Abstract

Time-correlated single photon counting (TCSPC) enables acquisition of fluorescence lifetime decays with high temporal resolution within the fluorescence decay. However, many thousands of photons per pixel are required for accurate lifetime decay curve representation, instrument response deconvolution, and lifetime estimation, particularly for two-component lifetimes. TCSPC imaging speed is inherently limited due to the single photon per laser pulse nature and low fluorescence event efficiencies (<10%) required to reduce bias towards short lifetimes. Here, simulated fluorescence lifetime decays are analyzed by SPCImage and SLIM Curve software to determine the limiting lifetime parameters and photon requirements of fluorescence lifetime decays that can be accurately fit. Data analysis techniques to improve fitting accuracy for low photon count data were evaluated. Temporal binning of the decays from 256 time bins to 42 time bins significantly (p<0.0001) improved fit accuracy in SPCImage and enabled accurate fits with low photon counts (as low as 700 photons/decay), a 6-fold reduction in required photons and therefore improvement in imaging speed. Additionally, reducing the number of free parameters in the fitting algorithm by fixing the lifetimes to known values significantly reduced the lifetime component error from 27.3% to 3.2% in SPCImage (p<0.0001) and from 50.6% to 4.2% in SLIM Curve (p<0.0001). Analysis of nicotinamide adenine dinucleotide–lactate dehydrogenase (NADH-LDH) solutions confirmed temporal binning of TCSPC data and a reduced number of free parameters improves exponential decay fit accuracy in SPCImage. Altogether, temporal binning (in SPCImage) and reduced free parameters are data analysis techniques that enable accurate lifetime estimation from low photon count data and enable TCSPC imaging speeds up to 6x and 300x faster, respectively, than traditional TCSPC analysis.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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  1. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).
  2. J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
    [Crossref] [PubMed]
  3. F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
    [Crossref] [PubMed]
  4. K. Sagolla, H.-G. Löhmannsröben, and C. Hille, “Time-resolved fluorescence microscopy for quantitative Ca2+ imaging in living cells,” Anal. Bioanal. Chem. 405(26), 8525–8537 (2013).
    [Crossref] [PubMed]
  5. B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
    [Crossref] [PubMed]
  6. M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
    [Crossref] [PubMed]
  7. M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
    [Crossref] [PubMed]
  8. A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
    [Crossref] [PubMed]
  9. A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
    [Crossref] [PubMed]
  10. X. F. Wang, T. Uchida, D. M. Coleman, and S. Minami, “A Two-Dimensional Fluorescence Lifetime Imaging System Using a Gated Image Intensifier,” Appl. Spectrosc. 45(3), 360–366 (1991).
    [Crossref]
  11. A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
    [Crossref] [PubMed]
  12. A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “High frame rate fluorescence lifetime imaging,” J. Phys. D Appl. Phys. 36(14), 1655–1662 (2003).
    [Crossref]
  13. M. G. Giacomelli, Y. Sheikine, H. Vardeh, J. L. Connolly, and J. G. Fujimoto, “Rapid imaging of surgical breast excisions using direct temporal sampling two photon fluorescent lifetime imaging,” Biomed. Opt. Express 6(11), 4317–4325 (2015).
    [Crossref] [PubMed]
  14. W. Becker, ed., Advanced Time-Correlated Single Photon Counting Applications (Springer, 2015).
  15. W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, 2005), Vol. 81.
  16. N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
    [PubMed]
  17. H. Wallrabe and A. Periasamy, “Imaging protein molecules using FRET and FLIM microscopy,” Curr. Opin. Biotechnol. 16(1), 19–27 (2005).
    [Crossref] [PubMed]
  18. W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
    [PubMed]
  19. S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. Walker, V. Devauges, J. a. Levitt, N. Dutton, T. Ng, R. Henderson, and S. Ameer-Beg, “A time-resolved multifocal multiphoton microscope for high speed fret imaging in vivo,” Microscience Microsc. Congr. 2014 39, 6013–6016 (2014).
    [Crossref]
  20. S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. J. Walker, V. Devauges, J. Richardson, N. Dutton, P. Barber, D. D.-U. Li, K. Suhling, T. Ng, R. K. Henderson, and S. M. Ameer-Beg, “A high speed multifocal multiphoton fluorescence lifetime imaging microscope for live-cell FRET imaging,” Biomed. Opt. Express 6(2), 277–296 (2015).
    [Crossref] [PubMed]
  21. A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
    [Crossref] [PubMed]
  22. T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
    [Crossref] [PubMed]
  23. R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61(1), 30–33 (1989).
    [Crossref]
  24. D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
    [Crossref] [PubMed]
  25. D. U. Campos-Delgado, O. G. Navarro, E. R. Arce-Santana, A. J. Walsh, M. C. Skala, and J. A. Jo, “Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials,” Opt. Express 23(18), 23748–23767 (2015).
    [Crossref] [PubMed]
  26. J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
    [Crossref] [PubMed]
  27. D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
    [Crossref] [PubMed]
  28. D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
    [Crossref] [PubMed]
  29. D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
    [Crossref] [PubMed]
  30. N. Krstajić, S. Poland, J. Levitt, R. Walker, A. Erdogan, S. Ameer-Beg, and R. K. Henderson, “0.5 billion events per second time correlated single photon counting using CMOS SPAD arrays,” Opt. Lett. 40(18), 4305–4308 (2015).
    [Crossref] [PubMed]
  31. L. Marcu, “Fluorescence lifetime techniques in medical applications,” Ann. Biomed. Eng. 40(2), 304–331 (2012).
    [Crossref] [PubMed]

