Waveform inversion with source encoding for breast sound speed reconstruction in ultrasound computed tomography

Vortex-encoded full-waveform inversion-based ultrasound computed tomography

Ultrasound imaging of musculoskeletal tissue has long been a challenge. As a novel medical ultrasound computed tomography (UCT) technique, full-waveform inversion (FWI) provides a promising solution for musculoskeletal imaging with high spatial resolution. However, FWI suffers from a substantial computational burden, primarily due to the multiple wavefield calculations involved in the inversion process, especially when dealing with a large number of sources. In order to minimize the number of wavefield calculations, we propose a source encoding technology for musculoskeletal FWI. In detail, based on the ring-shaped array within the UCT configuration, a novel vortex encoding strategy is developed and applied to FWI. Given the orthogonal properties of acoustic vortices, this strategy effectively mitigates the cross talk artifacts between the encoding sources. This vortex-encoded full-waveform inversion (VE-FWI) significantly reduces computation load by an order of magnitude compared to the conventional FWI. Besides, the vortex encoding strategy enhances the quality of reconstructed images, with a 2.9% increase in peak signal-to-noise ratio and a 4.7% increase in structure similarity index measure compared to other traditional encoding strategies. VE-FWI not only accelerates musculoskeletal UCT but also maintains high imaging quality, presenting a promising solution for practical applications with both accuracy and computational efficiency.

Optimal transport assisted full waveform inversion for multiparameter imaging of soft tissues in ultrasound computed tomography

Ultrasound computed tomography (USCT) has emerged as a promising platform for imaging tissue properties, offering non-ionizing and operator-independent capabilities. In this work, we demonstrate the feasibility of obtaining quantitative images of multiple acoustic parameters (sound speed and impedance) for soft tissues using full waveform inversion (FWI), which are justified with both numerical and experimental cases. A 3D reconstruction based on a series of 2D slice images is presented for the experimental case of ex vivo soft tissues. To improve the robustness of the reconstruction process, a hierarchical FWI strategy is adopted, gradually iterating from low to high frequencies. In parallel, we employ a graph-space optimal transport misfit function, avoiding convergence into local minima and minimizing inversion artifacts caused by skin-related supercritical reflections. Our method first carries out sound speed inversion based on transmitted waves in the low and middle frequency bands, and then uses all types of waves in the high frequency band for simultaneous inversion of both sound speed and impedance. Compared to conventional strategies, the proposed approach can accurately reconstruct physical models consistent with the actual soft tissue sample. These high-resolution ultrasound images of acoustic parameters are promising to allow for quantitative differentiation among different types of tissues (e.g., muscles and fats). These results have significant implications for advancing our understanding of tissue properties and for potentially contributing to disease diagnosis through USCT, which is a flexible and cost-effective alternative to X-ray computed tomography or magnetic resonance imaging at no significant sacrifices for resolution.

Full-Waveform Inversion Imaging of Cortical Bone Using Phased Array Tomography

Classic ultrasound bone imaging modalities usually demand either a prior knowledge or an advanced estimation on speed of sound (SoS), which not only renders to a burdensome imaging process but also supplies a limited resolution. To overcome these drawbacks, this article proposed a frequency-domain full-waveform inversion (FDFWI) modality using phased array tomography for high-accuracy cortical bone imaging. A transmission scenario of ultrasound wave in 2-D space was presented in the frequency domain to simulate the forward wavefield propagation. Iterations in the inversion process were performed by matching the simulation wavefield to the experimental one from low to high discrete frequency points. Moreover, the association between the maximum initial frequency and the initial SoS model was explored to prevent the occurrence of cycle-skipping phenomenon, which could lead to the outcomes being trapped in local minima. The feasibility and effectiveness of the proposed imaging scheme were testified by simulation, phantom, and ex-vivo studies, with mean relative errors of cortical part being 3.18%, 8.71%, and 9.36%, respectively. It is verified that the proposed FDFWI method is an effective way for parametric imaging of cortical bone without any prior knowledge of sound speed.

Angular spatial compounding of diffraction corrected images improves ultrasound attenuation measurements

Breast cancer is a leading cause of death for women. Quantitative ultrasound (QUS) and ultrasound computed tomography (USCT) are quantitative imaging techniques that have been investigated for management of breast cancer. QUS and USCT can generate ultrasound attenuation images. In QUS, the spectral log difference (SLD) is a technique that can provide estimates of the attenuation coefficient slope. Full angular spatial compounding (FASC) can be used with SLD to generate attenuation maps with better spatial resolution and lower estimate variance. In USCT, high quality speed of sound (SOS) images can be generated using full wave inversion (FWI) method, but attenuation images created using FWI are often of inferior quality. With the QTI Breast Acoustic CTTM Scanner (QT Imaging, Inc., Novato, CA), raw in-phase and quadrature data were used to implement SLD combined with FASC. The capabilities of SLD were compared with FWI through simulations, phantom experiments, and in vivo breast experiments. Results show the SLD resulted in improved accuracy in estimating lesion sizes compared to FWI. Further, SLD images had lower variance and mean absolute error (MAE) compared to FWI of the same samples with respect to the attenuation values (reducing MAE by three times) in the tissue mimicking phantoms.

Unveiling the potential of ultrasound in brain imaging: Innovations, challenges, and prospects

Within medical imaging, ultrasound serves as a crucial tool, particularly in the realms of brain imaging and disease diagnosis. It offers superior safety, speed, and wider applicability compared to Magnetic Resonance Imaging (MRI) and X-ray Computed Tomography (CT). Nonetheless, conventional transcranial ultrasound applications in adult brain imaging face challenges stemming from the significant acoustic impedance contrast between the skull bone and soft tissues. Recent strides in ultrasound technology encompass a spectrum of advancements spanning tissue structural imaging, blood flow imaging, functional imaging, and image enhancement techniques. Structural imaging methods include traditional transcranial ultrasound techniques and ultrasound elastography. Transcranial ultrasound assesses the structure and function of the skull and brain, while ultrasound elastography evaluates the elasticity of brain tissue. Blood flow imaging includes traditional transcranial Doppler (TCD), ultrafast Doppler (UfD), contrast-enhanced ultrasound (CEUS), and ultrasound localization microscopy (ULM), which can be used to evaluate the velocity, direction, and perfusion of cerebral blood flow. Functional ultrasound imaging (fUS) detects changes in cerebral blood flow to create images of brain activity. Image enhancement techniques include full waveform inversion (FWI) and phase aberration correction techniques, focusing on more accurate localization and analysis of brain structures, achieving more precise and reliable brain imaging results. These methods have been extensively studied in clinical animal models, neonates, and adults, showing significant potential in brain tissue structural imaging, cerebral hemodynamics monitoring, and brain disease diagnosis. They represent current hotspots and focal points of ultrasound medical research. This review provides a comprehensive summary of recent developments in brain imaging technologies and methods, discussing their advantages, limitations, and future trends, offering insights into their prospects.

