Adaptive finite element based tomography for fluorescence optical imaging in tissue

Abstract

A three-dimensional fluorescence-enhanced optical tomography scheme based upon an adaptive finite element formulation is developed and employed to reconstruct fluorescent targets in turbid media from frequency-domain measurements made in reflectance geometry using area excitation illumination. The algorithm is derived within a Lagrangian framework by treating the photon diffusion model as a constraint to the optimization problem. Adaptively refined meshes are used to separately discretize maps of the forward/adjoint variables and the unknown parameter of fluorescent yield. A truncated Gauss-Newton method with simple bounds is used as the optimization method. Fluorescence yield reconstructions from simulated measurement data with added Gaussian noise are demonstrated for one and two fluorescent targets embedded within a 512ml cubical tissue phantom. We determine the achievable resolution for the area-illumination/area-detection reflectance measurement geometry by reconstructing two 0.4cm diameter spherical targets placed at at a series of decreasing lateral spacings. The results show that adaptive techniques enable the computationally efficient and stable solution of the inverse imaging problem while providing the resolution necessary for imaging the signals from molecularly targeting agents.