Equally Sloped Tomography Research Articles

Quantitative, in situ visualization of intracellular insulin vesicles in pancreatic beta cells

Characterizing relationships between Zn2+, insulin, and insulin vesicles is of vital importance to the study of pancreatic beta cells. However, the precise content of Zn2+ and the specific location of insulin inside insulin vesicles are not clear, which hinders a thorough understanding of the insulin secretion process and diseases caused by blood sugar dysregulation. Here, we demonstrated the colocalization of Zn2+ and insulin in both single extracellular insulin vesicles and pancreatic beta cells by using an X-ray scanning coherent diffraction imaging (ptychography) technique. We also analyzed the elemental Zn2+ and Ca2+ contents of insulin vesicles using electron microscopy and energy dispersive spectroscopy (EDS) mapping. We found that the presence of Zn2+ is an important characteristic that can be used to distinguish insulin vesicles from other types of vesicles in pancreatic beta cells and that the content of Zn2+ is proportional to the size of insulin vesicles. By using dual-energy contrast X-ray microscopy and scanning transmission X-ray microscopy (STXM) image stacks, we observed that insulin accumulates in the off-center position of extracellular insulin vesicles. Furthermore, the spatial distribution of insulin vesicles and their colocalization with other organelles inside pancreatic beta cells were demonstrated using three-dimensional (3D) imaging by combining X-ray ptychography and an equally sloped tomography (EST) algorithm. This study describes a powerful method to univocally describe the location and quantitative analysis of intracellular insulin, which will be of great significance to the study of diabetes and other blood sugar diseases.

Three-dimensional ultrastructural imaging reveals the nanoscale architecture of mammalian cells

Knowledge of the interactions between nanomaterials and large-size mammalian cells, including cellular uptake, intracellular localization and translocation, has greatly advanced nanomedicine and nanotoxicology. Imaging techniques that can locate nanomaterials within the structures of intact large-size cells at nanoscale resolution play crucial roles in acquiring this knowledge. Here, the quantitative imaging of intracellular nanomaterials in three dimensions was performed by combining dual-energy contrast X-ray microscopy and an iterative tomographic algorithm termed equally sloped tomography (EST). Macrophages with a size of ∼20 µm that had been exposed to the potential antitumour agent [Gd@C82(OH)22]n were investigated. Large numbers of nanoparticles (NPs) aggregated within the cell and were mainly located in phagosomes. No NPs were observed in the nucleus. Imaging of the nanomedicine within whole cells advanced the understanding of the high-efficiency antitumour activity and the low toxicity of this agent. This imaging technique can be used to probe nanomaterials within intact large-size cells at nanometre resolution uniformly in three dimensions and may greatly benefit the fields of nanomedicine and nanotoxicology.

NUDIM: A non-uniform fast Fourier transform based dual-space constraint iterative reconstruction method in biological electron tomography

Electron tomography, a powerful imaging tool for studying 3D structures of macromolecular assemblies, always suffers from imperfect reconstruction with limited resolution due to the intrinsic low signal-to-noise ratio (SNR) and inaccessibility to certain tilt angles induced by radiation damage or mechanical limitation. In order to compensate for such insufficient data with low SNR and further improve imaging resolution, prior knowledge constraints about the objects in both real space and reciprocal space are thus exploited during tomographic reconstruction. However, direct Fast Fourier transform (FFT) between real space and reciprocal space remains extraordinarily challenging owing to their inconsistent grid sampling modes, e.g. regular and uniform grid sampling in real space whereas radial or polar grid sampling in reciprocal space. In order to solve such problem, a technique of non-uniform fast Fourier transform (NFFT) has been developed to transform efficiently between non-uniformly sampled grids in real and reciprocal space with sufficient accuracy. In this work, a Non-Uniform fast Fourier transform based Dual-space constraint Iterative reconstruction Method (NUDIM) applicable to biological electron tomography is proposed with a combination of basic concepts from equally sloped tomography (EST) and NFFT based reconstruction. In NUDIM, the use of NFFT can circumvent such grid sampling inconsistency and thus alleviate the stringent equally-sloped sampling requirement in EST reconstruction, while the dual-space constraint iterative procedure can dramatically enhance reconstruction quality. In comparison with conventional reconstruction methods, NUDIM is numerically and experimentally demonstrated to produce superior reconstruction quality with higher contrast, less noise and reduced missing wedge artifacts. More importantly, it is also capable of retrieving part of missing information from a limited number of projections.

