The introduction of dual energy CT, DECT, in the field of medical healthcare has made it possible to extract more information of the scanned objects. This in turn has the potential to improve the accuracy in radiation therapy dose planning. One problem that remains before successful material decomposition can be achieved however, is the presence of beam hardening and scatter artifacts that arise in a scan. Methods currently in clinical use for removal of beam hardening often bias the CT numbers. Hence, the possibility for an appropriate tissue decomposition is limited. Here a method for successful decomposition as well as removal of the beam hardening artifact is presented. The method uses effective linear attenuations for the five base materials, water, protein, adipose, cortical bone and marrow, to perform the decomposition on reconstructed simulated data. This is performed inside an iterative loop together with the polychromatic x-ray spectra to remove the beam hardening

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The phenomenon of x-ray beam hardening (BH) has significant impact on preclinical micro-CT imaging systems. The causal factors are the polyenergetic nature of x-ray beam used for imaging and the energy dependence of linear attenuation coefficient of the imaged material. With increase in length of propagation of beam in the imaged object, lower energy photons in the projected beam become preferentially absorbed. The beam "hardens" (as average energy increases) and progressively becomes more penetrating, causing underestimation of the attenuation coefficient. When this phenomenon is not accounted for during CT reconstruction, it results in images with nonuniform CT number values across regions of uniform density. It leads to severe errors in quantitative applications of micro-CT and degradation in diagnostic quality of images. Hence, correction for beam hardening effect is of foremost importance and has been an active area of research since the advent of micro -CT. The Siemens Inveon micro-CT system uses a common linearization approach for BH correction. It provides a set of standard default coefficients to be applied during CT reconstruction. However, our initial experiments with uniform water phantoms of varying diameters indicated that the correction coefficients provided by default in the Inveon system are applicable for imaging mouse-size (~28 mm) objects only. For larger objects the correction factors yielded incorrect CT values along with characteristic 'cupping' observed in the uniform region in the center of the phantom. This study provides an insight into the nature and characteristics of beam hardening on the Inveon CT system using water phantoms of varying sizes. We develop and test a beam hardening correction scheme based on linearization using cylindrical water phantoms of two different diameters - 28 mm and 71 mm, selected to represent mouse and rat sizes respectively. The measured non-linear relationship between attenuation and length of propagation is fitted to a polynomial function, which is used to estimate the effective monoenergetic attenuation coefficient for water. The estimated effective linear attenuation coefficient value is used to generate the expected sum of attenuation coefficients along each x-ray path through the imaged object. The acquired poly-energetic data is then linearized to expected projections using a third order polynomial fit, which is consistent with the Inveon BH model and software. The coefficients of this trinomial are then applied for BH correction during CT reconstruction. Correction achieved with the proposed model demonstrates effective removal of the characteristic cupping artifact that was observed when default BHC coefficients were applied. In addition to water phantoms, we also test the effectiveness of the proposed scheme using solid cylindrical phantoms of three different densities and composition. The proposed method was also used to measure the BH effect for 12 different kVp/filtration combinations. By generating twelve distinct sets of BHC coefficients, for each setting, we achieve a significant expansion in the quantitative performance of the Inveon CT system.

A reconstruction algorithm in computerized tomography is a procedure for reconstructing the attenuation coefficientscient, a real-valued function associated with the object of interest, from the measured projection data. Generally speaking, reconstruction algorithms in CT fall into two categories: direct, e.g., filtered back-projection (FBP), or iterative. In this thesis, we discuss a new fast matrix-free iterative reconstruction method based on a polyenergetic model. While most modern x-ray CT scanners rely on the well-known filtered back-projection algorithm, the corresponding reconstructions can be corrupted by beam hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. In this thesis, to compensate, we use an alternative model that accounts for differential absorption of polyenergetic x-ray photons and discretize it directly. We do not assume any prior knowledge about the physical properties of the scanned object. We study and implement different solvers and nonlinear unconstrained optimization methods, such as a Newton-like method and an extension of the Levenberg-Marquardt-Fletcher algorithm. We explain how we can use the structure of the Radon matrix and the properties of FBP to make our method matrix-free and fast. Finally, we discuss how we regularize our problem by applying different regularization methods, such as Tikhonov and regularization in the 1-norm. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization methods.

