3D printing in brachytherapy: A systematic review of gynecological applications.

PURPOSE: To provide a systematic review of the applications of 3D printing in gynecological brachytherapy. METHODS: Peer-reviewed articles relating to additive manufacturing (3D printing) from the 34 million plus biomedical citations in National Center for Biotechnology Information (NCBI/PubMed), and 53 million records in Web of Science (Clarivate) were queried for 3D printing applications. The results were narrowed sequentially to, (1) all literature in 3D printing with final publications prior to July 2022 (in English, and excluding books, proceedings, and reviews), and then to applications in, (2) radiotherapy, (3) brachytherapy, (4) gynecological brachytherapy. Brachytherapy applications were reviewed and grouped by disease site, with gynecological applications additionally grouped by study type, methodology, delivery modality, and device type. RESULTS: From 47,541 3D printing citations, 96 publications met the inclusion criteria for brachytherapy, with gynecological clinical applications compromising the highest percentage (32%), followed by skin and surface (19%), and head and neck (9%). The distribution of delivery modalities was 58% for HDR (Ir-192), 35% for LDR (I-125), and 7% for other modalities. In gynecological brachytherapy, studies included design of patient specific applicators and templates, novel applicator designs, applicator additions, quality assurance and dosimetry devices, anthropomorphic gynecological applicators, and in-human clinical trials. Plots of year-to-year growth demonstrate a rapid nonlinear trend since 2014 due to the improving accessibility of low-cost 3D printers. Based on these publications, considerations for clinical use are provided. CONCLUSIONS: 3D printing has emerged as an important clinical technology enabling customized applicator and template designs, representing a major advancement in the methodology for implantation and delivery in gynecological brachytherapy.

A robotically assisted 3D printed quality assurance lung phantom for Calypso.

Purpose. Radiation dose delivered to targets located near the upper-abdomen or in the thorax are significantly affected by respiratory-motion. Relatively large-margins are commonly added to compensate for this motion, limiting radiation-dose-escalation. Internal-surrogates of target motion, such as a radiofrequency (RF) tracking system, i.e. Calypso®System, are used to overcome this challenge and improve normal-tissue sparing. RF tracking systems consist of implanting transponders in the vicinity of the tumor to be tracked using radiofrequency-waves. Unfortunately, although the manufacture provides a universal quality-assurance (QA) phantom, QA-phantoms specifically for lung-applications are limited, warranting the development of alternative solutions to fulfil the tests mandated by AAPM's TG142. Accordingly, our objective was to design and develop a motion-phantom to evaluate Calypso for lung-applications that allows the Calypso®Beacons to move in different directions to better simulate truelung-motion.Methods and Materials.A Calypso lung QA-phantom was designed, and 3D-printed. The design consists of three independent arms where the transponders were attached. A pinpoint-chamber with a buildup-cap was also incorporated. A 4-axis robotic arm was programmed to drive the motion-phantom to mimic breathing. After acquiring a four-dimensional-computed-tomography (4DCT) scan of the motion-phantom, treatment-plans were generated and delivered on a Varian TrueBeam®with Calypso capabilities. Stationary and gated-treatment plans were generated and delivered to determine the dosimetric difference between gated and non-gated treatments. Portal cine-images were acquired to determine the temporal-accuracy of delivery by calculating the difference between the observed versus expected transponders locations with the known speed of the transponders' motion.Results.Dosimetric accuracy is better than the TG142 tolerance of 2%. Temporal accuracy is greater than, TG142 tolerance of 100 ms for beam-on, but less than 100 ms for beam-hold.Conclusions.The robotic QA-phantom designed and developed in this study provides an independent phantom for performing Calypso lung-QA for commissioning and acceptance testing of Calypso for lung treatments.

Automated multi-parameter high-dose-rate brachytherapy quality assurance via radioluminescence imaging.

