Hybrid Simplified Spherical Harmonics With Diffusion Equation Based Method For Fluorescence Molecular Tomography

Fluorescence molecular tomography(FMT),has become a powerful tool in the field of biological pharmacy, tumor diagnosis as it can accurately detect 3D distribution and concentration of fluorescent probes inside a living body using the boundary measurements from non-contact detector.Establishing an accurate and rapid forward model which well characterizes the fluorescence propagation in tissues, is crucial for FMT.Because diffusion equation(DE) is easy to be solved with high accuracy and efficiency in a diffuse medium, it had been initially employed in FMT reconstruction. However,DE becomes inaccurate in some cases, such as low scattering?high absorption?tissue boundary and light source attachment,so SPN is proposed.Compared with DE, SPN is much higher in accuracy while much lower in efficiency.Aiming at the limitations of the simplified spherical harmonics approximation(SPN) and diffusion equation(DE) in describing the fluorescent light propagation in tissues, a hybrid SPN-DE model(HSDM) is proposed. In the HSDM model, the SPN and DE are used to describe the light propagation in low and high scattering tissues respectively;and they are coupled using the established boundary coupling condition. The HSDM model makes full use of the advantages of SPN and DE, and abandons their disadvantages, so that it can provide a perfect balance between the accuracy and efficiency. Using the finite element method and hybrid multilevel regularization strategy, the forward model of FMT which is constructed by double use of the HSDM for the excitation and emission process of light propagation, is solved for the reconstructed images of the internal fluorescent probe. The accuracy and efficiency of the HSDM model was validated with regular geometries and digital mouse model based simulations;At the same time,The HSDM based reconstruction method was then demonstrated with the digital mouse based simulation, whose results revealed better performance than the SPN and DE based reconstruction methods. Finally, the feasibility of the proposed method in the applications of in vivo studies was illustrated with liver cancer bearing mouse based in situ experiment, which demonstrate the applicability and potential of the HSDM based method in FMT.