Martin D. Verweij

Acoustic droplet vaporization is initiated by superharmonic focusing.

Significance This work explains the long-standing puzzle of the physical mechanisms underlying acoustic droplet vaporization (ADV). ADV makes use of low-boiling-point perfluorocarbon droplets that become metastable once injected into the body, where they can be activated by high-intensity ultrasound. How ultrasound can physically trigger the vaporization remained elusive, also given the large mismatch between the ultrasound wavelength and the droplet size. Here we show that vaporization is preceded by nonlinear propagation of the ultrasound wave generating superharmonics. These high-frequency waves focus efficiently within the droplet, triggering vaporization. ADV shows great potential for advanced medical diagnosis and therapy. Our new understanding allows for further reduction of the required pressure amplitudes, thereby minimizing the adverse effects on healthy tissue. Acoustically sensitive emulsion droplets composed of a liquid perfluorocarbon have the potential to be a highly efficient system for local drug delivery, embolotherapy, or for tumor imaging. The physical mechanisms underlying the acoustic activation of these phase-change emulsions into a bubbly dispersion, termed acoustic droplet vaporization, have not been well understood. The droplets have a very high activation threshold; its frequency dependence does not comply with homogeneous nucleation theory and localized nucleation spots have been observed. Here we show that acoustic droplet vaporization is initiated by a combination of two phenomena: highly nonlinear distortion of the acoustic wave before it hits the droplet and focusing of the distorted wave by the droplet itself. At high excitation pressures, nonlinear distortion causes significant superharmonics with wavelengths of the order of the droplet size. These superharmonics strongly contribute to the focusing effect; therefore, the proposed mechanism also explains the observed pressure thresholding effect. Our interpretation is validated with experimental data captured with an ultrahigh-speed camera on the positions of the nucleation spots, where we find excellent agreement with the theoretical prediction. Moreover, the presented mechanism explains the hitherto counterintuitive dependence of the nucleation threshold on the ultrasound frequency. The physical insight allows for the optimization of acoustic droplet vaporization for therapeutic applications, in particular with respect to the acoustic pressures required for activation, thereby minimizing the negative bioeffects associated with the use of high-intensity ultrasound.

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 Greens 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.

A contrast source method for nonlinear acoustic wave fields in media with spatially inhomogeneous attenuation

Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.

Parallel transmit beamforming using orthogonal frequency division multiplexing applied to harmonic Imaging-A feasibility study

Real-time 2-D or 3-D ultrasound imaging systems are currently used for medical diagnosis. To achieve the required data acquisition rate, these systems rely on parallel beamforming, i.e., a single wide-angled beam is used for transmission and several narrow parallel beams are used for reception. When applied to harmonic imaging, the demand for high-amplitude pressure wave fields, necessary to generate the harmonic components, conflicts with the use of a wide-angled beam in transmission because this results in a large spatial decay of the acoustic pressure. To enhance the amplitude of the harmonics, it is preferable to do the reverse: transmit several narrow parallel beams and use a wide-angled beam in reception. Here, this concept is investigated to determine whether it can be used for harmonic imaging. The method proposed in this paper relies on orthogonal frequency division multiplexing (OFDM), which is used to create distinctive parallel beams in transmission. To test the proposed method, a numerical study has been performed, in which the transmit, receive, and combined beam profiles generated by a linear array have been simulated for the second-harmonic component. Compared with standard parallel beamforming, application of the proposed technique results in a gain of 12 dB for the main beam and in a reduction of the side lobes. Experimental verification in water has also been performed. Measurements obtained with a single-element emitting transducer and a hydrophone receiver confirm the possibility of exciting a practical ultrasound transducer with multiple Gaussian modulated pulses, each having a different center frequency, and the capability to generate distinguishable second-harmonic components.

A filtered convolution method for the computation of acoustic wave fields in very large spatiotemporal domains

The full-wave computation of transient acoustic fields with sizes in the order of 100 x 100 x 100 wavelengths by 100 periods requires a numerical method that is extremely efficient in terms of storage and computation. Iterative integral equation methods offer a good performance on these points, provided that the recurring spatiotemporal convolutions are computed with a coarse sampling and relatively few computational operations. This paper describes a method for the numerical evaluation of very large-scale, four-dimensional convolutions that employs a fast Fourier transformation and that uses a sampling rate close to or at the limit of two points per wavelength and per period. To achieve this, the functions involved are systematically filtered, windowed, and zero-padded with respect to all relevant coordinates prior to sampling. The method is developed in the context of the Neumann iterative solution of the acoustic contrast source problem for an inhomogeneous medium. The implementation of the method on a parallel computer is discussed. The obtained numerical results have a relative root mean square error of a few percent when sampling at two points per wavelength and per period. Further, the results prove that the method enables the computation of transient fields in the order of the indicated size.

Characterization of Integrated Optical Strain Sensors Based on Silicon Waveguides

Microscale strain gauges are widely used in micro electro-mechanical systems (MEMS) to measure strains such as those induced by force, acceleration, pressure or sound. We propose all-optical strain sensors based on micro-ring resonators to be integrated with MEMS. We characterized the strain-induced shift of the resonances of such devices. Depending on the width of the waveguide and the orientation of the silicon crystal, the linear wavelength shift per applied strain varies between 0.5 and 0.75 pm/microstrain for infrared light around 1550 nm wavelength. The influence of the increasing ring circumference is about three times larger than the influence of the change in waveguide effective index, and the two effects oppose each other. The strong dispersion in 220 nm high silicon sub-wavelength waveguides accounts for a decrease in sensitivity of a factor 2.2 to 1.4 for waveguide widths of 310 nm to 860 nm. These figures and insights are necessary for the design of strain sensors based on silicon waveguides.

