Abstract

Hyperspectral fluorescence lifetime imaging allows for the simultaneous acquisition of spectrally resolved temporal fluorescence emission decays. In turn, the acquired rich multidimensional data set enables simultaneous imaging of multiple fluorescent species for a comprehensive molecular assessment of biotissues. However, to enable quantitative imaging, inherent spectral overlap between the considered fluorescent probes and potential bleed-through must be considered. Such a task is performed via either spectral or lifetime unmixing, typically independently. Herein, we present “UNMIX-ME” (unmix multiple emissions), a deep learning-based fluorescence unmixing routine, capable of quantitative fluorophore unmixing by simultaneously using both spectral and temporal signatures. UNMIX-ME was trained and validated using an in silico framework replicating the data acquisition process of a compressive hyperspectral fluorescent lifetime imaging platform (HMFLI). It was benchmarked against a conventional LSQ method for tri and quadri-exponential simulated samples. Last, UNMIX-ME’s potential was assessed for NIR FRET in vitro and in vivo preclinical applications.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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  1. H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
    [Crossref]
  2. T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
    [Crossref]
  3. Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
    [Crossref]
  4. T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
    [Crossref]
  5. A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
    [Crossref]
  6. G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
    [Crossref]
  7. M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).
  8. R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
    [Crossref]
  9. F. Chollet, “Deep Learning with Separable Convolutions,” arXiv Prepr. arXiv1610.02357 (2016).
  10. F. Chollet, “Xception: Deep Learning with Depthwise Separable Convolutions,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 1800–1807.
  11. K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 770–778.
  12. J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
    [Crossref]
  13. D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
    [Crossref]
  14. J. T. Smith and M. Ochoa, “GitHub: “UNMIX-ME,”” https://github.com/jasontsmith2718/UNMIX-ME .
  15. K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
    [Crossref]
  16. C. Thaler, S. V. Koushik, P. S. Blank, and S. S. Vogel, “Quantitative multiphoton spectral imaging and its use for measuring resonance energy transfer,” Biophys. J. (2005).
  17. S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
    [Crossref]
  18. A. Rudkouskaya, N. Sinsuebphon, X. Intes, and M. Barroso, “Role of Tumor Heterogeneity in Imaging Breast Cancer Targeted Delivery using FLIM FRET in Vivo,” in Biomedical Optics 2016 (OSA, 2016), p. CTh2A.5.
    [Crossref]
  19. A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
    [Crossref]
  20. Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
    [Crossref]
  21. C. Li, “An Efficient Algorithm For Total Variation Regularization with Applications to the Single Pixel Camera and Compressive Sensing,” Rice Univ. (2009).
  22. S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
    [Crossref]

2020 (1)

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

2019 (3)

R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
[Crossref]

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

2018 (2)

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
[Crossref]

2017 (1)

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

2016 (1)

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

2015 (1)

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref]

2014 (1)

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[Crossref]

2013 (1)

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

2009 (1)

D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
[Crossref]

2008 (1)

G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
[Crossref]

2000 (1)

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

Abe, K.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

Albigès-Rizo, C.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Ardeshirpour, Y.

Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
[Crossref]

Barroso, M.

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

A. Rudkouskaya, N. Sinsuebphon, X. Intes, and M. Barroso, “Role of Tumor Heterogeneity in Imaging Breast Cancer Targeted Delivery using FLIM FRET in Vivo,” in Biomedical Optics 2016 (OSA, 2016), p. CTh2A.5.
[Crossref]

Beljonne, D.

D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
[Crossref]

Bidan, C. M.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Blank, P. S.

C. Thaler, S. V. Koushik, P. S. Blank, and S. S. Vogel, “Quantitative multiphoton spectral imaging and its use for measuring resonance energy transfer,” Biophys. J. (2005).

Chen, S.

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

Chollet, F.

F. Chollet, “Xception: Deep Learning with Depthwise Separable Convolutions,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 1800–1807.

F. Chollet, “Deep Learning with Separable Convolutions,” arXiv Prepr. arXiv1610.02357 (2016).

Coullomb, A.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Curutchet, C.

D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
[Crossref]

Dupont, A.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Enderlein, J.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Gadella, T. W. J.

G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
[Crossref]

Gandjbakhche, A. H.

Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
[Crossref]

Goedhart, J.

G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
[Crossref]

Gregor, I.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Hattori, S.

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

He, K.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 770–778.

Hirose, S.

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

Hogg, K.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[Crossref]

Intes, X.