Toward widespread use of virtual trials in medical imaging innovation and regulatory science

The rapid advancement in the field of medical imaging presents a challenge in keeping up to date with the necessary objective evaluations and optimizations for safe and effective use in clinical settings. These evaluations are traditionally done using clinical imaging trials, which while effective, pose several limitations including high costs, ethical considerations for repetitive experiments, time constraints, and lack of ground truth. To tackle these issues, virtual trials (aka in silico trials) have emerged as a promising alternative, using computational models of human subjects and imaging devices, and observer models/analysis to carry out experiments. To facilitate the widespread use of virtual trials within the medical imaging research community, a major need is to establish a common consensus framework that all can use. Based on the ongoing efforts of an AAPM Task Group (TG387), this article provides a comprehensive overview of the requirements for establishing virtual imaging trial frameworks, paving the way toward their widespread use within the medical imaging research community. These requirements include credibility, reproducibility, and accessibility. Credibility assessment involves verification, validation, uncertainty quantification, and sensitivity analysis, ensuring the accuracy and realism of computational models. A proper credibility assessment requires a clear context of use and the questions that the study is intended to objectively answer. For reproducibility and accessibility, this article highlights the need for detailed documentation, user-friendly software packages, and standard input/output formats. Challenges in data and software sharing, including proprietary data and inconsistent file formats, are discussed. Recommended solutions to enhance accessibility include containerized environments and data-sharing hubs, along with following standards such as CDISC (Clinical Data Interchange Standards Consortium). By addressing challenges associated with credibility, reproducibility, and accessibility, virtual imaging trials can be positioned as a powerful and inclusive resource, advancing medical imaging innovation and regulatory science.

Multi-angle speed-of-sound imaging with sparse sampling to characterize medical tissue properties

Medical Speed-of-sound (SoS) imaging, which can characterize medical tissue properties better by quantifying their different SoS, is an effective imaging method compared with conventional B-mode ultrasound imaging. As a commonly used diagnostic instrument, a hand-held array probe features convenient and quick inspection. However, artifacts will occur in the single-angle SoS imaging, resulting in indistinguishable tissue boundaries. In order to build a high-quality SoS image, a number of raw data are needed, which will bring difficulties to data storage and processing. Compressed sensing (CS) theory offers theoretical support to the feasibility that a sparse signal can be rebuilt with random but less sampling data. In this study, we proposed an SoS reconstruction method based on CS theory to process signals obtained from a hand-held linear array probe with a passive reflector positioned on the opposite side. The SoS reconstruction method consists of three parts. Firstly, a sparse transform basis is selected appropriately for a sparse representation of the original signal. Then, considering the mathematical principles of SoS imaging, the ray-length matrix is used as a sparse measurement matrix to observe the original signal, which represents the length of the acoustic propagation path. Finally, the orthogonal matching pursuit algorithm is introduced for image reconstruction. The experimental result of the phantom proves that SoS imaging can clearly distinguish tissues that show similar echogenicity in B-mode ultrasound imaging. The simulation and experimental results show that our proposed method holds promising potential for reconstructing precision SoS images with fewer signal samplings, transmission, and storage.

Investigating the Use of Traveltime and Reflection Tomography for Deep Learning-Based Sound-Speed Estimation in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) quantifies acoustic tissue properties such as the speed-of-sound (SOS). Although full-waveform inversion (FWI) is an effective method for accurate SOS reconstruction, it can be computationally challenging for large-scale problems. Deep learning-based image-to-image learned reconstruction (IILR) methods can offer computationally efficient alternatives. This study investigates the impact of the chosen input modalities on IILR methods for high-resolution SOS reconstruction in USCT. The selected modalities are traveltime tomography (TT) and reflection tomography (RT), which produce a low-resolution SOS map and a reflectivity map, respectively. These modalities have been chosen for their lower computational cost relative to FWI and their capacity to provide complementary information: TT offers a direct SOS measure, while RT reveals tissue boundary information. Systematic analyses were facilitated by employing a virtual USCT imaging system with anatomically realistic numerical breast phantoms (NBPs). Within this testbed, a supervised convolutional neural network (CNN) was trained to map dual-channel (TT and RT images) to a high-resolution SOS map. Single-input CNNs were trained separately using inputs from each modality alone (TT or RT) for comparison. The accuracy of the methods was systematically assessed using normalized root-mean-squared error (NRMSE), structural similarity index measure (SSIM), and peak signal-to-noise ratio (PSNR). For tumor detection performance, receiver operating characteristic (ROC) analysis was employed. The dual-channel IILR method was also tested on clinical human breast data. Ensemble average of the NRMSE, SSIM, and PSNR evaluated on this clinical dataset was 0.2355, 0.8845, and 28.33 dB, respectively.

2-D Slicewise Waveform Inversion of Sound Speed and Acoustic Attenuation for Ring Array Ultrasound Tomography Based on a Block LU Solver

Ultrasound tomography is an emerging imaging modality that uses the transmission of ultrasound through tissue to reconstruct images of its mechanical properties. Initially, ray-based methods were used to reconstruct these images, but their inability to account for diffraction often resulted in poor resolution. Waveform inversion overcame this limitation, providing high-resolution images of the tissue. Most clinical implementations, often directed at breast cancer imaging, currently rely on a frequency-domain waveform inversion to reduce computation time. For ring arrays, ray tomography was long considered a necessary step prior to waveform inversion in order to avoid cycle skipping. However, in this paper, we demonstrate that frequency-domain waveform inversion can reliably reconstruct high-resolution images of sound speed and attenuation without relying on ray tomography to provide an initial model. We provide a detailed description of our frequency-domain waveform inversion algorithm with open-source code and data that we make publicly available.

Cross-correlation adjustment full-waveform inversion with source encoding in ultrasound computed tomography

Full-waveform inversion (FWI) is one of the leading-edge techniques in ultrasound computed tomography (USCT). FWI reconstructs the images of sound speed by iteratively minimizing the difference between the predicted and measured signals. The challenges of FWI are to improve its stability and reduce its computational cost. In this paper, a new USCT algorithm based on cross-correlation adjustment FWI with source encoding (CCAFWI-SE) is proposed. In this algorithm, the gradient is adjusted using the intermediate signals as the inversion target rather than the measured signals during iteration. The intermediate signals are generated using the travel time difference calculated by cross-correlation. In the case of conventional FWI failure, using the proposed algorithm, the estimated sound speed can converge toward the ground truth. To reduce the computational cost, an intermittent update strategy is implemented. This strategy only requires one time for the calculation of the travel time difference per stage, so that the source encoding can be used. Simulation and laboratory experiments are implemented to validate this approach. The experiment results show it has successfully recovered the sound speed model, while conventional FWI failed when the initial model greatly differed from the ground truth. This verifies that our approach improves the stability of the reconstruction in USCT. In practice, additional computational costs can be reduced by combining our approach with existing methods. The proposed approach increases the robustness of the FWI and expands its application.

Breast Tomographic Ultrasound: The Spectrum from Current Dense Breast Cancer Screenings to Future Theranostic Treatments

This review provides unique insights to the scientific scope and clinical visions of the inventors and pioneers of the SoftVue breast tomographic ultrasound (BTUS). Their >20-year collaboration produced extensive basic research and technology developments, culminating in SoftVue, which recently received the Food and Drug Administration's approval as an adjunct to breast cancer screening in women with dense breasts. SoftVue's multi-center trial confirmed the diagnostic goals of the tissue characterization and localization of quantitative acoustic tissue differences in 2D and 3D coronal image sequences. SoftVue mass characterizations are also reviewed within the standard cancer risk categories of the Breast Imaging Reporting and Data System. As a quantitative diagnostic modality, SoftVue can also function as a cost-effective platform for artificial intelligence-assisted breast cancer identification. Finally, SoftVue's quantitative acoustic maps facilitate noninvasive temperature monitoring and a unique form of time-reversed, focused US in a single theranostic device that actually focuses acoustic energy better within the highly scattering breast tissues, allowing for localized hyperthermia, drug delivery, and/or ablation. Women also prefer the comfort of SoftVue over mammograms and will continue to seek out less-invasive breast care, from diagnosis to treatment.