A feasibility study for non-invasive thermometry using non-linear ultrasound

Purpose: High intensity focused ultrasound (HIFU) is used during hyperthermia cancer treatment to increase the tumour temperature. For an adequate and safe application it is important to measure the temperature in the heated region, preferably in a non-invasive manner and by the same modality as used for heating. The goal of this feasibility study is two-fold; first, it is investigated whether the acoustic non-linearity parameter B/A is most suitable for measuring temperature changes, second, a non-invasive thermometry method based on B/A is proposed and demonstrated. Material and methods: Water is used to confirm that B/A is a sensitive acoustic medium parameter that is practically applicable for non-invasive thermometry. Next, a thermometry method is proposed that employs the ratios between the fundamental and the higher harmonic frequency components of a non-linear acoustic wave. The method determines these ratios for a measured acoustic pulse that has traversed a certain medium, and compares these with temperature dependent reference ratios for the same medium. The method is demonstrated using simulated measurements of an acoustic plane wave propagating in glycerol. Results: Results obtained for water show that B/A is more sensitive for temperature changes than other practical acoustic parameters. For a combination of 16 simulated measurements, it is demonstrated that temperature can be predicted non-invasively with zero bias and a standard deviation of 2°C if the noise level does not exceed −40 dB. Conclusion: The suitability of B/A as a basis for non-invasive thermometry is confirmed, and a non-invasive thermometry method based on B/A is proposed and successfully demonstrated.

A Prototype PZT Matrix Transducer With Low-Power Integrated Receive ASIC for 3-D Transesophageal Echocardiography

This paper presents the design, fabrication, and experimental evaluation of a prototype lead zirconium titanate (PZT) matrix transducer with an integrated receive ASIC, as a proof of concept for a miniature three-dimensional (3-D) transesophageal echocardiography (TEE) probe. It consists of an array of 9 × 12 piezoelectric elements mounted on the ASIC via an integration scheme that involves direct electrical connections between a bond-pad array on the ASIC and the transducer elements. The ASIC addresses the critical challenge of reducing cable count, and includes front-end amplifiers with adjustable gains and microbeamformer circuits that locally process and combine echo signals received by the elements of each 3 × 3 subarray. Thus, an order-of-magnitude reduction in the number of receive channels is achieved. Dedicated circuit techniques are employed to meet the strict space and power constraints of TEE probes. The ASIC has been fabricated in a standard 0.18-μm CMOS process and consumes only 0.44 mW/channel. The prototype has been acoustically characterized in a water tank. The ASIC allows the array to be presteered across ±37° while achieving an overall dynamic range of 77 dB. Both the measured characteristics of the individual transducer elements and the performance of the ASIC are in good agreement with expectations, demonstrating the effectiveness of the proposed techniques.

Optimization of a phased-array transducer for multiple harmonic imaging in medical applications: frequency and topology

Second-harmonic imaging is currently one of the standards in commercial echographic systems for diagnosis, because of its high spatial resolution and low sensitivity to clutter and near-field artifacts. The use of nonlinear phenomena mirrors is a great set of solutions to improve echographic image resolution. To further enhance the resolution and image quality, the combination of the 3rd to 5th harmonics - dubbed the superharmonics - could be used. However, this requires a bandwidth exceeding that of conventional transducers. A promising solution features a phased-array design with interleaved low- and high-frequency elements for transmission and reception, respectively. Because the amplitude of the backscattered higher harmonics at the transducer surface is relatively low, it is highly desirable to increase the sensitivity in reception. Therefore, we investigated the optimization of the number of elements in the receiving aperture as well as their arrangement (topology). A variety of configurations was considered, including one transmit element for each receive element (1/2) up to one transmit for 7 receive elements (1/8). The topologies are assessed based on the ratio of the harmonic peak pressures in the main and grating lobes. Further, the higher harmonic level is maximized by optimization of the center frequency of the transmitted pulse. The achievable SNR for a specific application is a compromise between the frequency-dependent attenuation and nonlinearity at a required penetration depth. To calculate the SNR of the complete imaging chain, we use an approach analogous to the sonar equation used in underwater acoustics. The generated harmonic pressure fields caused by nonlinear wave propagation were modeled with the iterative nonlinear contrast source (INCS) method, the KZK, or the Burgers equation. The optimal topology for superharmonic imaging was an interleaved design with 1 transmit element per 6 receive elements. It improves the SNR by ~5 dB compared with the interleaved (1/2) design reported in literature. The optimal transmit frequency for superharmonic echocardiography was found to be 1.0 to 1.2 MHz. For superharmonic abdominal imaging this frequency was found to be 1.7 to 1.9 MHz. For 2nd-harmonic echocardiography, the optimal transmit frequency of 1.8 MHz reported in the literature was corroborated with our simulation results.

Green's function method for modeling nonlinear three-dimensional pulsed acoustic fields in diagnostic ultrasound including tissue-like attenuation

The iterative nonlinear contrast source (INCS) method, developed previously to predict the nonlinear acoustic pressure field excited by a medical diagnostic phased array transducer in a lossless medium, is extended to deal with media showing attenuation of a frequency power law type. For a linear case, comparison shows an excellent agreement between the results of the extended INCS method and the FieldII program. For a nonlinear case, the INCS method is used to show that the axial field profile of the second harmonic component in a medium with a frequency power law attenuation with a power b = 1.14 differs considerably from the field profiles in a lossless medium and in a medium with b = 2, i.e. square power law attenuation.