Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation.

Bioluminescence imaging has been extensively applied to in vivo small animal imaging. Quantitative three-dimensional bioluminescent source information obtained by using bioluminescence tomography can directly and much more accurately reflect biological changes as opposed to planar bioluminescence imaging. Preliminary simulated and experimental reconstruction results demonstrate the feasibility and promise of bioluminescence tomography. However, the use of multiple approximations, particularly the diffusion approximation theory, affects the quality of in vivo small animal-based image reconstructions. In the development of new reconstruction algorithms, high-order approximation models of the radiative transfer equation and spectrally resolved data introduce new challenges to the reconstruction algorithm and speed. In this paper, an SP(3)-based (the third-order simplified spherical harmonics approximation) spectrally resolved reconstruction algorithm is proposed. The simple linear relationship between the unknown source distribution and the spectrally resolved data is established in this algorithm. A parallel version of this algorithm is realized, making BLT reconstruction feasible for the whole body of small animals especially for fine spatial domain discretization. In simulation validations, the proposed algorithm shows improved reconstruction quality compared with diffusion approximation-based methods when high absorption, superficial sources and detection modes are considered. In addition, comparisons between fine and coarse mesh-based BLT reconstructions show the effects of numerical errors in reconstruction image quality. Finally, BLT reconstructions using in vivo mouse experiments further demonstrate the potential and effectiveness of the SP(3)-based reconstruction algorithm.