Comparison of algorithms to suppress artifacts from the natural lens in fluorescence lifetime imaging ophthalmoscopy (FLIO)

: Fluorescence lifetime imaging ophthalmoscopy (FLIO) has developed as a new diagnostic tool in ophthalmology. FLIO measurements are taken from 30° retinal ﬁelds in two spectral channels (short spectral channel (SSC): 498–560 nm, long spectral channel (LSC): 560–720 nm). Because of the layered structure of the eye, the detected signal is an interaction of the ﬂuorescence decay of the anterior part and of the fundus. By comparing FLIO measurements before and after cataract surgery, the impact of the natural lens was proven, despite the application of a confocal laser scanning (cSLO) technique. The goal of this work was to determine the best algorithmic solution to isolate the sole fundus ﬂuorescence lifetime from the measured signal, suppressing artifacts from the natural lens. Three principles based on a tri-exponential model were investigated: a tailﬁt, a layer-based approach with a temporally shifted component, and the inclusion of a separately measured ﬂuorescence decay of the natural lens. The mean ﬂuorescence lifetime τ m,12 is calculated using only the shortest and the intermediate exponential component. τ m,all is calculated using all three exponential components. The results of tri-exponential tailﬁt after cataract surgery were considered as a reference, because the implanted artiﬁcial lens can be assumed as non-ﬂuorescent. In SSC, the best accordance of τ m,all of the reference was determined with τ m,12 of the tailﬁt before surgery. If high-quality natural lens measurements are available, the correspondence of τ m,12 is best with τ m,all of the reference. In LSC, there is a good accordance for all models between τ m,12 before and after surgery. To study the pure fundus ﬂuorescence decay in eyes with natural lenses, we advise to utilize ﬂuorescence lifetime τ m,12 of a triple-exponential tailﬁt, as it corresponds well with the mean ﬂuorescence lifetime τ m,all of eyes with ﬂuorescence-less artiﬁcial intraocular lenses.


Introduction
FLIO, a time-resolved measurement of the autofluorescence of the eye, was developed as a tool to diagnose metabolic alterations [1,2], which offered sufficient repeatability (or retest reliability) [3][4][5]. FLIO is based on fluorescence lifetime imaging microscopy (FLIM), which is applied to many research fields. An extensive overview about the FLIM principles and its clinical applications is given by Marcu et al. [6]. Factors having an influence on FLIO measurements, such as macular pigmentation, photoreceptor bleaching, and pupil dilation have been investigated [7][8][9][10]. For the interpretation of FLIO data, the excitation and emission spectra, as well as the fluorescence decays of endogenous fluorophores, such as NADH (reduced nicotinamide adenine dinucleotide), FAD (flavin adenine dinucleotide), lipofuscin, AGE (advanced glycation end-products), melanin, collagen, and elastin were measured and compared with data from the literature [11,12]. As these fluorophores can be located in several anatomical structures of the eye, the corresponding measurements were performed on the cornea, lens, chamber water, vitreous, and retina of porcine eyes [13,14]. The summarized fluorescence of all fluorophores in all anatomical structures of the eye is detected during in vivo FLIO measurements. Based on such integral measurements, differences in fluorescence lifetimes were already detected between healthy volunteers and patients suffering from different diseases [2,[15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Good overviews about the physical background and the current state of clinical applications of FLIO are presented in [33,34]. FLIO has also been used in animal studies [35,36].
The eye can be considered as a structure of fluorescent layers, primarily comprised of anterior and posterior parts. The anterior part is dominated by the fluorescence of the natural lens. The posterior part consists of several retina layers, which are in FLIO often assumed as one layer because of its low depth resolution. The applied confocal detection principle is not as effective in suppressing the fluorescence signal from the anterior part [37] as it is in suppressing reflected light from the anterior part. Light is reflected on surfaces. In contrast, fluorescence is a volumetric event. Thus, the relation of the thickness of the fluorescent layers, i.e. natural lens vs. retina (4.0-4.7 mm vs. 0.2 mm), must to be taken into account.
