Fluorescence-lifetime imaging microscopy

A fluorophore which is excited by a photon will drop to the ground state with a certain probability based on the decay rates through a number of different (radiative and/or nonradiative) decay pathways. To observe fluorescence, one of these pathways must be by spontaneous emission of a photon. In the ensemble description, the fluorescence emitted will decay with time according to

${\displaystyle I(t)=I_{0}e^{-t/\tau }}$

where

${\displaystyle {\frac {1}{\tau }}=\sum k_{i}}$.

In the above, ${\displaystyle t}$ is time, ${\displaystyle \tau }$ is the fluorescence lifetime, ${\displaystyle I_{0}}$ is the initial fluorescence at ${\displaystyle t=0}$, and ${\displaystyle k_{i}}$ are the rates for each decay pathway, at least one of which must be the fluorescence decay rate ${\displaystyle k_{f}}$. More importantly, the lifetime, ${\displaystyle \tau }$ is independent of the initial intensity and of the emitted light. This can be utilized for making non-intensity based measurements in chemical sensing.[5]

Fluorescence-lifetime imaging yields images with the intensity of each pixel determined by ${\displaystyle \tau }$, which allows one to view contrast between materials with different fluorescence decay rates (even if those materials fluoresce at exactly the same wavelength), and also produces images which show changes in other decay pathways, such as in FRET imaging.

The goal of the analysis algorithm is to extract the pure decay curve from the measured decay and to estimate the lifetime(s). The latter is usually accomplished by fitting single or multi exponential functions. A variety of methods have been developed to solve this problem. The most widely used technique is the least square iterative re-convolution which is based on the minimization of the weighted sum of the residuals. In this technique theoretical exponential decay curves are convoluted with the instrument response function, which is measured separately, and the best fit is found by iterative calculation of the residuals for different inputs until a minimum is found. For a set of observations ${\displaystyle d({{t}_{i}})}$ of the fluorescence signal in time bin i, the lifetime estimation is carried out by minimization of:

${\displaystyle {{\chi }^{2}}=\sum \limits _{i}{{\left[{{d}_{i}}({{t}_{i}})-{{d}_{0i}}({{t}_{i}},a,\tau )\right]}^{2}}}$

Besides experimental difficulties, including the wavelength dependent instrument response function, mathematical treatment of the iterative de-convolution problem is not straight forward and it is a slow process which in the early days of FLIM made it impractical for a pixel-by-pixel analysis. Non fitting methods are attractive because they offer a very fast solution to lifetime estimation. One of the major and straightforward techniques in this category is the rapid lifetime determination (RLD) method. RLD calculates the lifetimes and their amplitudes directly by dividing the decay curve into two parts of equal width ${\displaystyle \delta }$t. The analysis is performed by integrating the decay curve in equal time intervals ${\displaystyle \delta }$t:

${\displaystyle {\begin{matrix}{{D}_{0}}=\sum \limits _{i=1}^{K/2}{{{I}_{i}}\delta t}&{{D}_{1}}=\sum \limits _{i=K/2}^{K}{{{I}_{i}}\delta t}\\\end{matrix}}}$

Ii is the recorded signal in the i-th channel and K is the number of channels. The lifetime can be estimated using:

${\displaystyle \tau =\delta t/\ln({{D}_{0}}/{{D}_{1}})}$

For multi exponential decays this equation provides the average lifetime. This method can be extended to analyze bi-exponential decays. One major drawback of this method is that it cannot take into account the instrument response effect and for this reason the early part of the measured decay curves should be ignored in the analyses. This means that part of the signal is discarded and the accuracy for estimating short lifetimes goes down.

One of the interesting features of the convolution theorem is that the integral of the convolution is the product of the factors that make up the integral. There are a few techniques which work in transformed space that exploit this property to recover the pure decay curve from the measured curve. Laplace and Fourier transformation along with Laguerre gauss expansion have been used to estimate the lifetime in transformed space. These approaches are faster than the deconvolution based methods but they suffer from truncation and sampling problems. Moreover, application of methods like Laguerre gauss expansion is mathematically complicated. In Fourier methods the lifetime of a single exponential decay curve is given by:

${\displaystyle \tau ={\frac {1}{n\omega }}{\frac {{A}_{n}}{{B}_{n}}}}$

Where:

${\displaystyle {\begin{matrix}{{A}_{n}}={\frac {\sum \limits _{t}{d(t)\sin(n\omega t)}}{\sum \limits _{t}{IRF(t)\sin(n\omega t)}}}={\frac {\omega \tau }{1+{{\omega }^{2}}{{\tau }^{2}}}},&{{B}_{n}}={\frac {\sum \limits _{t}{d(t)\cos(n\omega t)}}{\sum \limits _{t}{IRF\cos(n\omega t)}}}={\frac {1}{1+n{{\omega }^{2}}{{\tau }^{2}}}},&\omega ={\frac {2\pi }{T}}\\\end{matrix}}}$

and n is the harmonic number and T is the total time range of detection.

FLIM has primarily been used in biology as a method to detect photosensitizers in cells and tumors as well as FRET in instances where ratiometric imaging is difficult. The technique was developed in the late 1980s and early 1990s (Gating method: Bugiel et al. 1989. König 1989,[13] Phase modulation: Lakowicz at al. 1992,[14][15]) before being more widely applied in the late 1990s. In cell culture, it has been used to study EGF receptor signaling[16] and trafficking.[17] Time domain FLIM (tdFLIM) has also been used to show the interaction of both types of nuclear intermediate filament proteins lamins A and B1 in distinct homopolymers at the nuclear envelope, which further interact with each other in higher order structures.[18] FLIM imaging is particularly useful in neurons, where light scattering by brain tissue is problematic for ratiometric imaging.[19] In neurons, FLIM imaging using pulsed illumination has been used to study Ras,[20] CaMKII, Rac, and Ran[21] family proteins. FLIM has been used in clinical multiphoton tomography to detect intradermal cancer cells as well as pharmaceutical and cosmetic compounds.

More recently FLIM has also been used to detect flavanols in plant cells.[22]

• Phasor approach to fluorescence lifetime and spectral imaging

• Fluorescence Excited-State Lifetime Imaging
• Lifetime and spectral analysis tools in ImageJ: http://spechron.com Archived 2013-03-11 at the Wayback Machine
• Fluorescence Lifetime Imaging Microscopy
• Principle of TCSPC FLIM (Becker&Hickl GmbH)