Abstract

A pump-probe technique for the detection of fluorophores in tomographic PA images is introduced. It is based on inducing stimulated emission in fluorescent molecules, which in turn modulates the amount of thermalized energy, and hence the PA signal amplitude. A theoretical model of the PA signal generation in fluorophores is presented and experimentally validated on cuvette measurements made in solutions of Rhodamine 6G, a fluorophore of known optical and molecular properties. The application of this technique to deep tissue tomographic PA imaging is demonstrated by determining the spatial distribution of a near-infrared fluorophore in a tissue phantom.

© 2015 Optical Society of America

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2015 (1)

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

2014 (3)

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
[Crossref] [PubMed]

C. Lutzweiler, R. Meier, E. Rummeny, V. Ntziachristos, and D. Razansky, “Real-time optoacoustic tomography of indocyanine green perfusion and oxygenation parameters in human finger vasculature,” Opt. Lett. 39(14), 4061–4064 (2014).
[Crossref] [PubMed]

A. Krumholz, D. M. Shcherbakova, J. Xia, L. V. Wang, and V. V. Verkhusha, “Multicontrast photoacoustic in vivo imaging using near-infrared fluorescent proteins,” Sci. Rep. 4, 3939 (2014).
[Crossref] [PubMed]

2013 (3)

E. Morgounova, Q. Shao, B. J. Hackel, D. D. Thomas, and S. Ashkenazi, “Photoacoustic lifetime contrast between methylene blue monomers and self-quenched dimers as a model for dual-labeled activatable probes,” J. Biomed. Opt. 18(5), 056004 (2013).
[Crossref] [PubMed]

J. Laufer, A. Jathoul, M. Pule, and P. Beard, “In vitro characterization of genetically expressed absorbing proteins using photoacoustic spectroscopy,” Biomed. Opt. Express 4(11), 2477–2490 (2013).
[Crossref] [PubMed]

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
[Crossref] [PubMed]

2012 (5)

L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

G. S. Filonov, A. Krumholz, J. Xia, J. Yao, L. V. Wang, and V. V. Verkhusha, “Deep-tissue photoacoustic tomography of a genetically encoded near-infrared fluorescent probe,” Angew. Chem. Int. Ed. Engl. 51(6), 1448–1451 (2012).
[Crossref] [PubMed]

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012).

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, and P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[Crossref] [PubMed]

2011 (2)

P. Beard, “Biomedical photoacoustic imaging,” Interface Focus 1(4), 602–631 (2011).
[Crossref] [PubMed]

A. M. Brouwer, “Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report),” Pure Appl. Chem. 83(12), 2213–2228 (2011).
[Crossref]

2010 (3)

B. E. Treeby, E. Z. Zhang, and B. T. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26(11), 115003 (2010).
[Crossref]

J. Laufer, E. Zhang, and P. Beard, “Evaluation of Absorbing Chromophores Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging,” IEEE J. Sel. Top. Quantum Electron. 16(3), 600–607 (2010).
[Crossref]

A. Danielli, C. P. Favazza, K. Maslov, and L. V. Wang, “Picosecond absorption relaxation measured with nanosecond laser photoacoustics,” Appl. Phys. Lett. 97(16), 163701 (2010).
[Crossref] [PubMed]

2009 (3)

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature 461(7267), 1105–1109 (2009).
[Crossref] [PubMed]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

X. Yang, E. W. Stein, S. Ashkenazi, and L. V. Wang, “Nanoparticles for photoacoustic imaging,” Wiley Interdiscip Rev Nanomed Nanobiotechnol 1(4), 360–368 (2009).
[Crossref] [PubMed]

2008 (4)

A. De la Zerda, C. Zavaleta, S. Keren, S. Vaithilingam, S. Bodapati, Z. Liu, J. Levi, B. R. Smith, T.-J. Ma, O. Oralkan, Z. Cheng, X. Chen, H. Dai, B. T. Khuri-Yakub, and S. S. Gambhir, “Carbon nanotubes as photoacoustic molecular imaging agents in living mice,” Nat. Nanotechnol. 3(9), 557–562 (2008).
[Crossref] [PubMed]

S. Ashkenazi, S.-W. Huang, T. Horvath, Y.-E. L. Koo, and R. Kopelman, “Photoacoustic probing of fluorophore excited state lifetime with application to oxygen sensing,” J. Biomed. Opt. 13(3), 034023 (2008).
[Crossref] [PubMed]

J. Hendrix, C. Flors, P. Dedecker, J. Hofkens, and Y. Engelborghs, “Dark states in monomeric red fluorescent proteins studied by fluorescence correlation and single molecule spectroscopy,” Biophys. J. 94(10), 4103–4113 (2008).

