A coupled finite element-boundary element method for modeling Diffusion equation in 3D multi-modality optical imaging

Abstract

Three dimensional image reconstruction for multi-modality optical spectroscopy systems needs computationally efficient forward solvers with minimum meshing complexity, while allowing the flexibility to apply spatial constraints. Existing models based on the finite element method (FEM) require full 3D volume meshing to incorporate constraints related to anatomical structure via techniques such as regularization. Alternate approaches such as the boundary element method (BEM) require only surface discretization but assume homogeneous or piece-wise constant domains that can be limiting. Here, a coupled finite element-boundary element method (coupled FE-BEM) approach is demonstrated for modeling light diffusion in 3D, which uses surfaces to model exterior tissues with BEM and a small number of volume nodes to model interior tissues with FEM. Such a coupled FE-BEM technique combines strengths of FEM and BEM by assuming homogeneous outer tissue regions and heterogeneous inner tissue regions. Results with FE-BEM show agreement with existing numerical models, having RMS differences of less than 0.5 for the logarithm of intensity and 2.5 degrees for phase of frequency domain boundary data. The coupled FE-BEM approach can model heterogeneity using a fraction of the volume nodes (4-22%) required by conventional FEM techniques. Comparisons of computational times showed that the coupled FE-BEM was faster than stand-alone FEM when the ratio of the number of surface to volume nodes in the mesh (Ns/Nv) was less than 20% and was comparable to stand-alone BEM ( ± 10%).