Fully adaptive finite element based tomography using tetrahedral dual-meshing for fluorescence enhanced optical...

We have developed fluorescence enhanced optical tomography based upon fully adaptive finite element method (FEM) using tetrahedral dual-meshing wherein one of the two meshes discretizes the forward variables and the other discretizes the unknown parameters to be estimated. We used the 8-subtetrahedron subdivision scheme to create the nested dualmesh in which each are independently refined. However, two tetrahedrons from the two different meshes pose an intersection problem that needs to be resolved in order to find the common regions that the forward variables (the fluorescent diffuse photon fluence fields) and the parameter estimates (the fluorescent absorption coefficients) can be mutually assigned. Using an efficient intersection algorithm in the nested tetrahedral environments previously developed by the authors, we demonstrate fully adaptive tomography using a posteriori error estimates. Performing the iterative reconstructions using the simulated boundary measurement data, we demonstrate that small fluorescent targets embedded in the breast simulating phantom in point illumination/detection geometry can be resolved at reasonable computational cost.