Bioluminescence tomography using eigenvectors expansion and iterative solution for the optimized permissible source region

A reconstruction algorithm for bioluminescence tomography (BLT) has been developed. The algorithm numerically calculates the Green's function at different wavelengths using the diffusion equation and finite element method. The optical properties used in calculating the Green's function are reconstructed using diffuse optical tomography (DOT) and assuming anatomical information is provided by x-ray computed tomography or other methods. A symmetric system of equations is formed using the Green's function and the measured light fluence rate and the resulting eigenvalue problem is solved to get the eigenvectors of this symmetric system of equations. A space can be formed from the eigenvectors obtained and the reconstructed source is written as an expansion of the eigenvectors corresponding to non-zero eigenvalues. The coefficients of the expansion are found to obtain the reconstructed BL source distribution. The problem is solved iteratively by using a permissible source region that is shrunk by removing nodes with low probability to contribute to the source. Throughout this process the permissible region shrinks from the entire object to just a few nodes. The best estimate of the reconstructed source is chosen that which minimizes the difference between the calculated and measured light fluence rates. 3D simulations presented here show that the reconstructed source is in good agreement with the actual source in terms of locations, magnitudes, sizes, and total powers for both localized multiple sources and large inhomogeneous source distributions.