Three-dimensional polar representation for multispectral fluorescence lifetime imaging microscopy



Multispectral fluorescence lifetime imaging microscopy is a promising and powerful technique for discriminating multiply labeled samples and for detecting molecular interactions inside thick, heterogeneous, and light-scattering milieu such as tissue. The fast and correct analysis of the spectral and lifetime images constitutes a major challenge, which requires a high level of expertise. We present here a new approach that considerably simplifies this analysis avoiding complex fitting algorithm strategies and permitting a fast and visual graphical representation of the fluorescence lifetimes. By transforming the experimental data from time domain to frequency domain for each spectral channel, we calculate the multispectral polar representation and demonstrate its interest on multiply fluorescent labeled sample. We further apply it on Förster resonance energy transfer (FRET) experiments and demonstrate that FRET measurements with a high level of precision can be performed. With addition of emission wavelength as third dimension in the polar representation, autofluorescence emitted by the sample is thus clearly identified. Analysis artifacts induced by the sample or by fitting algorithm choice become then totally inexistent. © 2009 International Society for Advancement of Cytometry

In addition to intensity and wavelength, lifetime is a supplementary source of contrast in fluorescence microscopy, which greatly increases access to the biological information in living cells. Fluorescence Lifetime Imaging Microscopy (FLIM) has indeed been successfully applied to differentiate spectrally undistinguishable molecular species (1) and to map local modifications in labeled samples in terms of ion concentration (2), pH (3), and oxygen (4). FLIM has also been widely used to explore conformational change of proteins (5) or to separate interacting and non-interacting molecular fractions in Förster Resonance Energy Transfer (FRET) experiments (6, 7).

However, because of the low number of collected photons per pixel and the variability of the molecular environment inside a living cell, FLIM is usually limited to two lifetime components in the same pixel. This restriction makes it difficult to extract biologically relevant information from autofluorescent, heterogeneous, light-scattering samples such as biological tissue. Because of optical properties of tissue, a dedicated temporally and spectrally resolved system (called SLIM for Spectral and Lifetime Imaging Microscopy) is necessary for example to be able to explore molecular interactions on a nanometric scale (with FRET experiments).

Temporal and spectral measurements can be performed using two approaches, either frequency domain (8, 9) or time domain (10–12) measurements. In both cases, the determination of lifetimes and contributions of each molecular species are mainly achieved by fitting the collected data at each pixel using equations with multiple unknowns. Fast analysis of SLIM images constitutes then a major challenge. Indeed, because of the number of mathematical algorithms, the number of unknown parameters and the correlation between lifetimes and species contributions, obtaining reliable results with this fitting approach is time consuming and necessitates a high level of expertise (13, 14).

Recently, many efforts have been made to help simplify the results interpretation in classic FLIM experiments for nonspecialists (15–17). Among all these techniques, the polar plot or phasor (16, 18–20) is a promising approach that avoids complex fitting algorithm strategies and provides a fast, graphical representation of fluorescence lifetimes. This polar approach has successfully been applied in classic FLIM and FRET experiments (single spectral channel) by Digman et al. (16).

We propose to extend this concept on SLIM acquisitions by calculating the polar representation for each spectral channel to obtain a multispectral polar (MSP) representation (with emission wavelength as third dimension). Succinctly, this is done by calculating the Fourier sine and cosine transforms of all temporal decays and mapping the corresponding two-dimensional distributions to obtain a polar image for each spectral channel. Using this mathematical operation, each pixel of the intensity SLIM image corresponds to a point in the MSP representation and vice versa.

The main scope of this article is to demonstrate that this new and visual MSP representation is a useful method of SLIM image analysis, which should considerably facilitates the retrieval of biologically relevant information, thanks to the model free and nonfitting characteristics of this approach.

In a first part of this article, we describe the principle of this original MSP representation. We illustrate in a second part its interest for SLIM acquisition of a cross section of plant tissue; we then show its potential for measuring the FRET phenomenon occurring in living cells, which we can easily and visually differentiate from the cellular autofluorescence. Finally, we discuss the advantages and limitations of this method in the last section of this article.