E. Zhang, J. Laufer, and P. Beard, “Backward-mode multiwavelength photoacoustic scanner using a planar Fabry-Perot polymer film ultrasound sensor for high-resolution three-dimensional imaging of biological tissues,” Appl. Opt. 47(4), 561–577 (2008).
[Crossref] [PubMed]

2007 (2)

D. Razansky, C. Vinegoni, and V. Ntziachristos, “Multispectral photoacoustic imaging of fluorochromes in small animals,” Opt. Lett. 32(19), 2891–2893 (2007).
[Crossref] [PubMed]

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

2006 (1)

K. E. Sapsford, L. Berti, and I. L. Medintz, “Materials for fluorescence resonance energy transfer analysis: beyond traditional donor-acceptor combinations,” Angew. Chem. Int. Ed. Engl. 45(28), 4562–4589 (2006).
[Crossref] [PubMed]

2005 (1)

G. Jung, J. Wiehler, and A. Zumbusch, “The photophysics of green fluorescent protein: influence of the key amino acids at positions 65, 203, and 222,” Biophys. J. 88(3), 1932–1947 (2005).
[Crossref] [PubMed]

2002 (1)

D. Magde, R. Wong, and P. G. Seybold, “Fluorescence quantum yields and their relation to lifetimes of rhodamine 6G and fluorescein in nine solvents: improved absolute standards for quantum yields,” Photochem. Photobiol. 75(4), 327–334 (2002).
[Crossref] [PubMed]

1998 (1)

R. Menzel and E. Thiel, “Intersystem crossing rate constants of rhodamine dyes: influence of the amino-group substitution,” Chem. Phys. Lett. 291(1-2), 237–243 (1998).
[Crossref]

1997 (1)

P. Sathy and A. Penzkofer, “Absorption and fluorescence spectroscopic analysis of rhodamine 6G and oxazine 750 in porous sol-gel glasses,” J. Photochem. Photobiol. Chem. 109(1), 53–57 (1997).
[Crossref]

1995 (1)

S. Bedö, M. Pollnau, W. Lüthy, and H. P. Weber, “Saturation of the 2.71 μm laser output in erbium-doped ZBLAN fibers,” Opt. Commun. 116(1-3), 81–86 (1995).
[Crossref]

1994 (1)

P. Sathy, R. Philip, V. P. N. Nampoori, and C. P. G. Vallabhan, “Photoacoustic observation of excited singlet state absorption in the laser dye rhodamine 6G,” J. Phys. D Appl. Phys. 27(10), 2019–2022 (1994).
[Crossref]

1992 (1)

A. Grofcsik and W. J. Jones, “Stimulated emission cross-sections in fluorescent dye solutions: gain spectra and excited-state lifetimes of Nile blue A and oxazine 720,” J. Chem. Soc., Faraday Trans. 88(8), 1101 (1992).
[Crossref]

1987 (1)

P. Venkateswarlu, M. C. George, Y. V. Rao, H. Jagannath, G. Chakrapani, and A. Miahnahri, “Transient excited singlet state absorption in Rhodamine 6G,” Pramana 28(1), 59–71 (1987).
[Crossref]

1983 (1)

A. Penzkofer and W. Blau, “Theoretical analysis of S 1 state lifetime measurements of dyes with picosecond laser pulses,” Opt. Quantum Electron. 15, 325–347 (1983).

1976 (1)

A. Penzkofer, W. Falkenstein, and W. Kaiser, “Vibronic relaxation in the S1 state of rhodamine dye solutions,” Chem. Phys. Lett. 44(1), 82–87 (1976).
[Crossref]

1972 (1)

J. P. Hermann and J. Ducuing, “Dispersion of the two-photon cross section in rhodamine dyes,” Opt. Commun. 6(2), 101–105 (1972).
[Crossref]

Ale, A.

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
[Crossref] [PubMed]

Alqasemi, U.

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
[Crossref] [PubMed]

Arridge, S. R.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Ashkenazi, S.

E. Morgounova, Q. Shao, B. J. Hackel, D. D. Thomas, and S. Ashkenazi, “Photoacoustic lifetime contrast between methylene blue monomers and self-quenched dimers as a model for dual-labeled activatable probes,” J. Biomed. Opt. 18(5), 056004 (2013).
[Crossref] [PubMed]

X. Yang, E. W. Stein, S. Ashkenazi, and L. V. Wang, “Nanoparticles for photoacoustic imaging,” Wiley Interdiscip Rev Nanomed Nanobiotechnol 1(4), 360–368 (2009).
[Crossref] [PubMed]

S. Ashkenazi, S.-W. Huang, T. Horvath, Y.-E. L. Koo, and R. Kopelman, “Photoacoustic probing of fluorophore excited state lifetime with application to oxygen sensing,” J. Biomed. Opt. 13(3), 034023 (2008).
[Crossref] [PubMed]

Beard, P.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

J. Laufer, A. Jathoul, M. Pule, and P. Beard, “In vitro characterization of genetically expressed absorbing proteins using photoacoustic spectroscopy,” Biomed. Opt. Express 4(11), 2477–2490 (2013).
[Crossref] [PubMed]

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012).

