Quantised Angular Momentum Vectors and Projection Angle Distributions for Discrete Radon Transformations

International audienceA quantum mechanics based method is presented to generate sets of digital angles that may be well suited to describe projections on discrete grids. The resulting angle sets are an alternative to those derived using the Farey fractions from number theory. The Farey angles arise naturally through the definitions of the Mojette and Finite Radon Transforms. Often a subset of the Farey angles needs to be selected when reconstructing images from a limited number of views. The digital angles that result from the quantisation of angular momentum (QAM) vectors may provide an alternative way to select angle subsets. This paper seeks first to identify the important properties of digital angles sets and second to demonstrate that the QAM vectors are indeed a candidate set that fulfils these requirements. Of particular note is the rare occurrence of degeneracy in the QAM angles, particularly for the half-integral angular momenta angle sets

Modeling the Anisotropic Resolution and Noise Properties of Digital Breast Tomosynthesis

Digital breast tomosynthesis (DBT) is a 3D imaging modality in which a reconstruction of the breast is generated from various x-ray projections. Due to the newness of this technology, the development of an analytical model of image quality has been on-going. In this thesis, a more complete model is developed by addressing the limitations found in the previous linear systems (LS) model [Zhao, Med. Phys. 2008, 35(12): 5219-32]. A central assumption of the LS model is that the angle of x-ray incidence is approximately normal to the detector in each projection. To model the effect of oblique x-ray incidence, this thesis generalizes Swank\u27s calculations of the transfer functions of x-ray fluorescent screens to arbitrary incident angles. In the LS model, it is also assumed that the pixelation in the reconstruction grid is the same as the detector; hence, the highest frequency that can be resolved is the detector alias frequency. This thesis considers reconstruction grids with smaller pixelation to investigate super-resolution, or visibility of higher frequencies. A sine plate is introduced as a conceptual test object to analyze super-resolution. By orienting the long axis of the sine plate at various angles, the feasibility of oblique reconstruction planes is also investigated. This formulation differs from the LS model in which reconstruction planes are parallel to the breast support. It is shown that the transfer functions for arbitrary angles of x-ray incidence can be modeled in closed form. The high frequency modulation transfer function (MTF) and detective quantum efficiency (DQE) are degraded due to oblique x-ray incidence. In addition, using the sine plate, it is demonstrated that a reconstruction can resolve frequencies exceeding the detector alias frequency. Experimental images of bar patterns verified the existence of super-resolution. Anecdotal clinical examples showed that super-resolution improves the visibility of microcalcifications. The feasibility of oblique reconstructions was established theoretically with the sine plate and was validated experimentally with bar patterns. This thesis develops a more complete model of image quality in DBT by addressing the limitations of the LS model. In future studies, this model can be used as a tool for optimizing DBT

Multivalued Discrete Tomography Using Dynamical System That Describes Competition

Multivalued discrete tomography involves reconstructing images composed of three or more gray levels from projections. We propose a method based on the continuous-time optimization approach with a nonlinear dynamical system that effectively utilizes competition dynamics to solve the problem of multivalued discrete tomography. We perform theoretical analysis to understand how the system obtains the desired multivalued reconstructed image. Numerical experiments illustrate that the proposed method also works well when the number of pixels is comparatively high even if the exact labels are unknown

Imaging and 3D reconstruction of membrane protein complexes by cryo-electron microscopy and single particle analysis

Cryo-electron microscopy (cryo-EM) in combination with single particle image processing and volume reconstruction is a powerful technology to obtain medium-resolution structures of large protein complexes, which are extremely difficult to crystallize and not amenable to NMR studies due to size limitation. Depending on the stability and stiffness as well as on the symmetry of the complex, three-dimensional reconstructions at a resolution of 10-30 ˚ can be achieved. In this range of resolution, we may not be able to answer A chemical questions at the level of atomic interactions, but we can gain detailed insight into the macromolecular architecture of large multi-subunit complexes and their mechanisms of action. In this thesis, several prevalently large membrane protein complexes of great physiological importance were examined by various electron microscopy techniques and single particle image analysis. The core part of my work consists in the imaging of a mammalian V-ATPase, frozen-hydrated in amorphous ice and of the completion of the first volume reconstruction of this type of enzyme, derived from cryo-EM images. This ubiquitous rotary motor is essential in every eukaryotic cell and is of high medical importance due to its implication in various diseases such as osteoporosis, skeletal cancer and kidney disorders. My contribution to the second and third paper concerns the volume reconstruction of two bacterial outer membrane pore complexes from cryo-EM images recorded by my colleague Mohamed Chami. PulD from Klebsiella oxytoca constitutes a massive translocating pore capable of transporting a fully folded cell surface protein PulA through the membrane. It is part of the Type II secretion system, which is common for Gram-negative bacteria. The second volume regards ClyA, a pore-forming heamolytic toxin of virulent Escherichia coli and Salmonella enterica strains that kill target cells by inserting pores into their membranes. To the last two papers, I contributed with cryo-negative stain imaging of the cell division protein DivIVA from Bacillus subtilis and with image processing of the micrographs displaying the siderophore receptor FrpB from Neisseria meningitidis

