Abstract

Measurements of nanosecond and subnanosecond fluorescence lifetimes are restricted to dilute, nonscattering systems since excitation and emission photon times of flight significantly affect measured fluorescent decay kinetics. We provide the theoretical rationale for frequency-domain measurements of phase-shift and amplitude demodulation made at excitation and emission wavelengths for direct determination of lifetimes in tissues and other scattering media. We confirm our analytical expressions using standard laser dyes such as 3,3′-diethylthiatricarbocyanine iodide, IR-125, and IR-140 in polystyrene suspensions with similar scattering properties as tissues. Our results have significant implication for lifetime-based spectroscopy in tissues and other scattering media.

© 1996 Optical Society of America

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  1. J. Wu, M. S. Feld, R. P. Rava, “Analytical model for extracting intrinsic fluorescence in turbid media,” Appl. Opt. 32, 3585–3595 (1993).
  2. A. J. Durkin, S. Jaikumar, N. Ramanujam, R. Richards-Kortum, “Relation between fluorescence spectra of dilute and turbid samples,” Appl. Opt. 33, 414–423 (1993).
  3. M. S. Patterson, B. W. Pogue, “A mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissues,” Appl. Opt. 33, 1963–1974 (1994).
  4. B. Chance, R. R. Alfano, eds., Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389, (1995).
  5. S. Ahmed, Z. W. Zang, K. M. Yoo, M. A. Ali, “Effect of multiple light scattering and self-absorption on the fluorescence and excitation spectra of dyes in random media,” Appl. Opt. 33, 2746–2750 (1994).
  6. E. M. Sevick-Muraca, C. L. Burch, “Origin of phosphorescence signals reemitted in tissues,” Opt. Lett. 19, 1928–1930 (1994).
  7. D.A. Russell, R. H. Pottier, D. P. Valenzeno, “Continuous, noninvasive measurement of in vivo pH in conscious mice,” Photochem. Photobiol. 59, 309–313 (1994).
  8. R. Cubeddu, G. Canti, P. Taroni, G. Valentini, “Timegated fluorescence imaging for the diagnosis of tumors in a murine model,” Photochem. Photobiol. 57, 480–485 (1993).
  9. D. F. Wilson, “Measuring oxygen using oxygen dependent quenching of phosphorescence: a status report,” in Optical Imaging of Brain Function and Metabolism, E. Dirnagl, A. Arno, K. M. Einhapl, eds. (Plenum, New York, 1993), pp. 225–232.
  10. J. E. Roberts, S. J. Atherton, J. Dillon, “Detection of porphyrin excited states in the intact bovine lens,” Photochem. Photobiol. 54, 855–857 (1991).
  11. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1985).
  12. D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytical solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
  13. E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7, 24–28 (1996).
  14. C. L. Hutchinson, J. R. Lakowicz, E. M. Sevick-Muraca, “Fluorescence lifetime based sensing in tissues: a computational study,” Biophys. J. 68, 1574–1582 (1995).
  15. C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).
  16. R. B. Thompson, J. R. Frisoli, J. R. Lakowicz, “Phase fluorometry using a continuously modulated laser diode,” Anal. Chem. 64, 2075–2078 (1992).
  17. S. A. Soper, B. I. Legendre, “Error analysis of simple algorithms for determining fluorescence lifetimes in ultradilute dye solutions,” Appl. Spectrosc. 48, 400–405 (1994).
  18. H. Schneckenburger, K. Konig, “Fluorescence decay kinetics and imaging of NAD(P)H and flavins as metabolic indicators,” Opt. Eng. 31, 1447–1451 (1992).

1996 (1)

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7, 24–28 (1996).

1995 (1)

C. L. Hutchinson, J. R. Lakowicz, E. M. Sevick-Muraca, “Fluorescence lifetime based sensing in tissues: a computational study,” Biophys. J. 68, 1574–1582 (1995).