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, and P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[Crossref] [PubMed]

P. Beard, “Biomedical photoacoustic imaging,” Interface Focus 1(4), 602–631 (2011).
[Crossref] [PubMed]

J. Laufer, E. Zhang, and P. Beard, “Evaluation of Absorbing Chromophores Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging,” IEEE J. Sel. Top. Quantum Electron. 16(3), 600–607 (2010).
[Crossref]

E. Zhang, J. Laufer, and P. Beard, “Backward-mode multiwavelength photoacoustic scanner using a planar Fabry-Perot polymer film ultrasound sensor for high-resolution three-dimensional imaging of biological tissues,” Appl. Opt. 47(4), 561–577 (2008).
[Crossref] [PubMed]

J. Laufer, D. Delpy, C. Elwell, and P. Beard, “Quantitative spatially resolved measurement of tissue chromophore concentrations using photoacoustic spectroscopy: application to the measurement of blood oxygenation and haemoglobin concentration,” Phys. Med. Biol. 52(1), 141–168 (2007).
[Crossref] [PubMed]

Beard, P. C.

B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
[Crossref] [PubMed]

Bedö, S.

S. Bedö, M. Pollnau, W. Lüthy, and H. P. Weber, “Saturation of the 2.71 μm laser output in erbium-doped ZBLAN fibers,” Opt. Commun. 116(1-3), 81–86 (1995).
[Crossref]

Berti, L.

K. E. Sapsford, L. Berti, and I. L. Medintz, “Materials for fluorescence resonance energy transfer analysis: beyond traditional donor-acceptor combinations,” Angew. Chem. Int. Ed. Engl. 45(28), 4562–4589 (2006).
[Crossref] [PubMed]

Blau, W.

A. Penzkofer and W. Blau, “Theoretical analysis of S 1 state lifetime measurements of dyes with picosecond laser pulses,” Opt. Quantum Electron. 15, 325–347 (1983).

Bodapati, S.

A. De la Zerda, C. Zavaleta, S. Keren, S. Vaithilingam, S. Bodapati, Z. Liu, J. Levi, B. R. Smith, T.-J. Ma, O. Oralkan, Z. Cheng, X. Chen, H. Dai, B. T. Khuri-Yakub, and S. S. Gambhir, “Carbon nanotubes as photoacoustic molecular imaging agents in living mice,” Nat. Nanotechnol. 3(9), 557–562 (2008).
[Crossref] [PubMed]

Brouwer, A. M.

A. M. Brouwer, “Standards for photoluminescence quantum yield measurements in solution (IUPAC Technical Report),” Pure Appl. Chem. 83(12), 2213–2228 (2011).
[Crossref]

Burton, N. C.

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
[Crossref] [PubMed]

Chakrapani, G.

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W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature 461(7267), 1105–1109 (2009).
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A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

Oralkan, O.

A. De la Zerda, C. Zavaleta, S. Keren, S. Vaithilingam, S. Bodapati, Z. Liu, J. Levi, B. R. Smith, T.-J. Ma, O. Oralkan, Z. Cheng, X. Chen, H. Dai, B. T. Khuri-Yakub, and S. S. Gambhir, “Carbon nanotubes as photoacoustic molecular imaging agents in living mice,” Nat. Nanotechnol. 3(9), 557–562 (2008).
[Crossref] [PubMed]

Pedley, B.

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012).

Pedley, R. B.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

Penzkofer, A.

P. Sathy and A. Penzkofer, “Absorption and fluorescence spectroscopic analysis of rhodamine 6G and oxazine 750 in porous sol-gel glasses,” J. Photochem. Photobiol. Chem. 109(1), 53–57 (1997).
[Crossref]

A. Penzkofer and W. Blau, “Theoretical analysis of S 1 state lifetime measurements of dyes with picosecond laser pulses,” Opt. Quantum Electron. 15, 325–347 (1983).

A. Penzkofer, W. Falkenstein, and W. Kaiser, “Vibronic relaxation in the S1 state of rhodamine dye solutions,” Chem. Phys. Lett. 44(1), 82–87 (1976).
[Crossref]

Perrimon, N.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

Philip, B.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

Philip, R.

P. Sathy, R. Philip, V. P. N. Nampoori, and C. P. G. Vallabhan, “Photoacoustic observation of excited singlet state absorption in the laser dye rhodamine 6G,” J. Phys. D Appl. Phys. 27(10), 2019–2022 (1994).
[Crossref]

Pizzey, A. R.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

Pollnau, M.

