Temperature dependence of nickel ion release from nitinol medical devices.

Nitinol exhibits unique (thermo)mechanical properties that make it central to the design of many medical devices. However, nitinol nominally contains 50 atomic percent nickel, which if released in sufficient quantities, can lead to adverse health effects. While nickel release from nitinol devices is typically characterized using in vitro immersion tests, these evaluations require lengthy time periods. We have explored elevated temperature as a potential method to expedite this testing. Nickel release was characterized in nitinol materials with surface oxide thickness ranging from 12 to 1564 nm at four different temperatures from 310 to 360 K. We found that for three of the materials with relatively thin oxide layers, ≤ 87 nm nickel release exhibited Arrhenius behavior over the entire temperature range with activation energies of 80 to 85 kJ/mol. Conversely, the fourth ''black-oxide'' material, with a much thicker, complex oxide layer, was not well characterized by an Arrhenius relationship. Power law release profiles were observed in all four materials; however, the exponent from the thin oxide materials was approximately 1/4 compared with 3/4 for the black-oxide material. To illustrate the potential benefit of using elevated temperature to abbreviate nickel release testing, we demonstrated that a > 50 day 310 K release profile could be accurately recovered by testing for less than 1 week at 340 K. However, because the materials explored in this study were limited, additional testing and mechanistic insight are needed to establish a protective temperature scaling that can be applied to all nitinol medical device components.

A closer look at ultrasonic attenuation and heating in a tissue-mimicking material.

A well-characterized ultrasound tissue-mimicking material (TMM) can be important in determining the acoustic output and temperature rise from high intensity therapeutic ultrasound (HITU) devices and also in validating computer simulation models. A HITU TMM previously developed and characterized in our laboratory has been used in our acoustic and temperature measurements as well as modeled in our HITU simulation program. A discrepancy between thermal measurement and simulation, though, led us to further investigate the TMM properties. We found that the 2-parameter analytic fit commonly used to represent the attenuation of the TMM in the computer modeling was not adequate over the entire frequency range of interest, 1 MHz to 8 MHz in this study, indicating that we and others may have not been characterizing TMMs, and possibly tissue, optimally. By comparing measurements and simulations, we found that a 3-parameter analytic fit for attenuation gave a more accurate value for attenuation at 1 MHz and 2 MHz, and using that fit the temperature rise measurements in the TMM that agreed more closely with the simulation results.

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.

Experimental validation of a nonlinear derating technique based upon Gaussian-modal representation of focused ultrasound beams.

A technique useful for performing derating at acoustic powers where significant harmonic generation occurs is illustrated and validated with experimental measurements. The technique was previously presented using data from simulations. The method is based upon a Gaussian representation of the propagation modes, resulting in simple expressions for the modal quantities, but a Gaussian source is not required. The nonlinear interaction of modes within tissue is estimated from the nonlinear interaction in water, using appropriate amounts of source reduction and focal-point reduction derived from numerical simulations. An important feature of this nonlinear derating method is that focal temperatures can be estimated with little additional effort beyond that required to determine the focal pressure waveforms. Hydrophone measurements made in water were used to inform the derating algorithm, and the resulting pressure waveforms and increases in temperature were compared with values directly measured in tissue phantoms. For a 1.05 MHz focused transducer operated at 80 W and 128 W, the derated pressures (peak positive, peak negative) agreed with the directly measured values to within 11%. Focal temperature rises determined by the derating method agreed with values measured using a remote thermocouple technique with a difference of 17%.

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).

Thermal safety simulations of transient temperature rise during acoustic radiation force-based ultrasound elastography.

Ultrasound transient elastography is a new diagnostic imaging technique that uses acoustic radiation force to produce motion in solid tissue via a high-intensity, long-duration "push" beam. In our previous work, we developed analytical models for calculating transient temperature rise, both in soft tissue and at a bone/soft tissue interface, during a single acoustic radiation force impulse (ARFI) imaging frame. The present study expands on these temperature rise calculations, providing applicable range assessment and error analysis for a single ARFI frame. Furthermore, a "virtual source" approach is described for temperature and thermal dose calculation under multiple ARFI frames. By use of this method, the effect of inter-frame cooling duration on temperature prediction is analyzed, and a thermal buildup phenomenon is revealed. Thermal safety assessment indicates that the thermal dose values, especially at the absorptive bone/soft tissue interface, could approach recommended dose thresholds if the cooling interval of multiple-frame ARFI elastography is too short.

Nonlinear derating of high-intensity focused ultrasound beams using Gaussian modal sums.

A method is introduced for using measurements made in water of the nonlinear acoustic pressure field produced by a high-intensity focused ultrasound transducer to compute the acoustic pressure and temperature rise in a tissue medium. The acoustic pressure harmonics generated by nonlinear propagation are represented as a sum of modes having a Gaussian functional dependence in the radial direction. While the method is derived in the context of Gaussian beams, final results are applicable to general transducer profiles. The focal acoustic pressure is obtained by solving an evolution equation in the axial variable. The nonlinear term in the evolution equation for tissue is modeled using modal amplitudes measured in water and suitably reduced using a combination of "source derating" (experiments in water performed at a lower source acoustic pressure than in tissue) and "endpoint derating" (amplitudes reduced at the target location). Numerical experiments showed that, with proper combinations of source derating and endpoint derating, direct simulations of acoustic pressure and temperature in tissue could be reproduced by derating within 5% error. Advantages of the derating approach presented include applicability over a wide range of gains, ease of computation (a single numerical quadrature is required), and readily obtained temperature estimates from the water measurements.

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.

Thresholds for nonlinear effects in high- intensity focused ultrasound propagation and tissue heating.

For a variety of reasons, including their simplicity and ability to capitalize upon superposition, linear acoustic propagation models are preferable to nonlinear ones in modeling the propagation of high-intensity focused ultrasound (HIFU) beams. However, under certain conditions, nonlinear models are necessary to accurately model the beam propagation and heating. In analyzing the performance of a HIFU system, it is advantageous to know before the analysis whether a linear model suffices. This paper examines the problem of determining the thresholds at which nonlinear effects become important. It is demonstrated that nonlinear interaction has different effects on different physical and derived quantities, such as compressional pressure, rarefactional pressure, intensity, heat rate, temperature rise, and thermal lesion volume. Thresholds are determined as a function of the dimensionless gain, nonlinearity, and absorption parameters. The relative difference between linear and nonlinear predictions is plotted as a series of contours, enabling practitioners to locate their system in parameter space and determine whether nonlinearity significantly affects the quantities of interest.

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.

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.