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
[Crossref]

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

A. Rudkouskaya, N. Sinsuebphon, X. Intes, and M. Barroso, “Role of Tumor Heterogeneity in Imaging Breast Cancer Targeted Delivery using FLIM FRET in Vivo,” in Biomedical Optics 2016 (OSA, 2016), p. CTh2A.5.
[Crossref]

Knutson, J. R.

Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
[Crossref]

Koberling, F.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Koushik, S. V.

C. Thaler, S. V. Koushik, P. S. Blank, and S. S. Vogel, “Quantitative multiphoton spectral imaging and its use for measuring resonance energy transfer,” Biophys. J. (2005).

Krämer, B.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Kremers, G.-J.

G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
[Crossref]

Lamb, D. C.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Li, C.

C. Li, “An Efficient Algorithm For Total Variation Regularization with Applications to the Single Pixel Camera and Compressive Sensing,” Rice Univ. (2009).

Löschberger, A.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Marrison, J.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[Crossref]

Mazurkiewicz, J.

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

Michalet, X.

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

Niehörster, T.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Nishimura, H.

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

O’Toole, P.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[Crossref]

Ochoa, M.

R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
[Crossref]

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

J. T. Smith and M. Ochoa, “GitHub: “UNMIX-ME,”” https://github.com/jasontsmith2718/UNMIX-ME .

Oddou, C.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Okumura, K.

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

Patting, M.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Periasamy, A.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

Pian, Q.

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

Qian, C.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Rahn, H.-J.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Rajoria, S.

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref]

Ren, S.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 770–778.

Rudkouskaya, A.

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

A. Rudkouskaya, N. Sinsuebphon, X. Intes, and M. Barroso, “Role of Tumor Heterogeneity in Imaging Breast Cancer Targeted Delivery using FLIM FRET in Vivo,” in Biomedical Optics 2016 (OSA, 2016), p. CTh2A.5.
[Crossref]

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

Sackett, D. L.

Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
[Crossref]

Sauer, M.

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Scholes, G. D.

D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
[Crossref]

Shirai, T.

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

Silbey, R. J.

D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
[Crossref]

Sinsuebphon, N.

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

A. Rudkouskaya, N. Sinsuebphon, X. Intes, and M. Barroso, “Role of Tumor Heterogeneity in Imaging Breast Cancer Targeted Delivery using FLIM FRET in Vivo,” in Biomedical Optics 2016 (OSA, 2016), p. CTh2A.5.
[Crossref]

Smith, J. T.

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

J. T. Smith and M. Ochoa, “GitHub: “UNMIX-ME,”” https://github.com/jasontsmith2718/UNMIX-ME .

Sun, J.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 770–778.

Thaler, C.

C. Thaler, S. V. Koushik, P. S. Blank, and S. S. Vogel, “Quantitative multiphoton spectral imaging and its use for measuring resonance energy transfer,” Biophys. J. (2005).

Tsurui, H.

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

Tubbesing, K.

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

Un, N.

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

van Munster, E. B.

G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
[Crossref]

Vogel, S. S.

C. Thaler, S. V. Koushik, P. S. Blank, and S. S. Vogel, “Quantitative multiphoton spectral imaging and its use for measuring resonance energy transfer,” Biophys. J. (2005).

Ward, J.

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

Wehnekamp, F.

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Yan, P.

R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
[Crossref]

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

Yao, R.

R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
[Crossref]

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

Zhang, X.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 770–778.

Zhao, L.

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

Zimmermann, T.

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[Crossref]

Biophys. J. (1)

G.-J. Kremers, E. B. van Munster, J. Goedhart, and T. W. J. Gadella, “Quantitative Lifetime Unmixing of Multiexponentially Decaying Fluorophores Using Single-Frequency Fluorescence Lifetime Imaging Microscopy,” Biophys. J. 95(1), 378–389 (2008).
[Crossref]

Curr. Mol. Imaging (1)

S. Rajoria, L. Zhao, X. Intes, and M. Barroso, “FLIM-FRET for Cancer Applications,” Curr. Mol. Imaging 3(2), 144–161 (2015).
[Crossref]

EJNMMI Res. (1)

Y. Ardeshirpour, D. L. Sackett, J. R. Knutson, and A. H. Gandjbakhche, “Using in vivo fluorescence lifetime imaging to detect HER2-positive tumors,” EJNMMI Res. 8(1), 26 (2018).
[Crossref]

J. Biophotonics (1)

S. Chen, N. Sinsuebphon, A. Rudkouskaya, M. Barroso, X. Intes, and X. Michalet, “In vitro and in vivo phasor analysis of stoichiometry and pharmacokinetics using short-lifetime near-infrared dyes and time-gated imaging,” J. Biophotonics 12(3), 653–662 (2019).
[Crossref]

