287 research outputs found

    Computer-Aided, Multi-Modal, and Compression Diffuse Optical Studies of Breast Tissue

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    Diffuse Optical Tomography and Spectroscopy permit measurement of important physiological parameters non-invasively through ~10 cm of tissue. I have applied these techniques in measurements of human breast and breast cancer. My thesis integrates three loosely connected themes in this context: multi-modal breast cancer imaging, automated data analysis of breast cancer images, and microvascular hemodynamics of breast under compression. As per the first theme, I describe construction, testing, and the initial clinical usage of two generations of imaging systems for simultaneous diffuse optical and magnetic resonance imaging. The second project develops a statistical analysis of optical breast data from many spatial locations in a population of cancers to derive a novel optical signature of malignancy; I then apply this data-derived signature for localization of cancer in additional subjects. Finally, I construct and deploy diffuse optical instrumentation to measure blood content and blood flow during breast compression; besides optics, this research has implications for any method employing breast compression, e.g., mammography

    Analysis of homogeneous waveguides via the meshless radial basis function-generated-finite-difference method

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    The radial basis function generatedfinite difference (RBFFD) method is applied to the analysis of homogenous waveguides. To this end, the Helmholtz equation and the boundary conditions are collocated on the waveguide cross section. At each collocation node, derivatives are locally approximated by RBFFD formulas based on polyharmonic splines supplemented with highdegree polynomials. As a result, a sparse matrix eigenvalue problem is obtained which allows cutoff wavenumbers and axial fields to be calculated. To illustrate the accuracy of the method, we consider a semicircular and an eccentric circular waveguides.This work was supported in part by the Spanish Government (MCIU/AEI) and the European Commission (FEDER, UE) under Research Projects PGC2018-098350-B-C21and PGC2018-098350-B-C22

    Radial Basis Function Generated Finite Differences for the Nonlinear Schrodinger Equation

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    Solutions to the one-dimensional and two-dimensional nonlinear Schrodinger (NLS) equation are obtained numerically using methods based on radial basis functions (RBFs). Periodic boundary conditions are enforced with a non-periodic initial condition over varying domain sizes. The spatial structure of the solutions is represented using RBFs while several explicit and implicit iterative methods for solving ordinary differential equations (ODEs) are used in temporal discretization for the approximate solutions to the NLS equation. Splitting schemes, integration factors and hyperviscosity are used to stabilize the time-stepping schemes and are compared with one another in terms of computational efficiency and accuracy. This thesis shows that RBFs can be used to numerically solve the NLS with reasonable accuracy. Integration factors and splitting methods yield improvements in stability at the cost of computation time; both methods produce solutions of similar accuracy while splitting methods are slightly less expensive to implement than integration factors (computation times were of the same order of magnitude). The use of hyperviscosity can lead to an improvement in stability but can also lead to increased errors if the relevant parameters are not chosen carefully

    DIFFUSE OPTICAL MEASUREMENTS OF HEAD AND NECK TUMOR HEMODYNAMICS FOR EARLY PREDICTION OF CHEMO-RADIATION THERAPY OUTCOMES

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    Chemo-radiation therapy is a principal modality for the treatment of head and neck cancers, and its efficacy depends on the interaction of tumor oxygen with free radicals. In this study, we adopted a novel hybrid diffuse optical instrument combining a commercial frequency-domain tissue oximeter (Imagent) and a custom-made diffuse correlation spectroscopy (DCS) flowmeter, which allowed for simultaneous measurements of tumor blood flow and blood oxygenation. Using this hybrid instrument we continually measured tumor hemodynamic responses to chemo-radiation therapy over the treatment period of 7 weeks. We also explored monitoring dynamic tumor hemodynamic changes during radiation delivery. Blood flow data analysis was improved by simultaneously extracting multiple parameters from one single autocorrelation function curve measured by DCS. Patients were classified into two groups based on clinical outcomes: a complete response (CR) group and an incomplete response (IR) group with remote metastasis and/or local recurrence within one year. Interestingly, we found human papilloma virus (HPV-16) status largely affected tumor homodynamic responses to therapy. Significant differences in tumor blood flow index (BFI) and reduced scattering coefficient (μs’) between the IR and CR groups were observed in HPV-16 negative patients at Week 3. Significant differences in oxygenated hemoglobin concentration ([HbO2]) and blood oxygen saturation (StO2) between the two groups were found in HPV-16 positive patients at Week 1 and Week 3, respectively. Receiver operating characteristic curves were constructed and results indicated high sensitivities and specificities of these hemodynamic parameters for early (within the first three weeks of the treatment) prediction of one-year treatment outcomes. Measurement of tumor hemodynamics may serve as a predictive tool allowing treatment selection based on biologic tumor characteristics. Ultimately, reduction of side effects in patients not benefiting from radiation treatment may be feasible

