Learning a stable approximation of an existing but unknown inverse mapping: application to the half-time circular Radon transform.

Supervised deep learning-based methods have inspired a new wave of image reconstruction methods that implicitly learn effective regularization strategies from a set of training data. While they hold potential for improving image quality, they have also raised concerns regarding their robustness. Instabilities can manifest when learned methods are applied to find approximate solutions to ill-posed image reconstruction problems for which a unique and stable inverse mapping does not exist, which is a typical use case. In this study, we investigate the performance of supervised deep learning-based image reconstruction in an alternate use case in which a stable inverse mapping is known to exist but is not yet analytically available in closed form. For such problems, a deep learning-based method can learn a stable approximation of the unknown inverse mapping that generalizes well to data that differ significantly from the training set. The learned approximation of the inverse mapping eliminates the need to employ an implicit (optimization-based) reconstruction method and can potentially yield insights into the unknown analytic inverse formula. The specific problem addressed is image reconstruction from a particular case of radially truncated circular Radon transform (CRT) data, referred to as 'half-time' measurement data. For the half-time image reconstruction problem, we develop and investigate a learned filtered backprojection method that employs a convolutional neural network to approximate the unknown filtering operation. We demonstrate that this method behaves stably and readily generalizes to data that differ significantly from training data. The developed method may find application to wave-based imaging modalities that include photoacoustic computed tomography.

Volcanic arc rigidity variations illuminated by coseismic deformation of the 2011 Tohoku-oki M9.

Rock strength has long been linked to lithospheric deformation and seismicity. However, independent constraints on the related elastic heterogeneity are missing, yet could provide key information for solid Earth dynamics. Using coseismic Global Navigation Satellite Systems (GNSS) data for the 2011 M9 Tohoku-oki earthquake in Japan, we apply an inverse method to infer elastic structure and fault slip simultaneously. We find compliant material beneath the volcanic arc and in the mantle wedge within the partial melt generation zone inferred to lie above ~100 km slab depth. We also identify low-rigidity material closer to the trench matching seismicity patterns, likely associated with accretionary wedge structure. Along with traditional seismic and electromagnetic methods, our approach opens up avenues for multiphysics inversions. Those have the potential to advance earthquake and volcano science, and in particular once expanded to InSAR type constraints, may lead to a better understanding of transient lithospheric deformation across scales.

Spatiotemporal image reconstruction to enable high-frame-rate dynamic photoacoustic tomography with rotating-gantry volumetric imagers.

Significance: Dynamic photoacoustic computed tomography (PACT) is a valuable imaging technique for monitoring physiological processes. However, current dynamic PACT imaging techniques are often limited to two-dimensional spatial imaging. Although volumetric PACT imagers are commercially available, these systems typically employ a rotating measurement gantry in which the tomographic data are sequentially acquired as opposed to being acquired simultaneously at all views. Because the dynamic object varies during the data-acquisition process, the sequential data-acquisition process poses substantial challenges to image reconstruction associated with data incompleteness. The proposed image reconstruction method is highly significant in that it will address these challenges and enable volumetric dynamic PACT imaging with existing preclinical imagers. Aim: The aim of this study is to develop a spatiotemporal image reconstruction (STIR) method for dynamic PACT that can be applied to commercially available volumetric PACT imagers that employ a sequential scanning strategy. The proposed reconstruction method aims to overcome the challenges caused by the limited number of tomographic measurements acquired per frame. Approach: A low-rank matrix estimation-based STIR (LRME-STIR) method is proposed to enable dynamic volumetric PACT. The LRME-STIR method leverages the spatiotemporal redundancies in the dynamic object to accurately reconstruct a four-dimensional (4D) spatiotemporal image. Results: The conducted numerical studies substantiate the LRME-STIR method's efficacy in reconstructing 4D dynamic images from tomographic measurements acquired with a rotating measurement gantry. The experimental study demonstrates the method's ability to faithfully recover the flow of a contrast agent with a frame rate of 10 frames per second, even when only a single tomographic measurement per frame is available. Conclusions: The proposed LRME-STIR method offers a promising solution to the challenges faced by enabling 4D dynamic imaging using commercially available volumetric PACT imagers. By enabling accurate STIRs, this method has the potential to significantly advance preclinical research and facilitate the monitoring of critical physiological biomarkers.

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.

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.

