Time domain reconstruction of sound speed and attenuation in ultrasound computed tomography using full wave inversion

Deep Learning With Physics-Embedded Neural Network for Full Waveform Ultrasonic Brain Imaging

The convenience, safety, and affordability of ultrasound imaging make it a vital non-invasive diagnostic technique for examining soft tissues. However, significant differences in acoustic impedance between the skull and soft tissues hinder the successful application of traditional ultrasound for brain imaging. In this study, we propose a physics-embedded neural network with deep learning based full waveform inversion (PEN-FWI), which can achieve reliable quantitative imaging of brain tissues. The network consists of two fundamental components: forward convolutional neural network (FCNN) and inversion sub-neural network (ISNN). The FCNN explores the nonlinear mapping relationship between the brain model and the wavefield, replacing the tedious wavefield calculation process based on the finite difference method. The ISNN implements the mapping from the wavefield to the model. PEN-FWI includes three iterative steps, each embedding the F CNN into the ISNN, ultimately achieving tomography from wavefield to brain models. Simulation and laboratory tests indicate that PEN-FWI can produce high-quality imaging of the skull and soft tissues, even starting from a homogeneous water model. PEN-FWI can achieve excellent imaging of clot models with constant uniform distribution of velocity, randomly Gaussian distribution of velocity, and irregularly shaped randomly distributed velocity. Robust differentiation can also be achieved for brain slices of various tissues and skulls, resulting in high-quality imaging. The imaging time for a horizontal cross-sectional imag e of the brain is only 1.13 seconds. This algorithm can effectively promote ultrasound-based brain tomography and provide feasible solutions in other fields.

On the utilization of the adjoint method in microwave tomography

In microwave imaging, the adjoint method is widely used for the efficient calculation of the update direction, which is then used to update the unknown model parameter. However, the utilization and the formulation of the adjoint method differ significantly depending on the imaging scenario and the applied optimization algorithm. Because of the problem-specific nature of the adjoint formulations, the dissimilarities between the adjoint calculations may be overlooked. Here, we have classified the adjoint method formulations into two groups: the direct and indirect methods. The direct method involves calculating the derivative of the cost function, whereas, in the indirect method, the derivative of the predicted data is calculated. In this review, the direct and indirect adjoint methods are presented, compared, and discussed. The formulations are explicitly derived using the two-dimensional wave equation in frequency and time domains. Finite-difference time-domain simulations are conducted to show the different uses of the adjoint methods for both single source-multiple receiver, and multiple transceiver scenarios. This study demonstrated that an appropriate adjoint method selection is significant to achieve improved computational efficiency for the applied optimization algorithm.

Demonstration Study of Reflector-Based Volumetric Speed-of-Sound Imaging With Linear Ultrasound Arrays

Conventional B-mode ultrasound imaging has difficulty in delineating homogeneous soft tissues with similar acoustic impedances, as the reflectivity depends on the acoustic impedance at the interface. As a quantitative imaging biomarker sensitive to alteration of biomechanical properties, speed-of-sound (SoS) holds promising potential for tissue and disease differentiation such as delineation of different breast tissue types with similar acoustic impedance. Compared to two-dimensional (2D) SoS images, three-dimensional (3D) volumetric SoS images achieved through a full-angle ultrasound scan can reveal more intricate morphological structures of tissues; however, they generally require a ring transducer. In this study, we introduce a 3D SoS reconstruction system that utilizes hand-held linear arrays instead. This system employs a passive reflector positioned opposite the linear arrays, serving as an echogenic reference for time-of-flight (ToF) measurements, and a high-definition camera to track the location corresponding to each group of transmit-receive data. To merge these two streams of ToF measurements and location tracking, a voxel-based reconstruction algorithm is implemented. Experimental results with gelatin phantom and ex vivo tissue have demonstrated the stability of our proposed method. Moreover, the results underscore the potential of this system as a complementary diagnostic modality, particularly in the context of diseases such as breast cancer.

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.