S. Bedö, M. Pollnau, W. Lüthy, and H. P. Weber, “Saturation of the 2.71 μm laser output in erbium-doped ZBLAN fibers,” Opt. Commun. 116(1-3), 81–86 (1995).
[Crossref]

Pule, M.

Pule, M. a.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

Radrich, K.

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
[Crossref] [PubMed]

Rao, Y. V.

P. Venkateswarlu, M. C. George, Y. V. Rao, H. Jagannath, G. Chakrapani, and A. Miahnahri, “Transient excited singlet state absorption in Rhodamine 6G,” Pramana 28(1), 59–71 (1987).
[Crossref]

Razansky, D.

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
[Crossref] [PubMed]

C. Lutzweiler, R. Meier, E. Rummeny, V. Ntziachristos, and D. Razansky, “Real-time optoacoustic tomography of indocyanine green perfusion and oxygenation parameters in human finger vasculature,” Opt. Lett. 39(14), 4061–4064 (2014).
[Crossref] [PubMed]

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

D. Razansky, C. Vinegoni, and V. Ntziachristos, “Multispectral photoacoustic imaging of fluorochromes in small animals,” Opt. Lett. 32(19), 2891–2893 (2007).
[Crossref] [PubMed]

Roy, R.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature 461(7267), 1105–1109 (2009).
[Crossref] [PubMed]

Rummeny, E.

Sapsford, K. E.

K. E. Sapsford, L. Berti, and I. L. Medintz, “Materials for fluorescence resonance energy transfer analysis: beyond traditional donor-acceptor combinations,” Angew. Chem. Int. Ed. Engl. 45(28), 4562–4589 (2006).
[Crossref] [PubMed]

Sathy, P.

P. Sathy and A. Penzkofer, “Absorption and fluorescence spectroscopic analysis of rhodamine 6G and oxazine 750 in porous sol-gel glasses,” J. Photochem. Photobiol. Chem. 109(1), 53–57 (1997).
[Crossref]

P. Sathy, R. Philip, V. P. N. Nampoori, and C. P. G. Vallabhan, “Photoacoustic observation of excited singlet state absorption in the laser dye rhodamine 6G,” J. Phys. D Appl. Phys. 27(10), 2019–2022 (1994).
[Crossref]

Scambler, P.

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, and P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[Crossref] [PubMed]

Schaefer, K.

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
[Crossref] [PubMed]

Schmitt, F.-J.

J. Märk, C. Theiss, F.-J. Schmitt, and J. Laufer, “Photoacoustic imaging of a near-infrared fluorescent marker based on dual wavelength pump-probe excitation,” in Proc. of SPIE, Photons Plus Ultrasound: Imaging and Sensing, 2014, 8943, p. 894333.

Seybold, P. G.

D. Magde, R. Wong, and P. G. Seybold, “Fluorescence quantum yields and their relation to lifetimes of rhodamine 6G and fluorescein in nine solvents: improved absolute standards for quantum yields,” Photochem. Photobiol. 75(4), 327–334 (2002).
[Crossref] [PubMed]

Shao, Q.

E. Morgounova, Q. Shao, B. J. Hackel, D. D. Thomas, and S. Ashkenazi, “Photoacoustic lifetime contrast between methylene blue monomers and self-quenched dimers as a model for dual-labeled activatable probes,” J. Biomed. Opt. 18(5), 056004 (2013).
[Crossref] [PubMed]

Shcherbakova, D. M.

A. Krumholz, D. M. Shcherbakova, J. Xia, L. V. Wang, and V. V. Verkhusha, “Multicontrast photoacoustic in vivo imaging using near-infrared fluorescent proteins,” Sci. Rep. 4, 3939 (2014).
[Crossref] [PubMed]

Smith, B. R.

A. De la Zerda, C. Zavaleta, S. Keren, S. Vaithilingam, S. Bodapati, Z. Liu, J. Levi, B. R. Smith, T.-J. Ma, O. Oralkan, Z. Cheng, X. Chen, H. Dai, B. T. Khuri-Yakub, and S. S. Gambhir, “Carbon nanotubes as photoacoustic molecular imaging agents in living mice,” Nat. Nanotechnol. 3(9), 557–562 (2008).
[Crossref] [PubMed]

Stein, E. W.

X. Yang, E. W. Stein, S. Ashkenazi, and L. V. Wang, “Nanoparticles for photoacoustic imaging,” Wiley Interdiscip Rev Nanomed Nanobiotechnol 1(4), 360–368 (2009).
[Crossref] [PubMed]

Theiss, C.

J. Märk, C. Theiss, F.-J. Schmitt, and J. Laufer, “Photoacoustic imaging of a near-infrared fluorescent marker based on dual wavelength pump-probe excitation,” in Proc. of SPIE, Photons Plus Ultrasound: Imaging and Sensing, 2014, 8943, p. 894333.

Thiel, E.

