For the simulation of therapeutic ultrasound applications, a method including frequency-dependent attenuation effects directly in the time domain is highly desirable. This paper describes an efficient numerical time-domain implementation of the power-law attenuation model presented by Szabo [Szabo, J. Acoust. Soc. Am. 96, 491-500 (1994)]. Simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time-domain (FDTD) algorithm for nonlinear ultrasound propagation [Ginter et al., J. Acoust. Soc. Am. 111, 2049-2059 (2002)]. Szabo implemented the empirical frequency power-law attenuation using a causal convolutional operator directly in the time-domain equation. Though a variety of time-domain models has been published in recent years, no efficient numerical implementation has been presented so far for frequency power-law attenuation models. Solving a convolutional integral with standard time-domain techniques requires enormous computational effort and therefore often limits the application of such models to 1D problems. In contrast, the presented method is based on a recursive algorithm and requires only three time levels and a few auxiliary data to approximate the convolutional integral with high accuracy. The simulation results are validated by comparison with analytical solutions and measurements.

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The number of applications of high-intense, focused ultrasound for therapeutic purposes is growing. Besides established applications like lithotripsy, new applications like ultrasound in orthopedics or for the treatment of tumors arise. Therefore, new devices have to be developed which provide pressure waveforms and distributions in the focal zone specifically for the application. In this paper, a nonlinear full-wave simulation model is presented which predicts the therapeutically important characteristics of the generated ultrasound field for a given transducer and initial pressure signal. A nonlinear acoustic approximation in conservation form of the original hydrodynamic equations for ideal fluids rather than a wave equation provides the base for the nonlinear model. The equations are implemented with an explicit high-order finite-difference time-domain algorithm. The necessary coefficients are derived according to the dispersion relation preserving method. Simulation results are presented for two different therapeutic transducers: a self-focusing piezoelectric and one with reflector focusing. The computational results are validated by comparison with analytical solutions and measurements. An agreement of about 10% is observed between the simulation and experimental results.

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It is well known that fluorocarbon electrets, although thermally very stable, suffer a surface potential decay if exposed to high temperatures. This potential decay is of considerable interest in applications, for example, in the so-called prepolarized microphones. As a result, these devices suffer a loss in sensitivity approximately proportional to the decay of the electret surface potential. Since the potential and the related sensitivity losses are very slow at room temperature, a common approach in the literature is to perform accelerated isothermal depolarization experiments at elevated temperatures, and extrapolate the results to lower temperatures by assuming an Arrhenius-type behavior. In this paper, we investigate experimentally the potential decay of differently pre-annealed fluoroethylenepropylene electrets of different thicknesses, as well as the drop of sensitivity of commercially available measurement microphones from several manufacturers by the exposure to an ambient temperature of 95 °C for up to three years. Until now, no other reports compare electret and microphone decays over such a long period. The experimental data presented here could not be fitted with only one exponential decay function over the whole time-span investigated. However, assuming two or more discharge processes results in a good agreement between measurement and model functions. The time constants of these decay processes are specified in the text.

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