Polar Representation

The polar representation was initially described by Jameson et al. (18), successively improved by different groups (19, 20) and it has successfully been applied both to frequency domain (19) and time domain (16) FLIM experiments. In this article, we propose to extend this approach to SLIM data acquired in the temporal domain with time correlated single photon counting (TCSPC) technique. Polar calculations for each spectral interval were based on the previous work realized by E. Gratton and coworkers (16). Technically, for each pixel, the experimental results gathered with TCSPC technique are converted into frequency-domain data with a simple Fourier transform of the temporal decay I(t) and this complex value is separated into real (Re) and imaginary (Im) parts to obtain the [u; v] coordinates in the polar representation, also called an Argand diagram (Fig. 1). The normalized u- and v- coordinates in the polar representation for a decay I(t) are then simply given by the following expressions:

equation image(1)
equation image(2)

where FT [ ] is the Fourier Transform of the intensity decay. These values also correspond to the normalized Fourier sine and cosine transforms and they can then be written as:

equation image(3)
equation image(4)

where ω is the laser repetition frequency.

Figure 1.

Principle of the polar representation of fluorescence lifetime image for a single spectral channel. Each pixel of the FLIM image corresponds to a unique point of coordinates [u, v] in the polar plot, which corresponds also to a unique value of phase φ and modulation m.

With this mathematical operation, we can easily separate the lifetime components of different molecular species. For example, a sample with a single exponential decay satisfies this equality:

equation image(5)

This equation defines a semicircle centered at [u, v] = [0.5, 0] with a radius of 0.5. In other words, molecular species with single exponential decay are localized on this semicircle in the Argand diagram (see Fig. 1). Short lifetimes are close to the coordinates [1, 0], whereas long lifetimes approach the origin ([0, 0]). If multiple lifetime components are present in the sample, then we obtain this inequality:

equation image(6)

which indicates that the molecular species are located inside the semicircle. The case of a mixture of several molecular species and the case of FRET have already been studied (16, 19). They give different responses in terms of localization in the polar representation.

It is known (21, 22) that it is also possible to determine the lifetime components numerically for a sample with bi-exponential intensity decay equation image by fixing the donor lifetime in absence of acceptor τ2 and by solving the system of Eqs. (3)(4). The proportion a1 and the lifetime τ1 are then given by:

equation image(8)
equation image(9)

These expressions have never been reported before and permit to resolve quantitatively the lifetime components of the fluorescent sample.

Finally, it is interesting to note that we can easily make a parallel between (u, v) and the frequency-domain method (see Fig. 1). Indeed, phase φ and modulation m, which are well-known parameters in the frequency domain, are correlated to temporal decay I(t) given the following expressions:

equation image(10)
equation image(11)

where ‖ and Arg() are the absolute value and the argument of the complex number, respectively. We can therefore deduce phase and modulation lifetime values, τm and τϕ which are classically employed in the frequency-domain method (23, 24).

Cell Culture, DNA Cloning, and Transfection

Cos7 and U2OS cells were grown in plastic flasks at 37°C in 5% CO2 in Dulbecco's Modified Eagles's Medium (GIBCO/BRL, Carlsbad, CA) supplemented with 10% fetal calf serum with 4.5 g L−1 glucose and 1% penicillin/streptomycin.

Cells were plated on 32-mm large and 0.17-mm thick glass coverslips 24 hr before transfection. FuGENE HD (Roche Diagnostics, Basel, Switzerland) was used according to the manufacturer's recommendations for transfection 16 hr before observation. The transfection cocktail composed of 50 μL OPTI-MEM (Invitrogen, Cergy Pontoise, France), 2 μg plasmids, and 5 μL FuGENE was incubated for 30 min and was added to the culture medium. Culture medium was replaced by L15 medium (Invitrogen) before spectral and lifetime acquisition. U2OS cells were fixed in 4% paraformaldehyde (Sigma, Lyon, France) for 20 min, washed with PBS (Invitrogen), and mounted with Mowiol (Sigma).

BMI1-eGFP plasmid (BMI1 stands for BMI1 polycomb ring finger oncogene) was kindly provided by P.O. Angrand (Chromatinomics group, Interdisciplinary Research Institute).