J. Controlled Release (1)

A. Rudkouskaya, N. Sinsuebphon, J. Ward, K. Tubbesing, X. Intes, and M. Barroso, “Quantitative imaging of receptor-ligand engagement in intact live animals,” J. Controlled Release 286, 451–459 (2018).
[Crossref]

J. Histochem. Cytochem. (1)

H. Tsurui, H. Nishimura, S. Hattori, S. Hirose, K. Okumura, and T. Shirai, “Seven-color Fluorescence Imaging of Tissue Samples Based on Fourier Spectroscopy and Singular Value Decomposition,” J. Histochem. Cytochem. 48(5), 653–662 (2000).
[Crossref]

J. Phys. Chem. B (1)

D. Beljonne, C. Curutchet, G. D. Scholes, and R. J. Silbey, “Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems,” J. Phys. Chem. B 113(19), 6583–6599 (2009).
[Crossref]

Light: Sci. Appl. (1)

R. Yao, M. Ochoa, P. Yan, and X. Intes, “Net-FLICS: fast quantitative wide-field fluorescence lifetime imaging with compressed sensing – a deep learning approach,” Light: Sci. Appl. 8(1), 26 (2019).
[Crossref]

Methods Mol. Biol. (1)

T. Zimmermann, J. Marrison, K. Hogg, and P. O’Toole, “Clearing up the signal: Spectral imaging and linear unmixing in fluorescence microscopy,” Methods Mol. Biol. 1075, 129–148 (2014).
[Crossref]

Nat. Methods (1)

T. Niehörster, A. Löschberger, I. Gregor, B. Krämer, H.-J. Rahn, M. Patting, F. Koberling, J. Enderlein, and M. Sauer, “Multi-target spectrally resolved fluorescence lifetime imaging microscopy,” Nat. Methods 13(3), 257–262 (2016).
[Crossref]

Nat. Photonics (1)

Q. Pian, R. Yao, N. Sinsuebphon, and X. Intes, “Compressive hyperspectral time-resolved wide-field fluorescence lifetime imaging,” Nat. Photonics 11(7), 411–414 (2017).
[Crossref]

PLoS One (1)

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, “Non-Invasive In Vivo Imaging of Near Infrared-labeled Transferrin in Breast Cancer Cells and Tumors Using Fluorescence Lifetime FRET,” PLoS One 8(11), e80269 (2013).
[Crossref]

Proc. Natl. Acad. Sci. (1)

J. T. Smith, R. Yao, N. Sinsuebphon, A. Rudkouskaya, N. Un, J. Mazurkiewicz, M. Barroso, P. Yan, and X. Intes, “Fast fit-free analysis of fluorescence lifetime imaging via deep learning,” Proc. Natl. Acad. Sci. 116(48), 24019–24030 (2019).
[Crossref]

Sci. Rep. (1)

A. Coullomb, C. M. Bidan, C. Qian, F. Wehnekamp, C. Oddou, C. Albigès-Rizo, D. C. Lamb, and A. Dupont, “QuanTI-FRET: a framework for quantitative FRET measurements in living cells,” Sci. Rep. 10(1), 6504 (2020).
[Crossref]

Other (8)

F. Chollet, “Deep Learning with Separable Convolutions,” arXiv Prepr. arXiv1610.02357 (2016).

F. Chollet, “Xception: Deep Learning with Depthwise Separable Convolutions,” in 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2017), pp. 1800–1807.

K. He, X. Zhang, S. Ren, and J. Sun, “Deep Residual Learning for Image Recognition,” in 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) (IEEE, 2016), pp. 770–778.

C. Thaler, S. V. Koushik, P. S. Blank, and S. S. Vogel, “Quantitative multiphoton spectral imaging and its use for measuring resonance energy transfer,” Biophys. J. (2005).

A. Rudkouskaya, N. Sinsuebphon, X. Intes, and M. Barroso, “Role of Tumor Heterogeneity in Imaging Breast Cancer Targeted Delivery using FLIM FRET in Vivo,” in Biomedical Optics 2016 (OSA, 2016), p. CTh2A.5.
[Crossref]

J. T. Smith and M. Ochoa, “GitHub: “UNMIX-ME,”” https://github.com/jasontsmith2718/UNMIX-ME .

M. Ochoa, A. Rudkouskaya, R. Yao, P. Yan, M. Barroso, and X. Intes, “Deep Learning Enhanced Hyperspectral Fluorescence Lifetime Imaging,” bioRxiv (2020).

C. Li, “An Efficient Algorithm For Total Variation Regularization with Applications to the Single Pixel Camera and Compressive Sensing,” Rice Univ. (2009).