LUFT: A low-frequency ultrasound tomography system designed for lung imaging

Pulmonary imaging with ultrasound in the conventional MHz range suffers from significant artifacts, as the high frequency acoustic waves primarily reflect off of the lung pleura with little to no penetration through the lung tissue. Furthermore, B-mode ultrasound images are difficult to interpret and require a skilled technician to obtain. Motivated by the finding that acoustic frequencies in the kHz penetrate lung tissue, a low-frequency tomographic ultrasound system is presented. A Verasonics Vantage 64 low-frequency ultrasound system is programmed to work with a novel low-frequency Tonpilz transducers set arranged in a circular array on a belt. After signal processing, a time-of-flight (TOF) tomographic reconstruction algorithm with refraction correction is applied to estimate the sound speed in the plane of the transducer array. Data were collected on experimental phantoms made of ballistic gel containing targets of varying sound speeds, and reconstructions TOF were computed. Results demonstrate that the low-frequency ultrasound tomography system effectively detects targets in an experimental phantom with the ability to resolve multiple targets and distinguish between targets of high and low sound speed compared to the background medium.

Learned Full Waveform Inversion Incorporating Task Information for Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging imaging modality that holds great promise for breast imaging. Full-waveform inversion (FWI)-based image reconstruction methods incorporate accurate wave physics to produce high spatial resolution quantitative images of speed of sound or other acoustic properties of the breast tissues from USCT measurement data. However, the high computational cost of FWI reconstruction represents a significant burden for its widespread application in a clinical setting. The research reported here investigates the use of a convolutional neural network (CNN) to learn a mapping from USCT waveform data to speed of sound estimates. The CNN was trained using a supervised approach with a task-informed loss function aiming at preserving features of the image that are relevant to the detection of lesions. A large set of anatomically and physiologically realistic numerical breast phantoms (NBPs) and corresponding simulated USCT measurements was employed during training. Once trained, the CNN can perform real-time FWI image reconstruction from USCT waveform data. The performance of the proposed method was assessed and compared against FWI using a hold-out sample of 41 NBPs and corresponding USCT data. Accuracy was measured using relative mean square error (RMSE), structural self-similarity index measure (SSIM), and lesion detection performance (DICE score). This numerical experiment demonstrates that a supervised learning model can achieve accuracy comparable to FWI in terms of RMSE and SSIM, and better performance in terms of task performance, while significantly reducing computational time.

A Forward Model Incorporating Elevation-Focused Transducer Properties for 3-D Full-Waveform Inversion in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging medical imaging modality that holds great promise for improving human health. Full-waveform inversion (FWI)-based image reconstruction methods account for the relevant wave physics to produce high spatial resolution images of the acoustic properties of the breast tissues. A practical USCT design employs a circular ring-array comprised of elevation-focused ultrasonic transducers, and volumetric imaging is achieved by translating the ring-array orthogonally to the imaging plane. In commonly deployed slice-by-slice (SBS) reconstruction approaches, the 3-D volume is reconstructed by stacking together 2-D images reconstructed for each position of the ring-array. A limitation of the SBS reconstruction approach is that it does not account for 3-D wave propagation physics and the focusing properties of the transducers, which can result in significant image artifacts and inaccuracies. To perform 3-D image reconstruction when elevation-focused transducers are employed, a numerical description of the focusing properties of the transducers should be included in the forward model. To address this, a 3-D computational model of an elevation-focused transducer is developed to enable 3-D FWI-based reconstruction methods to be deployed in ring-array-based USCT. The focusing is achieved by applying a spatially varying temporal delay to the ultrasound pulse (emitter mode) and recorded signal (receiver mode). The proposed numerical transducer model is quantitatively validated and employed in computer simulation studies that demonstrate its use in image reconstruction for ring-array USCT.

Deep Learning Ultrasound Computed Tomography Under Sparse Sampling

Ultrasound computed tomography (USCT) is a fast-emerging imaging modality that is expected to help detect and characterize breast tumors by quantifying the distribution of the speed of sound (SOS) and acoustic attenuation in breast tissue. High-quality quantitative SOS reconstruction in USCT requires a large number of transducers, which incurs high system costs and slow computation. In contrast, sparsely distributed arrays are low-cost and fast but significantly degrade image quality. Thus, we propose a framework to achieve high-quality SOS reconstruction under sparse sampling based on a convolutional neural network (SRSS-Net) with faster computation. We first apply the bent-ray algorithm to sparsely sampled data and then apply the SRSS-Net to efficiently improve the image quality. Experimental results on synthetic and real datasets demonstrate that the proposed SRSS-Net provides reconstructions that are superior to those of state-of-the-art methods in terms of artifact suppression, structural preservation, quantitative restoration, and computational speed. As demonstrated in our experiments, the fine-tuning training strategy is suggested when applying SRSS-Net to real-world circumstances. The imaging and computational performance of SRSS-Net on the inhomogeneous breast phantom further demonstrates that SRSS-Net has great potential in real-time breast cancer detection.

A joint method of coherence factor and nonlinear beamforming for synthetic aperture imaging with a ring array

Ultrasound computed tomography (USCT) with a ring array is an emerging diagnostic method for breast cancer. In the literature, synthetic aperture (SA) imaging has employed the delay-and-sum (DAS) beamforming technique for ring-array USCT to obtain isotropic resolution reflection images. However, the images obtained by the conventional DAS beamformer suffer from off-axis clutter and low resolution due to inhomogeneity of the medium and phase distortion. To address these issues, researchers have developed adaptive beamforming methods, such as coherence factor (CF) and convolutional beamforming algorithm (COBA), that improve image quality. In this study, we propose a joint method that combines CF with short-lag COBA (SLCOBA). First, we estimate the average sound speed using CF to address tissue inhomogeneity. Based on the corrected sound speed map, SLCOBA effectively suppresses side lobes and enhances image quality. Numerical results show that the proposed method reduces clutter and noise, improving resolution performance. These findings suggest that the proposed method may be a practical option for breast imaging in inhomogeneous mediums in the future.

Frequency-domain full-waveform inversion-based musculoskeletal ultrasound computed tomography

Recently, full-waveform inversion (FWI) has become a promising tool for ultrasound computed tomography (USCT). However, as a computationally intensive technique, FWI suffers from computational burden, especially in conventional time-domain full-waveform inversion (TDFWI). On the contrary, frequency-domain full-waveform inversion (FDFWI) provides a relatively high computational efficiency as the propagation of discrete frequencies is much cheaper than full time-domain modeling. FDFWI has already been applied in soft tissue imaging, such as breast, but for the musculoskeletal model with high impedance contrast between hard and soft tissues, there is still a lack of an effective source estimation method. In this paper, a water-referenced data calibration method is proposed to address the source estimation challenge in the presence of bones, which achieves consistency between the measured and simulated data before the FDFWI procedure. To avoid the cycle-skipping local minimum effect and facilitate the algorithm convergence, a starting frequency criterion for musculoskeletal FDFWI is further proposed. The feasibility of the proposed method is demonstrated by numerical studies on retrieving the anatomies of the leg models and different musculoskeletal lesions. The study extends the advanced FDFWI method to the musculoskeletal system and provides an alternative solution for musculoskeletal USCT imaging with high computational efficiency.

Full-Waveform Inversion for Breast Ultrasound Tomography Using Line-Shape Modeled Elements

OBJECTIVE

The objective of the work described here was to incorporate the spatial shapes of the transducer elements into the framework of the full-waveform inversion.

METHODS

An element is treated as its cross-section in the 2-D imaging plane, that is, a line segment. The elements are not simply modeled as a set of point sources on their surface to avoid staircasing artifacts. By use of the Fourier collocation method, an element is spatially represented as the discrete convolution between its spatial distribution and a band-limited delta function. The excitation pulses on the emitters and recorded signals on the receivers are then weighted based on the discrete convolution results. Digital and physical experiments are implemented to validate the method.

DISCUSSION

It is meaningful to model the shapes of the elements if their spatial sizes are similar to or larger than the acoustic wavelengths. It should, however, be noted that because this article focuses on 2-D imaging, the inter-plane effects are not considered.

