Application And Research Of The Diffusion Equation In Vivo's Imaging

Molecular imaging is a new interdisciplinary subject, involving the molecular biology, physics, mathematics, the information science, the radiation medicine and so on. The emphasis research content is the molecular imaging theory. Bioluminescence Tomography (BLT) allows in vivo localization and quantification of bioluminescent sources inside a small animal to reveal various molecular and cellular activities. Photon propagation in biological tissues can be well described by a steady-state diffusion equation and Robin-type boundary conditions. In this paper, the overlap domain decomposition method (ODDM), non-overlap domain decomposition method, mixed finite element method and finite difference method are proposed respectively. Some kinds of discretization of the diffusion equation are obtained. The mathematic model of the inverse problem is constructed to determine the position of the light source. The simulation result of the ODDM is given. We can obtain the photon density distribution of the object surface, as well as reconstruct the position of the light source by using ODDM and genetic algorithm. The experimental region is partitioned into a certain number sub-regions. The stability and efficiency of the solution are enhanced by predefining the permissible region. Finally, we confirm the stability of MC algorithm in 3D and the real environment, comparing with the analytic solution by using MOSE platform.