Sequential slice object labeling in tomographic data via trajectory estimation

The increasing usage of volumetric imaging modalities, such as magnetic resonance imaging (MRI) and computed tomography (CT) in areas such as medicine and nondestructive evaluation (NDE) has placed a great importance on 3D visualization techniques. This growth of volume data in the form of cross sections has created the need for object labeling in volume data sets for 3D visualization. A sequential, slice-to-slice approach is proposed that is less computational and memory intensive than 3D connected-component labeling while achieving better results than the 2D overlap sequential processing approach. Labeling occurs while tracking each object through the 3D volume via updated trajectory approximation. This thesis is motivated by the desire to develop a labeling technique that captures key aspects of the human visual approach to the task. The proposed approach, while labeling 3D data, also provides a computationally efficient method by sequential processing of 2D slices instead of the whole 3D volume at once. Additionally, the proposed trajectory tracking approach performs correctly in many cases where current 2D sequential labeling techniques fail. Trajectory tracking for labeling is a new approach, representing the 3D objects as curves and performing 3D curve tracing to label the approximate trajectories of the objects. The labeled trajectories are then mapped back to the 3D objects to complete the labeling process. Development of the proposed labeling approach is discussed while multiple examples are presented. These examples are used to illustrate that the proposed approach performs correctly where the current overlap approach fails; examples are also used to show that the behavior of the proposed approach parallels that of the typical human approach to object tracking

An Overview of DNA Microarray Grid Alignment and Foreground Separation Approaches

This paper overviews DNA microarray grid alignment and foreground separation approaches. Microarray grid alignment and foreground separation are the basic processing steps of DNA microarray images that affect the quality of gene expression information, and hence impact our confidence in any data-derived biological conclusions. Thus, understanding microarray data processing steps becomes critical for performing optimal microarray data analysis. In the past, the grid alignment and foreground separation steps have not been covered extensively in the survey literature. We present several classifications of existing algorithms, and describe the fundamental principles of these algorithms. Challenges related to automation and reliability of processed image data are outlined at the end of this overview paper.</p

Optical projection tomography for whole organ imaging

In the past twenty years, far-reaching studies of molecular and cellular processes have reached a milestone in their maturation, and the knowledge from these studies was ready to apply at higher organizational levels. At that time, rodent models were long established. However, methods were inappropriate to image a whole rodent organ, such as the mouse brain, which drove the emergence of a new range of imaging techniques, later gathered under the name mesoscopy. Mesoscopic techniques filled a gap between classical microscopy and medical imaging techniques, such as magnetic resonance imaging, and X-ray computed tomography. They allow the acquisition of centimeter-sized samples. In this thesis, we focus on one of these mesoscopic imaging techniques called optical projection tomography, or OPT, and its potential application to Alzheimer's disease (AD) research. We review the fundamentals of OPT and describe the filtered back-projection algorithm, which is the primary tomographic reconstruction method of this technique. We also go through the implementation of OPT for whole mouse brain imaging, including sample preparation. We show that OPT is suitable to image the whole brain anatomy based on endogenous fluorescence, and the whole neural vasculature as well as amyloid plaques (a hallmark of AD) with adequate fluorescent markers. Then, we dwell on the characterization of OPT instruments. We give some insights on the instrument point spread function and discuss the influence of the number of projections on the quality of the reconstructed image. Afterward, we illustrate the application of OPT to study amyloidosis progression in a preliminary cross-sectional study, where we have used supervised learning to quantify the amyloid plaque load. In this study, we show that OPT can be used to quantify amyloidosis in whole mouse brains and that comparison between individuals of different age can be performed. Imaging of a whole mouse brain is unquestionably necessary. At this scale though, it has some constraints. We present the limitations of OPT, and we share how we think they can be circumvented by combining this modality with another microscopy technique, namely structured illumination microscopy. We see that this other microscopy technique has the potential to produce high-resolution zooms in selected regions of interest based on a prior OPT acquisition. The results presented in this work have led to the duplication of our OPT instrument in Lund University, and we hope they will help to foster advances in OPT and broaden its range of application. We also hope that this work will contribute to making OPT more accessible and user-friendly