The purpose of this study is to leverage radioluminescence imaging for the development of an automated high-dose-rate (HDR) brachytherapy quality assurance (QA) system that enables simultaneous measurements of dwell position, dwell time, wire velocity, and relative source strength in a single test. The system consists of a radioluminescence phosphor sheet (a mixture of Gd2O2S:Tb and PDMS) positioned atop a HDR needle applicator, a complementary metal-oxide-semiconductor digital camera used to capture the emitted radioluminescence signals from the scintillator sheet, and an in-house graphical user interface for signal processing. The signal processing was used to extract source intensity, location, and elapsed time, yielding the final measurements on dwell position, dwell time, and wire velocity. The source strength relative to the well chamber calibration (in unit of Air-Kerma strength, Sk ) is measured by establishing a calibration curve that correlates Sk with the detector response. Validation experiments are performed using three customized treatment plans. With these plans, the dwell position and dwell time are verified for a range of 110.0 cm-117.5 cm and 2 s-16 s, respectively, and the linear correlation with Sk is demonstrated for the source strength varying between 28 348 U (cGy cm2 h-1) and 41 906 U. The wire velocity, i.e. the speed of the radioactive source averaged over the distance in between dwell positions, is calculated for various distances ranging from 5 mm to 50 mm. Results show that the mean deviations of the measured dwell position and dwell time are 0.1 mm (range from 0 to 0.2 mm) and 32.5 ms (range from 0 to 60.0 ms) with respect to the planned values, respectively, and the system response is highly linear with Sk ( R2 = 0.998). Moreover, the measured wire velocities are comparable to previously reported values. Benefitting from the compact hardware design and image processing algorithms, the system provides a practical, reliable, and comprehensive solution for HDR QA.

Patient motion tracking for non-isocentric and non-coplanar treatments via fixed frame-of-reference 3D camera.

PURPOSE: As C-arm linac radiation therapy evolves toward faster, more efficient delivery, and more conformal dosimetry, treatments with increasingly complex couch motions are emerging. Monitoring the patient motion independently of the couch motion during non-coplanar, non-isocentric, or dynamic couch treatments is a key bottleneck to their clinical implementation. The goal of this study is to develop a prototype real-time monitoring system for unconventional beam trajectories to ensure a safe and accurate treatment delivery. METHODS: An in-house algorithm was developed for tracking using a couch-mounted three-dimensional (3D) depth camera. The accuracy of patient motion detection on the couch was tested on a 3D printed phantom created from the body surface contour exported from the treatment planning system. The technique was evaluated against a commercial optical surface monitoring system with known phantom displacements of 3, 5, and 7 mm in lateral, longitudinal, and vertical directions by placing a head phantom on a dynamic platform on the treatment couch. The stability of the monitoring system was evaluated during dynamic couch trajectories, at speeds between 10.6 and 65 cm/min. RESULTS: The proposed monitoring system agreed with the ceiling mounted optical surface monitoring system in longitudinal, lateral, and vertical directions within 0.5 mm. The uncertainty caused by couch vibration increased with couch speed but remained sub-millimeter for speeds up to 32 cm/min. For couch speeds of 10.6, 32.2, and 65 cm/min, the uncertainty ranges were 0.27- 0.73 mm, 0.15-0.87 mm, and 0.28-1.29 mm, respectively. CONCLUSION: By mounting a 3D camera in the same frame-of-reference as the patient and eliminating dead spots, this proof of concept demonstrates real-time patient monitoring during couch motion. For treatments with non-coplanar beams, multiple isocenters, or dynamic couch motion, this provides additional safety without additional radiation dose and avoids some of the complexity and limitations of room mounted systems.

Tungsten filled 3D printed field shaping devices for electron beam radiation therapy.

PURPOSE: Electron radiotherapy is a labor-intensive treatment option that is complicated by the need for field shaping blocks. These blocks are typically made from casting Cerrobend alloys containing lead and cadmium. This is a highly toxic process with limited precision. This work aims to provide streamlined and more precise electron radiotherapy by 3D using printing techniques. METHODS: The 3D printed electron cutout consists of plastic shells filled with 2 mm diameter tungsten ball bearings. Five clinical Cerrobend defined field were compared to the planned fields by measuring the light field edge when mounted in the electron applicator on a linear accelerator. The dose transmitted through the 3D printed and Cerrobend cutouts was measured using an IC profiler ion chamber array with 6 MeV and 16 MeV beams. Dose profiles from the treatment planning system were also compared to the measured dose profiles. Centering and full width half maximum (FWHM) metrics were taken directly from the profiler software. RESULTS: The transmission of a 16MeV beam through a 12 mm thick layer of tungsten ball bearings agreed within 1% of a 15 mm thick Cerrobend block (measured with an ion chamber array). The radiation fields shaped by ball bearing filled 3D printed cutout were centered within 0.4 mm of the planned outline, whereas the Cerrobend cutout fields had shift errors of 1-3 mm, and shape errors of 0.5-2 mm. The average shift of Cerrobend cutouts was 2.3 mm compared to the planned fields (n = 5). Beam penumbra of the 3D printed cutouts was found to be equivalent to the 15 mm thick Cerrobend cutout. The beam profiles agreed within 1.2% across the whole 30 cm profile widths. CONCLUSIONS: This study demonstrates that with a proper quality assurance procedure, 3D-printed cutouts can provide more accurate electron radiotherapy with reduced toxicity compared to traditional Cerrobend methods.

