Fluorescence decay data analysis correcting for detector pulse pile-up at very high count rates
Matthias Patting, Paja Reisch, Marcus Sackrow, Rhys Dowler, Marcelle Koenig, Michael Wahl
FFluorescence decay data analysis correcting for detector pulse pile-up at very high count rates
Matthias Patting, Paja Reisch, Marcus Sackrow, Rhys Dowler, Marcelle Koenig, Michael Wahl * PicoQuant GmbH, Rudower Chaussee 29, 12489 Berlin, Germany
Abstract . Using Time-Correlated Single Photon Counting (TCSPC) for the purpose of fluorescence lifetimemeasurements is usually limited in speed due to pile-up. With modern instrumentation this limitation can be liftedsignificantly but some artefacts due to frequent merging of closely spaced detector pulses (detector pulse pile-up)remains an issue to be addressed. We propose here a data analysis method correcting for this type of artefact and theresulting systematic errors. It physically models the photon losses due to detector pulse pile-up and incorporates theloss in the decay fit model employed to obtain fluorescence lifetimes and relative amplitudes of the decaycomponents. Comparison of results with and without this correction show a significant reduction of systematicerrors at count rates approaching the excitation rate. This allows quantitatively accurate fluorescense lifetimeimaging (FLIM) at very high frame rates.
Keywords : fluorescence lifetime, photon counting, TCSPC, data analysis, fitting, FLIM, FRET. * E-mail: [email protected]
Time-Correlated Single Photon Counting (TCSPC) is one of the most important methods todetermine fluorescence lifetimes on the nanosecond scale [O'Con 84]. It allows higher sensitivityand better time resolution than most analog detection methods and is well established also forfluorescence lifetime imaging (FLIM) in confocal microscopy for many important life scienceapplications [Lako 06].In TCSPC one repeatedly measures and histograms the elapsed time between sample excitationby a pulsed light source and the arrival of emitted fluorescence photons at the detector, typicallywith picosecond accuracy. However, classic TCSPC electronics as well as most single photon1ounting detectors have dead times on the order of several tens of nanoseconds. Within this timethe system is busy with data processing and cannot detect any other photon. The dead time istypically longer than the fluorescence decay processes of interest. Consequently, if more thanone photon is emitted per excitation cycle it cannot be detected. This causes a statistical over-representation of early photons and a corresponding distortion of the collected decay shape, aneffect called pile-up [O'Con 84, Kapu 15]. In order to avoid this situation it is necessary to workwith sufficiently low light intensities. Due to the statistical nature of photon flux this results inthe unfortunate situation that most of the excitation pulses lead to no emission at all and thespeed of photon collection is reduced to typically one out of every 50-100 laser pulses [O'Con84, Kapu 15]. In order to acquire a FLIM image with a confocal microscope, one typically scans the excitationand detection foci across the sample [Kobe 03, Ortm 04]. In case of a fast scanning system, thisvery often leads to only a few detected photons per pixel, which will not allow accurate lifetimeanalysis. It is therefore necessary to increase the number of detected photons per pixel either byreducing the scan speed or by accumulating several frames to sum up the photons. This is why ittypically takes several seconds up to half a minute to obtain a good FLIM image. A possible pathto speedier FLIM is to perform TCSPC with the highest possible photon rate. Even though it is feasible to correct for dead-time [Patt 07, Isba 17] the ultimate key to highthroughput TCSPC is eliminating dead-time. However, the highest time resolution and lowestdifferential nonlinearity (DNL) in timing can typically only be obtained with dedicated time-to-digital converters that incur a dead-time on the order of some tens of nanoseconds after each2hoton detection. It is possible to build faster timing circuits that allow effectively zero dead-time but compromise on timing resolution and DNL. We have recently developed a TCSPCboard that achieves 40 Mcps throughput, a dead-time < 1 ns, and a resolution of 250 ps, withoutcompromising on DNL [Pico 17]. Using such a TCSPC unit with negligible dead-time it ispossible to detect several photons within one excitation cycle. Although the temporal resolutionof the current hardware design is only 250 ps, it is still sufficient for most FLIM applications inthe life sciences. In addition to the timing electronics, the detector must also meet therequirement of short dead time. Currently the most suitable detectors in this regard are so calledhybrid photo detectors (HPD) based on a combination of two gain stages, a first one similar tothat of a photomultiplier tube and a second one in the form of an avalanche photo diode [Hama07]. With this combination of TCSPC unit and detector we have been able to demonstrateTCSPC data collection speeds of up to 40 Mcps at excitation rates of 40 MHz, which is about100 times faster than with conventional TCSPC and conservative pile-up constraints. Even whencompared with relaxed pile-up constraints (allowing more error, which is sometimes consideredtolerable in FLIM) a speedup by a factor of 10 is obtained. This speeds up FLIM acquisitionaccordingly, provided that the sample emits enough light.One issue that remains with the approach sketched so far is that of detector pulse pile-up. Thiseffect is caused by the fact that individual detector pulses have a certain width that cannot bemade infinitely small. With existing hardware as introduced above this is about 500 ps. At thedesired high count rates the actual photon statistics imply that there will quite frequently bephoton emissions closer than this, which means that successive detector pulses may overlap andmerge into one. Since the TCSPC electronics cannot distinguish the original pulses they will be3ounted as only one. This causes another form of histogram distortion where early photons areunder-represented. In the following we introduce a correction scheme for the systematic errorsresulting from this type of distortion. More precisely, we show how the underlying physicalmechanism of photon losses due to pulse pile-up can be incorporated in the fit model so that thefluorescence lifetime estimate is made robust against this type of histogram artefact, even at veryhigh count rates.
