Fast GPU-Based Global
Fit of TCSPC FLIM Data
W.
Becker, A. Bergmann, Becker & Hickl GmbH
Abstract: A global fit assumes that one or several of
the lifetimes of a multi-exponential decay are constant in all pixels of a FLIM
image. By using this a priori knowledge, the decay parameters can be obtained
at a better accuracy than by a multi-exponential fit with all decay parameters
floating. However, a global fit is enormously computation-intensive. Processing
times with standard CPU processing are therefore unacceptably long. We present
a Global Fit algorithm based on GPU processing that reduces the calculation
time from previously hours to a few minutes and less. Here, we demonstrate the
performance of the global fit for FLIM-FRET analysis and for metabolic-FLIM
analysis. The global fit is available in Becker & Hickl's
SPCImage NG data analysis software, version 9.073.
GPU-Based Global-Fit Procedure
A global fit assumes that one or several of
the lifetimes of a multi-exponential decay are constant in all pixels of a FLIM
image. Unlike a fit with 'fixed component lifetimes', which needs the component
lifetimes to be known, a global fit does not need a priori information on the values
of any of the lifetimes. The only information it uses is that one or several the
component lifetime do not change over the pixels of image.
Constant lifetimes often appear in
metabolic-FLIM data, where the lifetimes of the NADH or FAD / FMN decay
functions show no or little variation, and in FRET data where the lifetime of
the non-interacting donor component can be expected to be constant. In these
cases, it can be expected that global fitting improves the signal-to noise
ratio of the fit results. However, global fitting is extremely computation-intensive:
First, a 'normal' multi-exponential fit is performed with reasonable start
values. Then the values of the global parameters are varied and a new fit of
the image is performed. The procedure is continued until the error sum over the
entire image has been minimised. That means, in every cycle of the iteration a
full multi-exponential decay analysis for the entire image has to be performed.
Considering the fact that conventional multi-exponential FLIM analysis for an
average-size image takes 5 to 10 minutes a procedure like this must be expected
to be extremely time-consuming, if not impossible.
A few years ago bh introduced GPU
processing in their SPCImage NG data analysis software. On a GPU, a large
number of similar calculations are executed simultaneously. In a FLIM image,
the GPU is able to perform a multi-exponential-decay fit in hundreds of pixels
in parallel. As a result, the calculation time for one image is reduced from
formerly 5 to 10 minutes to a few seconds. A calculation time of a few seconds
for one FLIM image puts global analysis within reach: Assuming 20 analysis
cycles are needed to reach a perfect fit with a global parameter the
calculation time can be expected to be on the order of a few minutes or less.
Therefore, we implemented a GPU-based global fit algorithm in our
SPCImage NG FLIM data analysis software. Results for FLIM-FRET data and
for metabolic FLIM data are presented below.
Global Fit in SPCImage NG
The global fit is activated in the
Decay-Parameter Window in the upper right of the main panel. The desired decay
time is defined as 'Global' and checked for special treatment in the analysis.
Please see Fig. 1. In the figure lifetime t3 was declared as 'Global'. That
means the most appropriate value will be determined and used for all pixels. A
Global Fit can be run with a single global lifetime (as shown in the figure),
or with two or three global lifetimes. Of course, a global fit makes sense only
in combination with multi-exponential decay models. There is no point of declaring
a 'Global' lifetime for a single-exponential fit.
Fig. 1:
Activation of Global Fit in SPCImage NG. Parameter t3 was declared 'Global'.
Colour represents a1, the metabolic indicator. FAD image of pig skin.
FRET Analysis with Global Lifetime of the Non-Interacting
Donor
One potential application of global fitting
is FRET analysis [1, 3]. FRET analysis is based on a model which contains a
fast decay component from the interacting donor and a slow decay component from
the non-interacting donor. The technique not only delivers correct classic FRET
efficiencies [3], but also the fraction of interacting donor, the FRET
efficiency of the interacting donor, and the donor-acceptor distance. By using
the non-interacting donor lifetime as a reference lifetime the technique is
free of external calibration [4].