R. Menzel and E. Thiel, “Intersystem crossing rate constants of rhodamine dyes: influence of the amino-group substitution,” Chem. Phys. Lett. 291(1-2), 237–243 (1998).
[Crossref]

Thomas, D. D.

E. Morgounova, Q. Shao, B. J. Hackel, D. D. Thomas, and S. Ashkenazi, “Photoacoustic lifetime contrast between methylene blue monomers and self-quenched dimers as a model for dual-labeled activatable probes,” J. Biomed. Opt. 18(5), 056004 (2013).
[Crossref] [PubMed]

Treeby, B.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012).

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, and P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[Crossref] [PubMed]

Treeby, B. E.

B. E. Treeby, E. Z. Zhang, and B. T. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26(11), 115003 (2010).
[Crossref]

Vaithilingam, S.

A. De la Zerda, C. Zavaleta, S. Keren, S. Vaithilingam, S. Bodapati, Z. Liu, J. Levi, B. R. Smith, T.-J. Ma, O. Oralkan, Z. Cheng, X. Chen, H. Dai, B. T. Khuri-Yakub, and S. S. Gambhir, “Carbon nanotubes as photoacoustic molecular imaging agents in living mice,” Nat. Nanotechnol. 3(9), 557–562 (2008).
[Crossref] [PubMed]

Vallabhan, C. P. G.

P. Sathy, R. Philip, V. P. N. Nampoori, and C. P. G. Vallabhan, “Photoacoustic observation of excited singlet state absorption in the laser dye rhodamine 6G,” J. Phys. D Appl. Phys. 27(10), 2019–2022 (1994).
[Crossref]

Venkateswarlu, P.

P. Venkateswarlu, M. C. George, Y. V. Rao, H. Jagannath, G. Chakrapani, and A. Miahnahri, “Transient excited singlet state absorption in Rhodamine 6G,” Pramana 28(1), 59–71 (1987).
[Crossref]

Verkhusha, V. V.

A. Krumholz, D. M. Shcherbakova, J. Xia, L. V. Wang, and V. V. Verkhusha, “Multicontrast photoacoustic in vivo imaging using near-infrared fluorescent proteins,” Sci. Rep. 4, 3939 (2014).
[Crossref] [PubMed]

G. S. Filonov, A. Krumholz, J. Xia, J. Yao, L. V. Wang, and V. V. Verkhusha, “Deep-tissue photoacoustic tomography of a genetically encoded near-infrared fluorescent probe,” Angew. Chem. Int. Ed. Engl. 51(6), 1448–1451 (2012).
[Crossref] [PubMed]

Vinegoni, C.

D. Razansky, M. Distel, C. Vinegoni, R. Ma, N. Perrimon, R. W. Köster, and V. Ntziachristos, “Multispectral opto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics 3(7), 412–417 (2009).
[Crossref]

D. Razansky, C. Vinegoni, and V. Ntziachristos, “Multispectral photoacoustic imaging of fluorochromes in small animals,” Opt. Lett. 32(19), 2891–2893 (2007).
[Crossref] [PubMed]

Wang, L. V.

A. Krumholz, D. M. Shcherbakova, J. Xia, L. V. Wang, and V. V. Verkhusha, “Multicontrast photoacoustic in vivo imaging using near-infrared fluorescent proteins,” Sci. Rep. 4, 3939 (2014).
[Crossref] [PubMed]

G. S. Filonov, A. Krumholz, J. Xia, J. Yao, L. V. Wang, and V. V. Verkhusha, “Deep-tissue photoacoustic tomography of a genetically encoded near-infrared fluorescent probe,” Angew. Chem. Int. Ed. Engl. 51(6), 1448–1451 (2012).
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L. V. Wang and S. Hu, “Photoacoustic tomography: in vivo imaging from organelles to organs,” Science 335(6075), 1458–1462 (2012).

A. Danielli, C. P. Favazza, K. Maslov, and L. V. Wang, “Picosecond absorption relaxation measured with nanosecond laser photoacoustics,” Appl. Phys. Lett. 97(16), 163701 (2010).
[Crossref] [PubMed]

X. Yang, E. W. Stein, S. Ashkenazi, and L. V. Wang, “Nanoparticles for photoacoustic imaging,” Wiley Interdiscip Rev Nanomed Nanobiotechnol 1(4), 360–368 (2009).
[Crossref] [PubMed]

Weber, H. P.

S. Bedö, M. Pollnau, W. Lüthy, and H. P. Weber, “Saturation of the 2.71 μm laser output in erbium-doped ZBLAN fibers,” Opt. Commun. 116(1-3), 81–86 (1995).
[Crossref]

Wiehler, J.

G. Jung, J. Wiehler, and A. Zumbusch, “The photophysics of green fluorescent protein: influence of the key amino acids at positions 65, 203, and 222,” Biophys. J. 88(3), 1932–1947 (2005).
[Crossref] [PubMed]

Wong, R.

