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.
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.
BackgroundTo improve understanding of shockwave therapy mechanisms, in vitro experiments are conducted and the correlation between cell reaction and shockwave parameters like the maximum pressure or energy density is studied. If the shockwave is not measured in the experimental setup used, it is usually assumed that the device’s shockwave parameters (=manufacturer’s free field measurements) are valid. But this applies only for in vitro setups which do not modify the shockwave, e.g., by reflection or refraction. We hypothesize that most setups used for in vitro shockwave experiments described in the literature influence the sound field significantly so that correlations between the physical parameters and the biological reaction are not valid.MethodsTo reveal the components of common shockwave in vitro setups which mainly influence the sound field, 32 publications with 37 setups used for focused shockwave experiments were reviewed and evaluated regarding cavitation, cell container material, focal sound field size relative to cell model size, and distance between treated cells and air. For further evaluation of the severity of those influences, experiments and calculations were conducted.ResultsIn 37 setups, 17 different combinations of coupling, cell container, and cell model are described. The setup used mainly is a transducer coupled via water to a tube filled with a cell suspension. As changes of the shockwaves’ maximum pressure of 11 % can already induce changes of the biological reaction, the sound field and biological reactions are mainly disturbed by use of standard cell containers, use of coupling gel, air within the 5 MPa focal zone, and cell model sizes which are bigger than half the −6 dB focal dimensions.ConclusionsUntil now, correct and sufficient information about the shockwave influencing cells in vitro is only provided in 1 of 32 publications. Based on these findings, guidelines for improved in vitro setups are proposed which help minimize the influence of the setup on the sound field.Electronic supplementary materialThe online version of this article (doi:10.1186/s40349-016-0053-z) contains supplementary material, which is available to authorized users.
Abstract. Flywheel Energy Storage Systems represent an exciting alternative to traditional battery storage systems used to power satellites during periods of eclipse. The increasing demand for reliable communication and data access is driving explosive growth in the number of satenite systems being developed as well as their performance requirements. Power on orbit is the key to this performance, and batteries are becoming increasingly unattractive as an energy storage media. Flywheel systems offer very attractive characteristics for both energy storage in terms of energy density and the number of charge/discharge cycles, together with the important side benefit of spacecraft attitude control.
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