2015 (5)

2014 (3)

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

2013 (2)

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

K. Sagolla, H.-G. Löhmannsröben, and C. Hille, “Time-resolved fluorescence microscopy for quantitative Ca2+ imaging in living cells,” Anal. Bioanal. Chem. 405(26), 8525–8537 (2013).
[Crossref] [PubMed]

2012 (3)

A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
[Crossref] [PubMed]

L. Marcu, “Fluorescence lifetime techniques in medical applications,” Ann. Biomed. Eng. 40(2), 304–331 (2012).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

2011 (2)

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
[PubMed]

2010 (1)

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

2007 (2)

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

2005 (1)

H. Wallrabe and A. Periasamy, “Imaging protein molecules using FRET and FLIM microscopy,” Curr. Opin. Biotechnol. 16(1), 19–27 (2005).
[Crossref] [PubMed]

2004 (1)

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
[Crossref] [PubMed]

2003 (1)

A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “High frame rate fluorescence lifetime imaging,” J. Phys. D Appl. Phys. 36(14), 1655–1662 (2003).
[Crossref]

2002 (1)

A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
[Crossref] [PubMed]

1992 (1)

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
[Crossref] [PubMed]

1991 (1)

1989 (1)

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61(1), 30–33 (1989).
[Crossref]

1980 (1)

N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
[PubMed]

1979 (1)

T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
[Crossref] [PubMed]

Agronskaia, A. V.

A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “High frame rate fluorescence lifetime imaging,” J. Phys. D Appl. Phys. 36(14), 1655–1662 (2003).
[Crossref]

Ameer-Beg, S.

N. Krstajić, S. Poland, J. Levitt, R. Walker, A. Erdogan, S. Ameer-Beg, and R. K. Henderson, “0.5 billion events per second time correlated single photon counting using CMOS SPAD arrays,” Opt. Lett. 40(18), 4305–4308 (2015).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

Ameer-Beg, S. M.

Andrews, R.

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

Arce-Santana, E. R.

D. U. Campos-Delgado, O. G. Navarro, E. R. Arce-Santana, A. J. Walsh, M. C. Skala, and J. A. Jo, “Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials,” Opt. Express 23(18), 23748–23767 (2015).
[Crossref] [PubMed]

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

Arlt, J.

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

Arteaga, C. L.

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

Aurisicchio, L.

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

Ballew, R. M.

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61(1), 30–33 (1989).
[Crossref]

Barber, P.

Becker, W.

W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
[PubMed]

Bird, D. K.

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

Campos-Delgado, D. U.

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

D. U. Campos-Delgado, O. G. Navarro, E. R. Arce-Santana, A. J. Walsh, M. C. Skala, and J. A. Jo, “Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials,” Opt. Express 23(18), 23748–23767 (2015).
[Crossref] [PubMed]

Charbon, E.

