Meshless local Petrov-Galerkin method for bioluminescent photon propagation in the biological tissue

As a promising optical molecular imaging modality, bioluminescence tomography (BLT) has attracted remarkable attention for its excellent performance and high cost-effectiveness, which can be employed to speciffically and directly reveal physiological and pathological activities in vivo at molecular and cellular levels. The goal of BLT is to reconstruct the internal bioluminescent light source with surface measurements. Therefore, the calculation of surface light exitance plays an important role in the inverse source reconstruction, whereas photon propagation is complicated because of strongly scattering property of the biological tissue. In this contribution, a novel meshless local Petrov-Galerkin (MLPG) method based on diffusion approximation model is developed to avoid the complex and time-consuming mesh division in the conventional finite element method (FEM), and MLPG requires only a series of discretized nodes without consideration of element information and node connectivity. Compared with other meshless methods based on global weak-form, background cells used for Gauss quadrature are also omitted in the proposed method. In addition, the tissue optical parameters are incorporated as a priori knowledge in this algorithm. Finally, the performance of this method is valuated using two- and three-dimensional numerical simulation experiments. The results demonstrate the effectiveness and feasibility of the presented algorithm to predict boundary bioluminescent light power distribution.