1994 (6)

1993 (3)

1992 (2)

R. B. Thompson, J. R. Frisoli, J. R. Lakowicz, “Phase fluorometry using a continuously modulated laser diode,” Anal. Chem. 64, 2075–2078 (1992).

H. Schneckenburger, K. Konig, “Fluorescence decay kinetics and imaging of NAD(P)H and flavins as metabolic indicators,” Opt. Eng. 31, 1447–1451 (1992).

1991 (1)

J. E. Roberts, S. J. Atherton, J. Dillon, “Detection of porphyrin excited states in the intact bovine lens,” Photochem. Photobiol. 54, 855–857 (1991).

Ahmed, S.

Ali, M. A.

Atherton, S. J.

J. E. Roberts, S. J. Atherton, J. Dillon, “Detection of porphyrin excited states in the intact bovine lens,” Photochem. Photobiol. 54, 855–857 (1991).

Boas, D. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytical solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).

Bohren, C. F.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Burch, C. L.

Canti, G.

R. Cubeddu, G. Canti, P. Taroni, G. Valentini, “Timegated fluorescence imaging for the diagnosis of tumors in a murine model,” Photochem. Photobiol. 57, 480–485 (1993).

Chance, B.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytical solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).

Cubeddu, R.

R. Cubeddu, G. Canti, P. Taroni, G. Valentini, “Timegated fluorescence imaging for the diagnosis of tumors in a murine model,” Photochem. Photobiol. 57, 480–485 (1993).

Dillon, J.

J. E. Roberts, S. J. Atherton, J. Dillon, “Detection of porphyrin excited states in the intact bovine lens,” Photochem. Photobiol. 54, 855–857 (1991).

Durkin, A. J.

Feld, M. S.

Frisoli, J. R.

R. B. Thompson, J. R. Frisoli, J. R. Lakowicz, “Phase fluorometry using a continuously modulated laser diode,” Anal. Chem. 64, 2075–2078 (1992).

Huffman, D. R.

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

Hutchinson, C. L.

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7, 24–28 (1996).

C. L. Hutchinson, J. R. Lakowicz, E. M. Sevick-Muraca, “Fluorescence lifetime based sensing in tissues: a computational study,” Biophys. J. 68, 1574–1582 (1995).

Jaikumar, S.

Konig, K.

H. Schneckenburger, K. Konig, “Fluorescence decay kinetics and imaging of NAD(P)H and flavins as metabolic indicators,” Opt. Eng. 31, 1447–1451 (1992).

Lakowicz, J. R.

C. L. Hutchinson, J. R. Lakowicz, E. M. Sevick-Muraca, “Fluorescence lifetime based sensing in tissues: a computational study,” Biophys. J. 68, 1574–1582 (1995).

R. B. Thompson, J. R. Frisoli, J. R. Lakowicz, “Phase fluorometry using a continuously modulated laser diode,” Anal. Chem. 64, 2075–2078 (1992).

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1985).

Legendre, B. I.

O’Leary, M. A.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytical solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).

Paithankar, D. Y.

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7, 24–28 (1996).

Patterson, M. S.

Pogue, B. W.

Pottier, R. H.

D.A. Russell, R. H. Pottier, D. P. Valenzeno, “Continuous, noninvasive measurement of in vivo pH in conscious mice,” Photochem. Photobiol. 59, 309–313 (1994).

Ramanujam, N.

Rava, R. P.

Richards-Kortum, R.

Roberts, J. E.

J. E. Roberts, S. J. Atherton, J. Dillon, “Detection of porphyrin excited states in the intact bovine lens,” Photochem. Photobiol. 54, 855–857 (1991).

Russell, D.A.

D.A. Russell, R. H. Pottier, D. P. Valenzeno, “Continuous, noninvasive measurement of in vivo pH in conscious mice,” Photochem. Photobiol. 59, 309–313 (1994).

Schneckenburger, H.