A frequent objection against
double-exponential FRET analysis is that double-exponential fitting of the FLIM
data is required. A double-exponential fit needs more photons than a
single-exponential one. This raises concerns about the statistical accuracy of
the fit results and the FRET parameters derived from them. We have shown that
these concerns are not justified if the maximum-likelihood (MLE) fit of
SPCImage is used [2]. A global
fit can be expected to improve the accuracy even further: Apart from
environment-induced variations by non-FRET mechanisms, the lifetime of the
non-interacting donor component can be expected to be constant. A fit with a
global non-interacting donor lifetime therefore appears promising. A comparison
of FRET analysis with the traditional double-exponential fit and a fit with the
lifetime, t2, of the non-interfacing donor as a global parameter is given in Fig.
2.
Fig. 2: Upper row: FRET Analysis with free lifetime, t2, of the
non-interacting donor. Left to right: Mean lifetime of double-exponential
decay, tm, amount of interacting donor, a1, classic FRET efficiency, Eclass. Colour-coded
images and parameter histograms. Lower row: FRET Analysis with global lifetime,
t2, of the non-interacting donor. Left to right: Mean lifetime of
double-exponential decay, tm, amount of interacting donor, a1, classic FRET
efficiency, Eclass. Colour-coded images and parameter histograms.
There is clearly an increase in
signal-to-noise ratio for the global-fit (with t2 global) in comparison to the
classic fit (with both lifetimes freely floating). On average, the increase is
about a factor of 1.4 in SNR. This may not look like very much, but it is the
equivalent to an analysis of data with twice the number of photons per pixel.
Metabolic-FLIM Analysis with Global Lifetimes
Metabolic
FLIM uses the fluorescence decay functions of NADH or FAD to determine the
metabolic state of cells or tissues. Both compounds are present in a bound and
in an unbound form. The amounts of bound and unbound NADH and FAD depend on the
metabolic state. The fluorescence lifetimes of the decay components are
different, and can be separated by FLIM. Double-exponential decay analysis can
thus be used to determine the metabolic state: For NADH, small a1 indicates oxidative
phosphorylation, large a1 indicates glycolysis. For FAD it is the opposite:
Small a1 indicates glycolysis, large a1 indicates oxidative phosphorylation.
The problem of metabolic FLIM is the low
intensity of the NADH and the FAD fluorescence. It can therefore be difficult
to obtain enough photons for accurate double-exponential decay analysis. The
situation is further complicated by the presence of FNM fluorescence in FAD
data [1, 5]. Quantitative results for FAD are thus
only obtained by triple-exponential analysis. This makes the photon-budget
problem even more severe. Results can be obtained by analysis with 'fixed'
component lifetimes [5], but this opens the door to subjective influence of the
operator. A more promising solution is analysis with global parameters. It
turns out that the lifetimes of the fluorescence components, although different
in different cell and tissue types, are fairly stable within one and the same
sample. This is exactly the situation where global fitting helps.
An example is shown in Fig. 3. It shows FAD
data from freshly excised human bladder tissue. The upper row shows conventional
triple-exponential decay analysis with all three component lifetimes freely
floating. Left to right, it shows the amount of bound FAD, a1, the amount of
unbound FAD, a2, and the amount of FMN, a3. The photon number in the individual
pixels is about 100. To obtain reasonable a1, a2, and a3 data a binning radius
of 3 was used in SPCImage NG. This results in about 5000 photons per binned
pixel. Please see [2] for details of the binning procedure. It can be seen that
the MLE fit is generally able to derive reasonable triple-exponential decay parameters
form the data. However, the accuracy of the decay amplitudes is not really satisfactory.
Fig. 3 Left to right: amount of bound FAD, a1, the amount of unbound FAD,
a2, and the amount of FMN, a3. Upper row: Standard MLE fit. Lower row: Global
fit with component lifetimes t1, t2, t3 defined as global parameters.