Nanoscale Detection of Subcellular Nanoparticles by X-Ray Diffraction Imaging for Precise Quantitative Analysis of Whole Cancer Cells.

Nanoparticles show great potential for drug delivery systems in cancer treatment and diagnosis, which mainly rely on the interaction between nanoparticles and living cells. However, there is still a lack of accurate and large field-of-view imaging techniques to reveal the aggregation and distribution behavior of nanoparticles in whole cancer cells without being destroyed. Here, we demonstrated quantitative imaging of unstained and intact mouse breast cancer cells (4T1) containing 50 nm gold nanoparticles (Au@citrate NPs) using an X-ray scanning coherent diffraction imaging (ptychography) technique in a large field-of-view. A two-dimensional spatial resolution of 17 nm was achieved on the 4T1 cell. We combine X-ray ptychography and equally sloped tomography (EST) to perform three-dimensional structural mapping, distribution, and aggregation behavior of Au@citrate NPs in cancer cells. By taking full advantage of the large field-of-view, high-resolution, and quantitative imaging technique, the single intracellular Au@citrate NPs are observed and the amount of Au@citrate NPs in aggregations can be accurately quantified. In addition, the morphological changes of lysosomes containing Au@citrate NPs can be observed in the high-contrast mass density images. This study provides an approach for exploring quantitative analysis and physiological delivery of nanomaterials in intact cancer cells at nanoscale resolution, which may greatly benefit the interdisciplinary research of material science, nanomedicine, and nanotoxicology.

Equally sloped tomography based X-ray full-field nano-CT at Shanghai Synchrotron Radiation Facility

X-ray full-field nano-computed tomography (nano-CT) has non-destructive three-dimensional imaging capabilities with high spatial resolution, and has been widely applied to investigate morphology and structures in various areas. Conventional tomography reconstructs a 3D object from a large number of equal-angle projections. For nano-CT, it takes long collecting time due to the large projection numbers and long exposure time. Here, equally-sloped tomography (EST) based nano-CT was implemented and constructed on X-ray imaging beamline at the Shanghai Synchrotron Radiation Facility (SSRF) to overcome or alleviate these difficulties. Preliminary results show that hard TXM with the spatial resolution of 100 nm and the EST-based nano-CT with the ability of 3D nano non-destructive characterization have been realized. This technique promotes hard X-ray imaging capability to nano scales at SSRF and could have applications in many fields including nanomaterials, new energy and life sciences. The study will be helpful for the construction of the new full field X-ray nano-imaging beamline with the spatial resolution of 20 nm at SSRF phase II project.

Three-dimensional ultrastructural imaging reveals the nanoscale architecture of mammalian cells.

Knowledge of the interactions between nanomaterials and large-size mammalian cells, including cellular uptake, intracellular localization and translocation, has greatly advanced nanomedicine and nanotoxicology. Imaging techniques that can locate nanomaterials within the structures of intact large-size cells at nanoscale resolution play crucial roles in acquiring this knowledge. Here, the quantitative imaging of intracellular nanomaterials in three dimensions was performed by combining dual-energy contrast X-ray microscopy and an iterative tomographic algorithm termed equally sloped tomography (EST). Macrophages with a size of ∼20 µm that had been exposed to the potential antitumour agent [Gd@C82(OH)22] n were investigated. Large numbers of nanoparticles (NPs) aggregated within the cell and were mainly located in phagosomes. No NPs were observed in the nucleus. Imaging of the nanomedicine within whole cells advanced the understanding of the high-efficiency antitumour activity and the low toxicity of this agent. This imaging technique can be used to probe nanomaterials within intact large-size cells at nanometre resolution uniformly in three dimensions and may greatly benefit the fields of nanomedicine and nanotoxicology.

A modified equally sloped algorithm based on the total variation algorithm in computed tomography for insufficient data.

Computed tomography (CT) has become an important technique for analyzing the inner structures of material, biological and energy fields. However, there are often challenges in the practical application of CT due to insufficient data. For example, the maximum rotation angle of the sample stage is limited by sample space or image reconstruction from the limited number of views required to reduce the X-ray dose delivered to the sample. Therefore, it is difficult to acquire CT images with complete data. In this work, an iterative reconstruction algorithm based on the minimization of the image total variation (TV) has been utilized to develop equally sloped tomography (EST), and the reconstruction was carried out from limited-angle, few-view and noisy data. A synchrotron CT experiment on hydroxyapatite was also carried out to demonstrate the ability of the TV-EST algorithm. The results indicated that the new TV-EST algorithm was capable of achieving high-quality reconstructions from projections with insufficient data.