Ideal Observer Computation by Use of Markov-Chain Monte Carlo With Generative Adversarial Networks.

Medical imaging systems are often evaluated and optimized via objective, or task-specific, measures of image quality (IQ) that quantify the performance of an observer on a specific clinically-relevant task. The performance of the Bayesian Ideal Observer (IO) sets an upper limit among all observers, numerical or human, and has been advocated for use as a figure-of-merit (FOM) for evaluating and optimizing medical imaging systems. However, the IO test statistic corresponds to the likelihood ratio that is intractable to compute in the majority of cases. A sampling-based method that employs Markov-chain Monte Carlo (MCMC) techniques was previously proposed to estimate the IO performance. However, current applications of MCMC methods for IO approximation have been limited to a small number of situations where the considered distribution of to-be-imaged objects can be described by a relatively simple stochastic object model (SOM). As such, there remains an important need to extend the domain of applicability of MCMC methods to address a large variety of scenarios where IO-based assessments are needed but the associated SOMs have not been available. In this study, a novel MCMC method that employs a generative adversarial network (GAN)-based SOM, referred to as MCMC-GAN, is described and evaluated. The MCMC-GAN method was quantitatively validated by use of test-cases for which reference solutions were available. The results demonstrate that the MCMC-GAN method can extend the domain of applicability of MCMC methods for conducting IO analyses of medical imaging systems.

Stochastic three-dimensional numerical phantoms to enable computational studies in quantitative optoacoustic computed tomography of breast cancer.

Significance: When developing a new quantitative optoacoustic computed tomography (OAT) system for diagnostic imaging of breast cancer, objective assessments of various system designs through human trials are infeasible due to cost and ethical concerns. In prototype stages, however, different system designs can be cost-efficiently assessed via virtual imaging trials (VITs) employing ensembles of digital breast phantoms, i.e., numerical breast phantoms (NBPs), that convey clinically relevant variability in anatomy and optoacoustic tissue properties. Aim: The aim is to develop a framework for generating ensembles of realistic three-dimensional (3D) anatomical, functional, optical, and acoustic NBPs and numerical lesion phantoms (NLPs) for use in VITs of OAT applications in the diagnostic imaging of breast cancer. Approach: The generation of the anatomical NBPs was accomplished by extending existing NBPs developed by the U.S. Food and Drug Administration. As these were designed for use in mammography applications, substantial modifications were made to improve blood vasculature modeling for use in OAT. The NLPs were modeled to include viable tumor cells only or a combination of viable tumor cells, necrotic core, and peripheral angiogenesis region. Realistic optoacoustic tissue properties were stochastically assigned in the NBPs and NLPs. Results: To advance optoacoustic and optical imaging research, 84 datasets have been released; these consist of anatomical, functional, optical, and acoustic NBPs and the corresponding simulated multi-wavelength optical fluence, initial pressure, and OAT measurements. The generated NBPs were compared with clinical data with respect to the volume of breast blood vessels and spatially averaged effective optical attenuation. The usefulness of the proposed framework was demonstrated through a case study to investigate the impact of acoustic heterogeneity on OAT images of the breast. Conclusions: The proposed framework will enhance the authenticity of virtual OAT studies and can be widely employed for the investigation and development of advanced image reconstruction and machine learning-based methods, as well as the objective evaluation and optimization of the OAT system designs.

Bayesian Inference of Tissue Heterogeneity for Individualized Prediction of Glioma Growth.

Reliably predicting the future spread of brain tumors using imaging data and on a subject-specific basis requires quantifying uncertainties in data, biophysical models of tumor growth, and spatial heterogeneity of tumor and host tissue. This work introduces a Bayesian framework to calibrate the two-/three-dimensional spatial distribution of the parameters within a tumor growth model to quantitative magnetic resonance imaging (MRI) data and demonstrates its implementation in a pre-clinical model of glioma. The framework leverages an atlas-based brain segmentation of grey and white matter to establish subject-specific priors and tunable spatial dependencies of the model parameters in each region. Using this framework, the tumor-specific parameters are calibrated from quantitative MRI measurements early in the course of tumor development in four rats and used to predict the spatial development of the tumor at later times. The results suggest that the tumor model, calibrated by animal-specific imaging data at one time point, can accurately predict tumor shapes with a Dice coefficient 0.89. However, the reliability of the predicted volume and shape of tumors strongly relies on the number of earlier imaging time points used for calibrating the model. This study demonstrates, for the first time, the ability to determine the uncertainty in the inferred tissue heterogeneity and the model-predicted tumor shape.