A simulation study on the sensitivity of transcranial ray-tracing ultrasound modeling to skull properties

In transcranial focused ultrasound therapies, such as treating essential tremor via thermal ablation in the thalamus, acoustic energy is focused through the skull using a phased-array transducer. Ray tracing is a computationally efficient method that can correct skull-induced phase aberrations via per-element phase delay calculations using patient-specific computed tomography (CT) data. However, recent studies show that variations in CT-derived Hounsfield unit may account for only 50% of the speed of sound variability in human skull specimens, potentially limiting clinical transcranial ultrasound applications. Therefore, understanding the sensitivity of treatment planning methods to material parameter variations is essential. The present work uses a ray-tracing simulation model to explore how imprecision in model inputs, arising from clinically significant uncertainties in skull properties or considerations of acoustic phenomena, affects acoustic focusing quality through the skull. We propose and validate new methods to optimize ray-tracing skull simulations for clinical treatment planning, relevant for predicting intracranial target's thermal rise, using experimental data from ex-vivo human skulls.

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..

Location-Dependent Spatiotemporal Antialiasing in Photoacoustic Computed Tomography

Photoacoustic computed tomography (PACT) images optical absorption contrast by detecting ultrasonic waves induced by optical energy deposition in materials such as biological tissues. An ultrasonic transducer array or its scanning equivalent is used to detect ultrasonic waves. The spatial distribution of the transducer elements must satisfy the spatial Nyquist criterion; otherwise, spatial aliasing occurs and causes artifacts in reconstructed images. The spatial Nyquist criterion poses different requirements on the transducer elements' distributions for different locations in the image domain, which has not been studied previously. In this research, we elaborate on the location dependency through spatiotemporal analysis and propose a location-dependent spatiotemporal antialiasing method. By applying this method to PACT in full-ring array geometry, we effectively mitigate aliasing artifacts with minimal effects on image resolution in both numerical simulations and in vivo experiments.

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.

In Vivo Measurements of the Bulk Ultrasonic Attenuation Coefficient of Breast Tissue Using a Novel Phase-Insensitive Receiver

This study describes the first in vivo acoustic attenuation measurements of breast tissue undertaken using a novel phase-insensitive detection technique employing a differential pyroelectric sensor. The operation of the sensor is thermal in nature, with its output signal being dictated by the acoustic power integrated over its surface. The particularly novel feature of the sensor lies in its differential principle of operation, which significantly enhances its immunity to background acoustic and vibration noise. A large area variant of the sensor was used to detect ultrasonic energy generated by an array of 14 discrete 3.2-MHz plane piston transducers, transmitted through pendent breasts in water. The transduction and reception capability represent key parts of a prototype Quantitative Ultrasound Computed Tomography Test Facility developed at the National Physical Laboratory to study the efficacy of phase-insensitive ultrasound computed tomography of breast phantoms containing a range of appropriate inclusions, in particular, the measurement uncertainties associated with quantitative reconstructions of the acoustic attenuation coefficient. For this study, attenuation coefficient measurements were made using 1-D projections on 12 nominally healthy study volunteers, whose age ranged from 19 to 65 years. Averaged or bulk attenuation coefficient values were generated in the range 1.7-4.6 dBcm ^-1 at 3.2 MHz and have been compared with existing literature, derived from in vivo and ex vivo studies. Results are encouraging and indicate that the relatively simple technique could be applied as a robust method for assessing the properties of breast tissue, particularly the balance of fatty (adipose) and fibroglandular components.

Generation of Prior Information in a Dual-Mode Microwave-Ultrasound Breast Imaging System

A new breast imaging system capable of obtaining ultrasound and microwave scattered-field measurements with minimal or no movement of the breast between measurements has recently been reported. In this work, we describe the methodology that has been developed to generate prior information about the internal structures of the breast based on ultrasound data measured with the dual-mode system. This prior information, estimating both the geometry and complex-valued permittivity of tissues within the breast, is incorporated into the microwave inversion algorithm as a means of enhancing image quality. Several techniques to map reconstructed ultrasound speed to complex-valued relative permittivity are investigated. Quantitative images of two simplified dual-mode breast phantoms obtained using experimental data and the various forms of prior information are presented. Though preliminary, the results presented herein provide an understanding of the impacts of different forms of prior information on dual-mode reconstructions of the breast and can be used to inform future work on the subject.