B21-O-09Determination of Three-Dimensional Coordinates of Individual Atoms in Nano-Materials by Electron Tomography

Richard Feynman pointed out in his 1959 speech, “It would be very easy to make an analysis of any complicated chemical substance; all one would have to do would be to look at it and see where the atoms are… I put this out as a challenge: Is there no way to make the electron microscope more powerful?” Over more than 50 years, with significant achievements in electron microscope and the developments of aberration-corrected electron optics, scanning transmission electron microscopy (STEM) has reached spatial resolution of 0.5 Å. Recently, in combination of the state-of-the-art scanning transmission electron microscope (STEM) and a tomographic reconstruction technique known as equally sloped tomography (EST), we have achieved electron tomography at 2.4 angstrom resolution [ 1 ]. This general method has been applied to reveal almost all atoms inside a Pt nanoparticle with unprecedented details [ 2 ]. Most recently, Feynman's 1959 challenge has been tackled by successfully determining 3D coordinates of 3,769 individual atoms at the tip of a tungsten needle with a precision of ~19 picometers [ 3 ]. In this talk, I will present the achievements of this novel technique.

Beyond Crystallography: Coherent Diffraction Imaging and Atomic Resolution Electron Tomography

The discovery and interpretation of X-ray diffraction from crystals by von Laue, Henry and Lawrence Bragg about a century ago marked the beginning of a new era for visualizing the three-dimensional (3D) atomic structures in crystals. In 1999, the methodology of X-ray crystallography was extended to allow the structure determination of non-crystalline specimens, which is known as coherent diffraction imaging (CDI) or lensless imaging. In CDI, the diffraction pattern of a non-crystalline sample or a nanocrystal is first measured and then directly phased to obtain an image. The well-known phase problem is solved by combining the oversampling method with iterative algorithms. In the first part of the talk, I will present the principle of CDI and illustrate some applications using synchrotron radiation and X-ray free electron lasers (XFELs). In the second part of the talk, I will present a general tomographic method for determining the 3D local structure of materials at atomic resolution. By combining scanning transmission electron microscopy (STEM) with a novel data acquisition and image reconstruction method known as equally sloped tomography (EST), we achieve electron tomography at 2.4 Å resolution and observe nearly all the atoms in a multiply-twinned Pt nanoparticle. We find the existence of atomic steps at 3D twin boundaries of the Pt nanoparticle and, for the first time, image the 3D core structure of edge and screw dislocations in materials at atomic resolution. We expect this atomic resolution electron tomography method to find application in solid state physics, materials sciences, nanoscience, chemistry and biology.

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

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. 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. 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. 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.

SU‐E‐I‐144: Radiation Dose Reduction in Monochromatic Phase Contrast X‐Ray Mammography Using Equally Sloped Tomography

Purpose: In mammography, while maintaining the image quality, it is necessary to keep the delivered dose as low as possible since breast is a highly radiosensitive organ. Monochromatic phase contrast X‐ray mammography has shown its potential at higher sensitivity and lower impact in terms of dose delivery compared to absorption based diagnostic X‐ray mammography. An exact Fourier‐based iterative technique termed Equally Sloped Tomography(EST) has been newly developed and implemented on it. Using this technique, we conducted a series of comparative experiments to explore the further more radiation dose reduction in phase contrast mammography through reduction of projection numbers. Methods: Experiment took place at the biomedical beamline at ESRF(ID17). Full Human breasts samples were fixed in 4% formalin solution. Planar imaging and Computed Tomography(CT) modalities were combined to PCI techniques at 60KeV and using a 2kx2k taper optics CCD detector(45 micron pixel). The number of projections scanned was 2000 and digitally removed to 512 for reconstructions. Comparison reconstructions were produced by Filtered‐Back Projection(FBP) with a standard uncropped‐ramp filter. To optimize the result, Non‐local‐means regularization was applied for post‐processing in both cases. Results: Compared to the FBP reconstruction using 2000 projections, EST using 512 projections has comparable SNRs and CNRs, no obvious contrast degradation is observed between tumor and normal glandular tissue. In addition, the collagen exhibit similar visibility. Conclusions: Our results indicate that in the phase contrast mammography, EST technique can reduce the dose up to 50%∼75% by reducing number of projections, while images have comparable quality as the full dose FBP reconstruction. Furthermore, it makes the acquisition time 2∼4 times faster, which is important in in‐vivo imaging. The main reason for this is that EST is an exact Fourier‐based iterative algorithm that can incorporate different physical and mathematical constraints. It is always guided towards a lowest‐possible noisy state while keeping strictly consistent with measurements.Research sponsored by UC Discovery / TomoSoft Technologies Grant #ITL07‐10166.

