Fluorescence Lifetime Imaging

As applied mathematician I have been working in the field of biomedical optics, where inverse problems found many interesting and important applications. In particular, scattered light in biological tissue, which is generally modelled by the Radiative Transfer Equation, allows to obtain biologically relevant information from non-invasive boundary measurements. Solving the Radiative Transfer Equation numerically is very challenging and usually it's approximations are used. The most popular approximation for highly light scattering media is the diffusion approximation. While working at the University College London I have developed the finite volume and discontinuous Garlerkin methods for solving the diffusion approximation on adaptive meshes. Modern optical imaging technologies allow collecting time-dependent information, which is important for biologists. For instance, fluorescence lifetime imaging requires use of time-dependent information. In collaboration with Photonics Group, Imperial College London, we developed several novel reconstruction schemes utilizing time-gating imaging technology. Recently we used these methods for Fluorescence Resonance Energy Transfer in highly light scattering media. We also work on incorporating anatomical prior information obtained from other imaging modalities into reconstruction algorithms and data compression techniques.