Binary moving-blocker-based scatter correction in cone-beam computed tomography with width-truncated projections: proof of concept.

This paper proposes a binary moving-blocker (BMB)-based technique for scatter correction in cone-beam computed tomography (CBCT). In concept, a beam blocker consisting of lead strips, mounted in front of the x-ray tube, moves rapidly in and out of the beam during a single gantry rotation. The projections are acquired in alternating phases of blocked and unblocked cone beams, where the blocked phase results in a stripe pattern in the width direction. To derive the scatter map from the blocked projections, 1D B-Spline interpolation/extrapolation is applied by using the detected information in the shaded regions. The scatter map of the unblocked projections is corrected by averaging two scatter maps that correspond to their adjacent blocked projections. The scatter-corrected projections are obtained by subtracting the corresponding scatter maps from the projection data and are utilized to generate the CBCT image by a compressed-sensing (CS)-based iterative reconstruction algorithm. Catphan504 and pelvis phantoms were used to evaluate the method's performance. The proposed BMB-based technique provided an effective method to enhance the image quality by suppressing scatter-induced artifacts, such as ring artifacts around the bowtie area. Compared to CBCT without a blocker, the spatial nonuniformity was reduced from 9.1% to 3.1%. The root-mean-square error of the CT numbers in the regions of interest (ROIs) was reduced from 30.2 HU to 3.8 HU. In addition to high resolution, comparable to that of the benchmark image, the CS-based reconstruction also led to a better contrast-to-noise ratio in seven ROIs. The proposed technique enables complete scatter-corrected CBCT imaging with width-truncated projections and allows reducing the acquisition time to approximately half. This work may have significant implications for image-guided or adaptive radiation therapy, where CBCT is often used.

Quality control procedures for dynamic treatment delivery techniques involving couch motion.

In this study, the authors introduce and demonstrate quality control procedures for evaluating the geometric and dosimetric fidelity of dynamic treatment delivery techniques involving treatment couch motion synchronous with gantry and multileaf collimator (MLC). Tests were designed to evaluate positional accuracy, velocity constancy and accuracy for dynamic couch motion under a realistic weight load. A test evaluating the geometric accuracy of the system in delivering treatments over complex dynamic trajectories was also devised. Custom XML scripts that control the Varian TrueBeam™ STx (Serial #3) axes in Developer Mode were written to implement the delivery sequences for the tests. Delivered dose patterns were captured with radiographic film or the electronic portal imaging device. The couch translational accuracy in dynamic treatment mode was 0.01 cm. Rotational accuracy was within 0.3°, with 0.04 cm displacement of the rotational axis. Dose intensity profiles capturing the velocity constancy and accuracy for translations and rotation exhibited standard deviation and maximum deviations below 3%. For complex delivery involving MLC and couch motions, the overall translational accuracy for reproducing programmed patterns was within 0.06 cm. The authors conclude that in Developer Mode, TrueBeam™ is capable of delivering dynamic treatment delivery techniques involving couch motion with good geometric and dosimetric fidelity.

Enhancement of four-dimensional cone-beam computed tomography by compressed sensing with Bregman iteration.