Multi-Isotope Multi-Pinhole SPECT Bildgebung in kleinen Labortieren: Experimentelle Messungen und Monte Carlo Simulationen

Single photon emission computed tomography (SPECT) in small laboratory animals has become an integral part of translational medicine. It enables non-invasive validation of drug targeting, safety and efficacy in living organisms, which is progressively gaining importance in pharmaceutical industry. The increasing demand for efficiency in pharmaceutical research could be addressed by novel multitracer study designs. Multi-isotope multi-pinhole sampling allows validation of multiple tracers in a single experiment and consolidation of consecutive research trials. Due to physical and technical limitations, however, image quality and quantification can be substantially reduced. Advanced corrective procedures are required to establish multi-isotope multi-pinhole SPECT as a reliable and quantitative imaging technique for widespread use. For this purpose, the present work aimed to investigate the technical capabilities and physical limitations of multi-isotope multi-pinhole SPECT imaging in small laboratory animals. Based on experimental measurements and Monte Carlo simulations, specific error sources have been identified and procedures for quantitative image correction have been developed. A Monte Carlo simulation model of a state-of-the art SPECT/CT system has been established to provide a generalized framework for in-silico optimization of imaging hardware, acquisition protocols and reconstruction algorithms. The findings of this work can be used to improve image quality and quantification of SPECT in-vivo data for multi-isotope applications. They guide through the laborious process of multi-isotope protocol optimization and support the 3R welfare initiative that aims to replace, reduce and refine animal experimentation.Die Einzelphotonen-Emissionscomputertomographie (SPECT) in kleinen Labortieren hat sich als wichtiger Bestandteil der translationalen Medizin etabliert. Sie ermöglicht die nicht-invasive Validierung der Zielgenauigkeit, Wirksamkeit und Sicherheit von Wirkstoffen in lebenden Organismen und gewinnt zunehmend an Bedeutung in der pharmazeutischen Industrie. Die Forderung nach mehr Effizienz in der pharmazeutischen Forschung könnte durch neuartige Multitracer-Studien adressiert werden. Die Multi-Isotopen Akquisition mit Multi-Pinhole Kollimatoren ermöglicht die Validierung mehrerer Tracer in einem einzelnen Experiment und die Konsolidierung konsekutiver Bildgebungsstudien. Aufgrund physikalischer und technischer Limitationen ist die Bildqualität und Quantifizierbarkeit bei diesem Verfahren jedoch häufig reduziert. Um die Multi-Isotopen SPECT als zuverlässige und quantitative Bildgebungsmethode für den breiten Einsatz zu etablieren sind komplexe Korrekturverfahren erforderlich. Ziel der vorliegenden Arbeit war daher, die technischen Möglichkeiten und physikalischen Limitationen der Multi-Isotopen SPECT-Bildgebung in kleinen Labortieren systematisch zu untersuchen. Mithilfe von experimentellen Messungen und Monte Carlo Simulationen wurden spezifische Fehlerquellen identifiziert und Verfahren zur quantitativen Bildkorrektur entwickelt. Zudem wurde das Monte-Carlo Modell eines neuartigen SPECT/CT-Systems etabliert, um eine Plattform für die in-silico Optimierung von Bildgebungshardware, Aufnahmeprotokollen und Rekonstruktionsalgorithmen zu schaffen. Die Ergebnisse dieser Arbeit können die Bildqualität und Quantifizierbarkeit von SPECT in-vivo Daten für Multi-Isotopen Anwendungen verbessern. Sie führen beispielhaft durch den Prozess der Multi-Isotopen Protokolloptimierung und unterstützen die 3R-Initiative mit dem Ziel, experimentelle Tierversuche zu vermeiden (Replace), zu vermindern (Reduce) und zu verbessern (Refine)