K.W.A. van Dongen

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.

An ultrasound cylindrical phased array for deep heating in the breast: theoretical design using heterogeneous models

The objective of this theoretical study is to design an ultrasound (US) cylindrical phased array that can be used for hyperthermia (40-44 degrees C) treatment of tumours in the intact breast. Simultaneously, we characterize the influence of acoustic and thermal heterogeneities on the specific absorption rate (SAR) and temperature patterns to determine the necessity of using heterogeneous models for a US applicator design and treatment planning. Cylindrical configurations of monopole transducers are studied on their ability to generate interference patterns that can be steered electronically to the location of the target region. Hereto, design parameters such as frequency, number of transducers per ring, ring distance and number of rings are optimized to obtain a small primary focus, while suppressing secondary foci. The models account for local heterogeneities in both acoustic (wave velocity and absorption) and thermal (blood perfusion rate, heat capacity and conductivity) tissue properties. We used breast models with a central tumour (30x20x38 mm3) and an artificial thorax tumour (sphere with a radius of 25 mm) to test the design. Simulations predict that a US cylindrical phased array, consisting of six rings with 32 transducers per ring, a radius of 75 mm and 66 mm distance between the first and sixth transducer ring, operating at a frequency of 100 kHz, can be used to obtain 44 degrees C in the centre of tumours located anywhere in the intact breast. The dimensions of the volumes enclosed by the 41 degrees C iso-temperature are 19x19x21 mm3 and 21x21x32 mm3 for the central and the thorax tumours, respectively. It is demonstrated that acoustic and thermal heterogeneities do not disturb the SAR and temperature patterns.

Characterization of a photonic strain sensor in silicon-on-insulator technology

Recently there has been growing interest in sensing by means of optical microring resonators in photonic integrated circuits that are fabricated in silicon-on-insulator (SOI) technology. Taillaert et al. [Proc. SPIE 6619, 661914 (2007)] proposed the use of a silicon-waveguide-based ring resonator as a strain gauge. However, the strong lateral confinement of the light in SOI waveguides and its corresponding modal dispersion where not taken into account. We present a theoretical understanding, as well as experimental results, of strain applied on waveguide-based microresonators, and find that the following effects play important roles: elongation of the racetrack length, modal dispersion of the waveguide, and the strain-induced change in effective refractive index.

Modeling nonlinear acoustic wave fields in media with inhomogeneity in the attenuation and in the nonlinearity

Biomedical tissues usually show inhomogeneity in their acoustic medium parameters. These inhomogeneities cause refraction and scattering of diagnostic and therapeutic ultrasound waves. A method that is able to model the effects of inhomogeneity in the attenuation and in the nonlinearity is essential for the design of transducers for new ultrasound modalities and the development of novel ultrasound applications. The Iterative Nonlinear Contrast Source (INCS) method has originally been designed for the accurate modeling of nonlinear acoustic wave fields in homogeneous media. It considers the nonlinear term from the Westervelt equation as a distributed contrast source, and the corresponding integral equation is solved using an iterative Neumann scheme. This paper presents an extension of the INCS method that can handle inhomogeneity in the attenuation and in the coefficient of nonlinearity. Results are presented for the one-dimensional case. These show that in this case the presented method correctly predicts the effects related to nonlinear propagation and scattering by inhomogeneities in the attenuation and the coefficient of non-linearity.

Attenuation of ultrasound pressure fields described via contrast source formulation

Experimental data reveal that attenuation is an important phenomenon in medical ultrasound. The phenomenon is of particular importance for applications based on nonlinear propagation, as the higher frequency components of the pressure field generally experience greater attenuation. Therefore a method that is capable of modeling attenuation accurately is essential. In this paper we present a method to model attenuation via a contrast source formulation. We compare the obtained results with a version of the INCS method in which the attenuation is included in the Greens function. Both results are in excellent agreement with each other.

