Seismic and medical ultrasound imaging of velocity and density variations by nonlinear vectorial inverse scattering.

We present an iterative nonlinear inverse scattering algorithm for high-resolution acoustic imaging of density and velocity variations. To solve the multi-parameter nonlinear direct scattering problem, the acoustic wave equation for inhomogeneous media in the frequency domain is transformed into a vectorial integral equation of the Lippmann-Schwinger type for the combined pressure and pressure-gradient field. To solve the multi-parameter nonlinear inverse scattering problem, we use the Newton-Kantorovich method in conjunction with matrix-free representations of the Fréchet derivative operators and their adjoints. The approximate Hessian information that is accounted for in our iterative solution of the (nonlinear) multi-parameter inverse scattering problem is essential for the mitigation of multi-parameter cross talk effects. Numerical examples related to seismic and medical ultrasound breast imaging illustrate the performance of the new algorithm for multi-parameter acoustic imaging.

Multi-parameter inversion with the aid of particle velocity field reconstruction.

Multi-parameter inversion for medical ultrasound leads to an improved tissue classification. In general, simultaneous reconstruction of volume density of mass and compressibility would require knowledge of the particle velocity field along with the pressure field. However, in practice the particle velocity field is not measured. Here, the authors propose a method for multi-parameter inversion where the particle velocity field is reconstructed from the measured pressure field. To this end, the measured pressure field is described using outward propagating Hankel functions. For a synthetic setup, it is shown that the reconstructed particle velocity field matches the forward modelled particle velocity field. Next, the reconstructed particle velocity field is used together with the synthetically measured pressure field to reconstruct density and compressibility profiles with the aid of contrast source inversion. Finally, comparing the reconstructed speed of sound profiles obtained via single-parameter versus multi-parameter inversion shows that multi-parameter outperforms single-parameter inversion with respect to accuracy and stability.

On-chip silicon Mach-Zehnder interferometer sensor for ultrasound detection.

A highly sensitive ultrasound sensor based on an integrated photonics Mach-Zehnder interferometer (MZI) fabricated in silicon-on-insulator technology is reported. The sensing spiral is located on a membrane of size 121 µm×121 µm. Ultrasound waves excite the membrane's vibrational mode, which translates to modulation of the MZI transmission. The measured sensor transfer function is centered at 0.47 MHz and has a -6 dB bandwidth of 21.2%. The sensor sensitivity is linear in the optical input power and reaches a maximum 0.62 mV/Pa, which is limited by the interrogation method. At 0.47 MHz and for an optical power of 1.0 mW the detection limit is 0.38 mPa/Hz1/2 and the dynamic range is 59 dB. The MZI's gradual transmission function allows a wide range of wavelength operation points. This strongly facilitates sensor use and is promising for applications.

Wavefield finite time focusing with reduced spatial exposure.

Wavefield focusing is often achieved by time-reversal mirrors, where wavefields emitted by a source located at the focal point are evaluated at a closed boundary and sent back, after time-reversal, into the medium from that boundary. Mathematically, time-reversal mirrors are derived from closed-boundary integral representations of reciprocity theorems. In heterogeneous media, time-reversal focusing theoretically involves in- and output signals that are infinite in time and the resulting waves propagate through the entire medium. Recently, integral representations have been derived for single-sided wavefield focusing. Although the required input signals for this approach are finite in time, the output signals are not and, similar to time-reversal mirroring, the resulting waves propagate through the entire medium. Here, an alternative solution for double-sided wavefield focusing is derived. This solution is based on an integral representation where in- and output signals are finite in time, and where the energy of the waves propagating in the layer embedding the focal point is smaller than with time-reversal focusing. The potential of the proposed method is explored with numerical experiments involving a head model consisting of a skull enclosing a brain.

Sparsity constrained contrast source inversion.

