In full waveform inversion (FWI) for ultrasound computed tomography (CT), choosing the right sound source is essential for generating high-resolution images. We developed an optimized source estimation method for FWI to efficiently reduce the value of any cost function and evaluated its performance using simulation data and measurement data. In our optimized source estimation method, we obtain the sound source as α(k)·f, where f is a sound source (an arbitrary complex value), coefficient α(k) is cos(θk)+i·sin(θk), k is integer (0, 1, ⋯, N-1), θk is 2π/N·k, and the integer value of N is 360. We then determine the coefficient α(k) that minimizes the value of the cost function. In contrast to conventional source estimation, which only minimizes the value of the L2 norm cost function, our proposed source estimation can minimize the values of any cost function, such as the L1 norm or a hybrid of L1 and L2 norms. The advantage of our method is that it can be easily applied to FWI with various cost functions. In this preliminary study, we implemented FWI with the L2 norm cost function and compared the performance of our proposed method with that of the conventional method. In the simulation study, FWI with both the conventional and proposed source estimation methods improved the contrasts of inclusions of a numerical phantom compared to FWI with no source estimation. They both also improved the contrasts of inclusions of a measured oil-gel-based phantom compared to a bent-ray reconstruction method. The absolute mean errors between ROI and true values were 39, 11, and 11 [m/s] for the bent-ray reconstruction method, FWI with the conventional method, and FWI with the proposed method, respectively. In addition, FWI with both the conventional and proposed methods improved the contrasts of a patient’s tumor compared to the bentray reconstruction method. These results demonstrate that FWI with the proposed source estimation method can provide the same contrast and quantitative accuracy as FWI with the conventional source estimation method.
The performance of a reconstruction method in ultrasound computed tomography (CT) ideally should be evaluated using various kinds of phantoms at a wide range of speeds of sound when inclusions are made. However, generating real phantoms is more time consuming than generating simulated ones. In our previous study, we developed an oil-gel-based phantom by including water or salt water. In this study, we designed an evaluation method including various contrast conditions using the oil-gel-based phantom by changing the liquid and temperature. The phantom including water or salt water in 10-, 7-, 5-, or 3-mm holes was measured using our prototype ultrasound CT at temperatures of 15, 17.5, 20, 22.5, 25, 27.5, and 30°C, making the number of measurements 14. For these conditions, the difference (= contrast) in the speed of sound between the inclusions and the oil gel was −37 to 92 [m/s]. The filtered back projection (FBP) and full waveform inversion (FWI) were evaluated. The mean error of the speeds of sound in inclusions with the FBP and FWI were 17.1 ± 14.9 and 8.8 ± 10.1 [m/s], respectively. The mean percentage error of the sizes of the phantom (51 mm) and inclusions with the FBP and FWI were 22.5 ± 22.5% and 3.9 ± 4.3%, respectively. A single oil-gel-based phantom provided various contrast conditions after the temperature and liquid were changed. This kind of phantom can be used for comprehensive quantitative evaluations of the reconstruction method.
We are performing clinical studies on breast cancer examinations at Hokkaido University Hospital with an ultrasound computed tomography (USCT) system. Our studies have revealed that some reflection images exhibit intensity inhomogeneity because ultrasound waves, shot by a 1-D ring array transducer, go non-vertically into the object surface. This trend significantly increases the burden of interpretation. Therefore, we developed a calibration method to remove this heterogeneity based on the distribution of the incident angle of waves that are estimated from the slope of the subject surface morphologically extracted from multi-slice reflection images. Results showed that applying this correction method to clinical images enabled the image contrast and uniformity to be successfully recovered.