The memb-eGFP was constructed using memb-mCherry (25), which is derived from the PM-eGFP (26). It was achieved by swapping fluorescent protein coding sequences, mCherry for eGFP. Plasmid clones were propagated in XL1 blue (Stratagene, Cedar Creek, TX) and checked by sequencing.

The memb-eGFP-mCherry was also based on memb-mCherry (25). We inserted, upstream of the mCherry coding sequence using standard molecular biological techniques, a hydrophilic linker (27) of either 30 or 40 amino acids (AA) and the necessary restriction enzyme cleavage sites for the in-frame subcloning of the eGFP fragment derived from pEGFP-1 (Clontech, Saint-Germain-en-Laye, France).

The autofluorescent cross-section of Convallaria was kindly provided by Leica Microsystems (Mannheim, Germany).

Spectrally and Temporally Resolved System

A modelocked Ti:sapphire laser beam is focused into a sample, and the resulting two photon excitation fluorescence (TPEF) is epicollected and routed to a SLIM acquisition system with a dichroic mirror. This SLIM detector is a custom-made system named SPRC160, which simultaneously collects photon decay curves in each pixel of the TPEF image and fluorescence emission spectrum in 16 spectral intervals with TCSPC technique. This system has been rigorously characterized (10), ensuring accurate and reproducible acquisition of fluorescence lifetimes in each spectral channel.

SLIM Acquisition and Data Analysis

Spectrally and temporally resolved TPEF signals were acquired using the SPCM software (Becker & Hickl GmbH, Berlin, Germany). Object plane fields of respectively 150 × 150 μm2 for the Convallaria cross-section and 95 × 95 μm2 for the U2OS and Cos7 transfected cells were scanned with a 100× oil-immersion objective with cover slip correction (100×, NA = 1.4, Leica) and stored in a 128 × 128 pixel frame. The femtosecond Ti:Sa oscillator was tuned to the wavelength of 880 nm and the laser power was limited to about 3 mW (at objective focal point) to avoid photobleaching. The overall acquisition time of a complete image took 10 min. For each experiment, we verified that fluorophores had not been photodamaged and/or photobleached.

Determination of the lifetime value was then performed both with SPC Image (Becker & Hickl GmbH) and custom-made software developed in Matlab (Mathworks, Meudon, France). To improve the signal-to-noise ratio, the intensity images were binned with a factor n corresponding to a surface of (2n + 1)2 pixels. Images were processed differently, according to the software used. With SPC Image (Becker & Hickl GmbH), lifetimes were determined by fitting the experimental points with a single- or multiexponential intensity decay for each spectral channel [more details are presented in ref. (17)], whereas our custom-made software computes the polar image by calculating the Fourier sine and cosine transforms of the same experimental points (see Polar Representation section). By selecting an adequate region of interest on the polar representation, we isolated the lifetime interval and highlighted the corresponding pixels on the intensity image. Moreover, quantitative FRET measurements were done by calculating the lifetime components. Detailed calculations of these quantities are described previously. Finally, three-dimensional reconstructions of the polar representations for each spectral channel were performed with Imaris (Bitplane, Zurich, Switzerland).


To emphasize the interest of MSP representation, we illustrated its potential on a cross-section of plant tissue (Convallaria sp.), which presents multiple autofluorescent species with overlapping emission spectra. For this type of sample, both spectral and temporal resolutions were necessary to correctly discriminate the different structures. Spectrally and temporally resolved acquisitions were performed on a well-characterized SLIM system (see Materials and Methods).