Effects of Beamforming Techniques on Quality of Ultrasound Computed Tomography Images

BACKGROUND

In body tissues, tumors generally have different speeds of sound (SOS) than normal tissues. In this respect, ultrasound computed tomography (UCT) can generate a cross-sectional SOS map as an innovative ultrasound imaging method. This technique can produce images with a resolution of millimeters and a high signal-to-noise ratio.

OBJECTIVE

This study aimed to improve UCT image quality without increasing breast cancer screening and diagnosis time.

MATERIAL AND METHODS

In this analytical study, a ring-shaped UCT breast imaging system was simulated using the K-wave toolbox of MATLAB. The system has a 20 cm diameter and 256 ultrasonic piezoelectrics placed in the ring's circumference. Different beamforming techniques imaged two designed phantoms (i.e., resolution and contrast), and the resolution and contrast to noise ratio (CNR) were calculated.

RESULTS

The results of resolution phantom imaging without any beamforming showed that only bars with the value of 0.125 and 0.167 lp/mm were distinguishable, and the 0.1 bars were not recognizable in the imaging. In addition, increasing the number of transmitters led to no noticeable change in resolution for 0.125 and 0.167 lp/mm bars. In all beamforming techniques for imaging the contrast phantom, the CNR parameter up to an object with a diameter of 8 mm increases with increasing diameter without any change.

CONCLUSION

The beamforming technique using three simultaneous transmitters improved the resolution by about 1 mm compared to the normal strategy. In addition to high-contrast images, beamforming with 9 simultaneous transmitters led to a preferable technique.

Femoral neck phantom imaging using time-domain topological energy method

Ultrasonic bone imaging is a complex task, primarily because of the low energy contained in the signals reflected from the internal bone structures. In this study, the reconstruction of a bone-mimicking phantom echographic image using time-domain topological energy (TDTE) is proposed. A TDTE image results from a combination of forward and adjoint fields. The first is a solution of a numerical model that reproduces the setup of the experimental data acquisition to the best extent possible. The second has similar characteristics, but the source term is the time-reversed residue between the forward field and signals obtained from the experiment. The acquisition-reconstruction system used a linear phased-array transducer with a 5 MHz center frequency to acquire the signals and was coupled with a k-wave toolbox to implement the numerical models and perform the image reconstruction. The results showed good agreement between the geometry of the real phantom and the ultrasonic images. However, thickness evaluation errors were observed, which may be due to incorrect assumptions about the velocity models throughout the medium, a priori assumed to be known. Thus, this method has shown promising results and should be applied to the real femoral neck as a long-term objective.

Diffuse ultrasound computed tomography

An alternative approach to acquire transmission travel time data is proposed, exploiting the geometry of devices commonly used in ultrasound computed tomography for medical imaging or non-destructive testing with ultrasonic waves. The intent is to (i) shorten acquisition time for devices with a large number of emitters, (ii) to eliminate the calibration step, and (iii) to suppress instrument noise. Inspired by seismic ambient field interferometry, the method rests on the active excitation of diffuse ultrasonic wavefields and the extraction of deterministic travel time information by inter-station correlation. To reduce stochastic errors and accelerate convergence, ensemble interferograms are obtained by phase-weighted stacking of observed and computed correlograms, generated with identical realizations of random sources. Mimicking an imaging setup, the accuracy of the travel time measurements as a function of the number of emitters and random realizations can be assessed both analytically and with spectral-element simulations for phantoms mimicking the model parameter distribution. The results warrant tomographic reconstructions with straight- or bent-ray approaches, where the effect of inherent stochastic fluctuations can be made significantly smaller than the effect of subjective choices on regularisation. This work constitutes a first conceptual study and a necessary prelude to future implementations.

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.