A forward model incorporating elevation-focused transducer properties for 3D 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 volumentric imaging is achieved by translating the ring-array orthogonally to the imaging plane. In commonly deployed slice-by-slice (SBS) reconstruction approaches, the three-dimensional (3D) volume is reconstructed by stacking together two-dimensional (2D) images reconstructed for each position of the ring-array. A limitation of the SBS reconstruction approach is that it does not account for 3D wave propagation physics and the focusing properties of the transducers, which can result in significant image artifacts and inaccuracies. To perform 3D 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 3D computational model of an elevation-focused transducer is developed to enable 3D 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.

Heat-Resilient Schoolyards: Relations Between Temperature, Shade, and Physical Activity of Children During Recess.

BACKGROUND: Extreme heat may discourage physical activity of children while shade may provide thermal comfort. The authors determined the associations between ambient temperature, shade, and moderate to vigorous physical activity (MVPA) of children during school recess. METHODS: Children aged 8-10 (n = 213) wore accelerometers and global positioning system monitors during recess at 3 school parks in Austin, Texas (September-November 2019). Weather data originated from 10 sensors per park. The authors calculated shade from imagery using a geographic information system (GIS) and time-matched physical activity, location, temperature, and shade data. The authors specified piecewise multilevel regression to assess relations between average temperature and percentage of recess time in MVPA and shade. RESULTS: Temperature ranged 11 °C to 35 °C. Each 1 °C higher temperature was associated with a 0.7 percentage point lower time spent in MVPA, until 33 °C (91 °F) when the association changed to a 1.5 lower time (P < .01). Each 1 °C higher temperature was associated with a 0.3 percentage point higher time spent under shade, until 33 °C when the association changed to a 3.4 higher time (P < .001). At 33 °C or above, the direct association between shade and MVPA weakened (P < .05), with no interaction effect above 33 °C (P > .05). Children at the park with the most tree canopy spent 6.0 percentage points more time in MVPA (P < .01). CONCLUSIONS: Children engage in less MVPA and seek shade during extreme heat and engage in more MVPA in green schoolyards. With climate change, schools should consider interventions (eg, organizing shaded play, tree planting) to promote heat safe MVPA.

Computing a projection operator onto the null space of a linear imaging operator: tutorial.

Many imaging systems can be approximately described by a linear operator that maps an object property to a collection of discrete measurements. However, even in the absence of measurement noise, such operators are generally "blind" to certain components of the object, and hence information is lost in the imaging process. Mathematically, this is explained by the fact that the imaging operator can possess a null space. All objects in the null space, by definition, are mapped to a collection of identically zero measurements and are hence invisible to the imaging system. As such, characterizing the null space of an imaging operator is of fundamental importance when comparing and/or designing imaging systems. A characterization of the null space can also facilitate the design of regularization strategies for image reconstruction methods. Characterizing the null space via an associated projection operator is, in general, a computationally demanding task. In this tutorial, computational procedures for establishing projection operators that map an object to the null space of a discrete-to-discrete imaging operator are surveyed. A new machine-learning-based approach that employs a linear autoencoder is also presented. The procedures are demonstrated by use of biomedical imaging examples, and their computational complexities and memory requirements are compared.

Normalization of optical fluence distribution for three-dimensional functional optoacoustic tomography of the breast.

SIGNIFICANCE: In three-dimensional (3D) functional optoacoustic tomography (OAT), wavelength-dependent optical attenuation and nonuniform incident optical fluence limit imaging depth and field of view and can hinder accurate estimation of functional quantities, such as the vascular blood oxygenation. These limitations hinder OAT of large objects, such as a human female breast. AIM: We aim to develop a measurement-data-driven method for normalization of the optical fluence distribution and to investigate blood vasculature detectability and accuracy for estimating vascular blood oxygenation. APPROACH: The proposed method is based on reasonable assumptions regarding breast anatomy and optical properties. The nonuniform incident optical fluence is estimated based on the illumination geometry in the OAT system, and the depth-dependent optical attenuation is approximated using Beer-Lambert law. RESULTS: Numerical studies demonstrated that the proposed method significantly enhanced blood vessel detectability and improved estimation accuracy of the vascular blood oxygenation from multiwavelength OAT measurements, compared with direct application of spectral linear unmixing without optical fluence compensation. Experimental results showed that the proposed method revealed previously invisible structures in regions deeper than 15 mm and/or near the chest wall. CONCLUSIONS: The proposed method provides a straightforward and computationally inexpensive approximation of wavelength-dependent effective optical attenuation and, thus, enables mitigation of the spectral coloring effect in functional 3D OAT imaging.

