Thomas Dreyer

Full-wave modeling of therapeutic ultrasound: Nonlinear ultrasound propagation in ideal fluids

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.

Full wave modeling of therapeutic ultrasound: Efficient time-domain implementation of the frequency power-law attenuation

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.

Investigations of compact self focusing transducers using stacked piezoelectric elements for strong sound pulses in therapy

A new design for self-focusing piezoelectric transducers used in therapy is presented. Common transducers have large dimensions with diameters up to 500 mm in order to generate sufficiently high-pressure pulses. The reduction of the overall size can be achieved by a stacked placement of the single piezoelectric elements. Two prototype transducers of different dimensions are investigated considering their acoustic output compared to the former design. It is shown that similar focusing properties as well as comparable pressure pulse shapes and amplitudes can be achieved at significantly smaller transducer dimensions.

Experiments on the relation of shock wave parameters to stone disintegration

The sound field of different focusing piezoelectric transducers designed for lithotripsy was investigated. The shock wave parameters according to proposed standards, e.g., FDA Draft 1991, were determined. The parameters achieved are based on measurements using a fiber‐optical probe hydrophone. In contrast to PVDF‐based hydrophones, this hydrophone is able to give a correct representation also of the tensile components of a complete signal and provides a higher spatial resolution. Thus some shock wave parameters like beam energy can be calculated more precisely. The different lithotripter pulses were applied to model stones in vitro, recording the amounts of removed material. Fragmentation results were compared with the different parameters. Attempts were made to arrange these parameters according to their relevance to disintegration. The evaluation of these experiments revealed up to now that there is no significant relation between some of the shock wave parameters and fragmentation efficiency. It is concluded that most of the proposed parameters do not describe well the efficacy of different lithotripter sources on concrements.

Transient response of cylindrical piezoceramics used in self focusing transducers for therapy

Piezoelectric transducers used in therapy, for example in lithotripsy, consist of several thousand cylindrical piezoceramic elements which are driven by a high voltage pulse. In order to simulate the radiated pressure signal at the transducer surface the transient behaviour of a single cylindrical piezoceramic element was investigated using finite element analysis (FEA). The realistic electrical load conditions are integrated as well as the mechanical load given by the construction. Results show that the element does not behave like a piston source. Measurements agree to simulation results very well. It is concluded that the simulation results could provide valuable information for further design improvements of therapeutic transducers.

Modeling of piezoceramic composite transducer structures generating strong sound pulses in therapy

In order to simulate composite piezoelectric structures, which are applied in self-focusing transducers for therapy, a 3-D modeling approach is presented here. Assuming a plane and infinite transducer, a finite element model can be obtained using symmetry conditions. The realistic electrical drive by high voltage pulses was also included in the simulation. Transient FEM-analysis of transducer designs with a single layer of piezoelectric ceramics and stacked layers including water loads show good agreement to measured pressure pulses. The interaction of single elements expresses in a constructive superposition of their radiated pulses at relatively large distances of a few centimeters forming a nearly plane wave front. Variations of some geometric parameters of the composite structure show the ability to influence the pulse amplitude and shape.

Simulation of enhanced absorption in ultrasound thermotherapy due to nonlinear effects

Ultrasound thermotherapy (USTT) is used to induce thermal coagulation in human tissue by high intensity focused ultrasound. The absorbed ultrasound energy mainly determines the temperature achieved. It strongly depends on the counteracting processes of nonlinear ultrasound propagation and tissue absorption. To investigate the significance of these different effects for USTT, numerical simulations provide a useful tool for treatment planning. A nonlinear full‐wave ultrasound propagation model is presented to simulate USTT. It is based on a high‐order FDTD algorithm and combines nonlinear ultrasound propagation with a broadband frequency‐power‐law absorption. Calculations of temperature distributions are done using Penne’s bioheat‐transfer equation. The propagation model is verified by a comparison of measurements and simulations for pressure signals in water and tissue mimicking materials. Simulations with different source signals demonstrate that both higher amplitude and frequency of the source signal am...

Comparison of acoustic fields produced by the original and upgraded HM‐3 lithotripter

To reduce tissue injury in shock wave lithotripsy (SWL) while maintaining satisfactory stone comminution, an original HM‐3 lithotripter was upgraded by a reflector insert to suppress large intraluminal bubble expansion, which is a primary mechanism of vascular injury in SWL. The pressure waveforms produced by the original and upgraded HM‐3 lithotripter were measured by using a fiber optical probe hydrophone (FOPH), which was scanned both along and transverse to the lithotripter axis at 1‐mm step using a computer‐controlled 3‐D positioning system. At F2, the pressure waveform produced by the upgraded HM‐3 lithotripter at 22 kV has a distinct dual‐pulse structure, with a leading shock wave of ∼45 MPa from the reflector insert and a 4‐μs delayed second pulse of ∼15 MPa reflected from the uncovered bottom surface of the original HM‐3 reflector. The beam sizes of the original and upgraded HM‐3 lithotripter are comparable in both axial and lateral directions. The pressure waveforms measured at the reflector ape...

Design of compact piezoelectric transducers for shock wave applications

The application of focused intense sound pulses to treat several orthopedic diseases has gained in importance during the past years. Self‐focusing piezoelectric transducers known from ESWL are not well suited for this purpose due to their size. Therefore compact transducers have to be designed. This implies an increase of the pressure pulse amplitude generated at the radiating surface. A stacked placement of two piezoelectric layers driven by two high‐voltage pulses with an adjustable delay accomplishes this. Several designs are presented here representing transducers of different sizes. In principle piezoelectric transducers have the ability to vary the pressure pulse shape to a wider extent than other shock wave sources. Based on FEM simulations of the transducer the influence of some driving parameters, like a variation of the interpulse delay or shape of the driving voltage, on the resulting focal pressure signal is demonstrated. The results show the feasibility to control some parameters of the signa...

Combination of finite element simulations and linear systems theory for pulse shaping of piezoelectric transducers used in therapy

A simulation procedure is presented to calculate the focal ultrasound pressure pulse from the driving voltage of a piezoelectric composite transducer or to calculate the required voltage from a given focal pressure pulse. The description of the transducer system including the driving circuit is done by linear systems theory. A transducer transfer function is derived by transient finite element simulations of the transducer structure. Focusing is assumed to be linear, which is valid for small amplitudes. Measurements validate the model.