Fluorescence lifetime images are usually calculated by fitting the temporal data with either a mono- or a biexponential function, depending on the fluorescent species present in the sample, for each spectral channel. As expected, the calculated lifetimes were extremely dependent on the fitting parameters used (see Fig. 2). Our powerful MSP approach bypasses the drawback of fitting parameters by Fourier transforming the temporal data in the frequency domain to obtain a polar image for each spectral channel (Supporting Information Fig. S1). This approach therefore uses a nonfitting method. In addition, each molecular species has a unique spectral and lifetime signature, which correspond to a unique localization on the three dimensional polar image. In other words, lifetime and spectral differences between molecular species are immediately apparent in our MSP representation. The advantage of this approach is illustrated in Fig. 3. Each spectral channel unambiguously exhibits distinct molecular species whose localizations are well defined in the intensity image. These results corroborate those obtained with the fitting approach performed with optimized fitting parameters (Supporting Information Fig. S2), validating the relevance of our approach. By sliding the polar image across the spectral channels, we generated for the first time a three-dimensional polar representation, which makes it possible to separate both lifetime and spectral information at a glance (Fig. 3c). Because of the number of fluorescent molecular species in the sample, this spectral and temporal segmentation would not have been possible using either the classic polar approach (single spectral channel) or the fitting method.

Figure 2.

Fluorescence lifetime images of a cross-section of Convallaria for three selected spectral channels: 478–494 nm, 542–558 nm, and 622–638 nm (scale bar: 20 μm). Lifetimes are estimated by successively minimizing the difference between the experimental point and a mono-or biexponential fitting model. Corresponding lifetime distributions are represented by gray and black lines for the mono- and biexponential fit, respectively. Note that the number of fitting parameters used modifies the lifetime value and can consequently lead to misinterpretation of the results. [Color figure can be viewed in the online issue, which is available at]

Figure 3.

(a) Polar representations of a cross-section of Convallaria sp. for three selected spectral intervals: 478–494 nm, 542–558 nm, and 622–638 nm (1, 2, 3). The corresponding TPEF images are shown with a scale bar of 20 μm (b). The correspondence between the lifetime position on the polar image and the spatial localization on the intensity image is highlighted in color. The possibility of fast and visual discrimination of several fluorescent molecular species is clearly shown in the MSP reconstruction with emission wavelength as third dimension (see (c) and Supporting Information Movie S1).

We further demonstrated the pertinence of this approach to measure protein–protein interactions both in fixed and living cells. To visualize these molecular interactions, FRET experiments were performed on cells expressing eGFP (donor) and eGFP coupled to a red fluorescent protein, mCherry (acceptor), with two different linker sizes. Because of the known low quantum yield of mCherry, it is difficult to measure FRET by comparing the fluorescence intensities of the acceptor in the presence and absence of the donor (Fig. 4). These FRET interactions occurring between two fluorophores are easily measured in cell by using either the fitting approach or the classic polar plot. However, for multiply labeled samples presenting more than two fluorescent species, careful attention is needed to avoid experimental artifacts. As shown in Fig. 5, lifetime decrease was either caused by energy transfer from the donor to the acceptor or caused by shorter lifetime emission from other fluorescent species, such as those that arise from autofluorescence due to cell fixation. Furthermore, by comparing Fig. 6-c3 and -c4, we clearly see that classic polar representation is not sufficient to distinguish between these two samples. To facilitate the interpretation, SLIM acquisitions were therefore performed and the corresponding MSP representations (Fig. 5c) were generated as described earlier. It is well known that the eGFP emission spectrum is narrow (FWHM (40 nm), with a maximum at 507 nm and that eGFP decay is monoexponential. Consequently, as shown on Fig. 6-b1 and-c1, for living cells transfected with memb-eGFP, the second spectral channel (462–478 nm) polar plot is empty and the fourth (494–510 nm) exhibits a spot localized on the semi circle. When FRET occurs, the second channel polar representation is also empty (Figs. 6b2 and 6b3), but the fluorescence decay is now multiexponential; the spot is then located inside the semi circle for the 4th (Figs. 6c2 and 6c3). If we consider now the fixed cells expressing BMI1-eGFP, we clearly see that the second channel polar image is not empty (Fig 6b4) demonstrating the presence of autofluorescence. Owing to the unique polar signature of each molecular species, we can easily identify the lifetime components of the donor, the two FRET pairs with variable FRET efficiencies and the autofluorescence (Fig. 5c). However, the polar approach is not limited to a qualitative and visual approximation of the fluorescence lifetime. By fixing the donor lifetime in absence of acceptor τ2, it is indeed possible to numerically calculate lifetime components and mean lifetime from mathematical expressions reported in Eqs. (8) and (9). The results obtained with these calculations, which are presented in Table 1, are in excellent agreement with those obtained using an optimized fitting approach, demonstrating that our method is well suited for determining FRET components with a precision on the same order as that obtained using the fitting approach, but without the risk of fitting errors.