A key parameter for the photon loss model is the closest pulse spacing in time that the particularcombination of TCSPC electronics and detector can still resolve. Let this pulse pair resolution becalled D t here. Assuming Poisson statistics and a count rate n, the time intervals betweensuccessive photons will be exponentially distributed and the fraction of intervals shorter than D t will be 1 - e -n D t . A photon falling into D t after the detection of a previous photon will be lost. Thefraction of remaining photons will therefore be e -n D t [Reed 72]. TCSPC with pulsed excitation samples the photon distribution as a function of elapsed time tafter excitation. Let Dec(t) be the decay curve. With known excitation rate f exc and known pulsecount N each discrete time t i can be associated with a „differential“ or instantaneous count rate dn = f exc Dec(t i ) / N . (1)Applying Reed et al [Reed 72] for each time t i , one observes a lossy decay curve 4ec Exp (t i ) = Dec(t i ) e -dn D t = Dec(t i ) e -f exc Dec(t i ) / N D t . (2)The losses scale exponentially and distort the shape of the curve accordingly. Attempting to fitthis observed decay curve with a model function Dec Mod via nonlinear least squares methods (ormaximum likelihood estimation) in order to obtain physical parameters such as fluorescencelifetimes will result in systematic errors of the parameters.It is possible to correct the observed decay curve iteratively and thereby reconstruct the truedecay curve Dec(t), as shown previously for classic pile-up [Isba 16]. Unfortunately theprocedure is time consuming and would distort the experimental noise of the counting statistics.This is undesirable since the well defined Poisson statistics of the experimental error are ofcritical importance in the process of maximum likelihood estimation when fitting a model to theobserved data.The idea of the correction method proposed here is not to correct the observed decay curve but toincorporate the losses according to Eq. 2 into the fitted model function. This results in amodified model curve Dec
Corr (t) = Dec
Mod (t) e - f exc
Dec
Mod (t) / N D t . (3)This model curve is fitted to the data as usual by means of a nonlinear least squares algorithm ormaximum likelihood estimation. The pulse pair resolution D t can either be determined inadvance as an instrument specific constant or alternatively be obtained as an additional fit5arameter. The latter allows a calibration measurement of D t to be performed in reverse withoutadditional expenditure of apparatus or method. Nevertheless it must be noted that despite thecorrection, the loss of photons due to detector pulse pile-up will cause some loss in accuracy ofthe curve fitting and parameter estimation. These losses in accuracy, however, emerge only asstatistical errors, which is a substantial improvement over the uncorrected situation, wheresystematic errors dominate over statistical errors.A visual explanation of the proposed correction method is shown schematically in Fig. 1. Forsimplicity it uses a single-exponential decay and for clarity the photon losses due to detectorpulse pile-up are exaggerated. 6 ig. 1 Schematic illustration of the correction scheme by example of a single-exponential decaya) The original undistorted decay has a lifetime t ideal , symbolized by the slope triangle d/dt (ln(I)).Photon losses due to detector pulse pile-up (hashed area) lead to a compressed peak region in theobserved decay (dashed line). Only the latter is accessible by measurement.b) a nonlinear fit of the observed decay (dashed line) with an uncorrected model function resultsin lifetime t uncorr . The deformation results in a longer lifetime than expected.c) Adjustment of the model function (symbolized by arrows) ensures that the model curve (solidline) is in agreement with the observed decay curve (dashed line). The resulting lifetime t corr isnow in agreement with the expected value t ideal .7 Experimental Results