Ultrasound imaging is used for detecting and characterizing breast lesions. A state of the art imaging method is the contrast source inversion (CSI), which solves the full wave nonlinear inverse problem. However, when the measurements are acquired in noisy environments, CSI can diverge from the correct solution after several iterations. Problems associated with noisy data were originally solved by including total variation (TV) regularization. Unfortunately, for very noisy data, TV regularization alone is not sufficient. In this work, compressed sensing ideas are used to regularize the inversion process by restricting the solution of the CSI method to be sparse in a transformation domain. The proposed method estimates the contrast source and contrast function by minimizing the mean squared error between the measured and modeled data. An extra penalty term is added to measure sparsity in the transformation domain. A second method that combines sparsity of the contrast source and minimal TV in the contrast function is also presented. The proposed methods are tested on noise-free and noisy synthetic data sets representing a scan of a cancerous breast. Numerical experiments show that, for measurements contaminated with 1% noise, the sparsity constrained CSI improves the normalized mean squared error of the reconstructed speed-of-sound profiles up to 36% in comparison with traditional CSI. Also, for measurements contaminated with 5% noise, the proposed methods improve the quality of the reconstruction up to 70% in comparison with the traditional CSI method. Experimental results also show that the methods remain convergent to the correct speed-of-sound profile as the number of iterations increases.

A novel ultrasound technique for detection of osteochondral defects in the ankle joint: a parametric and feasibility study.

(Osteo)chondral defects (OCDs) in the ankle are currently diagnosed with modalities that are not convenient to use in long-term follow-ups. Ultrasound (US) imaging, which is a cost-effective and non-invasive alternative, has limited ability to discriminate OCDs. We aim to develop a new diagnostic technique based on US wave propagation through the ankle joint. The presence of OCDs is identified when a US signal deviates from a reference signal associated with the healthy joint. The feasibility of the proposed technique is studied using experimentally-validated 2D finite-difference time-domain models of the ankle joint. The normalized maximum cross correlation of experiments and simulation was 0.97. Effects of variables relevant to the ankle joint, US transducers and OCDs were evaluated. Variations in joint space width and transducer orientation made noticeable alterations to the reference signal: normalized root mean square error ranged from 6.29% to 65.25% and from 19.59% to 8064.2%, respectively. The results suggest that the new technique could be used for detection of OCDs, if the effects of other parameters (i.e., parameters related to the ankle joint and US transducers) can be reduced.

Computation of nonlinear ultrasound fields using a linearized contrast source method.

Nonlinear ultrasound is important in medical diagnostics because imaging of the higher harmonics improves resolution and reduces scattering artifacts. Second harmonic imaging is currently standard, and higher harmonic imaging is under investigation. The efficient development of novel imaging modalities and equipment requires accurate simulations of nonlinear wave fields in large volumes of realistic (lossy, inhomogeneous) media. The Iterative Nonlinear Contrast Source (INCS) method has been developed to deal with spatiotemporal domains measuring hundreds of wavelengths and periods. This full wave method considers the nonlinear term of the Westervelt equation as a nonlinear contrast source, and solves the equivalent integral equation via the Neumann iterative solution. Recently, the method has been extended with a contrast source that accounts for spatially varying attenuation. The current paper addresses the problem that the Neumann iterative solution converges badly for strong contrast sources. The remedy is linearization of the nonlinear contrast source, combined with application of more advanced methods for solving the resulting integral equation. Numerical results show that linearization in combination with a Bi-Conjugate Gradient Stabilized method allows the INCS method to deal with fairly strong, inhomogeneous attenuation, while the error due to the linearization can be eliminated by restarting the iterative scheme.

Simulation-to-real generalization for deep-learning-based refraction-corrected ultrasound tomography image reconstruction.

Objective. The image reconstruction of ultrasound computed tomography is computationally expensive with conventional iterative methods. The fully learned direct deep learning reconstruction is promising to speed up image reconstruction significantly. However, for direct reconstruction from measurement data, due to the lack of real labeled data, the neural network is usually trained on a simulation dataset and shows poor performance on real data because of the simulation-to-real gap.Approach. To improve the simulation-to-real generalization of neural networks, a series of strategies are developed including a Fourier-transform-integrated neural network, measurement-domain data augmentation methods, and a self-supervised-learning-based patch-wise preprocessing neural network. Our strategies are evaluated on both the simulation dataset and real measurement datasets from two different prototype machines.Main results. The experimental results show that our deep learning methods help to improve the neural networks' robustness against noise and the generalizability to real measurement data.Significance. Our methods prove that it is possible for neural networks to achieve superior performance to traditional iterative reconstruction algorithms in imaging quality and allow for real-time 2D-image reconstruction. This study helps pave the path for the application of deep learning methods to practical ultrasound tomography image reconstruction based on simulation datasets.