For breast cancer imaging by ultrasound computed tomography (CT) without dependence on patient breast size, we previously developed a high-sensitivity scan method in which a virtual fan-beam (vfan-beam) is generated from ultrasound waves emitted from 128 sources with unique delay times. Full waveform inversion (FWI) with multiple sound sources has not been previously applied to ultrasound CT using a ring transducer array. We have now developed a FWI calculation process that enables a vfan-beam to generate accurate sound speed images. A vfan-beam is accurately modeled by positioning the 128 sources and considering the delay times. The performance of the FWI calculation process with a vfan-beam was evaluated using a prototype ultrasound CT. For a circular phantom, the spatial resolution of a FWI image obtained with a vfan-beam was better than that of a filtered back projection (FBP) image. The image contrast of the FWI calculation process with a vfan-beam was comparable to that of the process with a conventional fanbeam generated from a single source. For a high-attenuation ellipse phantom, the sound speed image obtained with a conventional fan-beam had severe artifacts due to the low signal to noise ratio (SNR). Using a vfan-beam reduced the number of artifacts in the images due to the higher SNR. The FWI calculation process with a vfan-beam visualized a 3 mm inclusion more clearly than the FBP process. A measurement study demonstrated that the FWI process with a vfanbeam with a high SNR reduced the number of artifacts in the sound speed images and improved the spatial resolution for a high-attenuation breast.
Ultrasound Computed Tomography is a very promising medical imaging technology to be used to discover breast cancer early. The conventional ultrasound emission method (fan beam), which utilizes a single element for one emission, might result in a signal-to-noise ratio (SNR) too low for measuring dense breasts. This research proposes a virtual fan emission method that can maintain high accuracy, a large field of view, and a high SNR at the same time, using multiple elements while mimicking the wave field of single element emission. We experimentally proved its effectiveness in improving SNR by imaging a phantom with high attenuation to mimic a dense breast. Imaging of excised human breast tissues also suggested that the proposed virtual fan beam emission is more effective than conventional fan beam emission to screen for breast cancer correctly.
In breast imaging by ultrasound CT, ultrasound is refracted owing to the difference of the sound speed between the breast and background water. The sound speed of a dense breast is higher than that of the water, while that of a fatty breast is lower than that of the water. In this study, we developed an oil-gel-based phantom for mimicking the wave refraction from the fatty breast to the dense breast. An oil gel was generated by adding SEBS (Styrene-Ethylene/Butylenes-Styrene, 10 wt%) to paraffin oil. The oil-gel-based phantom has a cylindrical shape and contains rod shaped inclusions which can be filled with salty water (3.5%). When temperature increases, the sound speed of water increases, while that of the oil gel decreases; the sound speeds of the oil gel were higher than those of the water at less than 20°C, while the sound speeds of the oil gel were lower than those of water at higher than 20°C. By controlling the temperature, the oil-gel-based phantom was able to simulate the refraction from the fatty breast (1476 [m/s]) to the dense breast (1559 [m/s]). For 43 days, the variation of the sound speed and attenuation of the oil gel in the reconstructed images were 0.7[m/s] and 0.03[dB/MHz/cm], respectively. This phantom with high temporal stability is suitable for multi-center distribution and may be used for standardization of data acquisition and image reconstruction across centers.
We are developing an ultrasound computed tomography (USCT) system for early breast-cancer screening. USCT has great advantages over mammographies because of its lack of X-ray exposure and compression pain. USCT can show both the reflection boundary (structure) distribution and the sound speed (hardness) distribution in a subject, which is estimated from the time-of-flight (TOF) information of transmitted ultrasound waves on the basis of an X-ray CT algorithm. Considering the nature of ultrasound waves, improving the image quality generally increases the calculation burden. To achieve both high-quality images and high throughput, we developed an iterative refraction calibration method. The measured TOF sinogram was iteratively calibrated by the difference between the fastest wave arrival time and the arrival time of the wave along the geometrically shortest path in a section. This method was applied to the data of a gel phantom and a dog’s tumor extirpated at Tokyo University of Agriculture and Technology, which was measured by a USCT prototype with a 10 cm-diameter ring array. As a result, we achieved a calculation speed seven times faster than that of a conventional bent-ray reconstruction with the same contrast as that of a sound-speed image.
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