Improved AFEM algorithm for bioluminescence tomography based on dual-mesh alternation strategy

Abstract

Adaptive finite element method (AFEM) is broadly adopted to recover the internal source in biological tissues. In this letter, a novel dual-mesh alternation strategy (dual-mesh AFEM) is developed for bioluminescence tomography. By comprehensively considering the error estimation of the finite element method solution on each mesh, two different adaptive strategies based on the error indicator of the reconstructed source and the photon flux density are used alternately in the process. Combined with the constantly adjusted permissible region in the adaptive process, the new algorithm can achieve a more accurate source location compared with the AFEM in the previous experiments.OCIS codes: 170.6960, 170.3010. doi: 10.3788/COL201210.021701.Bioluminescence tomography (BLT), as a molecular imaging modality, has attracted considerable attention for the study of biological processes in vivo at the cellular and molecular levels. Moreover, it is a potential technique for cancer detection, drug discovery, and gene expression visualization [1,2] . The major advantages of BLT are sensitivity, low cost, ease of operation, and low noise (in contrast to fluorescence imaging). BLT also allows localization and quantification of internal biological sources generated by the luminescent enzyme and luciferase, which may reveal various molecular and cellular activities in three dimensions [3] . The source reconstruction algorithm has remained a challenging task due to the ill-posedness of the inverse problem in theory. Hence, sufficient a priori information including optical parameters, anatomical structure, and permissible source region have tremendous effect on the algorithm [3−6] . In addressing the irregular heterogeneous region, the finite element method (FEM), a classical technique has been widely used, particularly in the inverse problem [7−9] . Accurate numerical solutions require fine discretizations of the tissue volume and large computational resources. Adaptive FEM (AFEM) can achieve a relatively accurate result with low computation cost. In the adaptive process, the strategies of mesh refinement indicated by the error estimation are the core issue. These strategies have significant effect on the precision of the reconstruction result.In previous studies, Lv et al. proposed a multilevel AFEM method which employed two different a posteriori error estimations in the forbidden and permissible source regions on the same mesh [10] . Han et al. developed an hp-FEM for BLT using linear or quadratic interpolation basis functions for selected elements [11] . In this letter, a novel AFEM for BLT was extended. Both the discrete error estimation of the source and the flux density on the whole mesh were considered comprehensively. Consequently, both the direct maximum selection method and Kelly's error estimation of flux density were utilized as indicators. Subsequently, the mesh refinement was carried out alternately according to the two indicators on the two meshes to avoid overly detailed refinement which could aggravate the ill-po...