CONCLUSION

The approach helps reduce the root mean square errors and increase the structural similarity of the reconstructed images. It also helps to improve the stability of convergence and to accelerate the convergence speed.

Ultrasound computed tomography based on full waveform inversion with source directivity calibration

Ultrasound computed tomography based on full waveform inversion has the potential to provide high-resolution images of human tissues in a quantitative manner. A successful ultrasound computed tomography system requires the decent knowledge of acquisition array, including the spatial position and the directivity of each transducer, to meet the high-level demand of clinical applications. The conventional full waveform inversion algorithm assumes a point source with the omni-directional emission. Such assumption does not hold when the directivity of emitting transducer is not negligible. For a practical implementation, an efficient and accurate self-checking evaluation of directivity is crucial prior to the reconstruction of images. We propose to measure the directivity of each emitting transducer using the full-matrix captured data obtained with a water-immersed and target-free experiment. We introduce the weighted virtual point-source array to act as the proxy of emitting transducer during the numerical simulation. The weights of different points in the virtual array can be calculated from the observed data using the gradient-based local optimization method. Although the full waveform imaging method relies on the finite-difference solver of wave equation, such directivity estimation benefits from the introduction of analytical solver. The trick significantly reduces the numerical cost, enabling an automatic directivity self-check at boot. We verify the feasibility, efficiency, and accuracy of the virtual array method through simulated and experimental tests. For the experimental test, we also illustrate that full waveform inversion with directivity calibration can reduce the artifacts introduced by the conventional point source assumption, improving the quality of reconstructed images..

Optimization of reconstruction time of ultrasound computed tomography with a piecewise homogeneous region-based refract-ray model

In this article, a novel ultrasound computed tomography (USCT) reconstruction algorithm for breast imaging is proposed. This algorithm is based on an ultrasound propagation model, the refract-ray model (RRM). In this model, the field of imaging is assumed as piecewise homogenous and is divided into several regions. The ultrasound propagation paths are considered polylines that only refract at the borders of the regions. The edge information is provided by B-mode imaging. Both simulations and experiments are implemented to validate the proposed algorithm. Compared with the traditional bent-ray model (BRM), the time of reconstructions using RRM decreases by over 90 %. In simulations, the imaging qualities for RRM and BRM are comparable, in terms of the root mean square error, the Tenengrad value, and the deformation of digital phantom. In the experiments, a cylindrical agar phantom is imaged using a customized imaging system. When imaging using RRM, the estimate of the phantom radius is about 0.1 mm in error, while it is about 0.3 mm in error using BRM. Moreover, the Tenengrad value of the result using RRM is much higher than that using BRM (9.76 compared to 0.79). The results show that the proposed algorithm can better delineate the phantom within a water bath. In future work, further experimental work is required to validate the method for improving imaging quality under breast-mimicking imaging conditions.

Full Wave Inversion and Inverse Scattering in Ultrasound Tomography/Volography

Ultrasound breast tomography has been around for more than 40 years. Early approaches to reconstruction focused on simple algebraic reconstructions and bent ray techniques. These approaches were not able to provide high-quality and high spatial-resolution images. The advent of inverse scattering approaches resulted in a shift in image reconstruction approaches for breast tomography and a subsequent improvement in image quality. Full wave inverse solvers were developed to improve the reconstruction times without sacrificing image quality. The development of GPUs has markedly decreased the time for reconstruction using inverse scatting approaches. The development of fully 3D image solvers and hardware capable of capturing out of plane scattering have resulted in further improvement in breast tomography. This chapter discusses the state-of-the-art in ultrasound breast tomography, its history, the theory behind inverse scattering, approximations that are included to improve convergence, 3D image reconstruction, and hardware implementation of the constructions.

Deep-Learning-Based Ultrasound Sound-Speed Tomography Reconstruction with Tikhonov Pseudo-Inverse Priori

Ultrasound sound-speed tomography (USST) is a promising technology for breast imaging and breast cancer detection. Its reconstruction is a complex non-linear mapping from the projection data to the sound-speed image (SSI). The traditional reconstruction methods include mainly the ray-based methods and the waveform-based methods. The ray-based methods with linear approximation have low computational cost but low reconstruction quality; the full wave-based methods with the complex non-linear model have high quality but high cost. To achieve both high quality and low cost, we introduced traditional linear approximation as prior knowledge into a deep neural network and treated the complex non-linear mapping of USST reconstruction as a combination of linear mapping and non-linear mapping. In the proposed method, the linear mapping was seamlessly implemented with a fully connected layer and initialized using the Tikhonov pseudo-inverse matrix. The non-linear mapping was implemented using a U-shape Net (U-Net). Furthermore, we proposed the Tikhonov U-shape net (TU-Net), in which the linear mapping was done before the non-linear mapping, and the U-shape Tikhonov net (UT-Net), in which the non-linear mapping was done before the linear mapping. Moreover, we conducted simulations and experiments for evaluation. In the numerical simulation, the root-mean-squared error was 6.49 and 4.29 m/s for the UT-Net and TU-Net, the peak signal-to-noise ratio was 49.01 and 52.90 dB, the structural similarity was 0.9436 and 0.9761 and the reconstruction time was 10.8 and 11.3 ms, respectively. In this study, the SSIs obtained with the proposed methods exhibited high sound-speed accuracy. Both the UT-Net and the TU-Net achieved high quality and low computational cost.

Design and Construction of a Low-Frequency Ultrasound Acquisition Device for 2-D Brain Imaging Using Full-Waveform Inversion

The main techniques used to image the brain and obtain structural data are magnetic resonance imaging and X-ray computed tomography. These techniques produce images with high spatial resolution, but with the disadvantage of requiring very large equipment with special installation needs. In addition, X-ray tomography uses ionizing radiation, which limits their use. Ultrasound imaging is a safe technology that is delivered using compact and mobile devices. However, conventional ultrasound reconstruction techniques have failed to obtain images of the brain because of, fundamentally, the presence of the skull and the distortion that it produces on ultrasound. Recent studies have indicated that full-waveform inversion, a computational technique originally from Earth science, has the potential to generate accurate 3-D images of the brain. This technology can overcome the limitations of conventional ultrasound imaging, but a prototype for transcranial applications does not yet exist. Here, we investigate different designs of an annular array of ultrasound transducers to optimize the number of elements and rotations needed to conduct transcranial imaging with full-waveform inversion. This device uses small-diameter, low-frequency transducers that readily propagate ultrasound through the skull with good signal-to-noise ratios. It also incorporates the use of rotations to produce a high-density coverage of the target and acquire redundant traces that are beneficial for full-waveform inversion. We have built a ring of 40 transducers to illustrate that this design is capable of reconstructing images of the brain, retrieving its anatomy and acoustic properties with millimeter resolution. Laboratory results reveal the ability of this device to successfully image a 2.5-D brain- and skull-mimicking phantom using full-waveform inversion. To our knowledge, this is the first prototype ever used for transcranial-like imaging. The importance of these findings and their implications for the design of a 3-D reconstruction system with possible clinical applications are discussed.

Cross-correlation Full Waveform Inversion for Sound Speed Reconstruction in Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is considered to have great potential for breast cancer screening. Compared with the ray based methods, the reconstructed image using full waveform inversion (FWI) methods have higher spatial resolution. However, the results of FWI is difficult to converge to the real value when cycle skipping occurs. In this paper, a cross-correlation full waveform inversion(CC-FWI) is proposed for USCT image reconstruction. In the first stage, the ajoint source is adjusted as the residual of predicted signal and time-shifted measured signal to avoid cycle skipping. In the remaining stage, the FWI with source encoding is employed to accelerate convergence. The simulations are conducted to demonstrate the validity of the proposed algorithm. The root mean squared error (RMSE) of the proposed algorithm is much smaller than that of conventional FWI. The results suggest that CC-FWI is effective in avoiding cycle skipping. Clinical Relevance- Clinical relevance- New imaging modalities of high resolution, safety to examines for early-stage breast cancer imaging are urgently needed for researching and development. Ultra-sound computed tomography (USCT) is supposed to meet the above requirements and it can be potentially deployed in breast scanning.

