions of two solvers available in a commercial software package, pzflex, one using the finite-element-method (FEM) and the other a pseudo-spectral method, spectralflex, are compared with measurements and the Khokhlov-Zabolotskaya-Kuznetsov (KZK) Texas code (a finite-difference time-domain algorithm). The pzflex methods solve the continuity equation, momentum equation and equation of state where they account for nonlinearity to second order whereas the KZK code solves a nonlinear wave equation with a paraxial approximation for diffraction. Measurements of the field from a single element 3.3 MHz focused transducer were compared with the simulations and there was good agreement for the fundamental frequency and the harmonics; however the FEM pzflex solver incurred a high computational cost to achieve equivalent accuracy. In addition, pzflex results exhibited non-physical oscillations in the spatial distribution of harmonics when the amplitudes were relatively low. It was found that spectralflex was able to accurately capture the nonlinear fields at reasonable computational cost. These results emphasize the need to benchmark nonlinear simulations before using codes as predictive tools.

Modeling of wave propagation for medical ultrasound: a review

Numerical modeling of medical ultrasound has advanced tremendously in the past two decades. This opens up a great number of opportunities for medical ultrasound and associated technologies. Numerous new governing equations and algorithms have emerged and been applied to studying various medical ultrasound applications, including ultrasound imaging, photo-acoustic imaging, and therapeutic ultrasound. In addition, thanks to the rapid development of computers, modeling acoustic wave propagation in three-dimensional, large-scale domains has become a reality. This article will provide an indepth literature and technical review of recent progress on numerical modeling of medical ultrasound. Future challenges will also be discussed.

Computation of nonlinear ultrasound fields using a linearized contrast source method

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

A comparative evaluation of three hydrophones and a numerical model in high intensity focused ultrasound fields

The pressure fields of two different high intensity focused ultrasound (HIFU) transducers operated in burst mode were measured at acoustical power levels of 25 and 50 W (continuous wave equivalent) with three different hydrophones: A fiber-optic displacement sensor, a commercial HIFU needle hydrophone, and a prototype of a membrane hydrophone with a protective coating against cavitation effects. Additionally, the fields were modeled using a freely available simulations software package. The measured waveforms, the peak pressure profiles, as well as the spatial-peak temporal-average intensities from the different devices and from the modeling are compared and possible reasons for differences are discussed. The results clearly show that reliable pressure measurements in HIFU fields remain a difficult task concerning both the reliability of the measured values and the robustness of the sensors used: Only the fiber-optic hydrophone survived all four exposure regimes and the measured spatial-peak temporal-average intensities varied by a factor of up to 1.5 between the measurements and the modeling and between the measurements among themselves.

Membrane hydrophone phase characteristics through nonlinear acoustics measurements

This work considers the need for both the amplitude and phase to fully characterize polyvinylidene fluoride (PVDF) membrane hydrophones and presents a comprehensive discussion of the nonlinear acoustic measurements utilized to extract the phase information and the experimental results taken with two widely used PVDF membrane hydrophones up to 100 MHz. A semi-empirical computer model utilized the hyperbolic propagation operator to predict the nonlinear pressure field and provide the complex frequency response of the corresponding source transducer. The PVDF hydrophone phase characteristics, which were obtained directly from the difference between the computer-modeled nonlinear field simulation and the corresponding measured harmonic frequency phase values, agree to within 10% with the phase predictions obtained from receive-transfer-function simulations based on software modeling of the membrane's physical properties. Cable loading effects and membrane hydrophone resonances were distinguished and identified through a series of impedance measurements and receive transfer function simulations on the hydrophones including their hard-wired coaxial cables. The results obtained indicate that the PVDF membrane hydrophone's phase versus frequency plot exhibits oscillations about a monotonically decreasing line. The maxima and minima inflection point slopes occur at the membrane thickness resonances and antiresonances, respectively. A cable resonance was seen at 100 MHz for the hydrophone with a 1-m cable attached, but not seen for the hydrophone with a shorter 0.65-m cable.

Evaluation of a wave-vector-frequency-domain method for nonlinear wave propagation

A wave-vector-frequency-domain method is presented to describe one-directional forward or backward acoustic wave propagation in a nonlinear homogeneous medium. Starting from a frequency-domain representation of the second-order nonlinear acoustic wave equation, an implicit solution for the nonlinear term is proposed by employing the Green's function. Its approximation, which is more suitable for numerical implementation, is used. An error study is carried out to test the efficiency of the model by comparing the results with the Fubini solution. It is shown that the error grows as the propagation distance and step-size increase. However, for the specific case tested, even at a step size as large as one wavelength, sufficient accuracy for plane-wave propagation is observed. A two-dimensional steered transducer problem is explored to verify the nonlinear acoustic field directional independence of the model. A three-dimensional single-element transducer problem is solved to verify the forward model by comparing it with an existing nonlinear wave propagation code. Finally, backward-projection behavior is examined. The sound field over a plane in an absorptive medium is backward projected to the source and compared with the initial field, where good agreement is observed.

An iterative method for the computation of nonlinear, wide-angle, pulsed acoustic fields of medical diagnostic transducers

The development and optimization of medical ultrasound transducers and imaging modalities require a computational method that accurately predicts the nonlinear acoustic pressure field. A prospective method should provide the wide-angle, pulsed field emitted by an arbitrary planar source distribution and propagating in a three-dimensional, large scale domain holding a nonlinear acoustic medium. In this paper, a method is presented that is free of any assumed wavefield directionality. The nonlinear acoustic wave equation is solved by treating the nonlinear term as a contrast source. This formulation leads to an iterative scheme that involves the repetitive solution of a linear wave problem through Green's function method. It is shown that accurate field predictions may be obtained within a few iterations. Moreover, by employing a dedicated numerical convolution technique, the method allows for a discretization down to two points per wavelength or period of the highest frequency of interest. The performance of the method is evaluated through a number of nonlinear field predictions for pulsed transducers with various geometries. The results demonstrate the directional independence of the method. Moreover, comparison with results from several existing methods shows that the method accurately predicts the nonlinear field for weak to moderate nonlinearity.

Experimental validation of a tractable numerical model for focused ultrasound heating in flow-through tissue phantoms

Heating from high intensity focused ultrasound (HIFU) can be used to control bleeding, both from individual blood vessels as well as from gross damage to the capillary bed. The presence of vascularity can limit one's ability to elevate the temperature owing to convective heat transport. In an effort to better understand the heating process in tissues with vascular structure we have developed a numerical simulation that couples models for ultrasound propagation, acoustic streaming, ultrasound heating and blood cooling in a Newtonian viscous medium. The 3-D simulation allows for the study of complicated biological structures and insonation geometries. We have also undertaken a series of in vitro experiments employing non-uniform flow-through tissue phantoms and designed to provide verification of the model predictions. We show that blood flow of 2 cm/s (6.4 ml/min through a 2.6 mm 'vessel') can reduce peak temperature in a vessel wall by 25%. We also show that HIFU intensities of 6.5 x 10(5) W/m2 can induce acoustic streaming with peak velocities up to 5 cm/s and this can reduce heating near a vessel wall by more than 10%. These results demonstrate that convective cooling is important in HIFU and can be accounted for within simulation models.