The fluorescence of the natural lens is excited earlier in time than the fluorescence of the fundus because of the distance between them. This time-difference is visible in FLIO data, as shown in Fig. 1. Also visible in Fig. 1 is the much slower decay of the natural lens fluorescence of time in comparison to the fundus. The fluorescence lifetime of the natural lens is in the order of a few nanoseconds, while the fluorescence lifetimes of the fundus are mostly less than one nanosecond (in the fovea even less than 100 ps). Thus, the superposition of the fluorescence lifetimes from fundus and natural lens causes an elongation of the measured fluorescence lifetime compared to the pure fluorescence lifetime of the fundus.  Figure 2 shows the fluorescence spectrum of a natural lens, which was measured by a confocal laser scanner ophthalmoscope (cSLO) connected to a spectrograph [38]. The emission spectrum of the natural lens is predominantly in FLIO's short spectral channel. The fluorescence emissions of several expected fundus fluorophores (e.g. FAD, AGE (e.g. pentosidine, argpyrimidine), collagen, elastin, etc.) are mostly in the short spectral channel, [39], while the emission of e.g. A2E (N-retinylidene-N-retinylethanolamine, the component VIII of lipofuscin, maximum at 600 nm) is in the long spectral channel.
Hence, the fluorescence of the natural lens is considered an artifact which lowers the signal-tonoise ratio of the fundus fluorescence, possibly decreasing FLIO's sensitivity as a diagnostic tool for retinal diseases.
Intraocular lenses (IOL) are an artificial replacement for the natural lens, mostly used in therapy of strong cataract, and do not emit a considerable fluorescence signal. Consequently, FLIO measurements in patients with IOL do not suffer from artifacts caused by the natural lens fluorescence and contain only fluorescence signal from the fundus. Since FLIO should also work well in patients with natural lenses, the artifacts in FLIO data caused by the natural lens fluorescence have to be suppressed. As mentioned above, the confocal detection principle is not able to suppress the natural lens sufficiently and hardware modification of the FLIO device to solve this problem, e.g. [40], are currently not possible. In principle, the suppression of the disturbing fluorescent layer, located in front of the fluorescent layer of interest, is possible by multi-photon excitation. The required high exposure could damage the retina. According to Wang [41], there is only a factor of two in two-photon excitation between a fluorescence signal strong enough for imaging and damaging the retina. Despite this limitation, Hunter et al. [42] described the successful application of two-photon excitation in combination with adaptive optics for the detection of the pure fundus fluorescence in monkey eyes. The separation of the fluorescence of a single layer in a layered structure by combination of OCT and fluorescence is the goal of current research. Several approaches are described for the combination of OCT and fluorescence measurement in endoscopic applications [43,44]. The results are 3D OCT images but only 2D surface fluorescence images. Thus, the natural lens fluorescence in FLIO should be suppressed by means of software algorithms, which is the aim of this work. Therefore, FLIO measurements from patients with IOL will serve as the artifact free reference and FLIO measurements of the same patients from before the IOL insertion (cataract surgery) will be used as data basis to evaluate different algorithmic approaches to suppress the natural lens fluorescence.
A recommendation is given as to how FLIO measurements should be compared between healthy volunteers and patients.

Instrumentation
Time-resolved measurements were performed using the fourth version of a FLIO confocal laser scanning ophthalmoscope (cSLO), which was constructed by Heidelberg Engineering GmbH (Heidelberg, Germany) [4], according to their experiences with previous versions developed at the University eye clinic Jena.
In short, the basic device is a confocal laser scanning ophthalmoscope (cSLO, HRA-2, Heidelberg Engineering GmbH) using the SPECTRALIS system, an expandable diagnostic imaging platform that combines scanning laser fundus imaging with high-resolution optical coherence tomography (OCT). A picosecond pulsed diode laser excites the endogenous fluorescence at 473 nm (BDL-473-SMC, Becker & Hickl GmbH, Berlin, Germany) with a repetition rate of 80 MHz. The fluorescence decay is detected by time correlated single photon counting (TCSPC) from a 30-degree fundus field. The time resolution is 12.2 ps, the image repetition rate is 8.8 frames per second and the image size is 256 × 256 pixels.
Fluorescence decay is detected in a short spectral channel (SSC: 498 nm -560 nm) and in a long spectral channel (LSC: 560 nm -720 nm). The fluorescence is detected by a hybrid detector (HPM-100-40, Becker & Hickl GmbH), connected with a TCSPC board (SPC 150, Becker & Hickl GmbH) in each channel. For compensation of eye movements, infrared reflection images are recorded in parallel to the fluorescence images.
By combining the cSLO and the TCSPC technique [45,46] with multiple detectors, FLIO generates time-, space-, and spectrum-resolved fluorescence decay data sets. It takes approximately two minutes for each FLIO measurement to reach the target of 1000 photons per pixel [4] in the macular region in the SSC. Details of the FLIO device are described elsewhere [4,7,47].