Feasibility of ultrasound tomography-guided localized mild hyperthermia using a ring transducer: Ex vivo and in silico studies

BACKGROUND

As of 2022, breast cancer continues to be the most diagnosed cancer worldwide. This problem persists within the United States as well, as the American Cancer Society has reported that ∼12.5% of women will be diagnosed with invasive breast cancer over the course of their lifetime. Therefore, a clinical need continues to exist to address this disease from a treatment and therapeutic perspective. Current treatments for breast cancer and cancers more broadly include surgery, radiation, and chemotherapy. Adjuncts to these methods have been developed to improve the clinical outcomes for patients. One such adjunctive treatment is mild hyperthermia therapy (MHTh), which has been shown to be successful in the treatment of cancers by increasing effectiveness and reduced dosage requirements for radiation and chemotherapies. MHTh-assisted treatments can be performed with invasive thermal devices, noninvasive microwave induction, heating and recirculation of extracted patient blood, or whole-body hyperthermia with hot blankets.

PURPOSE

One common method for inducing MHTh is by using microwave for heat induction and magnetic resonance imaging for temperature monitoring. However, this leads to a complex, expensive, and inaccessible therapy platform. Therefore, in this work we aim to show the feasibility of a novel all-acoustic MHTh system that uses focused ultrasound (US) to induce heating while also using US tomography (UST) to provide temperature estimates. Changes in sound speed (SS) have been shown to be strongly correlated with temperature changes and can therefore be used to indirectly monitor heating throughout the therapy. Additionally, these SS estimates allow for heterogeneous SS-corrected phase delays when heating complex and heterogeneous tissue structures.

METHODS

Feasibility to induce localized heat in tissue was investigated in silico with a simulated breast model, including an embedded tumor using continuous wave US. Here, both heterogenous acoustic and thermal properties were modeled in addition to blood perfusion. We further demonstrate, with ex vivo tissue phantoms, the feasibility of using ring-based UST to monitor temperature by tracking changes in SS. Two phantoms (lamb tissue and human abdominal fat) with latex tubes containing varied temperature flowing water were imaged. The measured SS of the water at each temperature were compared against values that are reported in literature.

RESULTS

Results from ex vivo tissue studies indicate successful tracking of temperature under various phantom configurations and ranges of water temperature. The results of in silico studies show that the proposed system can heat an acoustically and thermally heterogenous breast model to the clinically relevant temperature of 42°C while accounting for a reasonable time needed to image the current cross section (200 ms). Further, we have performed an initial in silico study demonstrating the feasibility of adjusting the transmit waveform frequency to modify the effective heating height at the focused region. Lastly, we have shown in a simpler 2D breast model that MHTh level temperatures can be maintained by adjusting the transmit pressure intensity of the US ring.

CONCLUSIONS

This work has demonstrated the feasibility of using a 256-element ring array transducer for temperature monitoring; however, future work will investigate minimizing the difference between measured SS and the values shown in literature. A hypothesis attributes this bias to potential volumetric average artifacts from the ray-based SS inversion algorithm that was used, and that moving to a waveform-based SS inversion algorithm will greatly improve the SS estimates. Additionally, we have shown that an all-acoustic MHTh system is feasible via in silico studies. These studies have indicated that the proposed system can heat a tumor within a heterogenous breast model to 42°C within a narrow time frame. This holds great promise for increasing the accessibility and reducing the complexity of a future all-acoustic MHTh system.

Index-Rotated Fast Ultrasound Imaging of Cortical Bone Based on Predicted Velocity Model

Due to the significant acoustic impedance contrast at cortical boundaries, highly inside attenuation, and the unknown sound velocity distribution, accurate ultrasound cortical bone imaging remains a challenge, especially for the traditional pulse-echo modalities using unique sound velocity. Moreover, the large amounts of data recorded by multielement probe results in a relatively time-consuming reconstruction process. To overcome these limitations, this article proposed an index-rotated fast ultrasound imaging method based on predicted velocity model (IR-FUI-VP) for cortical cross section ultrasound tomography (UST) imaging, utilizing ray-tracing synthetic aperture (RTSA). In virtue of ring probe, the sound velocity model was predicted in advance using bent-ray inversion (BRI). With the predicted velocity model, index-rotated fast ultrasound imaging (IR-FUI) was further applied to image the cortical cross sections in the sectors corresponding to the dynamic apertures (DAs) and ring center. The final result was merged by all sector images. One cortical bone phantom and two ex vivo bovine femurs were utilized to demonstrate the performance of the proposed method. Compared to the conventional synthetic aperture (SA) imaging, the method can not only accurately image the outer cortical boundary but also precisely reconstruct the inner cortical surface. The mean relative errors of the predicted sound velocity in the region of interest (ROI) were all smaller than 7%, and the mean errors of cortical thickness are all less than 0.31 mm. The reconstructed images of bovine femurs were in good agreement with the reference images scanned by micro-computed tomography ( μ CT) with respect to the morphology and thickness. The speed of IR-FUI is about 3.73 times faster than the traditional SA. It is proved that the proposed IR-FUI-VP-based UST is an effective way for fast and accurate cortical bone imaging.

DeepUCT: Complex cascaded deep learning network for improved ultrasound tomography

Ultrasound computed tomography is an inexpensive and radiation-free medical imaging technique used to quantify the tissue acoustic properties for advanced clinical diagnosis. Image reconstruction in ultrasound tomography is often modeled as an optimization scheme solved by iterative methods like full-waveform inversion. These iterative methods are computationally expensive, while the optimization problem is ill-posed and nonlinear. To address this problem, we propose to use deep learning to overcome the computational burden and ill-posedness, and achieve near real-time image reconstruction in ultrasound tomography. We aim to directly learn the mapping from the recorded time-series sensor data to a spatial image of acoustical properties. To accomplish this, we develop a deep learning model using two cascaded convolutional neural networks with an encoder–decoder architecture. We achieve a good representation by first extracting the intermediate mapping-knowledge and later utilizing this knowledge to reconstruct the image. This approach is evaluated on synthetic phantoms where simulated ultrasound data are acquired from a ring of transducers surrounding the region of interest. The measurement data is acquired by forward modeling the wave equation using the k-wave toolbox. Our simulation results demonstrate that our proposed deep-learning method is robust to noise and significantly outperforms the state-of-the-art traditional iterative method both quantitatively and qualitatively. Furthermore, our model takes substantially less computational time than the conventional full-wave inversion method.

3D image reconstruction of terahertz computed tomography at sparse angles by total variation minimization

Continuous-wave terahertz computed tomography (THz-CT) is an important three-dimensional imaging method for probing the profile and inner properties of a sample's structure. We applied the total variation (TV) minimization iterative algorithm to squeeze 75% data acquisition time of THz-CT without the loss of reconstruction fidelity. The imaging system is built based on a 278.6 GHz avalanche diode source. A zero-order Bessel beam is generated by an axicon, for which the intensity profile remains essentially propagation invariant within the non-diffracting zone. The effectiveness of the proposed method is verified by using three optically opaque objects. The reconstruction results show that the TV-minimization algorithm can effectively suppress noise, artefacts, and shape distortion created in sparse angle reconstruction.