A reconstruction algorithm in computerized tomography is a procedure for reconstructing the attenuation coefficientscient, a real-valued function associated with the object of interest, from the measured projection data. Generally speaking, reconstruction algorithms in CT fall into two categories: direct, e.g., filtered back-projection (FBP), or iterative. In this thesis, we discuss a new fast matrix-free iterative reconstruction method based on a polyenergetic model. While most modern x-ray CT scanners rely on the well-known filtered back-projection algorithm, the corresponding reconstructions can be corrupted by beam hardening artifacts. These artifacts arise from the unrealistic physical assumption of monoenergetic x-ray beams. In this thesis, to compensate, we use an alternative model that accounts for differential absorption of polyenergetic x-ray photons and discretize it directly. We do not assume any prior knowledge about the physical properties of the scanned object. We study and implement different solvers and nonlinear unconstrained optimization methods, such as a Newton-like method and an extension of the Levenberg-Marquardt-Fletcher algorithm. We explain how we can use the structure of the Radon matrix and the properties of FBP to make our method matrix-free and fast. Finally, we discuss how we regularize our problem by applying different regularization methods, such as Tikhonov and regularization in the 1-norm. We present numerical reconstructions based on the associated nonlinear discrete formulation incorporating various iterative optimization methods.

<p>X-ray computed tomography (CT) is a non-destructive medical imaging technique for assessing the cross-sectional images of an object in terms of attenuation. As it is designed based on the physical processes involved in the x-ray and matter interactions, faithfully modeling the physics in the reconstruction procedure can yield accurate attenuation distribution of the scanned object. Otherwise, unrealistic physical assumptions can result in unwanted artifacts in reconstructed images. For example, the current reconstruction algorithms assume the photons emitted by the x-ray source are mono-energetic. This oversimplified physical model neglects the poly-energetic properties of the x-ray source and the nonlinear attenuations of the scanned materials, and results in the well-known beam-hardening artifacts (BHAs). The purpose of this work was to incorporate the poly-energetic nature of the x-ray spectrum and then to eliminate BHAs. By accomplishing this, I can improve the image quality, enable the quantitative reconstruction ability of the single-spectrum CT scanner, and potentially reduce unnecessary radiation dose to patients.</p><p>In this thesis, in order to obtain accurate spectrum for poly-energetic reconstruction, I first presented a novel spectral estimation technique, with which spectra across a large range of angular trajectories of the imaging field of view can be estimated with a single phantom and a single axial acquisition. The experimental results with a 16 cm diameter cylindrical phantom (composition: ultra-high-molecular-weight polyethylene [UHMWPE]) on a clinical scanner showed that the averaged absolute mean energy differences and the normalized root mean square differences with respect to the actual spectra across kVp settings (i.e., 80, 100, 120, 140) and angular trajectories were less than 0.61 keV and 3.41%, respectively</p><p>With the previous estimation of the x-ray spectra, three poly-energetic reconstruction algorithms are proposed for different clinical applications. The first algorithm (i.e., poly-energetic iterative FBP [piFBP]) can be applied to routine clinical CT exams, as the spectra of the x-ray source and the nonlinear attenuations of diverse body tissues and metal implant materials are incorporated to eliminate BHAs and to reduce metal artifacts. The simulation results showed that the variation range of the relative errors of various tissues across different phantom sizes (i.e., 16, 24, 32, and 40 cm in diameter) and kVp settings (80, 100, 120, 140) were reduced from [-7.5%, 17.5%] for conventional FBP to [-0.1%, 0.1%] for piFBP, while the noise was maintained at the same low level (about [0.3%, 1.7%]).</p><p>When iodinated contrast agents are involved and patient motions are not readily correctable (e.g., in myocardial perfusion exam), a second algorithm (i.e., poly-energetic simultaneous algebraic reconstruction technique [pSART]) can be applied to eliminate BHAs and to quantitatively determine the iodine concentrations of blood-iodine mixtures with our new technique. The phantom experiment on a clinical CT scanner indicated that the maximum absolute relative error across material inserts was reduced from 4.1% for conventional simultaneous algebraic reconstruction technique [SART] to 0.4% for pSART.</p><p>Extending the work beyond minimizing BHAs, if patient motions are correctable or negligible, a third algorithm (i.e., poly-energetic dynamic perfusion algorithm [pDP]) is developed to retrieve iodine maps of any iodine-tissue mixtures in any perfusion exams, such as breast, lung, or brain perfusion exams. The quantitative results of the simulations with a dynamic anthropomorphic thorax phantom indicated that the maximum error of iodine concentrations can be reduced from 1.1 mg/cc for conventional FBP to less than 0.1 mg/cc for pDP.</p><p>Two invention disclosure forms based on the work presented in this thesis have been submitted to Office of Licensing & Ventures of Duke University.</p> / Dissertation

