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Browsing by Author "Li, Xu"

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    Magnetoacoustic tomography with magnetic induction for electrical conductivity imaging of biological tissue.
    (2010-09) Li, Xu
    Electrical properties of biological tissue including conductivity and permittivity play important roles in many biomedical and clinical researches such as modeling neural or cardiac electrical activities and management of electromagnetic energy delivery to the body during clinical diagnosis and treatment. More importantly, these electrical properties may serve as an intrinsic contrast for anatomical or functional imaging. It is therefore of great value to noninvasively image the electrical properties of biological tissue with good accuracy and high spatial resolution. This dissertation research aims at developing and evaluating a new modality i.e. magnetoacoustic tomography with magnetic induction (MAT-MI), for imaging electrical conductivity distribution of biological tissue. In MAT-MI, a conductive object is placed in a static magnetic field and a time-varying magnetic stimulation is applied to induce eddy current inside the object volume. Within the static magnetic field, the Lorentz force acting on the induced eddy current causes mechanical movement of those charged particles in the object and leads to detectable ultrasound signals. These ultrasound signals can be acquired by ultrasound probes and used to reconstruct a high spatial resolution image that indicates the object's electrical conductivity contrast. We have proposed and investigated two types of MAT-MI approaches i.e. single-excitation MAT-MI and multi-excitation MAT-MI. The corresponding image reconstruction algorithms, simulation protocols and experiment systems have been developed for feasibility testing and performance evaluation. It is shown in our computer simulation and experiment studies that using the single-excitation MAT-MI we are able to image the conductivity boundaries of the object with several millimeter spatial resolution. In addition, we have also demonstrated that the multi-excitation MAT-MI approach allows us to further extract the internal information and reconstruct more completely the conductivity contrast of the object. For both approaches, two-dimensional (2D) and three-dimensional (3D) images of physical or tissue phantoms have been acquired and showed promising agreement with the target conductivity distribution. All the results we have collected so far from simulations and experiments suggest that the MAT-MI approach is potential to become an important noninvasive modality for electrical conductivity imaging of biological tissue.
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    On fully nonlinear elliptic and parabolic equations in domains with VMO coefficients
    (2013-04) Li, Xu
    We prove the solvability in Sobolev spaces Wp^(1,2), p>d+1, of the terminal-boundary value problem for a class of fully nonlinear parabolic equations, including parabolic Bellman's equations, in bounded cylindrical domains with VMO "coefficients". The solvability in Wp^2, p > d, of the corresponding elliptic boundary-value problem is also obtained.