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Ciliberto, G.

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

Coelho, S.

Coleman, D. M.

Connolly, J. L.

Cook, R. S.

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

Demas, J. N.

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61(1), 30–33 (1989).
[Crossref]

Devauges, V.

Dutton, N.

Duvall, C. L.

A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
[Crossref] [PubMed]

Eickhoff, J.

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

Eliceiri, K. W.

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

Erdogan, A.

Fang, Q.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
[Crossref] [PubMed]

Fierke, C. A.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Forster, L. S.

T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
[Crossref] [PubMed]

Friedrich, T.

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Fujimoto, J. G.

Gendron-Fitzpatrick, A.

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

Gerritsen, H. C.

A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “High frame rate fluorescence lifetime imaging,” J. Phys. D Appl. Phys. 36(14), 1655–1662 (2003).
[Crossref]

Giacomelli, M. G.

Gutierrez-Navarro, O.

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

Henderson, R.

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

Henderson, R. K.

S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. J. Walker, V. Devauges, J. Richardson, N. Dutton, P. Barber, D. D.-U. Li, K. Suhling, T. Ng, R. K. Henderson, and S. M. Ameer-Beg, “A high speed multifocal multiphoton fluorescence lifetime imaging microscope for live-cell FRET imaging,” Biomed. Opt. Express 6(2), 277–296 (2015).
[Crossref] [PubMed]

N. Krstajić, S. Poland, J. Levitt, R. Walker, A. Erdogan, S. Ameer-Beg, and R. K. Henderson, “0.5 billion events per second time correlated single photon counting using CMOS SPAD arrays,” Opt. Lett. 40(18), 4305–4308 (2015).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Hicks, D. J.

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

Hille, C.

K. Sagolla, H.-G. Löhmannsröben, and C. Hille, “Time-resolved fluorescence microscopy for quantitative Ca2+ imaging in living cells,” Anal. Bioanal. Chem. 405(26), 8525–8537 (2013).
[Crossref] [PubMed]

Holub, O.

W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
[PubMed]

Hurst, T.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Jo, J. A.

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

D. U. Campos-Delgado, O. G. Navarro, E. R. Arce-Santana, A. J. Walsh, M. C. Skala, and J. A. Jo, “Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials,” Opt. Express 23(18), 23748–23767 (2015).
[Crossref] [PubMed]

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
[Crossref] [PubMed]

Johnson, M. L.

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
[Crossref] [PubMed]

Junghans, C.

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Keely, P. J.

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

Krstajic, N.

Lafontant, A.

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

Lakowicz, J. R.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
[Crossref] [PubMed]

Levitt, J.

Li, D. D. U.

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Li, D. D.-U.

S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. J. Walker, V. Devauges, J. Richardson, N. Dutton, P. Barber, D. D.-U. Li, K. Suhling, T. Ng, R. K. Henderson, and S. M. Ameer-Beg, “A high speed multifocal multiphoton fluorescence lifetime imaging microscope for live-cell FRET imaging,” Biomed. Opt. Express 6(2), 277–296 (2015).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

Li, D.-U.

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

Löhmannsröben, H.-G.

K. Sagolla, H.-G. Löhmannsröben, and C. Hille, “Time-resolved fluorescence microscopy for quantitative Ca2+ imaging in living cells,” Anal. Bioanal. Chem. 405(26), 8525–8537 (2013).
[Crossref] [PubMed]

Manning, H. C.

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

Marcu, L.

L. Marcu, “Fluorescence lifetime techniques in medical applications,” Ann. Biomed. Eng. 40(2), 304–331 (2012).
[Crossref] [PubMed]

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
[Crossref] [PubMed]

Matthews, D. R.

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

McCranor, B. J.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Minami, S.

Mitchell, A. C.

A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
[Crossref] [PubMed]

Monypenny, J.

Morgan, C. G.

A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
[Crossref] [PubMed]

Murray, J. G.

A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
[Crossref] [PubMed]

Nakashima, N.

N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
[PubMed]

Navarro, O. G.

Ng, T.

Nowaczyk, K.

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
[Crossref] [PubMed]

O’Neal, C. C.

T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
[Crossref] [PubMed]

Papaioannou, T.

