Study And Enhancement Of A Finite Element Method Based Fluorescence Molecular Tomography Algorithm

Molecular imaging is a branch of medical imaging. With the potential to detect and diagnose cancers at relatively early stages, molecular imaging has been a hot spot in research these years. Fluorescence molecular tomography is a novel modality of molecular imaging, which aims to to recover the three dimensional distribution of fluorescent parameters in tissue by illuminating it with light source in visible or near infrared range, given the measurement of emitting fluorescence at the tissue boundary.In the context of fluorescence molecular tomography, the physical modal of light propagation in tissue can be converted to diffusion equation, which belongs to the family of elliptic partial differential equations. In this dissertation, we simulated the generation and propagation of fluorescence, making approximation of the coupled diffusion equations with finite element method. On the basis of the simulation, we established a reconstruction algorithm, which can use constant plain source and normal cooled CCD camara as experiment modules. The algorithm is split into two main parts. The first step is to solve the forward problem with matrix inversion in Matlab to get the error between the estimated values and the measurements of emitting fluorescence at the tissue boundary, given the initial guess of fluorescence parameter distribution. The second step is a gradient-based optimization approach, which iteratively updates the tomography of fluorescence parameters by minimizing the error function. Compared with the optimization approaches, ours simplified the target error function with the separation step, which reduced the unbalance among different terms in the target function. The separation step could also simplify the calculation of the gradient of target function with respect to the fluorescence parameter vector. Furthermore, during each iteration of the optimization process, we integrated a non-linear filter to make homogeneous regions smoother, which could improve the accuracy of the reconstruction. The equations and algorithm within this thesis were validated with numerical methods.The reconstruction algorithm was implemented on a simulated cube-shaped mesh dataset and its capability was further studied with artificial noise added. The result has shown that we can accurately localize the position of the fluorescent heterogeneity. When quantitatively recovering the three-dimensional distribution of fluorescence absorption coefficient, the algorithm has the system error of about 10% that reconstructed value at the node inside the fluorescent homogeneity is unphysically smaller that those at the peripheral nodes. The shield effect was significantly reduced after the integration of the non-linear filter as the error is controlled below the level of 1%.