Quantitative Sound Speed Imaging of Cortical Bone and Soft Tissue: Results From Observational Data Sets

This work presents the first quantitative ultrasonic sound speed images of ex vivo limb cross-sections containing both soft tissue and bone using Full Waveform Inversion (FWI) with level set (LS) and travel time regularization. The estimated bulk sound speed of bone and soft tissue are within 10% and 1%, respectively, of ground truth estimates. The sound speed imagery shows muscle, connective tissue and bone features. Typically, ultrasound tomography (UST) using FWI is applied to imaging breast tissue properties (e.g. sound speed and density) that correlate with cancer. With further development, UST systems have the potential to deliver volumetric operator independent tissue property images of limbs with non-ionizing and portable hardware platforms. This work addresses the algorithmic challenges of imaging the sound speed of bone and soft tissue by combining FWI with LS regularization and travel time methods to recover soft tissue and bone sound speed with improved accuracy and reduced soft tissue artifacts when compared to conventional FWI. The value of leveraging LS and travel time methods is realized by evidence of improved bone geometry estimates as well as promising convergence properties and reduced risk of final model errors due to un-modeled shear wave propagation. Ex vivo bulk measurements of sound speed and MRI cross-sections validates the final inversion results.

Local Sound Speed Estimation for Pulse-Echo Ultrasound in Layered Media

Our previous methodology in local sound speed estimation utilized time delays measured by the cross correlation of delayed full-synthetic aperture channel data to estimate the average speed of sound. However, focal distortions in this methodology lead to biased estimates of the average speed of sound, which, in turn, leads to biased estimates of the local speed of sound. Here, we demonstrate the bias in the previous methodology and introduce a coherence-based average sound speed estimator that eliminates this bias and is computationally much cheaper in practice. Because this coherence-based approach estimates the average sound speed in the medium over an equally spaced grid in depth rather than time, we derive a refined model that relates the local and average speeds of sound as a function of depth in layered media. A fast, closed-form inversion of this model yields highly accurate local sound speed estimates. The root-mean-square (rms) error of local sound speed reconstruction in simulations of two-layer media is 4.6 and 2.5 m/s at 4 and 8 MHz, respectively. This work examines the impact of frequency, f -number, aberration, and reverberation on sound speed estimation. Phantom and in vivo experiments in rats further validate the coherence-based sound speed estimator.

An Ultrasound Tomography Method for Monitoring CO2 Capture Process Involving Stirring and CaCO3 Precipitation

In this work, an ultrasound computed tomography (USCT) system was employed to investigate the fast-kinetic reactive crystallization process of calcium carbonate. USCT measurements and reconstruction provided key insights into the bulk particle distribution inside the stirred tank reactor and could be used to estimate the settling rate and settling time of the particles. To establish the utility of the USCT system for dynamical crystallization processes, first, the experimental imaging tasks were carried out with the stirred solid beads, as well as the feeding and stirring of the CaCO₃ crystals. The feeding region, the mixing process, and the particles settling time could be detected from USCT data. Reactive crystallization experiments for CO₂ capture were then conducted. Moreover, there was further potential for quantitative characterization of the suspension density in this process. USCT-based reconstructions were investigated for several experimental scenarios and operating conditions. This study demonstrates a real-time monitoring and fault detection application of USCT for reactive crystallization processes. As a robust noninvasive and nonintrusive tool, real-time signal analysis and reconstruction can be beneficial in the development of monitoring and control systems with real-world applications for crystallization processes. A diverse range of experimental studies shown here demonstrate the versatility of the USCT system in process application, hoping to unlock the commercial and industrial utility of the USCT devices.

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.