Participants
The FLIO data were measured in 31 patients before and after cataract surgery (17 males and 14 females). All patients underwent a detailed clinical ophthalmic examination, including funduscopy, slit-lamp examination, and intraocular pressure measurement. All patients were diagnosed with cataracta provecta (advanced cataracts). Three patients were excluded because of an extremely dense natural lens. The age range was 49 to 88 years with a mean of 72.6 ± 9.1 years. The pupil was dilated using tropicamide and phenylephrine HCl. All measurements were taken one day before cataract surgery and one month after surgery. Before cataract surgery, the fluorescence decay of the natural lens was measured separately.
The study was performed according to the tenets of the declaration of Helsinki and approved by the ethic committee of the University Hospital Jena. Written informed consent was obtained from all patients prior to study participation.

Data analysis
To improve the signal-to-noise ratio, spatial binning with a factor of 2 (5 × 5 pixels) was applied to the FLIO data before the following basic model functions were applied: Multi-exponential model: With I -fluorescence intensity, IRF -instrumental response function, α i -amplitude, τ ifluorescence lifetime, and b -background (offset). The background is fixed to 0.1 photons per pixel after binning, which was experimentally determined for typical acquisition times in the dark room, where all FLIO measurements were conducted. In this paper, a tri-and four-exponential fit is used (i = 3 and i = 4).
Layer-based approach with temporally shifted component: with tc i -time shift of the exponential component i. Lens-corrected approach: with I lens (t-tc lens ) -fluorescence intensity of the lens, time shifted by tc lens , α lens -amplitude of the lens fluorescence. The Eq. (1), (2), and (3) use in different manner specific conditions of the fluorescence lifetime measurement at the eye to isolate the pure fluorescence of the retina. The models according to Eq. (1) consider the multi-exponential approximation, which is commonly used in FLIM. The models according to Eq. (2) use the specific information that the fluorescence signal of the natural lens appears earlier at the detector than the retinal fluorescence signal to separate of both signals. The models according to Eq. (3) use the separately measured fluorescence of the natural lens to compensate its contribution in the detected sum fluorescence signal of the eye, ideally resulting in the pure retinal fluorescence signal.
Fluorescence measurements in two spectral channels permit to a certain degree the discrimination of endogenous fluorophores according to their emission spectra. According to Fig. 2, the impact of the fluorescence of the natural lens should be different in both spectral channels.
For the reference, it is assumed that the artificial lens emits no fluorescence and the impact of the fluorescence of the cornea is assumed to be negligible. Thus, there is no influence of the slow fluorescence decay from the natural lens and the fluorescence lifetimes are solely related to the fundus. Despite the lack of natural lens fluorescence, a multi-exponential model (Eq. 1) with three exponential components is required to model the reference data to achieve the best curve of residuals and the lowest χ 2 error (reduced form): where m is the number of time channels of the photon histogram, I M (t j ) is the number of measured photons, I c (t j ) is the number of calculated photons estimated using Eq. (1), (2) or (3), and p is the number of free parameters in the model. The model for the reference is applied in a tailfit manner, which means that only the decay of the fluorescence signal is used.
In the measurements taken before the cataract surgery, the fluorescence signal from the fundus is superimposed by the fluorescence signal of the natural lens. Nine different models (M1-M9) are applied to the measurements to minimize the impact of the natural lens fluorescence and to extract only the fundus fluorescence signal, as listed in Table 1.
Model M1 is identical to the reference, except that only measurements from before the cataract surgery are employed. M1 reflects the way data analysis is done in most clinical FLIO studies thus far. For M2, both the rising slope and the decay of the fluorescence are used to fit the model to the measured data. Otherwise, M2 is identical to M1.
The fluorescence of the natural lens causes a stepped slope in the measured fluorescence signal, which cannot be modelled with Eq. (1). Therefore, a layer-based approach (Eq. 2) is applied with d -distance between the fluorescent layers, c -the speed of light.
As the temporally shifted exponential component represents the natural lens fluorescence, only two exponential components would remain to model the fundus fluorescence signal in M3 and M4. Thus, M5 employs four exponential components: three exponential components to model the fundus fluorescence and the fourth exponential is temporally shifted to model the natural lens fluorescence.
A separately taken measurement of the natural lens was included in the modelling for M6 in addition to three exponential components (Eq. 3). For M7, the longest exponential component was temporally shifted by tc 3 to model residual fluorescence signals of the eye's anterior part, in addition to the measured fluorescence signal of the natural lens.