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.

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.

Redatuming of 2-D Wave Fields Measured on an Arbitrary-Shaped Closed Aperture.

Whole-breast ultrasound scanning systems are used to screen a women's breast for suspicious lesions. Typically, the transducers are located at fixed positions at relatively large distances from the breast to avoid any contact with the breast. Unfortunately, these large distances give rise to large spatial domains to be imaged. These large domains hamper the applicability of imaging by inversion. To reduce the size of the spatial computational domain, we present a 2-D redatuming method based on the Hankel decomposition of the measured field. With this method, the field measured over an arbitrary-shaped closed curve can be redatumed to a new curve enclosing a smaller spatial domain. Additional advantages of the proposed method are that it allows to account for the finite size and orientation of a transducer and that it is robust to noise. The proposed method is successfully validated using the synthetic and measured data, and the results show that the recorded field can be redatumed to any position in the embedding.

Ultrasound transmission tomography image reconstruction with a fully convolutional neural network.

Image reconstruction of ultrasound computed tomography based on the wave equation is able to show much more structural details than simpler ray-based image reconstruction methods. However, to invert the wave-based forward model is computationally demanding. To address this problem, we develop an efficient fully learned image reconstruction method based on a convolutional neural network. The image is reconstructed via one forward propagation of the network given input sensor data, which is much faster than the reconstruction using conventional iterative optimization methods. To transform the ultrasound measured data in the sensor domain into the reconstructed image in the image domain, we apply multiple down-scaling and up-scaling convolutional units to efficiently increase the number of hidden layers with a large receptive and projective field that can cover all elements in inputs and outputs, respectively. For dataset generation, a paraxial approximation forward model is used to simulate ultrasound measurement data. The neural network is trained with a dataset derived from natural images in ImageNet and tested with a dataset derived from medical images in OA-Breast Phantom dataset. Test results show the superior efficiency of the proposed neural network to other reconstruction algorithms including popular neural networks. When compared with conventional iterative optimization algorithms, our neural network can reconstruct a 110 × 86 image more than 20 times faster on a CPU and 1000 times faster on a GPU with comparable image quality and is also more robust to noise.

Ultrasonic Synthetic-Aperture Interface Imaging.

Synthetic-aperture (SA) imaging is a popular method to visualize the reflectivity of an object from ultrasonic reflections. The method yields an image of the (volume) contrast in acoustic impedance with respect to the embedding. Typically, constant mass density is assumed in the underlying derivation. Due to the band-limited nature of the recorded data, the image is blurred in space, which is quantified by the associated point spread function. SA volume imaging is valid under the Born approximation, where it is assumed that the contrast is weak. When objects are large with respect to the wavelength, it is questionable whether SA volume imaging should be the method-of-choice. Herein, we propose an alternative solution that we refer to as SA interface imaging. This approach yields a vector image of the discontinuities of acoustic impedance at the tissue interfaces. Constant wave speed is assumed in the underlying derivation. The image is blurred in space by a tensor, which we refer to as the interface spread function. SA interface imaging is valid under the Kirchhoff approximation, where it is assumed that the wavelength is small compared to the spatial dimensions of the interfaces. We compare the performance of volume and interface imaging on synthetic data and on experimental data of a gelatin cylinder with a radius of 75 wavelengths, submerged in water. As expected, the interface image peaks at the gelatin-water interface, while the volume image exposes a peak and trough on opposing sides of the interface.

A Broadband Polyvinylidene Difluoride-Based Hydrophone with Integrated Readout Circuit for Intravascular Photoacoustic Imaging.