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Measuring void fraction distribution in two-phase flow has been a challenging task for many decades because of its complex and fast-changing interfacial structure. In this study, a non-intrusive X-ray measurement system is developed and calibrated to mitigate this challenge. This approach has several advantages over the conventional methods such as the multi-sensor conductivity probe, wire-mesh sensor, impedance void meter, or direct optical imaging. The X-ray densitometry technique is non-intrusive, insensitive to flow regime changes, capable of measuring high temperature or high-pressure flows, and has reasonable penetration depth. With the advancement of detector technology, the system developed in this work can further achieve high spatial resolution (100 micron per pixel) and high temporal resolution (1000 frames per second). This work mainly focuses on the following aspects of the system development: establishing a geometrical model for the line detector system, conducting spectral analysis for X-ray attenuation in two-phase flow, and performing calibration tests. The geometrical model has considered the measurement plane, geometry of the test-section wall and flow channel, relative position of the X-ray source and detector pixels. By assuming axisymmetry, an algorithm has been developed to convert void fraction distribution along the detector pixels to the radial void profile in a circular pipe. The X-ray spectral analysis yielded a novel prediction model for non-chromatic X-rays and non-uniform structure materials such as the internal two-phase flow which contains gas, liquid and solid wall materials. A calibration experiment has been carried out to optimize the detector conversion factor for each detector pixels. Finally, the data measured by the developed X-ray system are compared with the double-sensor conductivity probe and gas flow meter for sample bubbly flow and slug flow conditions. The results show reasonable agreement between these different measuring techniques. / Master of Science / Two-phase flow is a widely observed phenomenon in a nuclear reactor operation and thermal hydraulic applications during thermal energy transfer process. Hence, precise understanding of two-phase flow model is essential to a thermal hydraulic design and safe operation of nuclear reactor operation systems. However, two-phase flow analysis, via measuring void fraction distribution of a two-phase flow, has been a challenging task for many decades because of its complex and dynamical interfacial characteristics. In this study, a nonintrusive X-ray measuring technique is developed to mitigate some of the conventional challenges of void fraction measurement of a two-phase flow. The void fraction imagery via X-ray densitometry technique is insensitive to flow regime changes at high temperature or high pressure flows conditions with reasonable penetration depth capabilities. Together, with the advanced detector technology and spectral analysis of the X-ray attenuation in two-phase flow, this study delivers both qualitative and quantitative geometrical model for the line detector system to provide a radial void profile of a circular pipe. Moreover, the X-ray spectral analysis yielded a novel prediction model of a non-chromatic X-rays and non-uniform structure materials such as the internal two-phase flow which contains gas, liquid, and solid pipe materials. A calibration experiment has been carried out to optimize the detector conversion factor for each detector pixels. Finally, the data measured by the developed X-ray system are compared with the double-sensor conductivity probe and gas flow meter for sample bubbly flow and slug flow conditions. The results show reasonable agreement between these different measuring techniques.

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