Deep-Learning-Driven Full-Waveform Inversion for Ultrasound Breast Imaging

Ultrasound breast imaging is a promising alternative to conventional mammography because it does not expose women to harmful ionising radiation and it can successfully image dense breast tissue. However, conventional ultrasound imaging only provides morphological information with limited diagnostic value. Ultrasound computed tomography (USCT) uses energy in both transmission and reflection when imaging the breast to provide more diagnostically relevant quantitative tissue properties, but it is often based on time-of-flight tomography or similar ray approximations of the wave equation, resulting in reconstructed images with low resolution. Full-waveform inversion (FWI) is based on a more accurate approximation of wave-propagation phenomena and can consequently produce very high resolution images using frequencies below 1 megahertz. These low frequencies, however, are not available in most USCT acquisition systems, as they use transducers with central frequencies well above those required in FWI. To circumvent this problem, we designed, trained, and implemented a two-dimensional convolutional neural network to artificially generate missing low frequencies in USCT data. Our results show that FWI reconstructions using experiment data after the application of the proposed method successfully converged, showing good agreement with X-ray CT and reflection ultrasound-tomography images.

Deep-Learning-Driven Full-Waveform Inversion for Ultrasound Breast Imaging

Ultrasound breast imaging is a promising alternative to conventional mammography because it does not expose women to harmful ionising radiation and it can successfully image dense breast tissue. However, conventional ultrasound imaging only provides morphological information with limited diagnostic value. Ultrasound computed tomography (USCT) uses energy in both transmission and reflection when imaging the breast to provide more diagnostically relevant quantitative tissue properties, but it is often based on time-of-flight tomography or similar ray approximations of the wave equation, resulting in reconstructed images with low resolution. Full-waveform inversion (FWI) is based on a more accurate approximation of wave-propagation phenomena and can consequently produce very high resolution images using frequencies below 1 megahertz. These low frequencies, however, are not available in most USCT acquisition systems, as they use transducers with central frequencies well above those required in FWI. To circumvent this problem, we designed, trained, and implemented a two-dimensional convolutional neural network to artificially generate missing low frequencies in USCT data. Our results show that FWI reconstructions using experiment data after the application of the proposed method successfully converged, showing good agreement with X-ray CT and reflection ultrasound-tomography images.

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Quantitative Inspection of Complex-Shaped Parts Based on Ice-Coupled Ultrasonic Full Waveform Inversion Technology

Ultrasonic methods have been extensively developed in nondestructive testing for various materials and components. However, accurately extracting quantitative information about defects still remains challenging, especially for complex structures. Although the immersion technique is commonly used for complex-shaped parts, the large mismatch of acoustic impedance between water and metal prevents effective ultrasonic transmission and leads to a low signal-to-noise ratio(SNR). In this paper, a quantitative imaging method is proposed for complex-shaped parts based on an ice-coupled full waveform inversion (FWI) method. Numerical experiments were carried out to quantitatively inspect the various defects in a turbine blade. Firstly, the k-space pseudospectral method was applied to simulate ice-coupled ultrasonic testing for the turbine blade. The recorded full wavefields were then applied for a frequency-domain FWI based on the Limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) method. With a carefully selected iterative number and frequency, a successive-frequency FWI can well detect half wavelength defects. Extended studies on an open notch with different orientations and multiple adjacent defects proved its capability to detect different types of defects. Finally, an uncertainty analysis was conducted with inaccurate initial velocity models with a relative error of ±2%, demonstrating its robustness even with a certain inaccuracy. This study demonstrates that the proposed method has a high potential to inspect complex-shaped structures with an excellent resolution.

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.

Biomedical Photoacoustic Imaging With Unknown Spatially Distributed Ultrasound Sensor Array

OBJECTIVE

With the growth of interest in different medical study on biological function, non-invasive photoacoustic imaging of biological tissue attracts the interests for researchers. To eliminate the limited angle effect of photoacoustic imaging based on ultrasound linear array, spatially distributed ultrasound sensor array is applied. The accurate sensor array position determines the quality of the imaging results. In this study, we proposed three methods based on photoacoustic and ultrasound signals to enhance the imaging quality using a 256-element full-ring array.

METHODS

Groups of photoacoustic and ultrasound signals are used to regress the position of each element sensor.

RESULT

In phantom study and mouse brain study, photoacoustic imaging results can both yield details clearly with average error rate of less than 1% (50 [Formula: see text]).