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Figures (12)

Fig. 1.
Fig. 1. UNMIX-ME model architecture. HMFLI input mapped to spatially independent unmixed fluorescence coefficient values (a) “XceptionBlock” [10] comprised of 1×1 separable convolutions [9]. (b) “CoefficientBlock” structure.
Fig. 2.
Fig. 2. Data simulation workflow. A binary MNIST image is assigned lifetime values within three bounds (c-e). Using these values, along with spatially unique spectra (average given in b) for gathering intensity multipliers, 16 TPSFs are created at each non-zero spatial pixel (a). The coefficients are calculated shortly after (f-h).
Fig. 3.
Fig. 3. Three-coefficient spectral unmixing in silico. Averaged spectra used for simulation (a) are given. (b-d) Ground-truth values are illustrated as well as the coefficients retrieved via DNN lifetime unmixing (e-g) and conventional LSQ + F fitting (h-j). Table 1 provides average and standard deviation MSE values calculated across 100 test samples as for additional performance quantification.
Fig. 4.
Fig. 4. HMFLI-FRET in vitro. Results from non-linear iterative spectral decomposition combined with lifetime fitting (LSQ + F) (a-j) and UNMIX-ME (k-t) are given. Boxplots of coefficient values retrieved at each ROI (labeled by acceptor/donor ratio) are given per reconstruction. Accepter/donor ratios are labeled per well in (a).
Fig. 5.
Fig. 5. HMFLI-FRET imaging of tumor xenograft in vivo. Mouse xenograft imaged at 76-hours post-injection of Trastuzumab (mix of AF700 & AF750 conjugates with A:D 2:1). Results from UNMIX-ME (a-c) and LSQ + F (d-f). Boxplots are given for further quantitative clarity (g-i).
Fig. 6.
Fig. 6. Additional information provided to complement the in vivo spectral lifetime quantification performed in Fig. 5. Histogram provides all acceptor/donor ratios obtained for each spatial location across the tumor ROI. The table provides averaged and standard deviation values for both coefficients and the FRET % values obtained through both methods.
Fig. 7.
Fig. 7. Information relevant for a two-spectra (a), four-specie (d-g) in silico spectral lifetime unmixing performance assessment. Example mono-specie HFLI data (b) along with an example containing a mix of all four (c) is given for illustrative purpose. Blue and red boxes indicate the spectra (a) to which each of the lifetime and coefficient (h-k) values belong.
Fig. 8.
Fig. 8. Metrics relevant to the UNMIX-ME deep convolutional neural network. The MSE validation loss curves were obtained for each coefficient separately over five separate training iterations for two separate cases - two-spectra, three-lifetime (Fig. 3) and two-spectra, four-lifetime (Fig. 8). The average and standard deviation of each is provided (a, b). Four the two-spectra/four-specie case, 1,000 separate samples were generated and fed into the network in order to perform a t-SNE assessment of each branch individually (c-f).
Fig. 9.
Fig. 9. Spectral lifetime unmixing performance obtained via both LSQ + F and UNMIX-ME versus ground-truth. A single illustration is given for qualitative assessment. Both SSIM (m) and MSE (n) were calculated for 250 test samples to provide quantification with regards to image-to-image similarity and direct one-to-one value comparison.
Fig. 10.
Fig. 10. HMFLI-FRET imaging of Transferrin receptor (TfR) engagement in vivo. Results from UNMIX-ME (a-d) and LSQ + F (e-h) are provided. Resolved liver and bladder areas are displayed per reconstruction.
Fig. 11.
Fig. 11. A detailed illustration of the Hyperspectral Macroscopic Fluorescence Lifetime Imaging (HMFLI) apparatus used for this work. An example depiction of the data acquired is given in Fig. 12.
Fig. 12.
Fig. 12. Averaged HMFLI TPSF data at two different regions of the tumor xenograft (b). The regions were chosen due to their high (a) and low (c) FRET quantification.

Tables (1)

Tables Icon

Table 1. Mean-squared error calculated for all three coefficient values through both techniques (complement to Fig. 3).

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Γ λ ( t ) = I × I R F λ ( t ) [ a 1 λ e t / τ 1 + a 2 λ e t / τ 2 + a 3 λ e t / τ 3 ]
( y 1 y 16 ) = ( a 1 1 a 2 1 a 3 1 a 1 16 a 2 16 a 3 16 ) ( c 1 c 3 )
Γ λ ( t ) = I × I R F λ ( t ) e t / τ n
a T = c D × ( 1 E ) × a D + a A × c A + c D × E × ( ϕ A / ϕ D ) × k ( λ ) × a A