3-D Stochastic Numerical Breast Phantoms for Enabling Virtual Imaging Trials of Ultrasound Computed Tomography

Ultrasound computed tomography (USCT) is an emerging imaging modality for breast imaging that can produce quantitative images that depict the acoustic properties of tissues. Computer-simulation studies, also known as virtual imaging trials, provide researchers with an economical and convenient route to systematically explore imaging system designs and image reconstruction methods. When simulating an imaging technology intended for clinical use, it is essential to employ realistic numerical phantoms that can facilitate the objective, or task-based, assessment of image quality (IQ). Moreover, when computing objective IQ measures, an ensemble of such phantoms should be employed, which displays the variability in anatomy and object properties that are representative of the to-be-imaged patient cohort. Such stochastic phantoms for clinically relevant applications of USCT are currently lacking. In this work, a methodology for producing realistic 3-D numerical breast phantoms for enabling clinically relevant computer-simulation studies of USCT breast imaging is presented. By extending and adapting an existing stochastic 3-D breast phantom for use with USCT, methods for creating ensembles of numerical acoustic breast phantoms are established. These breast phantoms will possess clinically relevant variations in breast size, composition, acoustic properties, tumor locations, and tissue textures. To demonstrate the use of the phantoms in virtual USCT studies, two brief case studies are presented, which addresses the development and assessment of image reconstruction procedures. Examples of breast phantoms produced by use of the proposed methods and a collection of 52 sets of simulated USCT measurement data have been made open source for use in image reconstruction development.

Breast Acoustic Parameter Reconstruction Method Based on Capacitive Micromachined Ultrasonic Transducer Array

Ultrasound computed tomography (USCT) systems based on capacitive micromachined ultrasonic transducer (CMUT) arrays have a wide range of application prospects. For this paper, a high-precision image reconstruction method based on the propagation path of ultrasound in breast tissue are designed for the CMUT ring array; that is, time-reversal algorithms and FBP algorithms are respectively used to reconstruct sound speed distribution and acoustic attenuation distribution. The feasibility of this reconstruction method is verified by numerical simulation and breast model experiments. According to reconstruction results, sound speed distribution reconstruction deviation can be reduced by 53.15% through a time-reversal algorithm based on wave propagation theory. The attenuation coefficient distribution reconstruction deviation can be reduced by 61.53% through FBP based on ray propagation theory. The research results in this paper will provide key technological support for a new generation of ultrasound computed tomography systems.

A Generalized Split-Step Angular Spectrum Method for Efficient Simulation of Wave Propagation in Heterogeneous Media

Angular spectrum (AS) methods enable efficient calculation of wave propagation from one plane to another inside homogeneous media. For wave propagation in heterogeneous media such as biological tissues, AS methods cannot be applied directly. Split-stepping techniques decompose the heterogeneous domain into homogeneous and perturbation parts, and provide a solution for forward wave propagation by propagating the incident wave in both frequency-space and frequency-wavenumber domains. Recently, a split-step hybrid angular spectrum (HAS) method was proposed for plane wave propagation of focused ultrasound beams. In this study, we extend these methods to enable simulation of acoustic pressure field for an arbitrary source distribution, by decomposing the source and reflection spectra into orthogonal propagation direction components, propagating each component separately, and summing all components to get the total field. We show that our method can efficiently simulate the pressure field of arbitrary sources in heterogeneous media. The accuracy of the method was analyzed comparing the resultant pressure field with pseudospectral time domain (PSTD) solution for breast tomography and hemispherical transcranial-focused ultrasound simulation models. Eighty times acceleration was achieved for a 3-D breast simulation model compared to PSTD solution with 0.005 normalized root mean-squared difference (NRMSD) between two solutions. For the hemispherical phased array, aberrations due to skull were accurately calculated in a single simulation run as evidenced by the resultant-focused ultrasound beam simulations, which had 0.001 NRMSD with 40 times acceleration factor compared to the PSTD method.

A Deep Learning-Based Automatic First-Arrival Picking Method for Ultrasound Sound-Speed Tomography

Ultrasound sound-speed tomography (USST) has shown great prospects for breast cancer diagnosis due to its advantages of nonradiation, low cost, 3-D breast images, and quantitative indicators. However, the reconstruction quality of USST is highly dependent on the first-arrival picking of the transmission wave. Traditional first-arrival picking methods have low accuracy and noise robustness. To improve the accuracy and robustness, we introduced a self-attention mechanism into the bidirectional long short-term memory (BLSTM) network and proposed the self-attention BLSTM (SAT-BLSTM) network. The proposed method predicts the probability of the first-arrival time and selects the time with maximum probability. A numerical simulation and prototype experiment were conducted. In the numerical simulation, the proposed SAT-BLSTM showed the best results. For signal-to-noise ratios (SNRs) of 50, 30, and 15 dB, the mean absolute errors (MAEs) were 48, 49, and 76 ns, respectively. The BLSTM had the second-best results, with MAEs of 55, 56, and 85 ns, respectively. The MAEs of the Akaike information criterion (AIC) method were 57, 296, and 489 ns, respectively. In the prototype experiment, the MAEs of the SAT-BLSTM, the BLSTM, and the AIC were 94, 111, and 410 ns, respectively.

Fourier-Domain Ultrasonic Imaging of Cortical Bone Based on Velocity Distribution Inversion

There is a significant acoustic impedance contrast between the cortical bone and the surrounding soft tissue, resulting in difficulty for ultrasound penetration into bone tissue with high frequency. It is challenging for the conventional pulse-echo modalities to give accurate cortical bone images using uniform sound velocity model. To overcome these limitations, an ultrasound imaging method called full-matrix Fourier-domain synthetic aperture based on velocity inversion (FM-FDSA-VI) was developed to provide accurate cortical bone images. The dual linear arrays were located on the upper and lower sides of the imaging region. After full-matrix acquisition with two identical linear array probes facing each other, travel-time inversion was used to estimate the velocity distribution in advance. Then, full-matrix Fourier-domain synthetic aperture (FM-FDSA) imaging based on the estimated velocity model was applied twice to image the cortical bone, utilizing the data acquired from top and bottom linear array, respectively. Finally, to further improve the image quality, the two images were merged to give the ultimate result. The performance of the method was verified by two simulated models and two bone phantoms (i.e., regular and irregular hollow bone phantom). The mean relative errors of estimated sound velocity in the region-of-interest (ROI) are all below 12%, and the mean errors of cortical section thickness are all less than 0.3 mm. Compared to the conventional synthetic aperture (SA) imaging, the FM-FDSA-VI method is able to accurately image cortical bone with respect to the structure. Moreover, the result of irregular bone phantom was close to the image scanned by microcomputed tomography ( μ CT) in terms of macro geometry and thickness. It is demonstrated that the proposed FM-FDSA-VI method is an efficient way for cortical bone ultrasonic imaging.

Ultrasonic Imaging of High-contrasted Objects Based on Full-waveform Inversion: Limits under Fluid Modeling

Quantitative ultrasound techniques have been previously used to evaluate biological hard tissues, characterized by a large acoustic impedance contrast. Here, we are interested in the imaging of experimental data from different test-targets with high acoustic impedance contrast, using the Full Waveform Inversion (FWI) method to solve the inverse problem. This method is based on high-resolution numerical modeling of the forward problem of interaction between waves and medium, considering the full time series. To reduce the complexity of the numerical implementation, the model considers a fluid medium. Therefore, the aim is to evaluate the precision of the reconstruction under this assumption for materials with a different level of attenuation of shear waves, to study the limits of this hypothesis. Images of the sound speed obtained using the experimental data are presented, and the precision of the reconstruction is evaluated. Future work should include viscoelastic materials.