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.

Physical activity, sedentary time and cardiometabolic health indicators among Mexican children.

We examined the independent associations of moderate to vigorous physical activity (MVPA) and sedentary time (ST) with cardiometabolic indicators in Mexican children (4-6 years of age). We conducted a cross-sectional study (n = 400) using the measures of MVPA and ST (7-day accelerometry) and the following indicators: % body fat, waist circumference, body mass index (BMI) z-score, glycated haemoglobin, blood glucose, triglycerides, total cholesterol, low-density lipoprotein (LDL) cholesterol, high-density lipoprotein (HDL) cholesterol, leptin, adiponectin and resting blood pressure. We examined the independent associations of MVPA and ST with cardiometabolic indicators through confounder-adjusted and mutually adjusted (including both MVPA and ST) linear regression models. Confounder-adjusted models showed that MVPA was associated with higher BMI z-scores and lower adiponectin levels in girls and lower body fat among boys. ST was associated with higher body fat, in the full sample, and lower LDL cholesterol among boys. After mutually adjusting for MVPA and ST, MVPA (10-minute increase) remained significantly associated with BMI z-score in girls (ß = 0.187, 95% CI: 0.019, 0.356) and ST (60-minute increase) remained significantly associated with higher body fat (ß = 1.11%, 95% CI: 0.019, 2.203) among boys and higher glycated haemoglobin (ß = 0.047% points, 95% CI: 0.000, 0.094) in the full sample. In preschool-aged children, the objective measures of ST and MVPA were associated with small differences in cardiometabolic health indicators. ST was unfavourably associated with some cardiometabolic indicators even after adjusting for MVPA, and thus appeared to have a more significant role than MVPA, especially in boys. Future longitudinal studies should confirm these results.

Accelerometer-based physical activity levels among Mexican adults and their relation with sociodemographic characteristics and BMI: a cross-sectional study.

BACKGROUND: The objectives of this study were to describe the accelerometer based total and bout-specific PA levels for a representative sample of adults from Cuernavaca, Mexico, and to examine the relationships with sociodemographic characteristics and BMI status. METHODS: Cross sectional study of adults from Cuernavaca, Mexico (2011, n = 677). Participants wore Actigraph GT3X accelerometers for seven days and sociodemographic data was collected through a survey. Weight and height were objectively measured. Total minutes/week of moderate-to-vigorous PA (MVPA) and of MVPA occurring within bouts of at least ten minutes were obtained. Intensity-specific (moderate and vigorous) total PA and bouted-PA was also obtained. The relation of each PA variable with sex, age, socioeconomic status, education, marital status and BMI status was assessed using unadjusted and adjusted linear models. RESULTS: The mean total MVPA among adults from Cuernavaca was 221.3 ± 10.0 (median = 178.3 min/week). Average MVPA within bouts was 65.8 ± 4.7 min/week (median = 30.0 min/week). 9.7 % of total MVPA occurred within bouts. Significant associations were found for total and bout-specific MVPA with being male (positive) and owning a motor vehicle (negative). Additional associations were found for intensity-specific PA outcomes. Mexican adults were more active during weekdays than weekends, suggesting that PA may be more strongly driven by necessity (transport) than by choice (leisure). CONCLUSIONS: This is the first study to objectively measure PA for a representative sample of Mexican adults in an urban setting. The sociodemographic correlates vary from those known from high income countries, stressing the need for more correlate studies from lower-to-middle income countries.

Characterizing the rheology of fluidized granular matter.

In this study we characterize the rheology of fluidized granular matter subject to secondary forcing. Our approach consists of first fluidizing granular matter in a drum half filled with grains via simple rotation and then superimposing oscillatory shear perpendicular to the downhill flow direction. The response of the system is mostly linear, with a phase lag between the grain motion and the oscillatory forcing. The rheology of the system can be well characterized by the GDR MiDi model if the system is forced with slow oscillations. The model breaks down when the forcing time scale becomes comparable to the characteristic time for energy dissipation in the flow.