The second row shows images of the same parameters
obtained by global fitting. All three component lifetimes, t1, t2, t3, were
defined 'global'. Again, a binning radius of 3, with a photon number of about
5000 per binned pixel, was used. The effect on the image quality is striking:
All component amplitudes, a1, a2, and a3, are obtained at high accuracy,
delivering clean images of the amounts of bound FAD, unbound FAD and FMN.
Precautions Against Fitting Artefacts
A global fit requires that the global
parameters are constant over the entire area in which the analysis is
performed. This is usually the case in NADH and FAD FLIM images, and in
FLIM FRET images. It may also be the case in molecular imaging
applications where the probe exists in a bound and unbound or a protonated and
deprotonated form. However, it should be scrutinized whether the component
lifetimes are really constant. Conventional analysis of reference data recorded
with long acquisition time and high photon number may help decide.
Importantly, image areas which contain atypical
decay data should be excluded from the analysis. This may be dead cells, spots
of contamination, or spots burned by excessive excitation power. These regions
have different component lifetimes and thus cannot be treated by the same
global parameter set as the rest of the image. Problems can also occur if a lifetime
that has been declared 'global' gets into the range of a non-global lifetime.
Moreover, make sure that the background is
excluded. Exclusion of background is easily achieved by the 'Threshold'
parameter of SPCImage NG. Exclusion of other contaminations may require
region-of-interest definition or image segmentation via the phasor plot [2]. We
also recommend not to use more model parameters in the fit than necessary. The
values of global parameters may not be entirely correct for every individual
pixel. If the model function is too flexible the fit procedure may attempt to
compensate with unnecessary changes in the remaining parameters. For best fit
accuracy, we recommend to use 'fixed' parameters for the 'Shift' and for the
'Offset'.
Calculation Times of GPU Processing
The calculation times depend on the number
of pixels used in the calculation, the number of time channels, and, of course,
on the size and speed of the GPU used. We determined the calculation times for
an NVIDIA GPU in a laptop and for a medium-size NVIDIA GPU in a standard PC. The
images contained about 80% pixels with useful data, the rest of the pixels were
background. The background pixels were excluded from the fit by the 'Threshold'
parameter of SPCImage NG.
Standard
Analysis Global Analysis
3-Exponential
Model 3-Exp.Model
All
3 Lifet. Floating All 3 Lifet. Global
256x256
pixels 512x512 pixels 256x256 pixels 512 x 512
pixels
256
time channels 1024 time channels 256 time channels 1024 time channels
Small-Size GPU in Laptop <1 second 6
seconds 12 seconds 160 seconds
Medium-Size GPU
in PC <1 second 1.2
seconds 2.4 seconds 32 seconds
Summary
A global-fit can significantly improve the
signal-to-noise ratio of a multi-exponential fit of FLIM data. In the past,
global fitting has only rarely been used because the calculation times were
unacceptably long. Now, GPU processing used in BH's SPCImage data analysis
software has put the calculation times in the range of a few 10 seconds to a
few minutes. The reduced data processing times make the global fit attractive
to a number of multi-exponential data analysis tasks in which the component
lifetimes are unknown but invariable over an area of interest within the
sample. We demonstrated global fitting for FLIM FRET data and for metabolic
FLIM data. In FLIM FRET data, global fitting improved the accuracy of FRET
parameters derived from double-exponential decay analysis. In FAD data, it
delivers quantitative values of the amounts of bound and unbound FAD, and the
amount of FMN.
References
1.
W. Becker, The bh TCSPC Handbook. 10th ed.
Becker & Hickl GmbH (2023)
2.
SPCImage Data Analysis, in W. Becker, The bh
TCSPC Handbook. 10th ed. Becker & Hickl GmbH (2023)
3.
W. Becker, A Common Mistake in Lifetime-Based
FRET Measurements. Application note, Becker & Hickl GmbH (2023)
4.
W. Becker, Axel Bergmann, Double-exponential
FLIM-FRET is free of calibration. Application note, www.becker-hickl.com (2023)
5.
W. Becker, L. Braun, DCS-120 FLIM System Detects
FMN in Live Cells, application note, available on www.becker-hickl.com (2023).