In four-dimensional (4D) cone-beam computed tomography (CBCT), there is a spatio-temporal tradeoff that currently limits the accuracy. The aim of this study is to develop a Bregman iteration based formalism for high quality 4D CBCT image reconstruction from a limited number of low-dose projections. The 4D CBCT problem is first divided into multiple 3D CBCT subproblems by grouping the projection images corresponding to the phases. To maximally utilize the information from the under-sampled projection data, a compressed sensing (CS) method with Bregman iterations is employed for solving each subproblem. We formulate an unconstrained optimization problem based on least-square criterion regularized by total-variation. The least-square criterion reflects the inconsistency between the measured and the estimated line integrals. Furthermore, the unconstrained problem is updated and solved repeatedly by Bregman iterations. The performance of the proposed algorithm is demonstrated through a series of simulation studies and phantom experiments, and the results are compared to those of previously implemented compressed sensing technique using other gradient-based methods as well as conventional filtered back-projection (FBP) results. The simulation and experimental studies have shown that artifact suppressed images can be obtained with as small as 41 projections per phase, which is adequate for clinical 4D CBCT reconstruction. With such small number of projections, the conventional FDK failed to yield meaningful 4D CBCT images, and CS technique using conjugate gradient was not able to recover sharp edges. The proposed method significantly reduces the radiation dose and scanning time to achieve the high quality images compared to the 4D CBCT imaging based on the conventional FDK technique and the existing CS techniques.

Radiation dose reduction in medical x-ray CT via Fourier-based iterative reconstruction.

PURPOSE: A Fourier-based iterative reconstruction technique, termed Equally Sloped Tomography (EST), is developed in conjunction with advanced mathematical regularization to investigate radiation dose reduction in x-ray CT. The method is experimentally implemented on fan-beam CT and evaluated as a function of imaging dose on a series of image quality phantoms and anonymous pediatric patient data sets. Numerical simulation experiments are also performed to explore the extension of EST to helical cone-beam geometry. METHODS: EST is a Fourier based iterative algorithm, which iterates back and forth between real and Fourier space utilizing the algebraically exact pseudopolar fast Fourier transform (PPFFT). In each iteration, physical constraints and mathematical regularization are applied in real space, while the measured data are enforced in Fourier space. The algorithm is automatically terminated when a proposed termination criterion is met. Experimentally, fan-beam projections were acquired by the Siemens z-flying focal spot technology, and subsequently interleaved and rebinned to a pseudopolar grid. Image quality phantoms were scanned at systematically varied mAs settings, reconstructed by EST and conventional reconstruction methods such as filtered back projection (FBP), and quantified using metrics including resolution, signal-to-noise ratios (SNRs), and contrast-to-noise ratios (CNRs). Pediatric data sets were reconstructed at their original acquisition settings and additionally simulated to lower dose settings for comparison and evaluation of the potential for radiation dose reduction. Numerical experiments were conducted to quantify EST and other iterative methods in terms of image quality and computation time. The extension of EST to helical cone-beam CT was implemented by using the advanced single-slice rebinning (ASSR) method. RESULTS: Based on the phantom and pediatric patient fan-beam CT data, it is demonstrated that EST reconstructions with the lowest scanner flux setting of 39 mAs produce comparable image quality, resolution, and contrast relative to FBP with the 140 mAs flux setting. Compared to the algebraic reconstruction technique and the expectation maximization statistical reconstruction algorithm, a significant reduction in computation time is achieved with EST. Finally, numerical experiments on helical cone-beam CT data suggest that the combination of EST and ASSR produces reconstructions with higher image quality and lower noise than the Feldkamp Davis and Kress (FDK) method and the conventional ASSR approach. CONCLUSIONS: A Fourier-based iterative method has been applied to the reconstruction of fan-bean CT data with reduced x-ray fluence. This method incorporates advantageous features in both real and Fourier space iterative schemes: using a fast and algebraically exact method to calculate forward projection, enforcing the measured data in Fourier space, and applying physical constraints and flexible regularization in real space. Our results suggest that EST can be utilized for radiation dose reduction in x-ray CT via the readily implementable technique of lowering mAs settings. Numerical experiments further indicate that EST requires less computation time than several other iterative algorithms and can, in principle, be extended to helical cone-beam geometry in combination with the ASSR method.

Single-scan patient-specific scatter correction in computed tomography using peripheral detection of scatter and compressed sensing scatter retrieval.