M8 uses the same equation as M6, but only high-quality natural lens measurements are utilized. Similarly, M9 corresponds to M7, and only the high-quality natural lens measurements are utilized. The reasoning behind M8 and M9 is the difficulty for the FLIO operator to find the correct focal point for a natural lens without any visible structure. Thus, only 11 measurements of the natural lens were high-quality, which means that the rising edge of its fluorescence signal is not stepped, but steep, and the decay part of the signal does not contain any sections with a rising signal. M8 and M9 demonstrate the potential to minimize the impact of the fluorescence decay of the natural lens, if the fluorescence of the natural lens is detected with high quality.
For comparison of the models, the following mean fluorescence lifetimes were calculated: Only the shortest (τ 1 ) and the intermediate (τ 2 ) fluorescence lifetime and their corresponding amplitudes (α 1 , α 2 ) are considered.
τ m, all All fluorescence lifetimes and corresponding amplitudes are considered. Measurements in different areas consider different distributions of fluorophores at the fundus. A standardized early treatment diabetic retinopathy study (ETDRS) grid, centered at the macula [48], was placed by an expert in each FLIO measurement. Its central area (C), as well as the inner ring (IR), and the outer ring (OR), were used for further analyses (see Fig. 3). For each region (C, IR, and OR) from each measurement, the mean values of the fluorescence lifetimes were used for further statistical evaluation. As not all data followed a normal distribution (Shapiro-Wilk test [49]), the non-parametric Wilcoxon signed-rank test was used to compare M1 to M7 against the reference, and the Wilcoxon rank-sum test was used for the comparison of M8 and M9 against the reference. show the mean fluorescence lifetime τ m,all using three exponential components while D (M1) shows τ m,12 using only the first two exponential components. There is a good correspondence between τ m,all after cataract surgery with τ m,12 before cataract surgery. The color scaling is identical for all fluorescence lifetimes.
The FLIMX [50] software package was used to determine and analyze the fluorescence lifetime in the time-resolved fluorescence data, which is documented and freely available for download under the open source BSD-license (http://www.flimx.de). Figure 3 shows images of fundus autofluorescence in SSC obtained with the FLIO device before and four weeks after cataract surgery with lens replacement. The preoperative fluorescence intensity image shows remarkably lower contrast than the image recorded after surgery. This can be attributed to the strong autofluorescence of the natural lens upon excitation at 473 nm [51]. In addition, a large difference of the mean fluorescence lifetime τ m,all before cataract surgery in comparison to after cataract surgery is visible, while the mean fluorescence lifetime τ m,12 from before cataract surgery is very similar to the mean fluorescence lifetime τ m,all after surgery. This excellent correspondence between τ m,all after surgery with τ m,12 before surgery, which corresponds to the retinal fluorescence, was achieved best by M1.

Results
The detailed fluorescence lifetimes τ m,all and τ m,12 of the considered locations in SSC and LSC are given for each model shown in Fig. 4.   Fig. 4. Mean fluorescence lifetimes τ m,all (dark color) and τ m,12 (light color) including standard deviation averaged over all patients for the reference (green) and all models (blue) for both spectral channels and all regions. Red * indicate no significant difference to τ m,all of the reference and purple # indicate no significant difference to τ m,12 of the reference.
The fluorescence lifetime depends, to a certain degree, on the location at the fundus. As shown in Fig. 4 (green bars), the mean fluorescence lifetimes τ m,all after surgery are shortest in the central area of the ETDRS grid and are longest in the outer ring. This behavior is valid in both spectral channels. This clear local difference of τ m,all is reduced before surgery because the long fluorescence decay of the natural lens overlays the fundus fluorescence decay.
Statistical tests were applied to determine non-significant median differences (p > 0.05) between τ m,12 of all models and τ m,all of the reference for SSC (Fig. 4, left side, red *). A good correspondence between measurements after surgery and measurements before surgery exists for M1 (three-exponential tailfit), M6 (three-exponential fit with additional natural lens measurement), as well as for M7 (three-exponential fit with shifted tc 3 and additional natural lens measurement) in the inner and the outer ring. The utilization of high-quality natural lens measurements in M8 and M9 resulted in good correspondence of their τ m,12 with τ m,all of the reference for all regions. For LSC, the median differences between τ m,all of all models and τ m,all of the reference (Fig. 4, right side, red *) were tested. The null-hypothesis was accepted for M5 und M8 in the inner ring and the outer ring. For M9, the distributions of τ m,all were comparable with τ m,all of the reference in all locations. In addition, the median differences between τ m,12 of all models and τ m,12 of the reference (Fig. 4, purple #) were tested in LSC. In the outer ring, a good agreement was found in M5, M8, and M9 and partly for M6 and M7.