CONCLUSION

The performance of our three methods have proved that they can be potentially applied to other ultrasound-based medical imaging studies with unknown distributed positions of sensor array to enhance the imaging quality.

SIGNIFICANCE

The proposed methods can contribute to precise biomedical imaging with unknown distributed positions of sensor array in different application scenarios.

Noninvasive multiparametric charac-terization of mammary tumors with transmission-reflection optoacoustic ultrasound

Development of imaging methods capable of furnishing tumor-specific morphological, functional, and molecular information is paramount for early diagnosis, staging, and treatment of breast cancer. Ultrasound (US) and optoacoustic (OA) imaging methods exhibit excellent traits for tumor imaging in terms of fast imaging speed, ease of use, excellent contrast, and lack of ionizing radiation. Here, we demonstrate simultaneous tomographic whole body imaging of optical absorption, US reflectivity, and speed of sound (SoS) in living mice. In vivo studies of 4T1 breast cancer xenografts models revealed synergistic and complementary value of the hybrid imaging approach for characterizing mammary tumors. While neovasculature surrounding the tumor areas were observed based on the vascular anatomy contrast provided by the OA data, the tumor boundaries could be discerned by segmenting hypoechoic structures in pulse-echo US images. Tumor delineation was further facilitated by enhancing the contrast and spatial resolution of the SoS maps with a full-wave inversion method. The malignant lesions could thus be distinguished from other hypoechoic regions based on the average SoS values. The reported findings corroborate the strong potential of the hybrid imaging approach for advancing cancer research in small animal models and fostering development of new clinical diagnostic approaches.

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.

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.

Ring Artifact Correction for Phase-Insensitive Ultrasound Computed Tomography

An algorithm was developed for the correction of ring artifacts in phase-insensitive ultrasound computed tomography attenuation images. Differences in the measurement sensitivity between the ultrasound transducer array elements cause discontinuities in the sinogram which manifest as rings and arcs in the reconstructed image. The magnitudes of the discontinuities are potentially time-varying and dependent on the attenuation being measured. The algorithm dynamically determines the measurement sensitivity of each transducer in the array during the scan by comparison with both the elements to its left and the elements to its right. Elements at either end of the array are corrected, assuming a zero-attenuation path. The two estimates of sensitivity are combined using a weighted mean similar to a Kalman filter. The algorithm was tested on simulated and experimentally acquired data. It was demonstrated to reduce the root-mean-square error (RMSE) of simulated images against ground-truth images by up to a factor of 50 compared with uncorrected images and to visibly reduce artifacts on images reconstructed from the experimentally acquired data.

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.

Therapeutic Systems and Technologies: State-of-the-Art Applications, Opportunities, and Challenges

In this review, we present current state-of-the-art developments and challenges in the areas of thermal therapy, ultrasound tomography, image-guided therapies, ocular drug delivery, and robotic devices in neurorehabilitation. Additionally, intellectual property and regulatory aspects pertaining to therapeutic systems and technologies are addressed.

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.

Ultrasonic wavefield inversion and migration in complex heterogeneous structures: 2D numerical imaging and nondestructive testing experiments

Delaminations, cracks and other defects in engineered structures often lie close to the theoretical resolution limit for ultrasonic waves. While ultrasonic waveform tomography has succeeded in detecting such features, recovery is difficult because it requires computationally expensive high-frequency numerical wave simulations and an accurate understanding of large-scale background variations of the engineered structure. Without such knowledge, small defects may be incorrectly imaged or go undetected altogether. To reduce computational cost and improve detection of small defects, a useful approach is to divide the waveform tomography procedure into two steps: first, a low-frequency model-building step aimed at recovering background structure, and second, a high-frequency imaging step targeting defects. The first is naturally formulated as waveform inversion for wavespeed parameters and the second as time reversal migration for reflectivity. Through synthetic test cases, we show that the two-step workflow appears more promising in most cases than a single-step inversion. In particular, we find that new workflow succeeds in the challenging scenario where the defect lies along preexisting layer interface in a composite bridge deck and in related experiments involving noisy data or inaccurate source parameters.