Intravascular photoacoustic (IVPA) imaging can visualize the coronary atherosclerotic plaque composition on the basis of the optical absorption contrast. Most of the photoacoustic (PA) energy of human coronary plaque lipids was found to lie in the frequency band between 2 and 15 MHz requiring a very broadband transducer, especially if a combination with intravascular ultrasound is desired. We have developed a broadband polyvinylidene difluoride (PVDF) transducer (0.6 × 0.6 mm, 52 µm thick) with integrated electronics to match the low capacitance of such a small polyvinylidene difluoride element (<5 pF/mm(2)) with the high capacitive load of the long cable (∼100 pF/m). The new readout circuit provides an output voltage with a sensitivity of about 3.8 µV/Pa at 2.25 MHz. Its response is flat within 10 dB in the range 2 to 15 MHz. The root mean square (rms) output noise level is 259 µV over the entire bandwidth (1-20 MHz), resulting in a minimum detectable pressure of 30 Pa at 2.25 MHz.

Comparing different ultrasound imaging methods for breast cancer detection.

Ultrasound is frequently used to evaluate suspicious masses in breasts. These evaluations could be improved by taking advantage of advanced imaging algorithms, which become feasible for low frequencies if accurate knowledge about the phase and amplitude of the wave field illuminating the volume of interest is available. In this study, we compare five imaging and inversion methods: time-of-flight tomography, synthetic aperture focusing technique, backpropagation, Born inversion, and contrast source inversion. All methods are tested on the same full-wave synthetic data representing a 2-D scan using a circular array enclosing a cancerous breast submerged in water. Of the tested methods, only contrast source inversion yielded an accurate reconstruction of the speed-ofsound profile of the tumor and its surroundings, because only this method takes effects such as multiple scattering, refraction, and diffraction into account.

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.

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.

A full vectorial contrast source inversion scheme for three-dimensional acoustic imaging of both compressibility and density profiles.

Imaging the two acoustic medium parameters density and compressibility requires the use of both the acoustic pressure and velocity wave fields, described via integral equations. Imaging is based on solving for the unknown medium parameters using known measured scattered wave fields, and it is difficult to solve this ill-posed inverse problem directly using a conjugate gradient inversion scheme. Here, a contrast source inversion method is used in which the contrast sources, defined via the product of changes in compressibility and density with the pressure and velocity wave fields, respectively, are computed iteratively. After each update of the contrast sources, an update of the medium parameters is obtained. Total variation as multiplicative regularization is used to minimize blurring in the reconstructed contrasts. The method successfully reconstructed three-dimensional contrast profiles based on changes in both density and compressibility, using synthetic data both with and without 50% white noise. The results were compared with imaging based only on the pressure wave field, where speed of sound profiles were solely based on changes in compressibility. It was found that the results improved significantly by using the full vectorial method when changes in speed of sound depended on changes in both compressibility and density.

A forward model and conjugate gradient inversion technique for low-frequency ultrasonic imaging.

Emerging methods of hyperthermia cancer treatment require noninvasive temperature monitoring, and ultrasonic techniques show promise in this regard. Various tomographic algorithms are available that reconstruct sound speed or contrast profiles, which can be related to temperature distribution. The requirement of a high enough frequency for adequate spatial resolution and a low enough frequency for adequate tissue penetration is a difficult compromise. In this study, the feasibility of using low frequency ultrasound for imaging and temperature monitoring was investigated. The transient probing wave field had a bandwidth spanning the frequency range 2.5-320.5 kHz. The results from a forward model which computed the propagation and scattering of low-frequency acoustic pressure and velocity wave fields were used to compare three imaging methods formulated within the Born approximation, representing two main types of reconstruction. The first uses Fourier techniques to reconstruct sound-speed profiles from projection or Radon data based on optical ray theory, seen as an asymptotical limit for comparison. The second uses backpropagation and conjugate gradient inversion methods based on acoustical wave theory. The results show that the accuracy in localization was 2.5 mm or better when using low frequencies and the conjugate gradient inversion scheme, which could be used for temperature monitoring.