The largest deviations between reference and M1-M9 for both τ m, 12 and τ m,all were found in the central area in SSC and LSC. The smallest differences were found in the outer ring.
Results for the figure of merit (Eq. 4), the calculated tc i values and the estimated fractional fluorescence of the natural lens are listed in Tables S1 and S2 in Supplement 1.
To reduce the complexity, the data shown in Fig. 5, 6 and 7 is restricted to the outer ring. Figure 5 depicts τ m,all in the outer ring from both spectral channels in more detail. In SSC, τ m,all of the tri-exponential model M2, which uses the entire fluorescence time range, is reduced from 497 ps before surgery to 199 ps after surgery (data not shown). M2's fluorescence lifetime τ m,all is 163% longer than the reference (tailfit after surgery). This is the largest deviation from the reference of all models. In M8 and M9, which use high-quality lens measurements in addition to the tri-exponential fit, the deviation of τ m,all from reference is reduced to 73%. In LSC, the deviations of τ m,all from the reference in all models and in all regions are considerably smaller than in SSC (Fig. 4). In the outer ring, the deviation from the reference is largest for τ m,all in M2 (21%), but much smaller than in SSC. τ m,all of M1 is 16% longer than in the reference. Nearly the same result as in the reference was obtained in M5 (-1%, four-exponential fit with variable tc4) and in M9 (-2%, tri-exponential fit with variable tc3 and high-quality lens measurements). In M8, τ m,all in LSC is 10% longer than the reference. The difference of τ m,12 in eyes with natural lens and τ m,all in eyes with artificial intra-ocular lenses is quite small for all models in SSC (Fig. 6). Especially in M1, this difference is only -0.5%. This is an important result because most FLIO measurements have been evaluated using M1 so far. In M6 and M7, τ m,12 was longer by only 12% and 9% respectively than τ m,all of the reference. In M3 (variable tc 3 ), the difference was only 15%. In case of a fixed tc 3 at 172 ps (M4), the difference was 20% (25% for tc 3 = 140 ps, data not shown).
The fundus fluorescence decay in SSC without the impact of the long fluorescence decay of the natural lens can be estimated, if the fluorescence lifetime τ m,12 is calculated in measurements before surgery. Figure 6 shows pairwise differences of the fluorescence lifetime τ m,12 from before  surgery (M1 -M9) and τ m,all from after surgery (reference) in SSC, as recommended by the CONSORT Group [52].
The pairwise differences shown in Fig. 6 provide more information than Fig. 4 by eliminating the influence of patient-specific fluorescence lifetime alterations, e.g. a longer fluorescence lifetime due to age. Thus, only the deviations caused by each model remain. A negative pairwise difference means, that the model estimated a shorter fluorescence lifetime than the reference (and vice versa for positive differences). The pairwise difference for M1, M8 and M9 possess a nearly ideal shape with a mean value of almost zero. The remaining models are biased towards positive pairwise differences, estimating longer fluorescence lifetimes than the reference. Similar to Fig. 6, Fig. 7 shows pairwise differences of the fluorescence lifetime τ m,12 from before surgery (M1 -M9) and τ m,12 from after surgery (reference) in LSC.
There is a good correspondence for τ m,12 before and after cataract surgery in LSC. A difference below 8% was calculated in M1, M3, M5, M6, M7, and M8. The largest difference of 17% was determined in M4. Even in M2, the model with the largest difference in SSC, the difference to τ m,12 of the reference was only 14% in LSC.

