Investigations on average fluorescence lifetimes for visualizing multi-exponential decays

Intensity- and amplitude-weighted average lifetimes, denoted as τ _I and τ _A hereafter, are useful indicators for revealing Förster resonance energy transfer (FRET) or fluorescence quenching behaviors. In this work, we discussed the differences between τ _I and τ _A and presented several model-free lifetime determination algorithms (LDA), including the center-of-mass, phasor, and integral equation methods for fast τ _I and τ _A estimations. For model-based LDAs, we discussed the model-mismatch problems, and the results suggest that a bi-exponential model can well approximate a signal following a multi-exponential model. Depending on the application requirements, suggestions about the LDAs to be used are given. The instrument responses of the imaging systems were included in the analysis. We explained why only using the τ _I model for FRET analysis can be misleading; both τ _I and τ _A models should be considered. We also proposed using τ _A/τ _I as a new indicator on two-photon fluorescence lifetime images, and the results show that τ _A/τ _I is an intuitive tool for visualizing multi-exponential decays.