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
[Crossref] [PubMed]

Periasamy, A.

H. Wallrabe and A. Periasamy, “Imaging protein molecules using FRET and FLIM microscopy,” Curr. Opin. Biotechnol. 16(1), 19–27 (2005).
[Crossref] [PubMed]

Poland, S.

Poland, S. P.

Poole, K. M.

A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
[Crossref] [PubMed]

Rae, B.

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

Ramanujam, N.

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

Richardson, J.

S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. J. Walker, V. Devauges, J. Richardson, N. Dutton, P. Barber, D. D.-U. Li, K. Suhling, T. Ng, R. K. Henderson, and S. M. Ameer-Beg, “A high speed multifocal multiphoton fluorescence lifetime imaging microscope for live-cell FRET imaging,” Biomed. Opt. Express 6(2), 277–296 (2015).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Riching, K. M.

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

Rupley, J. A.

T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
[Crossref] [PubMed]

Sagolla, K.

K. Sagolla, H.-G. Löhmannsröben, and C. Hille, “Time-resolved fluorescence microscopy for quantitative Ca2+ imaging in living cells,” Anal. Bioanal. Chem. 405(26), 8525–8537 (2013).
[Crossref] [PubMed]

Sanders, M. E.

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

Schmitt, F.-J.

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Sheikine, Y.

Skala, M. C.

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

D. U. Campos-Delgado, O. G. Navarro, E. R. Arce-Santana, A. J. Walsh, M. C. Skala, and J. A. Jo, “Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials,” Opt. Express 23(18), 23748–23767 (2015).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

Stoddard, A. K.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Stoppa, D.

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Su, B.

W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
[PubMed]

Suhling, K.

Szmacinski, H.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
[Crossref] [PubMed]

Tanaka, F.

N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
[PubMed]

Tertoolen, L.

A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “High frame rate fluorescence lifetime imaging,” J. Phys. D Appl. Phys. 36(14), 1655–1662 (2003).
[Crossref]

Thaa, B.

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Thompson, R. B.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Torikata, T.

T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
[Crossref] [PubMed]

Tyndall, D.

S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. J. Walker, V. Devauges, J. Richardson, N. Dutton, P. Barber, D. D.-U. Li, K. Suhling, T. Ng, R. K. Henderson, and S. M. Ameer-Beg, “A high speed multifocal multiphoton fluorescence lifetime imaging microscope for live-cell FRET imaging,” Biomed. Opt. Express 6(2), 277–296 (2015).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Uchida, T.

Vardeh, H.

Veit, M.

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Visitkul, V.

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

Vitali, M.

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Walker, R.

N. Krstajić, S. Poland, J. Levitt, R. Walker, A. Erdogan, S. Ameer-Beg, and R. K. Henderson, “0.5 billion events per second time correlated single photon counting using CMOS SPAD arrays,” Opt. Lett. 40(18), 4305–4308 (2015).
[Crossref] [PubMed]

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

Walker, R. J.

Wall, J. E.

A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
[Crossref] [PubMed]

Wallrabe, H.

H. Wallrabe and A. Periasamy, “Imaging protein molecules using FRET and FLIM microscopy,” Curr. Opin. Biotechnol. 16(1), 19–27 (2005).
[Crossref] [PubMed]

Walsh, A. J.

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

D. U. Campos-Delgado, O. G. Navarro, E. R. Arce-Santana, A. J. Walsh, M. C. Skala, and J. A. Jo, “Deconvolution of fluorescence lifetime imaging microscopy by a library of exponentials,” Opt. Express 23(18), 23748–23767 (2015).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
[Crossref] [PubMed]

Wang, X. F.

Weisshart, K.

W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
[PubMed]

White, J. G.

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

Yagi, K.

N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
[PubMed]

Yoshihara, K.

N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
[PubMed]

Zeng, H. H.