Summary
The fluorescence lifetime imaging ophthalmoscopy technique is in the process of evolving from prototype technology to clinical application. Part of this process is the identification and characterization of artifacts in the measured FLIO data and their suppression. This work describes the fluorescence of the natural lens as a noteworthy artifact in FLIO and how the effect of this artifact can be reduced by means of data processing. Therefore, FLIO data of 29 patients has been acquired before and after the replacement of the natural lens with a non-fluorescent artificial lens. By using the FLIO data after the surgery as artifact-free reference, the authors could evaluate 9 different models (based on three different algorithms) to analyze the FLIO data from before the surgery in combination with two different variants of a mean fluorescence lifetime. In SSC, τ m,12 of all models was generally much closer to τ m,all of the reference in comparison to each model's τ m,all . The mean fluorescence lifetime τ m,12 utilizing only the short and the intermediate fluorescence lifetime of M8 and M9, both tri-exponential models with an additionally included separately measured fluorescence signal of the natural lens of high quality, achieved the lowest deviations to the tri-exponential fluorescence lifetime τ m,all of reference in FLIO's short spectral channel in all regions. M1, a tri-exponential model, which is only applied to the decay of the fluorescence signal (tailfit) achieved even lower deviations to τ m,all of the reference in the inner and the outer ring of the short spectral channel. In the long spectral channel, τ m,all of M9 could match τ m,all of reference in all investigated regions while τ m,12 of M5 and M8 had the lowest deviations to τ m,12 of the reference. The authors recommend τ m,12 of M1 in SSC and τ m,12 of M5 in LSC because both models don't require a separate measurement of the patient's natural lens reducing FLIO's stress for the patient.

Fluorescence of the natural lens in FLIO
The eye has a structure of fluorescent layers: anterior and the posterior parts. The fluorescence of the natural lens dominates the fluorescence of the anterior part. The posterior part consists of several fundus layers, which are assumed as only one layer in FLIO because of insufficient depth resolution.
As demonstrated in Fig. 1, the fluorescence decay of the natural lens overlays the fundus fluorescence. Patients suffering from retinal diseases are predominantly of advanced age. The fluorescence of the natural lens increases with age, especially related to cataract formation. Thus, the artifacts caused by the fluorescence of the natural lens are most prominent in FLIO's typical patients. The mean fluorescence lifetime (bi-exponential fit) of the natural lens from a porcine eye is 1120 ps [11]. This value can be used for orientation, because the anatomical structure of a porcine eye is comparable to a human eye.
Independent of a bi-or tri-exponential approximation of the fluorescence lifetime in FLIO data, only prolongations of the mean fluorescence lifetime have been found in all clinical studies of patients and healthy volunteers with a natural lens so far [33,34]. Thus, it is possible that these prolongations of the fluorescence lifetime are influenced to a certain degree by the fluorescence lifetime of the natural lens. For example, comparing FLIO measurements of diabetic patients and healthy volunteers, considerable elongation of the fluorescence lifetime was found in diabetic patients [53]. Both groups had only eyes with natural lenses. In contrast, the difference in fluorescence lifetime was much smaller, when only patients and volunteers with artificial lenses were analyzed (6 participants per group). Karumanchi et al. [54] showed that diabetic patients and healthy volunteers can be discriminated according to fluorescence changes of the natural lens. Thus, it cannot be excluded that the prolongation of the fluorescence lifetime in diabetic patients found in FLIO data [18,19] may be caused to a certain degree by the fluorescence of the natural lens.

Comparison tri-exponential fits before and after surgery (ref, M1, M2)
The fluorescence decay after surgery is well fitted by τ m,all with a tri-exponential tailfit, which can also be seen in the fluorescence lifetimes of the reference: τ m,all is longer than τ m,12 in all regions. This means, beside the short fluorescence lifetime of the pigment epithelium and the neuronal retina [13], the longer fluorescence lifetimes of connective tissue, such as collagen and elastin [11,13], contribute to the fundus fluorescence decay.
The considerable impact of long fluorescence decay of the natural lens was demonstrated by the tri-exponential fit of the entire fluorescence time range (M2) before and after cataract surgery. The mean fluorescence lifetime τ m,all in SSC decreased from 497 ps before surgery down to 199 ps after cataract surgery (outer ring), which confirms the impact of fluorescence decay of the natural lens for subjects in an extended range of age.
A certain suppression of the natural lens fluorescence can be achieved by tailfit approximation (M1) in comparison to M2. In this case, τ m,all is reduced from 497 ps in M2 to 398 ps in M1 (SSC, outer ring).
Interestingly, the means and medians of the fluorescence lifetime τ m,12 of the fluorescence decay in M1 are nearly identical with the fluorescence lifetime τ m,all after cataract surgery. The mean value of τ m,12 of all patients in the outer ring in SSC is only 0.5% shorter than τ m,all of the reference. Thus, the fluorescence lifetime τ 3 in M1 corresponds to the fluorescence decay of the natural lens. This correspondence between τ m,all of the reference and τ m,12 before surgery was best for M1 in comparison with all other models in the outer ring. From this result, it can be advised that τ m,12 in tri-exponential tailfit (M1) should be used for the comparison of the fundus fluorescence decay in healthy volunteers with other types of patients, with natural lenses. It should be mentioned that the patients in this study were suffering from cataracts only. Fundus diseases can deteriorate this accordance.
