Medical imaging is critical for the detection and diagnosis of disease, guided biopsies, assessment of therapies, and administration of treatment. While computerized tomography (CT), magnetic resonance imaging (MRI), positron emission tomography (PET), and ultra-sound (US) are the more familiar modalities, interest in yet other modalities continues to grow. Among the motivations are reduction of cost, avoidance of ionizing radiation, and the search for new information, including biochemical and molecular processes. Fluorescence Molecular Tomography (FMT) is one such emerging technique and, like other techniques, has its advantages and limitations. FMT can reconstruct the distribution of fluorescent molecules in vivo using near-infrared radiation or visible band light to illuminate the subject. FMT is very safe since non-ionizing radiation is used, and inexpensive due to the comparatively low cost of the imaging system. This should make it particularly well suited for small animal studies for research. A broad range of cell activity can be identified by FMT, making it a potentially valuable tool for cancer screening, drug discovery and gene therapy. Since FMT imaging is scattering dominated, reconstruction of volume images is significantly more computationally intensive than for CT. For instance, to reconstruct a 32x32x32 image, a flattened matrix with approximately 10¹°, or 10 billion, elements must be dealt with in the inverse problem, while requiring more than 100 GB of memory. To reduce the error introduced by noisy measurements, significantly more measurements are needed, leading to a proportionally larger matrix. The computational complexity of reconstructing FMT images, along with inaccuracies in photon propagation models, has heretofore limited the resolution and accuracy of FMT. To surmount the problems stated above, we decompose the forward problem into a Khatri-Rao product. Inversion of this model is shown to lead to a novel reconstruction method that significantly reduces the computational complexity and memory requirements for overdetermined datasets. Compared to the well known SVD approach, this new reconstruction method decreases computation time by a factor of up to 25, while simultaneously reducing the memory requirement by up to three orders of magnitude. Using this method, we have reconstructed images up to 32x32x32. Also outlined is a two step approach which would enable imaging larger volumes. However, it remains a topic for future research. In achieving the above, the author studied the physics of FMT, developed an extensive set of original computer programs, performed COMSOL simulations on photon diffusion, and unavoidably, developed visual displays.

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To effectively design systems of microchannels it is necessary for scientists and engineers to understand thermal transport characteristics of microchannels. To experimentally determine the convective heat transfer coefficient of microchannels it is necessary to measure both the bulk and surface temperature fields. This investigation aims to develop a technique, named Total Internal Reflection Fluorescent Micro-Thermometry (TIR-FMT), to measure the temperature of water within several hundred nanometers of a wall--effectively, the surface temperature of the wall. In TIR-FMT, an evanescent-wave is generated in the water near the wall. The intensity of this evanescent-wave decays exponentially with distance from the wall. A fluorophore if illuminated by the evanescent-wave can absorb a photon. Excited fluorophores subsequently emit red-shifted photons, which are called fluorescence. The probability of a fluorescent emission is temperature-dependent. Therefore, by monitoring the intensity of the fluorescence a correlation can be made to the temperature of the region of illumination. Using the TIR-FMT technique the temperature dependence of the fluorescence intensity from buffered fluorescein (pH=9.2) was determined to be 1.35%/C. TIR-FMT can be used to measure the temperature of a fluorophore solution within 600 nm of a wall across a temperature range of 12.5-55C. The average uncertainties (95% confidence) of the temperature measured was determined to be 2.3C and 1.5C for a single 1.5x1.5 and #956;m pixel and the entire 715x950 and #956;m viewfield. By spatial averaging, average uncertainties of 2.0C and 1.8C were attained with spatial resolutions of 16x16 and 100x100 and #956;m, respectively.

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