D. Magde, R. Wong, and P. G. Seybold, “Fluorescence quantum yields and their relation to lifetimes of rhodamine 6G and fluorescein in nine solvents: improved absolute standards for quantum yields,” Photochem. Photobiol. 75(4), 327–334 (2002).
[Crossref] [PubMed]

Xia, J.

A. Krumholz, D. M. Shcherbakova, J. Xia, L. V. Wang, and V. V. Verkhusha, “Multicontrast photoacoustic in vivo imaging using near-infrared fluorescent proteins,” Sci. Rep. 4, 3939 (2014).
[Crossref] [PubMed]

G. S. Filonov, A. Krumholz, J. Xia, J. Yao, L. V. Wang, and V. V. Verkhusha, “Deep-tissue photoacoustic tomography of a genetically encoded near-infrared fluorescent probe,” Angew. Chem. Int. Ed. Engl. 51(6), 1448–1451 (2012).
[Crossref] [PubMed]

Xie, X. S.

W. Min, S. Lu, S. Chong, R. Roy, G. R. Holtom, and X. S. Xie, “Imaging chromophores with undetectable fluorescence by stimulated emission microscopy,” Nature 461(7267), 1105–1109 (2009).
[Crossref] [PubMed]

Xu, C.

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
[Crossref] [PubMed]

Xu, Y.

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
[Crossref] [PubMed]

Yang, X.

X. Yang, E. W. Stein, S. Ashkenazi, and L. V. Wang, “Nanoparticles for photoacoustic imaging,” Wiley Interdiscip Rev Nanomed Nanobiotechnol 1(4), 360–368 (2009).
[Crossref] [PubMed]

Yao, J.

G. S. Filonov, A. Krumholz, J. Xia, J. Yao, L. V. Wang, and V. V. Verkhusha, “Deep-tissue photoacoustic tomography of a genetically encoded near-infrared fluorescent probe,” Angew. Chem. Int. Ed. Engl. 51(6), 1448–1451 (2012).
[Crossref] [PubMed]

Zanganeh, S.

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
[Crossref] [PubMed]

Zavaleta, C.

A. De la Zerda, C. Zavaleta, S. Keren, S. Vaithilingam, S. Bodapati, Z. Liu, J. Levi, B. R. Smith, T.-J. Ma, O. Oralkan, Z. Cheng, X. Chen, H. Dai, B. T. Khuri-Yakub, and S. S. Gambhir, “Carbon nanotubes as photoacoustic molecular imaging agents in living mice,” Nat. Nanotechnol. 3(9), 557–562 (2008).
[Crossref] [PubMed]

Zhang, E.

A. P. Jathoul, J. Laufer, O. Ogunlade, B. Treeby, B. Cox, E. Zhang, P. Johnson, A. R. Pizzey, B. Philip, T. Marafioti, M. F. Lythgoe, R. B. Pedley, M. a. Pule, and P. Beard, “Deep in vivo photoacoustic imaging of mammalian tissues using a tyrosinase-based genetic reporter,” Nat. Photonics 9, 239–246 (2015).

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, and P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
[Crossref] [PubMed]

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012).

J. Laufer, E. Zhang, and P. Beard, “Evaluation of Absorbing Chromophores Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging,” IEEE J. Sel. Top. Quantum Electron. 16(3), 600–607 (2010).
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E. Zhang, J. Laufer, and P. Beard, “Backward-mode multiwavelength photoacoustic scanner using a planar Fabry-Perot polymer film ultrasound sensor for high-resolution three-dimensional imaging of biological tissues,” Appl. Opt. 47(4), 561–577 (2008).
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Zhang, E. Z.

B. E. Treeby, E. Z. Zhang, and B. T. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26(11), 115003 (2010).
[Crossref]

Zhu, Q.

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
[Crossref] [PubMed]

Zumbusch, A.

G. Jung, J. Wiehler, and A. Zumbusch, “The photophysics of green fluorescent protein: influence of the key amino acids at positions 65, 203, and 222,” Biophys. J. 88(3), 1932–1947 (2005).
[Crossref] [PubMed]

Angew. Chem. Int. Ed. Engl. (2)

G. S. Filonov, A. Krumholz, J. Xia, J. Yao, L. V. Wang, and V. V. Verkhusha, “Deep-tissue photoacoustic tomography of a genetically encoded near-infrared fluorescent probe,” Angew. Chem. Int. Ed. Engl. 51(6), 1448–1451 (2012).
[Crossref] [PubMed]

K. E. Sapsford, L. Berti, and I. L. Medintz, “Materials for fluorescence resonance energy transfer analysis: beyond traditional donor-acceptor combinations,” Angew. Chem. Int. Ed. Engl. 45(28), 4562–4589 (2006).
[Crossref] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