It was noted that τ m,12 increased in the ETDRS grid from the central area to the outer ring in both spectral channels, independent of the applied model. This confirms the results by Dylsi et al. [4], although they approximated the fluorescence decay only by a bi-exponential tailfit. The reason for the increasing τ m,12 might be an increased thickness of the neuronal retina. In SSC, an additional influence of the short fluorescence lifetime of the macular pigment xanthophyll can be assumed [7,8].
The lower effect of fluorescence decay of the natural lens in LSC compared to SSC was demonstrated by the difference of τ m,all before surgery (M1 through M9) and after surgery (reference). Whereas, in SSC, the difference was between 110% and 212%, in LSC the difference was considerably smaller, with a range of 16% to 45%, depending upon the location in the ETDRS grid. The differences for τ m,12 at the central area, and inner and outer rings between M1 and the reference were determined as 45%, 35%, and 30% in SSC, but as only 10%, 8%, and 5% in LSC.

Layer-based approach (M3, M4, M5)
The contribution of the layered structure of the eye on the decay of fluorescence in FLIO data was investigated in [50,[55][56][57]. The fluorescence signal of the natural lens appears by the time tc i earlier on the detector than the fundus fluorescence (Eq. 5). Both the excitation light and the fundus fluorescence light travel the distance between the natural lens and the fundus. This results in a shoulder of the rising edge of the fluorescence signal (Fig. 1). The visibility of this shoulder depends on the full width at half maximum (FWHM) of the instrument response function (IRF). This shoulder is clearly visible when using the ultra-fast hybrid detector HPM-100-06 (Becker & Hickl GmbH), which has an IRF of 40 ps (FWHM) after convolution with the laser pulse [56]. The shoulder was also visible using the microchannel plate photomultiplier tube R3809U-50 (Hamamatsu Photonics Europe GmbH, Herrsching am Ammersee, Germany) with an IRF of 80 ps (FWHM) in an earlier version of the FLIO device [57]. The current FLIO device utilizes GaAsP hybrid detectors (HPM-100-40, Becker & Hickl GmbH). This detector has a higher sensitivity than the microchannel plate photomultiplier and the ultra-fast hybrid detector, but the IRF is 120 ps (FWHM) [50]. Using the HPM-100-40 detector, the shoulder is only weakly visible. It seems that the product of sensitivity and dynamic behavior might be a constant for each detector type.
It might be possible to calculate a rough estimation of the distance between natural lens and fundus with FLIO's current time resolution using tc i from Eq. (2) and Eq. (5). The separation of the fluorescence from several fundus layers is the goal of current research. Therefore, the principle of time-shifted fluorescence measurement was investigated by Gräfe et al. [58]. In their experiments using a femtosecond pulse laser, a depth resolution of 100 µm was achieved by time gating and optical parametric amplification.
In M3, the time shift tc 3 of the third exponential component, which corresponds to the fluorescence decay of the natural lens, was assumed as a free parameter. The difference between τ m,all in tailfit after surgery (reference) to τ m,12 of M3 was 15% in the outer ring. In M4, with fixed tc 3 = 172 ps, this difference was 21%. The same difference was also calculated for tc 3 = 140 ps (data not shown). This comparatively large difference is in contrast to the results by Becker et al. [56]. Similar to M4, they also used a tri-exponential model with τ 3 shifted by a fixed tc 3 . They found a good correspondence between τ m,all after surgery τ m,12 before cataract surgery. Also, the shoulder in the rising edge was very well fitted. They noted comparable results with fixed tc 3 between 130 ps and 150 ps. There are some possible reasons for the different results in [56] compared to this work. Becker et al. used an ultra-fast hybrid detector for their measurements. A very short synthetic IRF instead of a measured IRF was applied in the modelling procedure. Thus, a better time resolution was possible. In addition, no ETDRS grid was applied. Instead, the entire fluorescence lifetime image was used for the analysis. Further, it is not clear how many patients were investigated.
In M5 (the fourth exponential component is temporally shifted by tc 4 , the parameter is not fixed) a good correspondence was found in SSC between τ m, 12 and τ m,all of reference in the central area. There were also only small deviations between M5's τ m,all and τ m,all of the reference for the inner ring and the outer ring in LSC. The correspondence between M5's τ m,12 and τ m,12 of the reference was very good for all regions. As described in methods, τ m,12 in M5 is calculated from the first three exponential components. Thus, it seems that the fourth exponential is able to model the weak fluorescence decay of the natural lens in LSC.
In the layer-based approach, the differences of the fluorescence lifetimes between before surgery and after surgery were smaller, when tc i was a free parameter and not fixed. The free tc i parameter allowed for a patient-individual adaptation, which seemed beneficial.
The application of the layer-based approach resulted in an inferior agreement of τ m,12 before surgery and τ m,all after surgery (reference) compared to the application of the simpler triexponential tailfit (M1). This result is only valid for the used FLIO hardware configuration. If detectors with a narrower IRF are used, a better correspondence between τ m,all after surgery and τ m,12 before surgery can be expected. The authors initially expected that models, which use an additional decay measurement of the natural lens would be best suited to estimate the fundus fluorescence decay after cataract surgery from data before the surgery. However, this was not always the case in this study.
Specifically, M6 and M7 (all natural lens measurements) yielded generally worse results when compared to M8 and M9 (high-quality natural lens measurements only). The measurement of the natural lens fluorescence decay is quite difficult because the operator has to focus correctly at the structure-less lens, and no standardization exists for this procedure. Furthermore, the complexity of the modelling is increased because of the inclusion of the single curve natural lens fluorescence decay.
As described above, the effect of the natural lens fluorescence is stronger in SSC compared to LSC. That can even be seen when utilizing the separate all natural lens measurements. In the outer ring of M6 (LSC), τ m,all before surgery is only 10% longer than τ m,all after surgery and the deviation of τ m,12 from τ m,12 of the reference is only 2%.
As shown in Fig. 4, there is an excellent accordance between τ m,12 in M8 and M9 with τ m,all of the reference in the inner and outer rings in SSC. In LSC, τ m,all of M9 corresponds well with τ m,all of the reference in all regions, while τ m,12 of M8 corresponds well with τ m,12 of the reference in all regions.
In comparison to models using a layer-based approach (Eq. (2); M3, M4, M5), an improved adaption of the rising edge of the measured time-resolved fluorescence curve was reached if the fluorescence of the natural lens was included (Eq. (3); M6 to M9) [57].
The higher the number of free parameters, the higher was the required number of photons in the decay curve for the calculation of the fluorescence lifetime with a pre-determined error. For tri-exponential fitting of a fluorescence decay with an error of 10%, about 20,000 photons per pixel are necessary, but 400,000 photons per pixel are needed in a case of 4-exponential fit [12,59]. With the current FLIO device, such high photon counts cannot be measured in a practical way unless the spatial resolution is largely reduced.

Conclusion
In FLIO, the measured time-resolved autofluorescence of the eye originates from a layered structure. Despite the application of a confocal laser scanning technique, the fluorescence of the natural lens considerably influences the measured fluorescence signal of the FLIO device, especially in older patients with strong natural lens fluorescence. In all patients of this study, the mean fluorescence lifetime τ m,all before cataract surgery was considerably longer than τ m,all after the surgery because the implanted artificial lens emits no fluorescence signal. The impact of the natural lens was largest when applying a tri-exponential model, which utilizes the entire time range of the fluorescence signal. The application of a tri-exponential tailfit, which utilizes only the decay of the fluorescence signal, already reduces the influence of the natural lens. The mean fluorescence lifetime τ m,12 calculated from a tri-exponential tailfit in eyes with a natural lens corresponds very well with the pure fundus fluorescence lifetime τ m,all of the same eyes after cataract surgery. The inclusion of a separate natural lens measurement in the fluorescence lifetime approximation yielded also good results, especially if high-quality natural lens measurements are used, but the achieved results cannot justify the extra effort and stress for the patient caused by the additional measurement of the natural lens. In contrast to Becker et al. [56], the results of the tri-or four-exponential fluorescence lifetime approximation using a temporal shift of the longest exponential component lead to inferior results compared to the tri-exponential tailfit for the utilized FLIO device. Thus, FLIO studies interested in investigating retinal physiology or pathology should use the mean fluorescence lifetime τ m,12 calculated from a tri-exponential tailfit instead of the currently used τ m,all to minimize the influence of the natural lens on their analysis.
The best solution to suppress the natural lens fluorescence in FLIO data would be a modification of the FLIO hardware, e.g. by introducing an annular stop into the detection light path [40] or the separate measurement of the natural lens fluorescence from a non-excited location during the scanning process.