Figure 4.

Normalized TPEF emission spectrum of living Cos7 cells expressing eGFP (solid black line) and eGFP coupled to mCherry with 30AA (solid gray line) or 40AA- (dashed black line) linkers. As expected according to FRET theory, a slight decrease in emission can be observed for the donor (eGFP) and a slight increase in emission can be observed for the acceptor (mCherry). TPEF emission spectrum of fixed U2OS cells transfected with BMI1-eGFP is also represented in dashed gray line. This emission spectrum exhibits also a weak decrease of eGFP and increase in emission for the low wavelengths caused by autofluorescent species. Because of the low intensity differences observed, it is therefore of primary importance to combine spectral and temporal information to avoid erroneous interpretation. Note that intensity threshold was fixed to 0.5% of the maximal TPEF intensity for each experiment and the binning factor n to 2.

Figure 5.

(a) TPEF intensity images of of labeled cells, overlaid with averaged lifetime images (the averaged lifetime is calculated by averaging the phase and modulation lifetimes for each pixel; see Polar representation section). Living cells expressing memb-eGFP (1), memb-eGFP in tandem with mCherry with two different linkers, 30AA (2) and 40AA (3) and fixed cells transfected with BMI1-eGFP plasmid (4) were analyzed. Scale bar: 20 μm; wavelength range: 494–510 nm. The lifetime distributions of each image are plotted in their corresponding colors in (b). Finally, MSP reconstruction of each cell is represented in (c) for two threshold values: 0.5% (in transparency) and 10% (in solid) of the maximum. Each cell has a clear and unique signature in the polar representation (see Supporting Information Movie S2). Coordinates [u;v] of the maximum are also indicated.

Figure 6.

(a) Maximum TPEF intensity projections of living Cos7 cells expressing memb-eGFP (1), eGFP coupled to mCherry with 30AA (2) or 40AA- (3) linkers and fixed U2OS cells transfected with BMI1-eGFP plasmid (4). Scale bar: 20 μm. The comparison of polar representations of each image for two spectral intervals: 462–478 nm (b) and 494–510 nm (c) is also represented. All the polar images are displayed in grayscale with a threshold fixed to 0.5% of the maximal polar image intensity for each experiment and a binning factor n = 5. Thanks to the use of multiple spectral channels, it is easy to determine if the lifetime decrease is provoked by energy transfer or by shorter lifetime emission from autofluorescence.

Table 1. Comparison of lifetime components deduced from the fitting method and from the polar analysis
 a1τ1 (NS)τm (ns)
  1. The mean value and corresponding standard deviations (σ) of each parameter (proportion a1 and lifetime τ1 and mean lifetime τm = a1τ1 + (1 − a12) determined for Cos7 cells labeled with memb-eGFP-mCherry with a linker size of 30 AA (clone 1) and 40 AA (clone 2) are indicated for a wavelength range of 494–510 nm. The donor lifetime in absence of acceptor was set to 2.5 ns, the binning factor n was set to 5 and the threshold was identical for each approach.

Clone 1Polar analysis0.720.
Fitting method0.730.
Clone 2Polar analysis0.550.
Fitting method0.610.


To provide a better knowledge of the potential utility of the polar approach for SLIM, we first clarify what this approach enables.

