Fluorescence optical tomography is an emerging tool for molecularly based medical imaging. In order to provide the required accuracy and resolution for imaging interior fluorescent yield and/or lifetime within the tissue, accurate experimental measurements as well as efficient and accurate numerical algorithms are needed. Herein, we present a new adaptive finite element approach to the inverse imaging problem that is able to significantly increase the resulting image resolution and accuracy, by (i) using finer meshes for the parameter
estimation where the dye concentration varies significantly, (ii) using finer meshes for the fluence prediction where gradients are significant, while (iii) choosing coarse meshes in other locations. The nonlinear iterative optimization scheme is formulated in function spaces, rather than on a fixed grid. Each step is discretized
separately, thus allowing for meshes that vary from one nonlinear step to the next. Furthermore, by employing adaptive schemes in the optimization, only the discretization level of the final mesh defines the achievable resolution, while the initial steps can be performed on coarse, cheap meshes. Using this technique, we can significantly reduce the total number of unknowns, which not only stabilizes the ill-posedness of the inverse problem, but also adapts the location and density of unknown parameters to achieve higher image resolution
where it is needed. Specifically, we use an a posteriori error criterion to iteratively and adaptively refine meshes for both the forward and inverse problems based on derivatives of excitation and emission fluences as well as the sought parameter. We demonstrate this scheme on synthetically generated data similar to available experimental measurements.
Fluorescence enhance optical tomography is an emerging imaging tool for investigating the molecular tissue environments in vivo. Owing to the scattering nature of near infrared radiation in tissue, iterative tomography approaches must employ the coupled diffusion equations for three-dimensional recovery of fluorescent properties from tissue boundary measurements. Unfortunately, the inverse problem suffers from computational inefficiency and ill-posed ness. Furthermore, the resolution attained in fluorescence tomography is limited by a priori fixed discretization of finite element/finite difference schemes used. These difficulties can be ameliorated by employing adaptive discretization strategies. To date, the efficacy of adaptive mesh refinement techniques has yet to be demonstrated in clinically relevant medical imaging situations. In this contribution we present a novel fluorescence tomography scheme which employs dual adaptive finite element meshes for three dimensional reconstructions of fluorescent targets beneath the simulated tissue surface. Image reconstructions for 1cm3 fluorescent target placed at the depth of 1 cm from the illumination surface are presented for target to background rations (TBRs) of 1:0 and 100:1 on the basis of dye concentration.
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