PURPOSE: X-ray scatter results in a significant degradation of image quality in computed tomography (CT), representing a major limitation in cone-beam CT (CBCT) and large field-of-view diagnostic scanners. In this work, a novel scatter estimation and correction technique is proposed that utilizes peripheral detection of scatter during the patient scan to simultaneously acquire image and patient-specific scatter information in a single scan, and in conjunction with a proposed compressed sensing scatter recovery technique to reconstruct and correct for the patient-specific scatter in the projection space. METHODS: The method consists of the detection of patient scatter at the edges of the field of view (FOV) followed by measurement based compressed sensing recovery of the scatter through-out the projection space. In the prototype implementation, the kV x-ray source of the Varian TrueBeam OBI system was blocked at the edges of the projection FOV, and the image detector in the corresponding blocked region was used for scatter detection. The design enables image data acquisition of the projection data on the unblocked central region of and scatter data at the blocked boundary regions. For the initial scatter estimation on the central FOV, a prior consisting of a hybrid scatter model that combines the scatter interpolation method and scatter convolution model is estimated using the acquired scatter distribution on boundary region. With the hybrid scatter estimation model, compressed sensing optimization is performed to generate the scatter map by penalizing the L1 norm of the discrete cosine transform of scatter signal. The estimated scatter is subtracted from the projection data by soft-tuning, and the scatter-corrected CBCT volume is obtained by the conventional Feldkamp-Davis-Kress algorithm. Experimental studies using image quality and anthropomorphic phantoms on a Varian TrueBeam system were carried out to evaluate the performance of the proposed scheme. RESULTS: The scatter shading artifacts were markedly suppressed in the reconstructed images using the proposed method. On the Catphan©504 phantom, the proposed method reduced the error of CT number to 13 Hounsfield units, 10% of that without scatter correction, and increased the image contrast by a factor of 2 in high-contrast regions. On the anthropomorphic phantom, the spatial nonuniformity decreased from 10.8% to 6.8% after correction. CONCLUSIONS: A novel scatter correction method, enabling unobstructed acquisition of the high frequency image data and concurrent detection of the patient-specific low frequency scatter data at the edges of the FOV, is proposed and validated in this work. Relative to blocker based techniques, rather than obstructing the central portion of the FOV which degrades and limits the image reconstruction, compressed sensing is used to solve for the scatter from detection of scatter at the periphery of the FOV, enabling for the highest quality reconstruction in the central region and robust patient-specific scatter correction.

Scatter correction in cone-beam CT via a half beam blocker technique allowing simultaneous acquisition of scatter and image information.

PURPOSE: X-ray scatter incurred to detectors degrades the quality of cone-beam computed tomography (CBCT) and represents a problem in volumetric image guided and adaptive radiation therapy. Several methods using a beam blocker for the estimation and subtraction of scatter have been proposed. However, due to missing information resulting from the obstruction of the blocker, such methods require dual scanning or dynamically moving blocker to obtain a complete volumetric image. Here, we propose a half beam blocker-based approach, in conjunction with a total variation (TV) regularized Feldkamp-Davis-Kress (FDK) algorithm, to correct scatter-induced artifacts by simultaneously acquiring image and scatter information from a single-rotation CBCT scan. METHODS: A half beam blocker, comprising lead strips, is used to simultaneously acquire image data on one side of the projection data and scatter data on the other half side. One-dimensional cubic B-Spline interpolation/extrapolation is applied to derive patient specific scatter information by using the scatter distributions on strips. The estimated scatter is subtracted from the projection image acquired at the opposite view. With scatter-corrected projections where this subtraction is completed, the FDK algorithm based on a cosine weighting function is performed to reconstruct CBCT volume. To suppress the noise in the reconstructed CBCT images produced by geometric errors between two opposed projections and interpolated scatter information, total variation regularization is applied by a minimization using a steepest gradient descent optimization method. The experimental studies using Catphan504 and anthropomorphic phantoms were carried out to evaluate the performance of the proposed scheme. RESULTS: The scatter-induced shading artifacts were markedly suppressed in CBCT using the proposed scheme. Compared with CBCT without a blocker, the nonuniformity value was reduced from 39.3% to 3.1%. The root mean square error relative to values inside the regions of interest selected from a benchmark scatter free image was reduced from 50 to 11.3. The TV regularization also led to a better contrast-to-noise ratio. CONCLUSIONS: An asymmetric half beam blocker-based FDK acquisition and reconstruction technique has been established. The proposed scheme enables simultaneous detection of patient specific scatter and complete volumetric CBCT reconstruction without additional requirements such as prior images, dual scans, or moving strips.