In order to assess the effectiveness of the proposed correction scheme we performed FLIMmeasurements on a mixture of two types of polymer microspheres stained with dyes of differentlifetimes. The sample was prepared by mixing 20 µl Dragon Green beads (Bangs LaboratoriesInc., Fishers, IN, USA), 20 µl Nile Red beads (Spherotech Inc., Lake Forest, IL, USA) and0.5 ml of purified water. A 2 µl droplet of the mixture was then dried on a glass cover slip.Imaging was performed on a MicroTime 200 confocal microscope (PicoQuant, Berlin,Germany). The sample was excited by a pulsed diode laser at 485 nm and 20 MHz pulse rate(PicoQuant GmbH, Berlin, Germany). Emission was separated out via a filter LP488 (SemrockInc., Rochester, NY, USA) and dichroic zt488/640rpc (Chroma Technology Corp, Bellows Falls,VT, USA). The photon detector was a PMA-Hybrid 40 and the TCSPC electronics were aTimeHarp 260 N (both PicoQuant GmbH, Berlin, Germany). Figure 2 shows the uncorrected andcorrected fitting results for the two lifetimes in the brightest pixel of the image (80x80 µm,256x256 pixels). The calculated lifetimes of the two bead types are plotted against the count rate.As the beads were spatially well separated (meaning that all pixels exhibited a mono-exponentialbehavior), a mono-exponential reconvolution model was applied. The lifetimes were taken fromtheir corresponding peak positions in the lifetime histogram of the image, whereas the error barsindicate the FWHM of the lifetime peak. The uncorrected fits (solid square) show a strongdependency on the count rate, whereas the corrected fits (open triangle) stay constant within thetolerance level, as indicated by the dotted line. 8 ig. 2
Fitting results for the brightest pixel of the image (80x80 µm, 256x256 px) of a beadsample (PMA-Hybrid 40, TimeHarp 260 N, 20 µl Dragon Green beads + 20 µl Nile Red beads +0,5 ml water, 2 µl droplet dried on glass cover slip, filter: LP488, dichroic: zt488/640rpc,excitation at 485nm and 20 MHz rate). The calculated lifetimes of the two bead types (left andright panel, respectively) are plotted against the count rate.Note that the width of the uncorrected lifetime peaks shows a pronounced increase withincreasing count rate. The reason lies in the intensity gradient along each individual bead (brightcenter, dark rim). In the center the lifetime distortions by the detector pulse pile-up are strongest,whereas at the rim the effects are less pronounced. For the corrected fits the width of the lifetimepeaks stays small and constant, a further indication that the correction helps to reduce thedetector pulse pile-up effects. 9bove 60 Mcps there appears to be a slight trend towards systematically increased lifetimes evenfor the corrected lifetimes, indicating that the correction starts to become less precise. The reasonfor this lies in count rate dependent systematic errors in the decay curves that probably originatefrom the front end analog electronics or the detector and cannot be described in terms of detectorpulse pile-up. Nevertheless, the relative error associated with the trend is still smaller than 5%.In order to demonstrate the effectiveness of the correction also in Förster Resonant EnergyTransfer (FRET) imaging with typically more complex decay shapes we have analyzed threedata sets from chinese hamster ovary (CHO) cells with EGFP-N-WASP and mRFP-Toca-1(courtesy of S. Ahmed and T. Sudhaharan, Institute of Medical Biology, Singapore) with andwithout correction. Imaging was performed at average count rates of 5, 20, and 30 Mcps on aMicroTime 200 confocal microscope (PicoQuant, Berlin, Germany). The excitation wavelengthwas 485 nm at 40 MHz repetition rate and emitted photons were collected between 500 - 540 nmusing a PMA Hybrid 40 detector module and a TimeHarp 260 N TCSPC unit (both PicoQuant,Berlin, Germany). TCSPC histograms of each pixel were fitted with a double exponential model.Average lifetime results mapped to color are shown in Figure 3. The corrected version is free ofvisible artefacts up to 20 MHz count rate. At 30 MHz a trend towards falsely long lifetimes isvisible but lifetime contrast is still substantially better than uncorrected.10 ig. 3
FRET imaging results with and without correction at different count rates. Sample: CHOcells with EGFP-N-WASP and mRFP-Toca-1, courtesy of S. Ahmed and T. Sudhaharan,Institute of Medical Biology, Singapore.
We have shown a correction method for detector pulse pile-up in fluorescence lifetimemeasurements with TCSPC that allows for data collection at very high count rates. Experimentalresults indicate that this allows measuring at count rates approaching the excitation rate withlifetime errors below the 5% level. This facilitates quantitatively accurate confocal FLIMmeasurements at very high frame rates. 11
Acknowledgements
The authors thank Sandra Orthaus-Müller (formerly PicoQuant GmbH) for pushing and inspiringthe project. This work was partially funded by BMBF grant 13N12672 "tCAm4Life". [O'Con 84] D. V. O'Connor and D. Phillips,
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