3D cone-beam breast ultrasonic tomography imaging for capacitive micromachined ultrasonic transducer cylindrical array

In this paper, a 3D cone-beam ultrasonic transmission tomography method for capacitive micromachined ultrasonic transducer (CMUT) cylindrical phased array was proposed. The performance of the proposed method was evaluated by numerical simulation experiments. After beam focusing of the transmitting array, the deviation of reconstructed sound attenuation distribution and sound speed distribution were respectively reduced by at least 71.4% and 46.4%. The research results in this paper will provide a good theoretical and practical foundation for the realization of ultrasonic imaging based on CMUT cylindrical array in the future.

Flexible ultrasonic array for breast-cancer diagnosis based on a self-shape-estimation algorithm

Breast cancer is a very common malignant tumour that typically occurs in women aged 35-70 years (accounting for 85% of patients). Recently, it has been appearing in younger women as well. Traditional ultrasonic transducers usually use a fixed array, which avoids the radiation from mammography, has a low cost, and can be used for repeated testing. This substantially benefits the clinical diagnosis of breast cancer. However, the fixed transducer-array diagnosis process exerts considerable pressure on the human body, which can easily cause mass displacement or unnecessary pain. Therefore, ultrasound breast cancer diagnosis without compression has attracted attention. In this study, we used a flexible ultrasonic array to record the ultrasound information of the mass, and proposed a mathematical model suitable for breast-cancer diagnosis. Then, we used a self-shape-estimation algorithm to obtain a two-dimensional (2D) ultrasound image of the breast cancer. The algorithm was tested with simulated and experimental array data, and its performance was evaluated according to the tumour location. The surface-shape error obtained through the numerical simulation was less than 0.8 mm, and the deviation in the estimated mass position was less than 1.24 mm. The tumour location was also obtained experimentally in a breast-cancer model. Therefore, the method proposed in this paper can realize ultrasound diagnoses and represents a new diagnostic tool for breast cancer.

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.

Source encoding for viscoacoustic ultrasound computed tomography

Ultrasound computed tomography (USCT) is a noninvasive imaging modality that has shown its clinical relevance for breast cancer diagnostics. As opposed to traveltime inversions, waveform-based inversions can exploit the full content of ultrasound data, thereby providing increased resolution. However, this is only feasible when modeling the full physics of wave propagation, accounting for 3D effects such as refraction and diffraction, and this comes at a significant computational cost. To mitigate this cost, a crosstalk-free source encoding method for explicit time-domain solvers is proposed. The gradient computation is performed with only two numerical "super" wave simulations, independent of the number of sources and receivers. Absence of crosstalk is achieved by considering orthogonal frequencies attributed to each source. By considering "double-difference" measurements, no a priori knowledge of the source time function is required. With this method, full-physics based 3D waveform inversions can be performed within minutes using reasonable computational resources, fitting clinical requirements.

Speed of sound ultrasound transmission tomography image reconstruction based on Bézier curves

Speed of Sound (SoS) maps from ultrasound tomography (UST) provide valuable quantitative information for soft tissue characterization and identification of lesions, making this technique interesting for breast cancer detection. However, due to the complexity of the processes that characterize the interaction of ultrasonic waves with matter, classic and fast tomographic algorithms such as back-projection are not suitable. Consequently, the image reconstruction process in UST is generally slow compared to other more conventional medical tomography modalities. With the aim of facilitating the translation of this technique into real clinical practice, several reconstruction algorithms are being proposed to make image reconstruction in UST to be a fast and accurate process. The geometrical acoustic approximation is often used to reconstruct SoS with less computational burden in comparison with full-wave inversion methods. In this work, we propose a simple formulation to perform on-the-flight reconstruction for UST using geometrical acoustics with refraction correction based on quadratic Bézier polynomials. Here we demonstrate that the trajectories created with these polynomials are an accurate approximation to reproduce the refracted acoustic paths connecting the emitter and receiver transducers. The method is faster than typical acquisition times in UST. Thus, it can be considered a step towards real-time reconstructions, which may contribute to its future clinical translation.

Breast Cancer Assessment With Pulse-Echo Speed of Sound Ultrasound From Intrinsic Tissue Reflections: Proof-of-Concept

PURPOSE

The aim of this study was to differentiate malignant and benign solid breast lesions with a novel ultrasound (US) technique, which measures speed of sound (SoS) using standard US transducers and intrinsic tissue reflections and scattering (speckles) as internal reference.

MATERIALS AND METHODS

This prospective, institutional review board-approved, Health Insurance Portability and Accountability Act-compliant prospective comparison study was performed with prior written informed consent from 20 women. Ten women with histological proven breast cancer and 10 with fibroadenoma were measured. A conventional US system with a linear probe was used for SoS-US (SonixTouch; Ultrasonix, Richmond, British Columbia, Canada). Tissue speckle reflections served as a timing reference for the US signals transmitted through the breasts. Relative phase inconsistencies were detected using plane wave measurements from different angular directions, and SoS images with 0.5-mm resolution were generated using a spatial domain reconstruction algorithm. The SoS of tumors were compared with the breast density of a larger cohort of 106 healthy women.

RESULTS

Breast lesions show focal increments ΔSoS (meters per second) with respect to the tissue background. Peak ΔSoS values were evaluated. Breast carcinoma showed significantly higher ΔSoS than fibroadenomas ([INCREMENT]SoS > 41.64 m/s: sensitivity, 90%; specificity, 80%; area under curve, 0.910) and healthy breast tissue of different densities (area under curve, 0.938; sensitivity, 90%; specificity, 96.5%). The lesion localization in SoS-US images was consistent with B-mode imaging and repeated SoS-US measurements were reproducible.

CONCLUSIONS

Using SoS-US, based on conventional US and tissue speckles as timing reference, breast carcinoma showed significantly higher SoS values than fibroadenoma and healthy breast tissue of different densities. The SoS presents a promising technique for differentiating solid breast lesions.

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.

Optimal experimental design for joint reflection-transmission ultrasound breast imaging: From ray- to wave-based methods

Ultrasound computed tomography (USCT) is an emerging modality to image the acoustic properties of the breast tissue for cancer diagnosis. With the need of improving the diagnostic accuracy of USCT, while maintaining the cost low, recent research is mainly focused on improving (1) the reconstruction methods and (2) the acquisition systems. D-optimal sequential experimental design (D-SOED) offers a method to integrate these aspects into a common systematic framework. The transducer configuration is optimized to minimize the uncertainties in the estimated model parameters, and to reduce the time to solution by identifying redundancies in the data. This work presents a formulation to jointly optimize the experiment for transmission and reflection data and, in particular, to estimate the speed of sound and reflectivity of the tissue using either ray-based or wave-based imaging methods. Uncertainties in the parameters can be quantified by extracting properties of the posterior covariance operator, which is analytically computed by linearizing the forward problem with respect to the prior knowledge about parameters. D-SOED is first introduced by an illustrative toy example, and then applied to real data. This shows that the time to solution can be substantially reduced, without altering the final image, by selecting the most informative measurements.

Quantitative assessment of breast density using transmission ultrasound tomography

Purpose

Breast density is important in the evaluation of breast cancer risk. At present, breast density is evaluated using two‐dimensional projections from mammography with or without tomosynthesis using either (a) subjective assessment or (b) a computer‐aided approach. The purpose of this work is twofold: (a) to establish an algorithm for quantitative assessment of breast density using quantitative three‐dimensional transmission ultrasound imaging; and (b) to determine how these quantitative assessments compare with both subjective and objective mammographic assessments of breast density.

Methods

We described and verified a threshold‐based segmentation algorithm to give a quantitative breast density (QBD) on ultrasound tomography images of phantoms of known geometric forms. We also used the algorithm and transmission ultrasound tomography to quantitatively determine breast density by separating fibroglandular tissue from fat and skin, based on imaged, quantitative tissue characteristics, and compared the quantitative tomography segmentation results with subjective and objective mammographic assessments.