A Bayesian approach to real-time 3D tumor localization via monoscopic x-ray imaging during treatment delivery.

PURPOSE: Monoscopic x-ray imaging with on-board kV devices is an attractive approach for real-time image guidance in modern radiation therapy such as VMAT or IMRT, but it falls short in providing reliable information along the direction of imaging x-ray. By effectively taking consideration of projection data at prior times and/or angles through a Bayesian formalism, the authors develop an algorithm for real-time and full 3D tumor localization with a single x-ray imager during treatment delivery. METHODS: First, a prior probability density function is constructed using the 2D tumor locations on the projection images acquired during patient setup. Whenever an x-ray image is acquired during the treatment delivery, the corresponding 2D tumor location on the imager is used to update the likelihood function. The unresolved third dimension is obtained by maximizing the posterior probability distribution. The algorithm can also be used in a retrospective fashion when all the projection images during the treatment delivery are used for 3D localization purposes. The algorithm does not involve complex optimization of any model parameter and therefore can be used in a "plug-and-play" fashion. The authors validated the algorithm using (1) simulated 3D linear and elliptic motion and (2) 3D tumor motion trajectories of a lung and a pancreas patient reproduced by a physical phantom. Continuous kV images were acquired over a full gantry rotation with the Varian TrueBeam on-board imaging system. Three scenarios were considered: fluoroscopic setup, cone beam CT setup, and retrospective analysis. RESULTS: For the simulation study, the RMS 3D localization error is 1.2 and 2.4 mm for the linear and elliptic motions, respectively. For the phantom experiments, the 3D localization error is < 1 mm on average and < 1.5 mm at 95th percentile in the lung and pancreas cases for all three scenarios. The difference in 3D localization error for different scenarios is small and is not statistically significant. CONCLUSIONS: The proposed algorithm eliminates the need for any population based model parameters in monoscopic image guided radiotherapy and allows accurate and real-time 3D tumor localization on current standard LINACs with a single x-ray imager.

Low-dose x-ray phase-contrast and absorption CT using equally sloped tomography.

Tomographic reconstruction from undersampled and noisy projections is often desirable in transmission CT modalities for purposes of low-dose tomography and fast acquisition imaging. However under such conditions, due to the violation of the Nyquist sampling criteria and the presence of noise, reconstructions with acceptable accuracy may not be possible. Recent experiments in transmission electron tomography and coherent diffraction microscopy have shown that the technique of equally sloped tomography (EST), an exact tomographic method utilizing an oversampling iterative Fourier-based reconstruction, provides more accurate image reconstructions when the number of projections is significantly undersampled relative to filtered back projection and algebraic iterative methods. Here we extend this technique by developing new reconstruction algorithms which allow for the incorporation of advanced mathematical regularization constraints, such as the nonlocal means total variational model, in a manner that is consistent with experimental projections. We then evaluate the resulting image quality of the developed algorithm through simulations and experiments at the European Synchrotron Radiation Facility on image quality phantoms using the x-ray absorption and phase contrast CT modalities. Both our simulation and experimental results have indicated that the method can reduce the number of projections by 60-75% in parallel beam modalities, while achieving comparable or better image quality than the conventional reconstructions. As large-scale and compact synchrotron radiation facilities are currently under rapid development worldwide, the implementation of low-dose x-ray absorption and phase-contrast CT can find broad applications in biology and medicine using these advanced x-ray sources.

Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy.