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.

TU-B-201B-01: Radiation Dose Reduction in Medical X-Ray CT Using Equally-Sloped Tomography

Purpose: An exact Fourier‐based iterative reconstruction technique termed Equally‐Sloped Tomography (EST) has recently been developed to allow a reduction of radiation dose while maintaining image quality. Here we optimize this technique by incorporating a Gradient Descent algorithm with mathematical regularization constraints, including the Non‐Local Means Total Variation model. Using this technique, we conducted a series of comparative experiments to quantify the image quality, and explore radiation dose reduction in CT through reduction of X‐ray flux. Method and Materials: A standard quality control phantom containing multiple contrastvisibility and resolution inserts was imaged using a Siemens Somatom Sensation 64 scanner. The X‐ray flux was systematically lowered from 583mAs to 39mAs. All scans were performed under axial mode with constant tube current. Comparison reconstructions were produced by Filtered‐Back Projection (FBP) with a standard uncropped ramp filter. The resolution, signal‐to‐noise ratio (SNR) and contrast‐to‐noise ratio (CNR) were measured and compared as a function of flux. Results: Compared to the FBP reconstruction of 500mAs, the optimized EST reconstruction of 50mAs has comparable SNRs and CNRs. The low‐contrast regions of the phantom exhibit similar visibility. In addition, no resolution degradation is observed in the low‐dose EST reconstruction.Conclusion: As radiation dose is linearly proportional to the X‐ray flux, our results indicate that the optimized EST technique may potentially reduce the CT dose up to 90%, while producing comparable image resolution, quality and contrast as the full‐dose FBP reconstruction. The reasons that EST allows for significant reduction of the CT dose are because (i) an exact Fourier‐based iterative algorithm is used in the reconstruction where both physical and mathematical constraints can be naturally incorporated, (ii) the algorithm is guided towards a lowest‐possible noisy state, which is also strictly consistent with the measured data. Conflict of Interest: Research sponsored by UC Discovery / TomoSoft Technologies Grant #ITL07‐10166.

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.

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.

MO-D-332-06: Dose Reduction in CT Using a Novel Fourier-Based Iterative Reconstruction Method

Purpose: A novel Fourier‐based iterative acquisition and reconstruction method, termed Equally‐Sloped Tomography (EST), has been developed for reconstructing an image from an undersampled number of projections. We review this method and present the first series of comparative experiments and simulations quantifying the image quality and the dose reduction through this method. Method and Materials: Using the MOBY whole body mouse phantom and the Zubal whole body human phantom, CT simulations of EST vs. filtered back projection (FBP) and iterative algebraic methods were performed as function of number of projections and flux. The reconstruction image quality was quantified using SNR and CNR of contoured organs,modulation transfer function(MTF), and Fourier ring correlation (FRC). The simulations were experimentally verified using a cone‐beam x‐ray microCT scanner. A microfluidic resolution phantom and a MTF phantom were manufactured to quantify the experimental image quality. Using the microCT phantoms, the resolution, SNR, and CNR were tabulated as a function of flux and number of projections. Using this data, a dose reduction factor was calculated by determining the flux and number of projections that resulted in an equivalent SNR and resolution for EST relative to conventional reconstructions.Results: For the same number of projections and flux, all simulated and experimental reconstructions via EST resulted in better or equivalent SNR, FRC, and resolution relative to FBP. The dose reduction factor based on the SNR and resolution equivalence criteria was 35–45% for reconstructions with the number of projections above the Nyquist criteria and 40–50% dose reduction when the number of projections is undersampled. Conclusion: The results indicate that EST provides an effective method for dose reduction in CT and warrants further investigation. Conflict of Interest: Research sponsored by TomoSoft Technologies corporation.