Koen W. A. van Dongen

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 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.

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.

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.

Extension of Marcatili's Analytical Approach for Rectangular Silicon Optical Waveguides

Marcatilis famous approximate analytical description of light propagating through rectangular dielectric waveguides, published in 1969, gives accurate results for low-index-contrast waveguides. However, photonic-integrated circuit technology has advanced to high-index-contrast (HIC) waveguides. In this paper, we improve Marcatilis model by adjusting the amplitudes of the components of the electromagnetic fields in his description. We find that Marcatilis eigenvalue equation for the propagation constant is also valid for HIC waveguides. Our improved method shows much better agreement with rigorous numerical simulations, in particular for the case of HIC waveguides. We also derive explicit expressions for the effective group index and the effects of external forces on the propagation constant. Furthermore, with our method, the phenomenon of avoided crossing of modes is observed and studied.

Modeling three-dimensional nonlinear acoustic wave fields in media with spatially varying coefficient of nonlinearity, attenuation and speed of sound

Numerical methods capable of modeling nonlinear pressure wave fields propagating through inhomogeneous biomedical tissue are essential for the design and optimization of ultrasound transducers or devices. The Iterative Nonlinear Contrast Source (INCS) method is an accurate method for modeling three-dimensional nonlinear acoustic wave fields. Originally it was capable of modeling nonlinear wave fields in homogeneous lossy tissue. Recently, it has been extended to deal with spatially varying coefficient of nonlinearity and attenuation. The method recasts a generalized form of the Westervelt equation into an integral equation which was originally solved using a Neumann scheme. This scheme allows to model moderate losses and nonlinearity. Problems with the convergence may occur for realistic speed of sound contrast. Here, we present a different solution method which makes it possible to treat, besides spatially varying coefficient of nonlinearity and attenuation, also realistic speed of sound contrasts. The nonlinear integral equation is solved using a steepest descent scheme. The method has been used to compute the three-dimensional nonlinear pressure wave field generated by a 40 element linear array and propagating through a medium with spatially varying coefficient of nonlinearity, attenuation and speed of sound. Simulations have been performed up to the 5th harmonic component.

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.

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.

Sensitivity study of the acoustic nonlinearity parameter for measuring temperatures during High Intensity Focused Ultrasound treatment

The aim of High Intensity Focused Ultrasound (HIFU) is to locally increase the temperature in a body. For an adequate application of the treatment it is important to measure non‐invasively the temperature profiles in the heated region. Most efficiently, this is done with the same modality as being used for heating. Consequently, the preferred measuring method should rely on the temperature dependence of an acoustic medium parameter. The goal of this study is to determine which parameter is most sensitive to temperature changes. To find the most suitable parameter, the temperature dependence of the speed of sound (SOS), the density of mass and the acoustic nonlinearity parameter B/A are compared for water. The temperature dependence of the SOS and the mass density are obtained by interpolating values found in literature. Since measured values of the B/A parameter are only known for a few coarsely distributed temperature values, it has been synthesised from a two‐dimensional function describing the SOS vers...

Wave equation based transmission tomography

For iterative image reconstruction of transmission tomography we apply the paraxial approximation of the Helmholtz equation for a spherical transducer arrangement. We choose this approach due to its three order of magnitude lower complexity than full wave solutions with the same precision for transmission tomography. In homogeneous media we prove that our forward solution is exact. With the help of this forward solution 2D and 3D ultrasound measurements could be simulated for transmission tomography. 2D reconstructions of a breast-like numerical phantom had a deviation in sound speed of 0.14 m/s and a deviation in attenuation of 6.5% from the ground truth. Applications up to now are breast cancer diagnostics and non-destructive testing.