Illumination pattern optimization for fluorescence tomography: theory and simulation studies.

Fluorescence molecular tomography is a powerful tool for 3D visualization of molecular targets and pathways in vivo in small animals. Owing to the high degrees of absorption and scattering of light through tissue, the fluorescence tomographic inverse problem is inherently ill-posed. In order to improve source localization and the conditioning of the light propagation model, multiple sets of data are acquired by illuminating the animal surface with different spatial patterns of near-infrared light. However, the choice of these patterns in most experimental setups is ad hoc and suboptimal. This paper presents a systematic approach for designing efficient illumination patterns for fluorescence tomography. Our objective here is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. We achieve this by improving the conditioning of the Fisher information matrix. We parameterize the spatial illumination patterns and formulate our problem as a constrained optimization problem that, for a fixed number of illumination patterns, yields the optimal set of patterns. For geometric insight, we used our method to generate a set of three optimal patterns for an optically homogeneous, regular geometrical shape and observed expected symmetries in the result. We also generated a set of six optimal patterns for an optically homogeneous cuboidal phantom set up in the transillumination mode. Finally, we computed optimal illumination patterns for an optically inhomogeneous realistically shaped mouse atlas for different given numbers of patterns. The regularized pseudoinverse matrix, generated using the singular value decomposition, was employed to reconstruct the point spread function for each set of patterns in the presence of a sample fluorescent point source deep inside the mouse atlas. We have evaluated the performance of our method by examining the singular value spectra as well as plots of average spatial resolution versus estimator variance corresponding to different illumination schemes.