Results

Quantitative breast density (QBD) measured in phantoms demonstrates high quantitative accuracy with respect to geometric volumes with average difference of less than 0.1% of the total phantom volumes. There is a strong correlation between QBD and both subjective mammographic assessments of Breast Imaging ‐ Reporting and Data System (BI‐RADS) breast composition categories and Volpara density scores — the Spearman correlation coefficients for the two comparisons were calculated to be 0.90 (95% CI: 0.71–0.96) and 0.96 (95% CI: 0.92–0.98), respectively.

Conclusions

The calculation of breast density using ultrasound tomography and the described segmentation algorithm is quantitatively accurate in phantoms and highly correlated with both subjective and Food and Drug Administration (FDA)‐cleared objective assessments of breast density.

Error analysis of speed of sound reconstruction in ultrasound limited angle transmission tomography

We have investigated limited angle transmission tomography to estimate speed of sound (SOS) distributions for breast cancer detection. That requires both accurate delineations of major tissues, in this case by segmentation of prior B-mode images, and calibration of the relative positions of the opposed transducers. Experimental sensitivity evaluation of the reconstructions with respect to segmentation and calibration errors is difficult with our current system. Therefore, parametric studies of SOS errors in our bent-ray reconstructions were simulated. They included mis-segmentation of an object of interest or a nearby object, and miscalibration of relative transducer positions in 3D. Close correspondence of reconstruction accuracy was verified in the simplest case, a cylindrical object in homogeneous background with induced segmentation and calibration inaccuracies. Simulated mis-segmentation in object size and lateral location produced maximum SOS errors of 6.3% within 10 mm diameter change and 9.1% within 5 mm shift, respectively. Modest errors in assumed transducer separation produced the maximum SOS error from miscalibrations (57.3% within 5 mm shift), still, correction of this type of error can easily be achieved in the clinic. This study should aid in designing adequate transducer mounts and calibration procedures, and in specification of B-mode image quality and segmentation algorithms for limited angle transmission tomography relying on ray tracing algorithms.

Quantitative transmission ultrasound tomography: Imaging and performance characteristics

PURPOSE

Quantitative Transmission (QT) ultrasound has shown promise as a breast imaging modality. This study characterizes the performance of the latest generation of QT ultrasound scanners: QT Scanner 2000.

METHODS

The scanner consists of a 2048-element ultrasound receiver array for transmission imaging and three transceivers for reflection imaging. Custom fabricated phantoms were used to quantify the imaging performance parameters. The specific performance parameters that have been characterized are spatial resolution (as point spread function), linear measurement accuracy, contrast to noise ratio, and image uniformity, in both transmission and reflection imaging modalities.

RESULTS

The intrinsic in-plane resolution was measured to be better than 1.5 mm and 1.0 mm for transmission and reflection modalities respectively. The linear measurement accuracy was measured to be, on average, approximately 1% for both the modalities. Speed of sound image uniformity and measurement accuracy were calculated to be 99.5% and <0.2% respectively. Contrast to noise ratio (CNR) measurements vary as a function of object size.

CONCLUSIONS

The results show an improvement in the imaging performance of the system in comparison to earlier ultrasound tomography systems, which are applicable to clinical applications of the system, such as breast imaging.

Numerical Modeling of Ultrasound Propagation in Weakly Heterogeneous Media Using a Mixed-Domain Method

A mixed-domain method (MDM) is presented in this paper for modeling one-way linear/nonlinear wave propagation in biological tissue with arbitrary heterogeneities, in which sound speed, density, attenuation coefficients, and nonlinear coefficients are all spatial varying functions. The present method is based on solving an integral equation derived from a Westervelt-like equation. One-dimensional problems are first studied to verify the MDM and to reveal its limitations. It is shown that this method is accurate for cases with small variation of sound speed. A 2-D case is further studied with focused ultrasound beams to validate the application of the method in the medical field. Results from the MATLAB toolbox k-Wave are used as the benchmark. Normalized root-mean-square (rms) error estimated at the focus of the transducer is 0.0133 when the coarsest mesh (1/3 of the wavelength) is used in the MDM. Fundamental and second-harmonic fields throughout the considered computational domains are compared and good agreement is observed. Overall, this paper demonstrates that the MDM is a computationally efficient and accurate method when used to model wave propagation in biological tissue with relatively weak heterogeneities.

The Application of an Ultrasound Tomography Algorithm in a Novel Ring 3D Ultrasound Imaging System

Currently, breast cancer is one of the most common cancers in women all over the world. A novel 3D breast ultrasound imaging ring system using the linear array transducer is proposed to decrease costs, reduce processing difficulties, and improve patient comfort as compared to modern day breast screening systems. The 1 × 128 Piezoelectric Micromachined Ultrasonic Transducer (PMUT) linear array is placed 90 degrees cross-vertically. The transducer surrounds the mammary gland, which allows for non-contact detection. Once the experimental platform is built, the breast model is placed through the electric rotary table opening and into a water tank that is at a constant temperature of 32 °C. The electric rotary table performs a 360° scan either automatically or mechanically. Pulse echo signals are captured through a circular scanning method at discrete angles. Subsequently, an ultrasonic tomography algorithm is designed, and a horizontal slice imaging is realized. The experimental results indicate that the preliminary detection of mass is realized by using this ring system. Circular scanning imaging is obtained by using a rotatable linear array instead of a cylindrical array, which allows the size and location of the mass to be recognized. The resolution of breast imaging is improved through the adjustment of the angle interval (>0.05°) and multiple slices are gained through different transducer array elements (1 × 128). These results validate the feasibility of the system design as well as the algorithm, and encourage us to implement our concept with a clinical study in the future.

Joint reconstruction of the initial pressure and speed of sound distributions from combined photoacoustic and ultrasound tomography measurements

The initial pressure and speed of sound (SOS) distributions cannot both be stably recovered from photoacoustic computed tomography (PACT) measurements alone. Adjunct ultrasound computed tomography (USCT) measurements can be employed to estimate the SOS distribution. Under the conventional image reconstruction approach for combined PACT/USCT systems, the SOS is estimated from the USCT measurements alone and the initial pressure is estimated from the PACT measurements by use of the previously estimated SOS. This approach ignores the acoustic information in the PACT measurements and may require many USCT measurements to accurately reconstruct the SOS. In this work, a joint reconstruction method where the SOS and initial pressure distributions are simultaneously estimated from combined PACT/USCT measurements is proposed. This approach allows accurate estimation of both the initial pressure distribution and the SOS distribution while requiring few USCT measurements.

Automatic Segmentation of Ultrasound Tomography Image

Ultrasound tomography (UST) image segmentation is fundamental in breast density estimation, medicine response analysis, and anatomical change quantification. Existing methods are time consuming and require massive manual interaction. To address these issues, an automatic algorithm based on GrabCut (AUGC) is proposed in this paper. The presented method designs automated GrabCut initialization for incomplete labeling and is sped up with multicore parallel programming. To verify performance, AUGC is applied to segment thirty-two in vivo UST volumetric images. The performance of AUGC is validated with breast overlapping metrics (Dice coefficient (D), Jaccard (J), and False positive (FP)) and time cost (TC). Furthermore, AUGC is compared to other methods, including Confidence Connected Region Growing (CCRG), watershed, and Active Contour based Curve Delineation (ACCD). Experimental results indicate that AUGC achieves the highest accuracy (D = 0.9275 and J = 0.8660 and FP = 0.0077) and takes on average about 4 seconds to process a volumetric image. It was said that AUGC benefits large-scale studies by using UST images for breast cancer screening and pathological quantification.