Information Fusion of Magnetic Resonance Images and Mammographic Scans for Improved Diagnostic Management of Breast Cancer

Medical imaging is critical to non-invasive diagnosis and treatment of a wide spectrum of medical conditions. However, different modalities of medical imaging employ/apply di erent contrast mechanisms and, consequently, provide different depictions of bodily anatomy. As a result, there is a frequent problem where the same pathology can be detected by one type of medical imaging while being missed by others. This problem brings forward the importance of the development of image processing tools for integrating the information provided by different imaging modalities via the process of information fusion. One particularly important example of clinical application of such tools is in the diagnostic management of breast cancer, which is a prevailing cause of cancer-related mortality in women. Currently, the diagnosis of breast cancer relies mainly on X-ray mammography and Magnetic Resonance Imaging (MRI), which are both important throughout different stages of detection, localization, and treatment of the disease. The sensitivity of mammography, however, is known to be limited in the case of relatively dense breasts, while contrast enhanced MRI tends to yield frequent 'false alarms' due to its high sensitivity. Given this situation, it is critical to find reliable ways of fusing the mammography and MRI scans in order to improve the sensitivity of the former while boosting the specificity of the latter. Unfortunately, fusing the above types of medical images is known to be a difficult computational problem. Indeed, while MRI scans are usually volumetric (i.e., 3-D), digital mammograms are always planar (2-D). Moreover, mammograms are invariably acquired under the force of compression paddles, thus making the breast anatomy undergo sizeable deformations. In the case of MRI, on the other hand, the breast is rarely constrained and imaged in a pendulous state. Finally, X-ray mammography and MRI exploit two completely di erent physical mechanisms, which produce distinct diagnostic contrasts which are related in a non-trivial way. Under such conditions, the success of information fusion depends on one's ability to establish spatial correspondences between mammograms and their related MRI volumes in a cross-modal cross-dimensional (CMCD) setting in the presence of spatial deformations (+SD). Solving the problem of information fusion in the CMCD+SD setting is a very challenging analytical/computational problem, still in need of efficient solutions. In the literature, there is a lack of a generic and consistent solution to the problem of fusing mammograms and breast MRIs and using their complementary information. Most of the existing MRI to mammogram registration techniques are based on a biomechanical approach which builds a speci c model for each patient to simulate the effect of mammographic compression. The biomechanical model is not optimal as it ignores the common characteristics of breast deformation across different cases. Breast deformation is essentially the planarization of a 3-D volume between two paddles, which is common in all patients. Regardless of the size, shape, or internal con guration of the breast tissue, one can predict the major part of the deformation only by considering the geometry of the breast tissue. In contrast with complex standard methods relying on patient-speci c biomechanical modeling, we developed a new and relatively simple approach to estimate the deformation and nd the correspondences. We consider the total deformation to consist of two components: a large-magnitude global deformation due to mammographic compression and a residual deformation of relatively smaller amplitude. We propose a much simpler way of predicting the global deformation which compares favorably to FEM in terms of its accuracy. The residual deformation, on the other hand, is recovered in a variational framework using an elastic transformation model. The proposed algorithm provides us with a computational pipeline that takes breast MRIs and mammograms as inputs and returns the spatial transformation which establishes the correspondences between them. This spatial transformation can be applied in different applications, e.g., producing 'MRI-enhanced' mammograms (which is capable of improving the quality of surgical care) and correlating between different types of mammograms. We investigate the performance of our proposed pipeline on the application of enhancing mammograms by means of MRIs and we have shown improvements over the state of the art

Evaluation of a diffraction-enhanced imaging (DEI) prototype and exploration of novel applications for clinical implementation of DEI

Conventional mammographic image contrast is derived from x-ray absorption, resulting in breast structure visualization due to density gradients that attenuate radiation without distinction between transmitted, scattered, or refracted x-rays. Diffraction-enhanced imaging (DEI) allows for increased contrast with decreased radiation dose compared to conventional mammographic imaging due to monochromatic x-rays, its unique refraction-based contrast mechanism, and excellent scatter rejection. Although laboratory breast imaging studies have demonstrated excellent breast imaging, important clinical translation and application studies are needed before the DEI system can be established as a useful breast imaging modality. This dissertation focuses on several important studies toward the development of a clinical DEI system. First, contrast-enhanced DEI was explored using commercially available contrast agents. Phantoms were imaged at a range of x-ray energies and relevant contrast agent concentrations. Second, we performed a reader study to determine if superior DEI contrast mechanisms preserve image quality as tissue thickness increases. Breast specimens were imaged at several thicknesses, and radiologist perception of lesion visibility was recorded. Lastly, a prototype DEI system utilizing an x-ray tube source was evaluated through a reader study. Breast tissue specimens were imaged on the traditional and prototype DEI systems, and expert radiologists evaluated image quality and pathology correlation. This dissertation will demonstrate proof-of-principle for contrast-enhanced DEI, establishing the feasibility of contrast-enhanced DEI using commercially available contrast agents. Further, it will show that DEI might be able to reduce breast compression, and thus the perception of pain during mammography, without significantly decreasing breast lesion visibility. Finally, this research shows the successful implementation of a DEI prototype, displaying breast features with approximately statistically equivalent visibility to the traditional DEI system. Together, this research is an important step toward the clinical translation of DEI, a technology with the potential to facilitate early breast cancer detection and diagnosis

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal