## Effects of incomplete decay in fluorescence lifetime estimation |

Biomedical Optics Express, Vol. 2, Issue 9, pp. 2517-2531 (2011)

http://dx.doi.org/10.1364/BOE.2.002517

Acrobat PDF (1000 KB)

### Abstract

Fluorescence lifetime imaging has emerged as an important microscopy technique, where high repetition rate lasers are the primary light sources. As fluorescence lifetime becomes comparable to intervals between consecutive excitation pulses, incomplete fluorescence decay from previous pulses can superimpose onto the subsequent decay measurements. Using a mathematical model, the incomplete decay effect has been shown to lead to overestimation of the amplitude average lifetime except in mono-exponential decays. An inverse model is then developed to correct the error from this effect and the theoretical simulations are tested by experimental results.

© 2011 OSA

## 1. Introduction

1. K. Suhling, P. M. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. **4**(1), 13–22 (2005). [CrossRef] [PubMed]

2. M. T. Kelleher, G. Fruhwirth, G. Patel, E. Ofo, F. Festy, P. R. Barber, S. M. Ameer-Beg, B. Vojnovic, C. Gillett, A. Coolen, G. Kéri, P. A. Ellis, and T. Ng, “The potential of optical proteomic technologies to individualize prognosis and guide rational treatment for cancer patients,” Target Oncol **4**(3), 235–252 (2009). [CrossRef] [PubMed]

3. I. Munro, J. McGinty, N. Galletly, J. Requejo-Isidro, P. M. P. Lanigan, D. S. Elson, C. Dunsby, M. A. A. Neil, M. J. Lever, G. W. H. Stamp, and P. M. W. French, “Toward the clinical application of time-domain fluorescence lifetime imaging,” J. Biomed. Opt. **10**(5), 051403 (2005). [CrossRef] [PubMed]

5. G. O. Fruhwirth, S. Ameer-Beg, R. Cook, T. Watson, T. Ng, and F. Festy, “Fluorescence lifetime endoscopy using TCSPC for the measurement of FRET in live cells,” Opt. Express **18**(11), 11148–11158 (2010). [CrossRef] [PubMed]

8. Y. Chen and A. Periasamy, “Characterization of two-photon excitation fluorescence lifetime imaging microscopy for protein localization,” Microsc. Res. Tech. **63**(1), 72–80 (2004). [CrossRef] [PubMed]

9. J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, W. J. Lederer, M. S. Kirby, and M. L. Johnson, “Fluorescence lifetime imaging of intracellular calcium in COS cells using Quin-2,” Cell Calcium **15**(1), 7–27 (1994). [CrossRef] [PubMed]

10. A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “Fast fluorescence lifetime imaging of calcium in living cells,” J. Biomed. Opt. **9**(6), 1230–1237 (2004). [CrossRef] [PubMed]

11. G. Wagnières, J. Mizeret, A. Studzinski, and H. van den Bergh, “Frequency-domain fluorescence lifetime imaging for endoscopic clinical cancer photodetection: apparatus design and preliminary results,” J. Fluoresc. **7**(1), 75–83 (1997). [CrossRef]

12. Y. Sun, N. Hatami, M. Yee, J. Phipps, D. S. Elson, F. Gorin, R. J. Schrot, and L. Marcu, “Fluorescence lifetime imaging microscopy for brain tumor image-guided surgery,” J. Biomed. Opt. **15**(5), 056022 (2010). [CrossRef] [PubMed]

13. J. A. Russell, K. R. Diamond, T. Collins, H. F. Tiedje, J. E. Hayward, T. J. Farrell, M. S. Patterson, and Q. Fang, “Characterization of fluorescence lifetime of photofrin and delta-aminolevulinic acid induced protoporphyrin IX in living cells using single and two-photon excitation,” IEEE J. Sel. Top. Quantum Electron. **14**(1), 158–166 (2008). [CrossRef]

14. A. Rück, Ch. Hülshoff, I. Kinzler, W. Becker, and R. Steiner, “SLIM: a new method for molecular imaging,” Microsc. Res. Tech. **70**(5), 485–492 (2007). [CrossRef] [PubMed]

*F*(

*t*) is the measured fluorescence intensity as a function of time

*t*;

*τ*are the individual exponential components; and

_{i}*a*are the coefficients of each exponential term. The measured intensity decay is a convolution of

_{i}*F*(

*t*) with the Instrument Response Function (IRF); thus deconvolution is sometimes necessary to recover the

*F*(

*t*) when the IRF is not negligible [4].

16. H. C. Gerritsen, “High-speed fluorescence lifetime imaging,” Proc. SPIE **5323**, 77–87 (2004). [CrossRef]

16. H. C. Gerritsen, “High-speed fluorescence lifetime imaging,” Proc. SPIE **5323**, 77–87 (2004). [CrossRef]

16. H. C. Gerritsen, “High-speed fluorescence lifetime imaging,” Proc. SPIE **5323**, 77–87 (2004). [CrossRef]

^{®}, is a typical long-lived fluorophore with its average lifetime of around 13 ns in bulk solutions or 6 −10 ns in live cells [13

13. J. A. Russell, K. R. Diamond, T. Collins, H. F. Tiedje, J. E. Hayward, T. J. Farrell, M. S. Patterson, and Q. Fang, “Characterization of fluorescence lifetime of photofrin and delta-aminolevulinic acid induced protoporphyrin IX in living cells using single and two-photon excitation,” IEEE J. Sel. Top. Quantum Electron. **14**(1), 158–166 (2008). [CrossRef]

14. A. Rück, Ch. Hülshoff, I. Kinzler, W. Becker, and R. Steiner, “SLIM: a new method for molecular imaging,” Microsc. Res. Tech. **70**(5), 485–492 (2007). [CrossRef] [PubMed]

7. E. A. Jares-Erijman and T. M. Jovin, “Imaging molecular interactions in living cells by FRET microscopy,” Curr. Opin. Chem. Biol. **10**(5), 409–416 (2006). [CrossRef] [PubMed]

8. Y. Chen and A. Periasamy, “Characterization of two-photon excitation fluorescence lifetime imaging microscopy for protein localization,” Microsc. Res. Tech. **63**(1), 72–80 (2004). [CrossRef] [PubMed]

18. P. R. Barber, S. M. Ameer-Beg, J. Gilbey, L. M. Carlin, M. Keppler, T. C. Ng, and B. Vojnovic, “Multiphoton time-domain fluorescence lifetime imaging microscopy: practical application to protein-protein interactions using global analysis,” J. R. Soc. Interface **6**(0), S93–S105 (2009). [CrossRef]

*et al.,*initially reported an analytical model in a conference paper [19

19. P. R. Barber, S. M. Ameer-Beg, J. Gilbey, R. J. Edens, I. Ezike, and B. Vojnovic, “Global and pixel kinetic data analysis for FRET detection by multi-photon time-domain FLIM,” Proc. SPIE **5700**, 171–181 (2005). [CrossRef]

*et al.*to simulate the effects of the incomplete decay and quantitatively determine the influence of the incomplete decay to the accuracy of lifetime parameter estimation either in noise-free or noisy conditions. The theoretical simulation is experimentally tested using standard fluorophores with a multiphoton microscope and a 80 MHz Ti:sapphire laser. Most importantly, correction methods were developed to recover original lifetime parameters from the measured lifetime values. Table 1 illustrated the abbreviations used in the rest of this article.

## 2. Methods

### 2.1. Analytical model of incomplete decay

*et al.*in Ref. [19

19. P. R. Barber, S. M. Ameer-Beg, J. Gilbey, R. J. Edens, I. Ezike, and B. Vojnovic, “Global and pixel kinetic data analysis for FRET detection by multi-photon time-domain FLIM,” Proc. SPIE **5700**, 171–181 (2005). [CrossRef]

*I*

_{0}(

*t*) is different from the measured decay curve

*I*(

*t*), where the period of the excitation laser pulses are short compared to the fluorophore’s lifetime. If

*I*

_{0}(

*t*) is represented with

*N*exponential terms, it can be described as:

*i*term,

^{th}*τ*

_{0}

*is the lifetime component. Then, the original amplitude weighted lifetime*

_{i}*τ*

_{0}is determined by [4]

*A*

_{01}

*, A*

_{02}

_{,}…, A_{0}

_{N}, τ_{01}

*,τ*

_{02}

*,…,τ*

_{0}

*) are known and that the measured parameters affected by incomplete decay (*

_{N}*A*

_{1}

*, A*

_{2}

_{,}…, A_{N}, τ_{1}

*,τ*

_{2}

*,…,τ*) are unknown. In practice, one would always obtain the measured values experimentally and try to estimate the original set of decay parameters. An inverse model was then derived from the forward model and assumes the opposite: the measured parameters are known and the original parameters are unknown. The goal of the inverse model is to predict the original lifetime parameters from the measured data by correcting errors in lifetime estimation due to incomplete decay.

_{N}#### 2.1.1. Forward Model

*I*(

*t*) is a summation of

*I*

_{0}(

*t*) and the tails of the

*n*previous decay curves where

*I*

_{0}(

*t*) is the original decay curve,

*I*(

*t*) is the resulting measured decay curve, and

*t*is the time interval between two consecutive excitation pulses:

_{o}*t*and

_{o}*τ*

_{0}

*are always positive, the final expression for*

_{i}*I*(

*t*) can be significantly simplified to [20]

_{id}) can be calculated from original parameters by substituting Eqs. (9) and (10) into Eq. (5):

#### 2.1.2. Inverse Model

_{id}) since the τ

_{id}is the same as the original individual lifetime while the coefficient is normalized.

*N =*2. Expressing the measured coefficients and component lifetimes affected by incomplete decay in terms of the original parameters using Eq. (9) and (10),

_{id}) as shown in Eq. (21a) is expressed in terms of the original parameters by substituting Eq. (17) to Eq. (20) into Eq. (21). Again, applying the general analytical model developed above, the inverse model is applied to the bi-exponential case where

*N =*2 to obtain the following equations to express the original parameters in terms of measured parameters:

#### 2.1.3. Incomplete Decay Simulations

_{0}) and simulated measured amplitude weighted lifetime (τ

_{id}) as defined in Eq. (12) or (16) is calculated using the derived analytical models and examined under each condition.

### 2.2. Noise simulation

_{1}= 1.5 ns and Case 2 with τ

_{2}= 4.9 ns which correspond to the lifetimes of Rhodamine B (RdmB) and Lucifer Yellow (LY) respectively. For bi-exponential, various cases were generated with different A

_{1}:A

_{2}ratios where A

_{1}ranged from 0.1 – 0.9 and A

_{2}is normalized to be 1 – A

_{1}. In all the cases, the original coefficient values were chosen such that A

_{1}+ A

_{2}= 516, τ

_{1}= 1.5 ns (RdmB), and τ

_{2}= 4.9 ns (LY). The absolute original coefficient values were set as 516 based on typical original peak decay intensities obtained from the real TCSPC experiments; however, it will not affect the actual calculation of amplitude weighted lifetime, where the normalized coefficients were used. Although the fitting coefficient A in mono-exponential decay is not critical, we performed and plotted simulation to demonstrate the effect of noise on parameter estimations.

_{1}, A

_{2,}τ

_{1,}τ

_{2}) were used to calculate lifetime values and the fractional error for various SNR. The fractional error between the data with and without the noise is defined as (τ

*-τ*

_{idn}_{0})/τ

_{0}* 100, where τ

*represents the amplitude weighted average lifetime of the noisy incomplete decay curve and τ*

_{idn}_{0}represents the amplitude weighted average lifetime of the original decay curve.

### 2.3. Time-domain multi-photon fluorescence lifetime measurements

## 3. Results

### 3.1. Simulated results of the incomplete decay

_{id}) does depend on the coefficients

*A*

_{1}and

*A*

_{2}, where

_{0}) and measured (τ

_{id}) decay curves are shown on a linear and log scale. As shown in Fig. 2, incomplete decay only affects the estimation of amplitude weighted lifetimes for bi-exponential decays. Table 2 shows the time-domain parameters distorted by the incomplete decay in mono- and bi-exponential cases used in Fig. 2.

*i*measured and original coefficients which is defined as the fractional error

^{th}*E*(

_{i}=*A*

_{i}– A_{0}

*)*

_{i}*/A*where

_{oi,}*i*= 1, 2 for bi-exponential cases. According to Eq. (9),

*E*can be rewritten as

_{i}^{th}fractional error (

*E*) is only dependent on the i

_{i}^{th}individual lifetime (τ

_{i}), the threshold value of individual lifetimes(τ

_{i(thld)}) that would give fractional errors of 5% is determined by rearranging Eq. (26). The threshold value is expressed as:

*E*is a monotonically increasing function with respect to

_{i}*τ*, which means if τ

_{i}_{i}< τ

_{i(}

_{thld}_{)}, the estimation errors due to incomplete decay are less than 5% and may be negligible. The τ

_{i(thresh)}values corresponding to various laser repetition rates are shown in Table 3 . As expected, the higher the repetition rate, the lower the threshold individual lifetime value, and thus the more likely incomplete decay will cause fractional errors between coefficients and cause errors in lifetime parameter estimation.

*E*scales linearly with the laser repetition period

_{i}*t*and thus the individual threshold lifetime values (τ

_{o}_{i(thld)}) that would give fractional errors of 5% can instead be expressed as a fraction of the repetition period,

*t*

_{o}/ τ_{i}_{(}

_{thld}_{)}. This threshold ratio between repetition period

*t*and threshold lifetime value τ

_{o}_{i(thld)}can be denoted as

*R*

_{i}_{(}

_{thld}_{)}. By re-arranging Eq. (28),

*R*

_{i}_{(}

_{thld}_{)}=

*t*

_{o}/ τ_{i}_{(}

_{thld}_{)}= -ln(0.05/1.05) = 3.045. Since

*E*is a monotonically decreasing function with respect to

_{i}*t*, this means that as long as the time interval between laser pulses (

_{o}/ τ_{i}*t*) is 3 times longer than the individual lifetime τ

_{o}_{i,}the estimation errors due to incomplete decay are less than 5% and may be negligible.

*A*

_{01}

*= A*

_{02}

*=*0

*.*5, τ

_{01}= 1 ns,

*τ*

_{02}varies from 0 to 20 ns) was plotted with respect to

*τ*

_{2}at various repetition rates as shown by the multiple curves. It was observed that at each

*τ*

_{2}value, the error increased as the repetition rate increased. For example, the error of the τ

_{id}at

*τ*

_{2}of 20 ns at the highest repetition rate (100 MHz) resulted in the maximum error of all cases with 40% error from the original average lifetime value (

*τ*

_{0}). Figure 3 also illustrated the negligible incomplete decay effect when τ

_{1}= 1 ns and τ

_{2}< τ

_{i(thld)}; the error is always less than 5%. Similarly, Fig. 3 illustrates that when the time window between laser excitation pulses (

*t*) is around three times longer than both τ

_{o}_{1}and τ

_{2}, the error due to incomplete decay is less than 5%.

_{id}and τ

_{0}values as defined in Eq. (16) was also investigated at a constant repetition rate of 80 MHz as shown in Fig. 4 . Figure 4 shows a contour plot where the y-axis corresponds to

*A*

_{1}and is varied from 0 to 1 (

*A*

_{2}

*=*1

*– A*

_{1}) and the x-axis corresponds to the difference between measured lifetime components (

*τ*

_{1}

*– τ*

_{2}) where

*τ*

_{2}(10 ns) was chosen to be constant and

*τ*

_{1}varies from

*τ*

_{2}

*–*8(2ns) to

*τ*

_{2}

*+*8 (18 ns). The varying gray scale color of the contour map corresponds to the calculated absolute fractional errors for the various corresponding measured coefficient and lifetime component values where the darker the color, the larger the error.

_{1}approaches 0.5. In other words, since

*A*

_{2}

*=*1

*– A*

_{1}, the fractional error increases as

*A*

_{1}and

*A*

_{2}approach 0.5.

_{1}. The behavior, as observed in Fig. 4, follows this pattern: if

*τ*

_{2}

*> τ*

_{1}(negative difference), the maximum error tends to occur at values greater than A

_{1}= 0.5 whereas if

*τ*

_{2}

*< τ*

_{1}(positive difference), maximum error tends to occur at values less than A

_{1}= 0.5. Therefore, it is difficult to determine

*the specific A*

_{1}values that would give the maximum error for all cases. However, it is clear that the error from incomplete decay increases for measured coefficients that converge towards 0.5. It is also interesting that although all cases of measured parameters in Fig. 4 followed this error trend with respect to amplitude variations, the magnitude of the error varied drastically between different cases. The reason for this large difference between different cases of measured parameters (lifetime components) will be investigated in the following section.

_{id}) and original (τ

_{0}) amplitude weighted lifetime values (as defined by Eq. (16) also depends on the measured lifetime components. However, where incomplete decay has an effect, the error does not depend on the magnitude of the measured lifetime components but actually on the differences between the measured lifetime components (

*τ*

_{1}

*– τ*

_{2}). It can be observed from Fig. 4 that as the difference between

*τ*

_{1}and

*τ*

_{2}increases, the error increases as well. The error trend is not symmetric with respect to the difference between measured lifetime components where positive differences will result in lower error values. This is an indication that larger lifetime component values with the same differences will result in relatively lower fractional error values. Moreover, Fig. 4 demonstrate that in cases with small differences in measured lifetimes (i.e. 4 ns), incomplete decay effects may be negligible (<5%) for all possible coefficient values, which further verifies the threshold values determined by the model.

### 3.2. The dependency of measured lifetimes *(*τ_{idn}*)* on the SNR level

_{01}:A

_{02}ratios (τ

_{01}= 1.5 ns (RdmB), and τ

_{02}= 4.9 ns (LY)) were fitted using the nonlinear least squares algorithm to obtain the predicted measured amplitude weighted lifetimes (affected by incomplete decay) with noise (τ

_{idn}).The corresponding residuals were plotted (data not shown) and at each SNR level showed no pattern, indicating the good quality of fitting process. The original amplitude weighted lifetime values (τ

_{0}) for various A

_{01}to A

_{02}ratios were also calculated for the original decay signal. Using the inverse model on τ

_{idn,}the corrected amplitude weighted lifetimes were obtained (τ

_{corr}). . The original amplitude weighted lifetime (τ

_{0}), predicted measured amplitude weighted lifetimes (with noise) (τ

_{idn}), and corrected amplitude weighted lifetimes (τ

_{corr}) for various A

_{01}:A

_{02}ratios at SNR = 16 are shown in Table 4 below. As shown in Table 4, it is demonstrated that the corrected amplitude weighted lifetimes (τ

_{corr}) by the inverse model under low SNR = 16 are almost equivalent to the original amplitude weighted lifetimes (τ

_{0}) (less than 1% difference). This further verifies the accuracy of the inverse model and indicates that the effect on estimation error from noise itself is actually minor in comparison with the effect of incomplete decay and is always negligible. This shows that the correction for incomplete decay is indeed necessary.

### 3.3. Experimental results

*τ*

_{0}) without the effects of incomplete decay, the dye mixture was calculated with respect to the original fluorescence lifetime of each dye obtained from the frequency domain system (4.9 ns and 1.5 ns). Also, to determine the real relative contribution of RdmB and LY (ie correct original coefficients to obtain real original coefficients), the quantum efficiency (QE) of each fluorescence dye was also determined by taking the average of integrated photon intensities from three repetitive LY and RdmB measurements using TCSPC. The results showed the relative QE of RdmB is 36% against LY. Therefore, the quantum efficiency corrected original coefficients can represent the real relative contribution of RdmB (

*QE*

_{c}A_{01}) and LY (

*QE*

_{c}A_{02}) where

*QE*

_{c}A_{02}

*=*1

*– QE*

_{c}A_{01}.

*τ*

_{0}), the TCSPC measurements (τ

*), and correction of τ*

_{idn}*using the inverse model (τ*

_{idn}*). Except for the measurement at*

_{corr}*QE*

_{c}A_{01}

*59.1% (*

_{ =}*τ*

_{0}

*=*2.89 ns), the measured TCSPC lifetime (

*τ*) consistently overestimated the original amplitude weighted lifetime of the solution (

_{idn}*τ*

_{0}) as obtained from the frequency domain system. The overestimation of measured amplitude weighted lifetime values is predicted and agrees with the incomplete decay model. Using the inverse model, the measured amplitude weighted lifetime values (

*τ*) were corrected and is close enough to the original amplitude weighted lifetime (

_{idn}*τ*

_{0}) to be within the uncertainties of the experimental measurement. Differences between τ

_{0}and τ

_{idn}(Diff

_{id}) and between τ

_{0}and τ

_{corr}(Diff

_{corr}) were evaluated to see whether lifetime estimation error caused by incomplete decay is comparable to errors from random experimental noise. As shown in Table 5, Diff

_{id}is always larger than Diff

_{corr}for all mixtures indicating that the effect on estimation error from incomplete decay is larger than the effect on error from noise and that the correction for incomplete decay is indeed necessary. The outlier value at 59.1% (

*τ*

_{0}

*=*2.89 ns) may be due to low SNR in the experimental measurements, which led to large uncertainties in lifetime estimation for bi-exponential decays.

## 4. Discussion and Conclusion

*E*

_{id}) became significant with (i) increased laser repetition rate, (ii) converge of coefficients to be equal, and (iii) increased difference between individual lifetime components, while the error is not significantly increased by the noise. These facts offer guidelines that allow researchers to have a better idea for measurement values that may require correction for incomplete decay.

^{®}and ALA induced protoporphyrin IX (PpIX), which are clinically approved photosensitizers with fluorescence lifetimes of more than 10 ns [13

13. J. A. Russell, K. R. Diamond, T. Collins, H. F. Tiedje, J. E. Hayward, T. J. Farrell, M. S. Patterson, and Q. Fang, “Characterization of fluorescence lifetime of photofrin and delta-aminolevulinic acid induced protoporphyrin IX in living cells using single and two-photon excitation,” IEEE J. Sel. Top. Quantum Electron. **14**(1), 158–166 (2008). [CrossRef]

8. Y. Chen and A. Periasamy, “Characterization of two-photon excitation fluorescence lifetime imaging microscopy for protein localization,” Microsc. Res. Tech. **63**(1), 72–80 (2004). [CrossRef] [PubMed]

*et al.*described a technique that uses fibers with different lengths to multiplex multiple spectral channels of fluorescence decay using a single detector [23

23. Y. Yuan, T. Papaioannou, and Q. Fang, “Single-shot acquisition of time-resolved fluorescence spectra using a multiple delay optical fiber bundle,” Opt. Lett. **33**(8), 791–793 (2008). [CrossRef] [PubMed]

## Acknowledgments

## References and links

1. | K. Suhling, P. M. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. |

2. | M. T. Kelleher, G. Fruhwirth, G. Patel, E. Ofo, F. Festy, P. R. Barber, S. M. Ameer-Beg, B. Vojnovic, C. Gillett, A. Coolen, G. Kéri, P. A. Ellis, and T. Ng, “The potential of optical proteomic technologies to individualize prognosis and guide rational treatment for cancer patients,” Target Oncol |

3. | I. Munro, J. McGinty, N. Galletly, J. Requejo-Isidro, P. M. P. Lanigan, D. S. Elson, C. Dunsby, M. A. A. Neil, M. J. Lever, G. W. H. Stamp, and P. M. W. French, “Toward the clinical application of time-domain fluorescence lifetime imaging,” J. Biomed. Opt. |

4. | J. R. Lakowicz, |

5. | G. O. Fruhwirth, S. Ameer-Beg, R. Cook, T. Watson, T. Ng, and F. Festy, “Fluorescence lifetime endoscopy using TCSPC for the measurement of FRET in live cells,” Opt. Express |

6. | T. Ng, A. Squire, G. Hansra, F. Bornancin, C. Prevostel, A. Hanby, W. Harris, D. Barnes, S. Schmidt, H. Mellor, P. I. H. Bastiaens, and P. J. Parker, “Imaging protein kinase Calpha activation in cells,” Science |

7. | E. A. Jares-Erijman and T. M. Jovin, “Imaging molecular interactions in living cells by FRET microscopy,” Curr. Opin. Chem. Biol. |

8. | Y. Chen and A. Periasamy, “Characterization of two-photon excitation fluorescence lifetime imaging microscopy for protein localization,” Microsc. Res. Tech. |

9. | J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, W. J. Lederer, M. S. Kirby, and M. L. Johnson, “Fluorescence lifetime imaging of intracellular calcium in COS cells using Quin-2,” Cell Calcium |

10. | A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “Fast fluorescence lifetime imaging of calcium in living cells,” J. Biomed. Opt. |

11. | G. Wagnières, J. Mizeret, A. Studzinski, and H. van den Bergh, “Frequency-domain fluorescence lifetime imaging for endoscopic clinical cancer photodetection: apparatus design and preliminary results,” J. Fluoresc. |

12. | Y. Sun, N. Hatami, M. Yee, J. Phipps, D. S. Elson, F. Gorin, R. J. Schrot, and L. Marcu, “Fluorescence lifetime imaging microscopy for brain tumor image-guided surgery,” J. Biomed. Opt. |

13. | J. A. Russell, K. R. Diamond, T. Collins, H. F. Tiedje, J. E. Hayward, T. J. Farrell, M. S. Patterson, and Q. Fang, “Characterization of fluorescence lifetime of photofrin and delta-aminolevulinic acid induced protoporphyrin IX in living cells using single and two-photon excitation,” IEEE J. Sel. Top. Quantum Electron. |

14. | A. Rück, Ch. Hülshoff, I. Kinzler, W. Becker, and R. Steiner, “SLIM: a new method for molecular imaging,” Microsc. Res. Tech. |

15. | W. Becker, A. Bergmann, and C. Biskup, “Multispectral fluorescence lifetime imaging by TCSPC,” Microsc. Res. Tech. |

16. | H. C. Gerritsen, “High-speed fluorescence lifetime imaging,” Proc. SPIE |

17. | W. Becker, |

18. | P. R. Barber, S. M. Ameer-Beg, J. Gilbey, L. M. Carlin, M. Keppler, T. C. Ng, and B. Vojnovic, “Multiphoton time-domain fluorescence lifetime imaging microscopy: practical application to protein-protein interactions using global analysis,” J. R. Soc. Interface |

19. | P. R. Barber, S. M. Ameer-Beg, J. Gilbey, R. J. Edens, I. Ezike, and B. Vojnovic, “Global and pixel kinetic data analysis for FRET detection by multi-photon time-domain FLIM,” Proc. SPIE |

20. | J. Stewart, |

21. | J. R. Taylor, |

22. | D. J. Schroeder, |

23. | Y. Yuan, T. Papaioannou, and Q. Fang, “Single-shot acquisition of time-resolved fluorescence spectra using a multiple delay optical fiber bundle,” Opt. Lett. |

**OCIS Codes**

(170.3650) Medical optics and biotechnology : Lifetime-based sensing

**ToC Category:**

Spectroscopic Diagnostics

**History**

Original Manuscript: May 2, 2011

Revised Manuscript: July 21, 2011

Manuscript Accepted: July 31, 2011

Published: August 2, 2011

**Citation**

Regina Won Kay Leung, Shu-Chi Allison Yeh, and Qiyin Fang, "Effects of incomplete decay in fluorescence lifetime estimation," Biomed. Opt. Express **2**, 2517-2531 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-9-2517

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### References

- K. Suhling, P. M. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. 4(1), 13–22 (2005). [CrossRef] [PubMed]
- M. T. Kelleher, G. Fruhwirth, G. Patel, E. Ofo, F. Festy, P. R. Barber, S. M. Ameer-Beg, B. Vojnovic, C. Gillett, A. Coolen, G. Kéri, P. A. Ellis, and T. Ng, “The potential of optical proteomic technologies to individualize prognosis and guide rational treatment for cancer patients,” Target Oncol 4(3), 235–252 (2009). [CrossRef] [PubMed]
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