To begin, we emphasize that MSP representation is a powerful method to segment fluorescence lifetime with spectral resolution. Owing to the addition of the emission wavelength as third dimension, we extend the capacity of the well-known classic polar plot to the SLIM image analysis. We thus demonstrated here that our promising approach allows both to discriminate multiply labelled fluorescent samples and also to easily identify autofluorescence emitted by transfected cells. Like the classic polar plot, this approach further circumvents the complexity of optimizing fitting parameters and eliminates any analysis artifacts that arise from the choice of fitting algorithm. Obtaining reliable results from biological tissues with MSP approach is then greatly simplified and becomes accessible to nonexperts without using the complex and time consuming fitting procedure generally associated with SLIM image analysis. It is thus conceivable to apply our MSP approach to facilitate tumor detections for instance, which are performed until now with simultaneous time- and wavelength-resolved spectroscopy due to the complexity of the data analysis (28, 29). Thanks to the spectrally and temporally resolved visual segmentation of our MSP approach, we might indeed envisage to realize a fast and visual diagnostic of cancerous tumor imaging without risk of error.

One might imagine that an alternative and even simpler nonfitting method to discriminate fluorescence lifetime might be the area calculation of the intensity decay curve (which corresponds to: ∫I(t)dt = ∑jNjΔt, where Nj is the photons number in the jth temporal channel) for each pixel and each spectral channel, to obtain the mean lifetime τm according to this following relation: ∫I(t)dt = ∑iaiτi = τm. However, this nonfitting approach is clearly limited to the mean lifetime determination and therefore it does not give access to the different lifetime components (even if we fix an unknown parameter), which makes it impossible to perform quantitative FRET experiment. Thus, a significant advantage of the MSP representation is that quantitative FRET measurements can be performed with a high level of precision by fixing one parameter only (the donor lifetime), parameter which is always measured at the beginning of FRET experiments.

Moreover, we emphasize that in this report, we calculated the fluorescence lifetime components numerically from the Eqs. (8) and (9); this method is hence totally different from the FRET trajectory calculations described by Digman et al. (16) insofar as the FRET trajectory necessitates an adjusting procedure to deduce the FRET efficiency.

However, lifetime measurements by using MSP representation as described in this paper are limited for samples emitting fluorescence whose intensity curve exhibits a mono- or biexponential decay. Furthermore, in FRET experiments, the fluorescence intensity decay curve of the donor has to be mono exponential, in other words the polar spot has to be localized on the semi circle to determine correctly lifetimes and contributions of molecular species; otherwise the Eqs. (8) and (9) are not valid and the calculations fail. In practice, there exists a wide range of FRET experiments where MSP representation is effective at performing FRET experiments. These calculations could also be extended to resolve fluorescent samples emitting more than biexponential intensity decay. For example, if the fluorescence intensity decay is described by a triexponential function: equation image it is necessary to determine five unknown parameters (three lifetime components τ1, τ2, and τ3 and two proportions a1 and a2) from the two Eqs. (3) and (4). To numerically resolve this system, it is then required to fix three unknown parameters. Experimentally, it is difficult to measure them with MSP representation. It is of course possible to realize this measurement with standard fitting method and to reinsert them a posteriori in MSP representation. However, with this two steps procedure, we lose the main advantage of MSP, which is a model free and non fitting method.

We remind the reader that the experimental data used to perform MSP representation are acquired with a standard time domain SLIM acquisition system. The signal to noise ratio is then intrinsically limited by the acquisition system and thus this ratio is not modified by the SLIM image analysis employed. However, these two image processing methods are not exactly equivalent. Indeed, one additional benefit of MSP representation is that it leads to somewhat reduces the importance of the offset compared with the standard fitting method (a detailed comparison including an error propagation of these two image processing methods will be presented elsewhere).

In this article, MSP representation was applied to simplify the interpretation of time domain multispectral FLIM experiments. This approach can of course be easily extended to analyze the frequency domain SLIM images or might also be applied to a wider range of fluorescence lifetime experiments, like the time lapse FLIM acquisitions for example. By using the acquisition time as the third dimension of our MSP representation, we could detect easily and visually any slight lifetime modification induced by local molecular environment modifications (pH, ions concentration, FRET, cellular stress,etc) during time progression. Because of its simplicity and ease-of-use, this nonfitting analysis method should make a significant impact in the biological and microscopy community.


We thank Jim Smith for generously providing the pCS-memb-mCherry plasmid. We are indebted to Franck Riquet for creating both memb-eGFP and memb-eGFP-mCherry plasmids. The SPRC-160 was developed in collaboration with J. Barbillat (CNRS, UMR 8516).