A. Danielli, C. P. Favazza, K. Maslov, and L. V. Wang, “Picosecond absorption relaxation measured with nanosecond laser photoacoustics,” Appl. Phys. Lett. 97(16), 163701 (2010).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

Biophys. J. (2)

G. Jung, J. Wiehler, and A. Zumbusch, “The photophysics of green fluorescent protein: influence of the key amino acids at positions 65, 203, and 222,” Biophys. J. 88(3), 1932–1947 (2005).
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Chem. Phys. Lett. (2)

A. Penzkofer, W. Falkenstein, and W. Kaiser, “Vibronic relaxation in the S1 state of rhodamine dye solutions,” Chem. Phys. Lett. 44(1), 82–87 (1976).
[Crossref]

R. Menzel and E. Thiel, “Intersystem crossing rate constants of rhodamine dyes: influence of the amino-group substitution,” Chem. Phys. Lett. 291(1-2), 237–243 (1998).
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IEEE J. Sel. Top. Quantum Electron. (1)

J. Laufer, E. Zhang, and P. Beard, “Evaluation of Absorbing Chromophores Used in Tissue Phantoms for Quantitative Photoacoustic Spectroscopy and Imaging,” IEEE J. Sel. Top. Quantum Electron. 16(3), 600–607 (2010).
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Interface Focus (1)

P. Beard, “Biomedical photoacoustic imaging,” Interface Focus 1(4), 602–631 (2011).
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B. E. Treeby, E. Z. Zhang, and B. T. Cox, “Photoacoustic tomography in absorbing acoustic media using time reversal,” Inverse Probl. 26(11), 115003 (2010).
[Crossref]

J. Biomed. Opt. (6)

C. Xu, P. D. Kumavor, U. Alqasemi, H. Li, Y. Xu, S. Zanganeh, and Q. Zhu, “Indocyanine green enhanced co-registered diffuse optical tomography and photoacoustic tomography,” J. Biomed. Opt. 18(12), 126006 (2013).
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B. Cox, J. G. Laufer, S. R. Arridge, and P. C. Beard, “Quantitative spectroscopic photoacoustic imaging: a review,” J. Biomed. Opt. 17(6), 061202 (2012).
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S. Ashkenazi, S.-W. Huang, T. Horvath, Y.-E. L. Koo, and R. Kopelman, “Photoacoustic probing of fluorophore excited state lifetime with application to oxygen sensing,” J. Biomed. Opt. 13(3), 034023 (2008).
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E. Morgounova, Q. Shao, B. J. Hackel, D. D. Thomas, and S. Ashkenazi, “Photoacoustic lifetime contrast between methylene blue monomers and self-quenched dimers as a model for dual-labeled activatable probes,” J. Biomed. Opt. 18(5), 056004 (2013).
[Crossref] [PubMed]

J. Laufer, P. Johnson, E. Zhang, B. Treeby, B. Cox, B. Pedley, and P. Beard, “In vivo preclinical photoacoustic imaging of tumor vasculature development and therapy,” J. Biomed. Opt. 17(5), 056016 (2012).

J. Laufer, F. Norris, J. Cleary, E. Zhang, B. Treeby, B. Cox, P. Johnson, P. Scambler, M. Lythgoe, and P. Beard, “In vivo photoacoustic imaging of mouse embryos,” J. Biomed. Opt. 17(6), 061220 (2012).
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A. Grofcsik and W. J. Jones, “Stimulated emission cross-sections in fluorescent dye solutions: gain spectra and excited-state lifetimes of Nile blue A and oxazine 720,” J. Chem. Soc., Faraday Trans. 88(8), 1101 (1992).
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J. Photochem. Photobiol. Chem. (1)

P. Sathy and A. Penzkofer, “Absorption and fluorescence spectroscopic analysis of rhodamine 6G and oxazine 750 in porous sol-gel glasses,” J. Photochem. Photobiol. Chem. 109(1), 53–57 (1997).
[Crossref]

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

P. Sathy, R. Philip, V. P. N. Nampoori, and C. P. G. Vallabhan, “Photoacoustic observation of excited singlet state absorption in the laser dye rhodamine 6G,” J. Phys. D Appl. Phys. 27(10), 2019–2022 (1994).
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Mol. Imag. Biol. (1)

