Computation of ultrasound propagation in a population of nonlinearly oscillating microbubbles including multiple scattering.

In contrast-enhanced echography, the simulation of nonlinear propagation of ultrasound through a population of oscillating microbubbles imposes a computational challenge. Also, the numerical complexity increases because each scatterer has individual properties. To address these problems, the Iterative Nonlinear Contrast Source (INCS) method has been extended to include a large population of nonlinearly responding microbubbles. The original INCS method solves the Westervelt equation in a four-dimensional spatiotemporal domain by generating increasingly accurate field corrections to iteratively update the acoustic pressure. The field corrections are computed by the convolution of a nonlinear contrast source with the Green's function of the linear background medium. Because the convolution integral allows a coarse discretization, INCS can efficiently deal with large-scale problems. To include a population of microbubbles, these are considered as individual contrast point sources with their own nonlinear response. The field corrections are computed as before, but now, in each iteration, the temporal signature of each contrast point source is computed by solving the bubble's Marmottant equation. Physically, each iteration adds an order of multiple scattering. Here, the performance of the extended INCS method and the significance of multiple scattering is demonstrated through various results from different configurations.

A spatial and temporal characterisation of single proton acoustic waves in proton beam cancer therapy.

An in vivo range verification technology for proton beam cancer therapy, preferably in real-time and with submillimeter resolution, is desired to reduce the present uncertainty in dose localization. Acoustical imaging technologies exploiting possible local interactions between protons and microbubbles or nanodroplets might be an interesting option. Unfortunately, a theoretical model capable of characterising the acoustical field generated by an individual proton on nanometer and micrometer scales is still missing. In this work, such a model is presented. The proton acoustic field is generated by the adiabatic expansion of a region that is locally heated by a passing proton. To model the proton heat deposition, secondary electron production due to protons has been quantified using a semi-empirical model based on Rutherford's scattering theory, which reproduces experimentally obtained electronic stopping power values for protons in water within 10% over the full energy range. The electrons transfer energy into heat via electron-phonon coupling to atoms along the proton track. The resulting temperature increase is calculated using an inelastic thermal spike model. Heat deposition can be regarded as instantaneous, thus, stress confinement is ensured and acoustical initial conditions are set. The resulting thermoacoustic field in the nanometer and micrometer range from the single proton track is computed by solving the thermoacoustic wave equation using k-space Green's functions, yielding the characteristic amplitudes and frequencies present in the acoustic signal generated by a single proton in an aqueous medium. Wavefield expansion and asymptotic approximations are used to extend the spatial and temporal ranges of the proton acoustic field.

Error analysis and reliability of zero-order Lamb mode inversion for waveguide characterization.

In recent years, several fitting techniques have been presented to reconstruct the parameters of a plate from its Lamb wave dispersion curves. Published studies show that these techniques can yield high accuracy results and have the potential of reconstructing several parameters at once. The precision with which parameters can be reconstructed by inverting Lamb wave dispersion curves, however, remains an open question of fundamental importance to many applications. In this work, we introduce a method of analyzing dispersion curves that yields quantitative information on the precision with which the parameters can be extracted. In our method, rather than employing error minimization algorithms, we compare a target dispersion curve to a database of theoretical ones that covers a given parameter space. By calculating a measure of dissimilarity (error) for every point in the parameter space, we reconstruct the distribution of the error in that space, beside the location of its minimum. We then introduce dimensionless quantities that describe the distribution of this error, thus yielding information about the spread of similar curves in the parameter space. We demonstrate our approach by considering both idealized and realistic scenarios, analyzing the dispersion curves obtained numerically for a plate and experimentally for a pipe. Our results show that the precision with which each parameter is reconstructed depends on the mode used, as well as the frequency range in which it is considered.

Tapering of the interventricular septum can affect ultrasound shear wave elastography: An in vitro and in silico study.

Shear wave elastography (SWE) has the potential to determine cardiac tissue stiffness from non-invasive shear wave speed measurements, important, e.g., for predicting heart failure. Previous studies showed that waves traveling in the interventricular septum (IVS) may display Lamb-like dispersive behaviour, introducing a thickness-frequency dependency in the wave speed. However, the IVS tapers across its length, which complicates wave speed estimation by introducing an additional variable to account for. The goal of this work is to assess the impact of tapering thickness on SWE. The investigation is performed by combining in vitro experiments with acoustic radiation force (ARF) and 2D finite element simulations, to isolate the effect of the tapering curve on ARF-induced and natural waves in the heart. The experiments show a 11% deceleration during propagation from the thick to the thin end of an IVS-mimicking tapered phantom plate. The numerical analysis shows that neglecting the thickness variation in the wavenumber-frequency domain can introduce errors of more than 30% in the estimation of the shear modulus, and that the exact tapering curve, rather than the overall thickness reduction, determines the dispersive behaviour of the wave. These results suggest that septal geometry should be accounted for when deriving cardiac stiffness with SWE.

Fundamental modeling of wave propagation in temporally relaxing media with applications to cardiac shear wave elastography.

Shear wave elastography (SWE) might allow non-invasive assessment of cardiac stiffness by relating shear wave propagation speed to material properties. However, after aortic valve closure, when natural shear waves occur in the septal wall, the stiffness of the muscle decreases significantly, and the effects of such temporal variation of medium properties on shear wave propagation have not been investigated yet. The goal of this work is to fundamentally investigate these effects. To this aim, qualitative results were first obtained experimentally using a mechanical setup, and were then combined with quantitative results from finite difference simulations. The results show that the amplitude and period of the waves increase during propagation, proportional to the relaxation of the medium, and that reflected waves can originate from the temporal stiffness variation. These general results, applied to literature data on cardiac stiffness throughout the heart cycle, predict as a major effect a period increase of 20% in waves propagating during a healthy diastolic phase, whereas only a 10% increase would result from the impaired relaxation of an infarcted heart. Therefore, cardiac relaxation can affect the propagation of waves used for SWE measurements and might even provide direct information on the correct relaxation of a heart.

Multiline 3D beamforming using micro-beamformed datasets for pediatric transesophageal echocardiography.

Until now, no matrix transducer has been realized for 3D transesophageal echocardiography (TEE) in pediatric patients. In 3D TEE with a matrix transducer, the biggest challenges are to connect a large number of elements to a standard ultrasound system, and to achieve a high volume rate (>200 Hz). To address these issues, we have recently developed a prototype miniaturized matrix transducer for pediatric patients with micro-beamforming and a small central transmitter. In this paper we propose two multiline parallel 3D beamforming techniques (µBF25 and µBF169) using the micro-beamformed datasets from 25 and 169 transmit events to achieve volume rates of 300 Hz and 44 Hz, respectively. Both the realizations use angle-weighted combination of the neighboring overlapping sub-volumes to avoid artifacts due to sharp intensity changes introduced by parallel beamforming. In simulation, the image quality in terms of the width of the point spread function (PSF), lateral shift invariance and mean clutter level for volumes produced by µBF25 and µBF169 are similar to the idealized beamforming using a conventional single-line acquisition with a fully-sampled matrix transducer (FS4k, 4225 transmit events). For completeness, we also investigated a 9 transmit-scheme (3 × 3) that allows even higher frame rates but found worse B-mode image quality with our probe. The simulations were experimentally verified by acquiring the µBF datasets from the prototype using a Verasonics V1 research ultrasound system. For both µBF169 and µBF25, the experimental PSFs were similar to the simulated PSFs, but in the experimental PSFs, the clutter level was ~10 dB higher. Results indicate that the proposed multiline 3D beamforming techniques with the prototype matrix transducer are promising candidates for real-time pediatric 3D TEE.

A sensitive optical micro-machined ultrasound sensor (OMUS) based on a silicon photonic ring resonator on an acoustical membrane.

With the increasing use of ultrasonography, especially in medical imaging, novel fabrication techniques together with novel sensor designs are needed to meet the requirements for future applications like three-dimensional intercardiac and intravascular imaging. These applications require arrays of many small elements to selectively record the sound waves coming from a certain direction. Here we present proof of concept of an optical micro-machined ultrasound sensor (OMUS) fabricated with a semi-industrial CMOS fabrication line. The sensor is based on integrated photonics, which allows for elements with small spatial footprint. We demonstrate that the first prototype is already capable of detecting pressures of 0.4 Pa, which matches the performance of the state of the art piezo-electric transducers while having a 65 times smaller spatial footprint. The sensor is compatible with MRI due to the lack of electronical wiring. Another important benefit of the use of integrated photonics is the easy interrogation of an array of elements. Hence, in future designs only two optical fibers are needed to interrogate an entire array, which minimizes the amount of connections of smart catheters. The demonstrated OMUS has potential applications in medical ultrasound imaging, non destructive testing as well as in flow sensing.

Single pulse frequency compounding protocol for superharmonic imaging.

Second harmonic imaging is currently accepted as the standard in commercial echographic systems. A new imaging technique, coined as superharmonic imaging (SHI), combines the third till the fifth harmonics, arising during nonlinear sound propagation. It could further enhance the resolution and quality of echographic images. To meet the bandwidth requirement for SHI a dedicated phased array has been developed: a low frequency subarray, intended for transmission, interleaved with a high frequency subarray, used in reception. As the bandwidth of the elements is limited, the spectral gaps in between the harmonics cause multiple (ghost) reflection artifacts. A dual-pulse frequency compounding method aims at suppressing those artifacts at a price of a reduced frame rate. In this study we explore a possibility of performing frequency compounding within a single transmission. The traditional frequency compounding method suppresses the ripples by consecutively emitting two short Gaussian bursts with a slightly different center frequency. In the newly proposed method, the transmit aperture is divided into two parts: the first half is used to send a pulse at the lower center frequency, while the other half simultaneously transmits at a slightly higher center frequency. The suitability of the protocol for medical imaging applications in terms of the steering capabilities was performed in a simulation study with INCS and the hydrophone measurements. Moreover, an experimental study was carried out to find the optimal parameters for the clinical imaging protocol. The latter was subsequently used to obtain the images of a tissue mimicking phantom containing strongly reflecting wires. Additionally, the images of a human heart in the parasternal projection were acquired. The scanning aperture with the developed protocol amounts to approximately 90°, which is sufficient to capture the cardiac structures in the standard anatomical projections. The theoretically estimated and experimentally measured grating lobe levels are equal to -28.3 dB and -35.9 dB, respectively. A considerable improvement in the axial resolution of the SHI component (0.73 mm) at -6 dB in comparison with the third harmonic (2.23 mm) was observed. A similar comparison in terms of the lateral resolution slightly favored the superharmonic component by 0.2 mm. Additionally, the images of the tissue mimicking phantom exhibited the absence of the multiple reflection artifacts. The in-vivo acquisition allows one to clearly observe the dynamic of the mitral valve leaflets. The new method is equally effective in eliminating the ripple artifacts associated with SHI as the dual-pulse technique, while the full frame rate is maintained.

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.

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 Green's 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.