Microscopy has greatly advanced our understanding of biology. Although significant progress has recently been made in optical microscopy to break the diffraction-limit barrier, reliance of such techniques on fluorescent labeling technologies prohibits quantitative 3D imaging of the entire contents of cells. Cryoelectron microscopy can image pleomorphic structures at a resolution of 3-5 nm, but is only applicable to thin or sectioned specimens. Here, we report quantitative 3D imaging of a whole, unstained cell at a resolution of 50-60 nm by X-ray diffraction microscopy. We identified the 3D morphology and structure of cellular organelles including cell wall, vacuole, endoplasmic reticulum, mitochondria, granules, nucleus, and nucleolus inside a yeast spore cell. Furthermore, we observed a 3D structure protruding from the reconstructed yeast spore, suggesting the spore germination process. Using cryogenic technologies, a 3D resolution of 5-10 nm should be achievable by X-ray diffraction microscopy. This work hence paves a way for quantitative 3D imaging of a wide range of biological specimens at nanometer-scale resolutions that are too thick for electron microscopy.

Development and optimization of regularized tomographic reconstruction algorithms utilizing equally-sloped tomography.

We develop two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints. The founding structure of the developed algorithms is EST, a technique of tomographic acquisition and reconstruction first proposed by Miao in 2005 for performing tomographic image reconstructions from a limited number of noisy projections in an accurate manner by avoiding direct interpolations. EST has recently been successfully applied to coherent diffraction microscopy, electron microscopy, and computed tomography for image enhancement and radiation dose reduction. However, the bottleneck of EST lies in its slow speed due to its higher computation requirements. In this paper, we formulate the EST approach as a constrained problem and subsequently transform it into a series of linear problems, which can be accurately solved by the operator splitting method. Based on these mathematical formulations, we develop two iterative algorithms for tomographic image reconstructions through EST, which incorporate Bregman and continuative regularization. Our numerical experiment results indicate that the new tomographic image reconstruction algorithms not only significantly reduce the computational time, but also improve the image quality. We anticipate that EST coupled with the novel iterative algorithms will find broad applications in X-ray tomography, electron microscopy, coherent diffraction microscopy, and other tomography fields.

Three-dimensional structure determination from a single view.

The ability to determine the structure of matter in three dimensions has profoundly advanced our understanding of nature. Traditionally, the most widely used schemes for three-dimensional (3D) structure determination of an object are implemented by acquiring multiple measurements over various sample orientations, as in the case of crystallography and tomography, or by scanning a series of thin sections through the sample, as in confocal microscopy. Here we present a 3D imaging modality, termed ankylography (derived from the Greek words ankylos meaning 'curved' and graphein meaning 'writing'), which under certain circumstances enables complete 3D structure determination from a single exposure using a monochromatic incident beam. We demonstrate that when the diffraction pattern of a finite object is sampled at a sufficiently fine scale on the Ewald sphere, the 3D structure of the object is in principle determined by the 2D spherical pattern. We confirm the theoretical analysis by performing 3D numerical reconstructions of a sodium silicate glass structure at 2 A resolution, and a single poliovirus at 2-3 nm resolution, from 2D spherical diffraction patterns alone. Using diffraction data from a soft X-ray laser, we also provide a preliminary demonstration that ankylography is experimentally feasible by obtaining a 3D image of a test object from a single 2D diffraction pattern. With further development, this approach of obtaining complete 3D structure information from a single view could find broad applications in the physical and life sciences.

Radiation dose reduction and image enhancement in biological imaging through equally-sloped tomography.

Electron tomography is currently the highest resolution imaging modality available to study the 3D structures of pleomorphic macromolecular assemblies, viruses, organelles and cells. Unfortunately, the resolution is currently limited to 3-5nm by several factors including the dose tolerance of biological specimens and the inaccessibility of certain tilt angles. Here we report the first experimental demonstration of equally-sloped tomography (EST) to alleviate these problems. As a proof of principle, we applied EST to reconstructing frozen-hydrated keyhole limpet hemocyanin molecules from a tilt-series taken with constant slope increments. In comparison with weighted back-projection (WBP), the algebraic reconstruction technique (ART) and the simultaneous algebraic reconstruction technique (SART), EST reconstructions exhibited higher contrast, less peripheral noise, more easily detectable molecular boundaries and reduced missing wedge effects. More importantly, EST reconstructions including only two-thirds the original images appeared to have the same resolution as full WBP reconstructions, suggesting that EST can either reduce the dose required to reach a given resolution or allow higher resolutions to be achieved with a given dose. EST was also applied to reconstructing a frozen-hydrated bacterial cell from a tilt-series taken with constant angular increments. The results confirmed similar benefits when standard tilts are utilized.