    Forward modelling 3-D geophysical electromagnetic field data with meshfree methods

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    Simulating geophysical electromagnetic (EM) data over real-life conductivity models requires numerical algorithms that can incorporate realistically complex geometry and topography. The most successful way to incorporate them is to use unstructured meshes in the discretization of an Earth model. Current mesh-based numerical methods that are capable of using such meshes have inherent drawbacks caused by generating 3-D unstructured meshes conforming to irregular geometries. Such a mesh generation process may become computationally expensive and unstable, and particularly so for EM inversion computations in which the forward modelling may be required many times. In this thesis I investigate the feasibility and applicability of radial basis function-based finite difference (RBF-FD), a meshfree method, in forward modelling 3-D EM data. In the meshfree method, the physical model is represented using only a set of unconnected points, effectively overcoming the issues related to the mesh generation. To improve numerical efficiency, unstructured point sets are used in the computation for the first time for EM problems. The computation is further accelerated by introducing a new type of radial basis function in the RBFFD method. The convergence and accuracy of the proposed RBF-FD method are demonstrated first via forward modelling gravity and gravity gradient data. The computational efficiency of the meshfree method is compared with that of using a more traditional finite element method. The meshfree method is then applied to forward model magnetotelluric data of which the effectiveness is demonstrated using three benchmark conductivity models from the literature. Faithful reproduction of the physics in the EM fields, e.g. discontinuous electric fields across the conductivity contrasts, is achieved by proposing a hybrid meshfree scheme which is a modification to standard meshfree algorithms. The hybrid method is also applied to simulate controlled-source EM data in the frame of both total-field and primary-secondary field approaches, in which the problems in dealing with singular source functions that cause singularities in the EM fields are addressed. For these two approaches, the accuracies of the proposed hybrid meshfree method in forward modelling the controlled-source EM data are demonstrated by using idealized 1-D layered models and a 3-D marine canonical disk model. The successful applications of the proposed meshfree method in modelling the above EM data suggest that the meshfree technique has the potential of becoming an important numerical method for simulating EM responses over complicated conductivity models

    General Relativity as a Biconformal Gauge Theory

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    We consider the conformal group of a space of dim n=p+q, with SO(p,q) metric. The quotient of this group by its homogeneous Weyl subgroup gives a principal fiber bundle with 2n-dim base manifold and Weyl fibers. The Cartan generalization to a curved 2n-dim geometry admits an action functional linear in the curvatures. Because symmetry is maintained between the translations and the special conformal transformations in the construction, these spaces are called biconformal; this same symmetry gives biconformal spaces overlapping structures with double field theories, including manifest T-duality. We establish that biconformal geometry is a form of double field theory, showing how general relativity with integrable local scale invariance arises from its field equations. While we discuss the relationship between biconformal geometries and the double field theories of T-dual string theories, our principal interest is the study of the gravity theory. We show that vanishing torsion and vanishing co-torsion solutions to the field equations overconstrain the system, implying a trivial biconformal space. With co-torsion unconstrained, we show that (1) the torsion-free solutions are foliated by copies of an n-dim Lie group, (2) torsion-free solutions generically describe locally scale-covariant general relativity with symmetric, divergence-free sources on either the co-tangent bundle of n-dim (p,q)-spacetime or the torus of double field theory, and (3) torsion-free solutions admit a subclass of spacetimes with n-dim non-abelian Lie symmetry. These latter cases include the possibility of a gravity-electroweak unification. It is notable that the field equations reduce all curvature components to dependence only on the solder form of an n-dim Lagrangian submanifold, despite the increased number of curvature components and doubled number of initial independent variables

    Geodetic Sciences

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    Space geodetic techniques, e.g., global navigation satellite systems (GNSS), Very Long Baseline Interferometry (VLBI), satellite gravimetry and altimetry, and GNSS Reflectometry & Radio Occultation, are capable of measuring small changes of the Earth�s shape, rotation, and gravity field, as well as mass changes in the Earth system with an unprecedented accuracy. This book is devoted to presenting recent results and development in space geodetic techniques and sciences, including GNSS, VLBI, gravimetry, geoid, geodetic atmosphere, geodetic geophysics and geodetic mass transport associated with the ocean, hydrology, cryosphere and solid-Earth. This book provides a good reference for geodetic techniques, engineers, scientists as well as user community
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