Subsurface imaging using measured near-field antenna footprints

Images of the subsurface are made for the detection of land-mines using a bistatic steppedfrequency continuous-wave spiral-antenna system. While the system moves along the surface, the emitted electromagnetic wavefields are scattered by objects in the subsurface and cause changes in the voltages measured at the receiver. These changes are formulated as a convolution of a sensitivity function and a complex contrast function. Within the Born approximation, this sensitivity function is equal to the inner product of the wavefield emitted by the transmitter and the field from the receiver operating in transmitting mode. For true amplitude imaging purposes, knowledge of the wavefields in the subsurface is needed. Since it is difficult to obtain a model which describes the radiation characteristics accurately, we measure the footprints of the antennae at one level in the near-field region and propagate the emitted wavefields using Huygens’ principle. We use both synthetic and experimental data to localize objects in a homogeneous space. First, we apply time-domain synthetic-aperture-radar (SAR) imaging in its most basic appearance. Next, we apply a single-step inversion algorithm to the data, where we use the measured radiation characteristics of the antenna system. This results in an increase in resolution.We refer to this method as ‘minimized back-propagation’.

Perfectly matched layers for frequency-domain integral equation acoustic scattering problems

Simulations of acoustic wavefields in inhomogeneous media are always performed on finite numerical domains. If contrasts actually extend over the domain boundaries of the numerical volume, unwanted, non-physical reflections from the boundaries will occur. One technique to suppress these reflections is to attenuate them in a locally reflectionless absorbing boundary layer enclosing the spatial computational domain, a perfectly matched layer (PML). This technique is commonly applied in time-domain simulation methods like finite element methods or finite-difference time-domain, but has not been applied to the integral equation method. In this paper, a PML formulation for the three-dimensional frequency-domain integral-equation-based acoustic scattering problem is derived. Three-dimensional acoustic scattering configurations are used to test the PML formulation. The results demonstrate that strong attenuation (a factor of 200 in amplitude) of the scattered pressure field is achieved for thin layers with a thickness of less than a wavelength, and that the PMLs themselves are virtually reflectionless. In addition, it is shown that the integral equation method, both with and without PMLs, accurately reproduces pressure fields by comparing the obtained results with analytical solutions.

Modeling acoustic wave field propagation in 3D breast models

Ultrasound is a women friendly breast cancer examination method. To facilitate the design of new imaging modalities and imaging algorithms, software is required to compute the transient acoustic pressure wave field in inhomogeneous media. A frequency domain integral equation is formulated to model attenuative acoustic wave fields in three-dimensional breast models. The method allows for multiple scattering caused by inhomogeneities in the speed of sound and attenuation. The resulting integral equation is solved using an iterative conjugate gradient scheme. The accuracy of the method is tested by comparing a plane wave scattering off a spherical contrast to an analytical solution. In addition, various simulations are performed to investigate the effect of inhomogenities in the speed of sound and attenuation on A-scans.

Modeling nonlinear medical ultrasound via a linearized contrast source method

Research on nonlinear medical ultrasound has been increased over the last decade and has resulted in a wide range of numerical methods for the modeling of the nonlinear distortion of a propagating pressure wave. However, when applied to realistic configurations, the majority of these methods are either computationally expensive or limited by the applied approximations. The Iterative Nonlinear Contrast Source (INCS) method is able to accurately compute the pulsed nonlinear pressure wave field that is generated in a large three-dimensional domain by an arbitrary transducer transmitting under a large steering angle. The method is based on the Neumann iterative solution of a nonlinear integral equation that is equivalent to the Westervelt equation. To improve the performance of the method, it would be beneficial to employ iterative schemes (e.g. Conjugate Gradient based schemes) that are efficient for solving linear integral equations. This motivates the development of a linearized version of the INCS method, as presented in this paper. To test the presented approach, a Bi-CGSTAB scheme is used to solve the linearized Westervelt equation. For the one-dimensional case, results are obtained and compared with the solution obtained with the original INCS method, and the Fubini solution. All the results have been obtained up to the third harmonic component and are in agreement with each other.