N. C. Deliolanis, A. Ale, S. Morscher, N. C. Burton, K. Schaefer, K. Radrich, D. Razansky, and V. Ntziachristos, “Deep-tissue reporter-gene imaging with fluorescence and optoacoustic tomography: a performance overview,” Mol. Imag. Biol. 16(5), 652–660 (2014).
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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of the electronic and vibrational transitions in a fluorophore during pump-probe excitation (S0 – electronic ground state, S1 - first excited electronic state, S0* and S1* - vibrationally excited energy levels, kvib - vibrational relaxation rate, knr - non-radiative relaxation rate from S1 to S0*, kf - rate of spontaneous fluorescence emission, kse - rate of SE). ΔES1, ΔES10, ΔES0 indicate the relative energies of the transitions. (b) Wavelength dependence of the absorption cross section, σa, and the SE cross section, σse, of Rhodamine 6G.
Fig. 2
Fig. 2 Experimental setup for (i) measuring PA signals in a cuvette and (ii) acquiring tomographic PA images using time delayed pump and probe excitation pulses (PZT - piezoelectric ultrasound transducer, FM - flipper mirror, L - lenses).
Fig. 3
Fig. 3 Illustration of the initial compressive part of time-resolved PA signals generated in (i) a non-fluorescent absorber (grey dashed line), (ii) a fluorophore with SE (blue line), i.e. simultaneous pump and probe pulses, and (iii) a fluorophore without SE (black solid line), i.e. separate pump and probe pulses. A difference signal (red line), which provides a measure of the change in the local thermalized energy, is obtained by subtracting (ii) and (iii). The signals were predicted using the forward model (Eq. (13)).
Fig. 4
Fig. 4 Experimental setup for tomographic PA imaging of a tissue phantom, which consisted of capillary tubes filled with an aqueous solution of Atto680 (c = 160 µM) or blood immersed in a scattering lipid suspension. Image data sets were acquired in backward mode using a Fabry-Pérot based PA scanner using simultaneous and time delayed (Δt = 7.7 ns) pump-probe pulses.
Fig. 5
Fig. 5 PA signals measured in R6G solutions (c = 85 µM) in a cuvette (dotted lines) and those predicted by the forward model (solid lines) for different pump-probe fluences (t0 = 4.45 µs). The black lines correspond to the signal without SE (1), the blue lines correspond to the signal with SE (2) and red line represents the calculated difference signal (3).
Fig. 6
Fig. 6 PA signals measured in R6G solutions of different concentration (dotted lines) and those predicted by the forward model (solid lines): (a) 170 µM, (b) 85 µM, and (c) 42.5 µM. The pump fluence was 6 mJ/cm2, the probe fluence was 24 mJ/cm2, and t0 was 4.3 µs.
Fig. 7
Fig. 7 (a) Difference signal amplitude (peak-to-peak) measured in R6G as a function of probe pulse wavelength together with the model prediction (c = 85 µM, Φpump = 9 mJ/cm2, Φprobe = 16 mJ/cm2). σse(λ) is shown for comparison. (b) Difference signal amplitude (peak-to-peak) measured in an R6G solution as a function of time delay together with the model prediction (c = 170 µM, Φpump = 4 mJ/cm2, Φprobe = 10 mJ/cm2). The error bars in (a) and (b) correspond to the standard deviation of three measurements.
Fig. 8
Fig. 8 Difference imaging of a tissue phantom consisting of polymer capillaries filled with Atto680 (c = 160 µM) and whole murine blood immersed in a scattering medium. 2-D x-z cross sectional images of 3-D PA image data sets acquired using (a) simultaneous pump-probe pulses, (b) time delayed pump-probe pulses, and (c) the difference image obtained by subtracting (b) and (c). (d) Fused volume-rendered 3-D image of (b) and (c).

Equations (13)

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N 1 * ( t ) t = ( N 0 ( t ) N 1 * ( t ) ) σ a Φ R pump N 1 * ( t ) k vib
τ = 1 k nr + k f
η = k f τ
N 1 ( t ) t = N 1 * ( t ) k vib N 1 ( t ) τ ( N 1 ( t ) N 0 * ( t ) ) σ se Φ R probe
N 0 * ( t ) t = N 1 ( t ) τ + ( N 1 ( t ) N 0 * ( t ) ) σ se Φ R probe N 0 * ( t ) k vib
N 0 ( t ) t = N 0 * ( t ) k vib ( N 0 ( t ) N 1 * ( t ) ) σ a Φ R pump
Φ R pump ( x , t ) = Φ R 0pump G ( t ) e μ a ( x , t ) x
Φ R probe ( x , t ) = Φ R 0probe G ( t ) e μ se ( x , t ) x
μ a ( x , t ) = ( N 0 ( x , t ) N 1 * ( x , t ) ) c σ a ,
μ se ( x , t ) = ( N 0 * ( x , t ) N 1 ( x , t ) ) c σ se
p 0 ( x ) = Γ p u l s e μ a Φ pump ( x , t ) d t
p 0 ( x ) = Γ c p u l s e s ( ( Δ E S1 E ) N 1 * ( x , t ) k vib + ( Δ E S10 E ) ( N 1 ( x , t ) τ ) ( 1 η ) + ( Δ E S0 E ) N 0 * ( x , t ) k vib ) d t
S ( t ) = K f ( c , Φ pump ( λ ) , Φ probe ( λ ) , Δ t , c s , t t 0 )

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