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Anal. Bioanal. Chem. (1)

K. Sagolla, H.-G. Löhmannsröben, and C. Hille, “Time-resolved fluorescence microscopy for quantitative Ca2+ imaging in living cells,” Anal. Bioanal. Chem. 405(26), 8525–8537 (2013).
[Crossref] [PubMed]

Anal. Chem. (1)

R. M. Ballew and J. N. Demas, “An error analysis of the rapid lifetime determination method for the evaluation of single exponential decays,” Anal. Chem. 61(1), 30–33 (1989).
[Crossref]

Ann. Biomed. Eng. (1)

L. Marcu, “Fluorescence lifetime techniques in medical applications,” Ann. Biomed. Eng. 40(2), 304–331 (2012).
[Crossref] [PubMed]

Appl. Spectrosc. (1)

Biochemistry (1)

T. Torikata, L. S. Forster, C. C. O’Neal, and J. A. Rupley, “Lifetimes and NADH quenching of tryptophan fluorescence in pig heart lactate dehydrogenase,” Biochemistry 18(2), 385–390 (1979).
[Crossref] [PubMed]

Biochim. Biophys. Acta (1)

F.-J. Schmitt, B. Thaa, C. Junghans, M. Vitali, M. Veit, and T. Friedrich, “eGFP-pHsens as a highly sensitive fluorophore for cellular pH determination by fluorescence lifetime imaging microscopy (FLIM),” Biochim. Biophys. Acta 1837(9), 1581–1593 (2014).
[Crossref] [PubMed]

Biomed. Opt. Express (2)

Cancer Res. (2)

A. J. Walsh, R. S. Cook, H. C. Manning, D. J. Hicks, A. Lafontant, C. L. Arteaga, and M. C. Skala, “Optical metabolic imaging identifies glycolytic levels, subtypes, and early-treatment response in breast cancer,” Cancer Res. 73(20), 6164–6174 (2013).
[Crossref] [PubMed]

A. J. Walsh, R. S. Cook, M. E. Sanders, L. Aurisicchio, G. Ciliberto, C. L. Arteaga, and M. C. Skala, “Quantitative optical imaging of primary tumor organoid metabolism predicts drug response in breast cancer,” Cancer Res. 74(18), 5184–5194 (2014).
[Crossref] [PubMed]

Curr. Opin. Biotechnol. (1)

H. Wallrabe and A. Periasamy, “Imaging protein molecules using FRET and FLIM microscopy,” Curr. Opin. Biotechnol. 16(1), 19–27 (2005).
[Crossref] [PubMed]

J. Biol. Chem. (1)

N. Nakashima, K. Yoshihara, F. Tanaka, and K. Yagi, “Picosecond fluorescence lifetime of the coenzyme of D-amino acid oxidase,” J. Biol. Chem. 255(11), 5261–5263 (1980).
[PubMed]

J. Biomed. Opt. (6)

M. C. Skala, K. M. Riching, D. K. Bird, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, P. J. Keely, and N. Ramanujam, “In vivo multiphoton fluorescence lifetime imaging of protein-bound and free nicotinamide adenine dinucleotide in normal and precancerous epithelia,” J. Biomed. Opt. 12(2), 024014 (2007).
[Crossref] [PubMed]

A. J. Walsh, K. M. Poole, C. L. Duvall, and M. C. Skala, “Ex vivo optical metabolic measurements from cultured tissue reflect in vivo tissue status,” J. Biomed. Opt. 17(11), 116015 (2012).
[Crossref] [PubMed]

D. U. Campos-Delgado, O. Gutierrez-Navarro, E. R. Arce-Santana, M. C. Skala, A. J. Walsh, and J. A. Jo, “Blind deconvolution estimation of fluorescence measurements through quadratic programming,” J. Biomed. Opt. 20(7), 075010 (2015).
[Crossref] [PubMed]

J. A. Jo, Q. Fang, T. Papaioannou, and L. Marcu, “Fast model-free deconvolution of fluorescence decay for analysis of biological systems,” J. Biomed. Opt. 9(4), 743–752 (2004).
[Crossref] [PubMed]

D.-U. Li, B. Rae, R. Andrews, J. Arlt, and R. Henderson, “Hardware implementation algorithm and error analysis of high-speed fluorescence lifetime sensing systems using center-of-mass method,” J. Biomed. Opt. 15(1), 017006 (2010).
[Crossref] [PubMed]

D. D. U. Li, J. Arlt, D. Tyndall, R. Walker, J. Richardson, D. Stoppa, E. Charbon, and R. K. Henderson, “Video-rate fluorescence lifetime imaging camera with CMOS single-photon avalanche diode arrays and high-speed imaging algorithm,” J. Biomed. Opt. 16(9), 096012 (2011).
[Crossref] [PubMed]

