Sensor optimization for fluorescence optical tomography by experimental design methods

With the increasing importance of molecular imaging fluorescence based methods are continuously gaining impact. In fluorescence optical tomography excitation light is injected into the tissue where the fluorophore converts it to radiation of another wavelength. From the emitted light reaching the boundary the 3-D distribution of the fluorophore is reconstructed. This paper aims at finding the optimal spatial distribution of optodes in order to keep their number (hardware costs) low while gaining maximum information from the target object. The implemented algorithm starts with an arbitrary pool of feasible optodes. The optimal subset is searched by minimizing the mutual information between the different measurements. This goal is reached by subsequently removing those sources and detectors which add the least independent information until a stopping criterion is reached. Mutual information is estimated by calculating the inner products between the rows of the sensitivity matrix i.e. the first derivative of the forward mapping with respect to the optical parameters to be reconstructed. We assembled this matrix with a finite element implementation of the diffusion approximation of light propagation in scattering tissues. When starting with an initial pool of 96 optodes regularly spaced on a cylindrical surface and focusing on different target regions within the cylinder, the algorithm always converged towards physically reasonable optimal sets. Optimal source/detector patterns are be presented graphically and numerically.