A Fully Constrained Optimization Method for Time-Resolved Multispectral Fluorescence Lifetime Imaging Microscopy Data Unmixing

Abstract

This paper presents a new unmixing methodology of multispectral fluorescence lifetime imaging microscopy (m-FLIM) data, in which the spectrum is defined as the combination of time-domain fluorescence decays at multiple emission wavelengths. The method is based on a quadratic constrained optimization (CO) algorithm that provides a closed-form solution under equality and inequality restrictions. In this paper, it is assumed that the time-resolved fluorescence spectrum profiles of the constituent components are linearly independent and known a priori. For comparison purposes, the standard least squares (LS) solution and two constrained versions nonnegativity constrained least squares (NCLS) and fully constrained least squares (FCLS) (Heinz and Chang, 2001) are also tested. Their performance was evaluated by using synthetic simulations, as well as imaged samples from fluorescent dyes and ex vivo tissue. In all the synthetic evaluations, the CO obtained the best accuracy in the estimations of the proportional contributions. CO could achieve an improvement ranging between 41% and 59% in the relative error compared to LS, NCLS, and FCLS at different signal-to-noise ratios. A liquid mixture of fluorescent dyes was also prepared and imaged in order to provide a controlled scenario with real data, where CO and FCLS obtained the best performance. The CO and FCLS were also tested with 20 ex vivo samples of human coronary arteries, where the expected concentrations are qualitatively known. A certainty measure was employed to assess the confidence in the estimations made by each algorithm. The experiments confirmed a better performance of CO, since this method is optimal with respect to equality and inequality restrictions in the linear unmixing formulation. Thus, the evaluation showed that CO achieves an accurate characterization of the samples. Furthermore, CO is a computational efficient alternative to estimate the abundance of components in m-FLIM data, since a global optimal solution is always guaranteed in a closed form.