J. Microsc. (1)

A. C. Mitchell, J. E. Wall, J. G. Murray, and C. G. Morgan, “Measurement of nanosecond time-resolved fluorescence with a directly gated interline CCD camera,” J. Microsc. 206(3), 233–238 (2002).
[Crossref] [PubMed]

J. Phys. D Appl. Phys. (1)

A. V. Agronskaia, L. Tertoolen, and H. C. Gerritsen, “High frame rate fluorescence lifetime imaging,” J. Phys. D Appl. Phys. 36(14), 1655–1662 (2003).
[Crossref]

Metallomics (1)

B. J. McCranor, H. Szmacinski, H. H. Zeng, A. K. Stoddard, T. Hurst, C. A. Fierke, J. R. Lakowicz, and R. B. Thompson, “Fluorescence lifetime imaging of physiological free Cu(II) levels in live cells with a Cu(II)-selective carbonic anhydrase-based biosensor,” Metallomics 6(5), 1034–1042 (2014).
[Crossref] [PubMed]

Microsc. Res. Tech. (1)

W. Becker, B. Su, O. Holub, and K. Weisshart, “FLIM and FCS detection in laser-scanning microscopes: increased efficiency by GaAsP hybrid detectors,” Microsc. Res. Tech. 74(9), 804–811 (2011).
[PubMed]

Opt. Express (1)

Opt. Lett. (1)

Proc. Natl. Acad. Sci. U.S.A. (2)

J. R. Lakowicz, H. Szmacinski, K. Nowaczyk, and M. L. Johnson, “Fluorescence lifetime imaging of free and protein-bound NADH,” Proc. Natl. Acad. Sci. U.S.A. 89(4), 1271–1275 (1992).
[Crossref] [PubMed]

M. C. Skala, K. M. Riching, A. Gendron-Fitzpatrick, J. Eickhoff, K. W. Eliceiri, J. G. White, and N. Ramanujam, “In vivo multiphoton microscopy of NADH and FAD redox states, fluorescence lifetimes, and cellular morphology in precancerous epithelia,” Proc. Natl. Acad. Sci. U.S.A. 104(49), 19494–19499 (2007).
[Crossref] [PubMed]

Sensors (Basel) (1)

D. D.-U. Li, S. Ameer-Beg, J. Arlt, D. Tyndall, R. Walker, D. R. Matthews, V. Visitkul, J. Richardson, and R. K. Henderson, “Time-Domain Fluorescence Lifetime Imaging Techniques Suitable for Solid-State Imaging Sensor Arrays,” Sensors (Basel) 12(12), 5650–5669 (2012).
[Crossref] [PubMed]

Other (4)

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, 2006).

S. P. Poland, N. Krstajić, J. Monypenny, S. Coelho, D. Tyndall, R. Walker, V. Devauges, J. a. Levitt, N. Dutton, T. Ng, R. Henderson, and S. Ameer-Beg, “A time-resolved multifocal multiphoton microscope for high speed fret imaging in vivo,” Microscience Microsc. Congr. 2014 39, 6013–6016 (2014).
[Crossref]

W. Becker, ed., Advanced Time-Correlated Single Photon Counting Applications (Springer, 2015).

W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, 2005), Vol. 81.

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Figures (8)

Fig. 1
Fig. 1

(A) Percent error of the SPCImage and SLIM Curve calculated lifetime values for a single-exponential decay, insert shows errors for lifetimes less than 2 ns. (B) Error in calculated lifetime of SPCImage and SLIM Curve for single component lifetime decays where τ = 0.6 ns. (C) Minimum number of photons for SPCImage and SLIM Curve to calculate the lifetime of a single-exponential decay within 5%. (D) Minimum number of photons for SPCImage and SLIM Curve to calculate the lifetime of a single-exponential decay within 1%. Mean +/− SD (256 simulations).

Fig. 2
Fig. 2

α1 (A), τ1 (B), and τ2 (C) error for simulated two-component fluorescence decay curves analyzed in SPCImage. α1 (D), τ1 (E), and τ2 (F) error for simulated two-component fluorescence decay curves analyzed in SLIM Curve. Average of 256 simulations, 10,000 photons/curve (SNR = 100).

