Computationally efficient perturbative forward modeling for 3D multispectral bioluminescence and fluorescence tomography

The forward problem of optical bioluminescence and fluorescence tomography seeks to determine, for a given 3D source distribution, the photon density on the surface of an animal. Photon transport through tissues is commonly modeled by the diffusion equation. The challenge, then, is to accurately and efficiently solve the diffusion equation for a realistic animal geometry and heterogeneous tissue types. Fast analytical solvers are available that can be applied to arbitrary geometries but assume homogeneity of tissue optical properties and hence have limited accuracy. The finite element method (FEM) with volume tessellation allows reasonably accurate modeling of both animal geometry and tissue heterogeneity, but this approach is computationally intensive. The computational challenge is heightened when one is working with multispectral data to improve source localization and conditioning of the inverse problem. Here we present a fast forward model based on the Born approximation that falls in between these two approaches. Our model introduces tissue heterogeneity as perturbations in diffusion and absorption coefficients at rectangular grid points inside a mouse atlas. These reflect as a correction term added to the homogeneous forward model. We have tested our model by performing source localization studies first with a biolumnescence simulation setup and then with an experimental setup using a fluorescent source embedded in an inhomogeneous phantom that mimicks tissue optical properties.