Fig. 3
Fig. 3

Minimum number of photons required in a decay curve for α1 error < 10% (A), τ1 error < 25% (B), and τ2 error < 25% (C) when simulated decays are analyzed in SPCImage. Minimum number of photons required in a decay curve for α1 error < 10% (D), τ1 error < 25% (E), and τ2 error < 25% (F) when simulated decays are analyzed in SLIM Curve. Average of 256 simulations.

Fig. 4
Fig. 4

α1 (A), τ1 (B), and τ2 (C) error for simulated lifetime decays where τ1 = 0.5 ns and τ2 = 1.2 ns analyzed in SPCImage. α1 (D), τ1 (E), and τ2 (F) error for simulated lifetime decays where τ1 = 0.5 ns and τ2 = 1.2 ns analyzed in SLIM Curve. Average +/− SD of 256 simulations.

Fig. 5
Fig. 5

(A) Component error improvement (mean +/− SD) for all simulated data sets analyzed in SPCImage as a function of time bins. * p<0.05 versus 256 time bins (error improvement = 0%). (B) Error improvement of the extracted lifetime components analyzed in SPCImage as a function of the number of photons in the curve. (C) Minimum number of photons required (mean +/− SD) for decay curves with total error less than 25% (SPCImage). (D) Component error improvement (mean +/− SD) for all simulated data sets analyzed in SLIM Curve as a function of time bins. * p<0.05 versus 256 time bins (error improvement = 0%).

Fig. 6
Fig. 6

α1 error (mean +/− SD) when τ1 and τ2 are free or fixed in SPCImage (A) or SLIM Curve (B). Average for all simulated curves generated in Methods 2.2. **** p< 0.0001.

Fig. 7
Fig. 7

α error (average +/− SD) for all simulated decay curves analyzed in SPCImage with free (A) and fixed (B) τ1 and τ2 values. α error (average +/− SD) for all simulated decay curves analyzed in SLIM Curve with free (C) and fixed (D) τ1 and τ2 values.

Fig. 8
Fig. 8

(A) Representative α1 image of the α1 = 0.5 NADH-LDH solution with 800 photons, evaluated with 256 time bins. (B) Representative α1 image of the α1 = 0.5 NADH-LDH solution with 800 photons, evaluated in SPCImage with lifetime values fixed to τ1 = 0.52 ns and τ2 = 1.25 ns, (C) Representative α1 image of the α1 = 0.5 NADH-LDH solution with 800 photons, evaluated with 64 time bins. (D) Total error (τ1 error + τ2 error + α error) improvement for SPCImage analysis of NADH-LDH solutions with 800 photons per curve with temporal binning versus no temporal binning. * p< 0.05 vs. 256 time bins (error improvement = 0%). (E) α error as a function of number of photons per decay curve for NADH-LDH solutions analyzed in SPCImage with short and long lifetimes either free or fixed to τ1 = 0.52 ns and τ2 = 1.25 ns. For α1 = 0.3 and 0.5, the p-value between the α1 errors from free and fixed lifetime estimation is less than 0.0001 at each photon count. (F) Mean lifetime (τm) error for NADH decreases with increased photons collected (α1 = 0.5). (G) Mean lifetime (τm) error for images with 800 photons per pixel is reduced with temporal binning (NADH α1 = 0.5).

Tables (3)

Tables Icon

Table 1 Concentrations of NADH and LDH for solutions with certain α1 values.

Tables Icon

Table 2 Percent Simulations with Total Error < 25%

Tables Icon

Table 3 Photons and time (s) required for a 256x256 pixel image of a two-component fluorescence decay where τ1 = 0.5, τ2 = 1.2 and α1 = 0.8, with and without noise reduction techniques. Calculations assume a 80MHz laser source and 10% photon efficiency. Minimum photons required for total error < 10%

Equations (4)

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F ( t ) = i = 1 x α i e t τ i + C
I ( t ) = I R F ( t ) F ( t )
F ( t ) = α 1 e t τ 1 + α 2 e t τ 2 + C
F ( t ) = α 1 e t τ 1 + α 2 e t τ 2

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