H. Schneckenburger, K. Konig, “Fluorescence decay kinetics and imaging of NAD(P)H and flavins as metabolic indicators,” Opt. Eng. 31, 1447–1451 (1992).

Sevick-Muraca, E. M.

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7, 24–28 (1996).

C. L. Hutchinson, J. R. Lakowicz, E. M. Sevick-Muraca, “Fluorescence lifetime based sensing in tissues: a computational study,” Biophys. J. 68, 1574–1582 (1995).

E. M. Sevick-Muraca, C. L. Burch, “Origin of phosphorescence signals reemitted in tissues,” Opt. Lett. 19, 1928–1930 (1994).

Soper, S. A.

Taroni, P.

R. Cubeddu, G. Canti, P. Taroni, G. Valentini, “Timegated fluorescence imaging for the diagnosis of tumors in a murine model,” Photochem. Photobiol. 57, 480–485 (1993).

Thompson, R. B.

R. B. Thompson, J. R. Frisoli, J. R. Lakowicz, “Phase fluorometry using a continuously modulated laser diode,” Anal. Chem. 64, 2075–2078 (1992).

Valentini, G.

R. Cubeddu, G. Canti, P. Taroni, G. Valentini, “Timegated fluorescence imaging for the diagnosis of tumors in a murine model,” Photochem. Photobiol. 57, 480–485 (1993).

Valenzeno, D. P.

D.A. Russell, R. H. Pottier, D. P. Valenzeno, “Continuous, noninvasive measurement of in vivo pH in conscious mice,” Photochem. Photobiol. 59, 309–313 (1994).

Wilson, D. F.

D. F. Wilson, “Measuring oxygen using oxygen dependent quenching of phosphorescence: a status report,” in Optical Imaging of Brain Function and Metabolism, E. Dirnagl, A. Arno, K. M. Einhapl, eds. (Plenum, New York, 1993), pp. 225–232.

Wu, J.

Yodh, A. G.

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytical solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).

Yoo, K. M.

Zang, Z. W.

Anal. Chem. (1)

R. B. Thompson, J. R. Frisoli, J. R. Lakowicz, “Phase fluorometry using a continuously modulated laser diode,” Anal. Chem. 64, 2075–2078 (1992).

Appl. Opt. (4)

Appl. Spectrosc. (1)

Biophys. J. (1)

C. L. Hutchinson, J. R. Lakowicz, E. M. Sevick-Muraca, “Fluorescence lifetime based sensing in tissues: a computational study,” Biophys. J. 68, 1574–1582 (1995).

Opt. Eng. (1)

H. Schneckenburger, K. Konig, “Fluorescence decay kinetics and imaging of NAD(P)H and flavins as metabolic indicators,” Opt. Eng. 31, 1447–1451 (1992).

Opt. Lett. (1)

Opt. Photon. News (1)

E. M. Sevick-Muraca, C. L. Hutchinson, D. Y. Paithankar, “Optical tissue biodiagnostics using fluorescence lifetime,” Opt. Photon. News 7, 24–28 (1996).

Photochem. Photobiol. (3)

J. E. Roberts, S. J. Atherton, J. Dillon, “Detection of porphyrin excited states in the intact bovine lens,” Photochem. Photobiol. 54, 855–857 (1991).

D.A. Russell, R. H. Pottier, D. P. Valenzeno, “Continuous, noninvasive measurement of in vivo pH in conscious mice,” Photochem. Photobiol. 59, 309–313 (1994).

R. Cubeddu, G. Canti, P. Taroni, G. Valentini, “Timegated fluorescence imaging for the diagnosis of tumors in a murine model,” Photochem. Photobiol. 57, 480–485 (1993).

Proc. Natl. Acad. Sci. USA (1)

D. A. Boas, M. A. O’Leary, B. Chance, A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytical solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).

Other (4)

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1985).

C. F. Bohren, D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

D. F. Wilson, “Measuring oxygen using oxygen dependent quenching of phosphorescence: a status report,” in Optical Imaging of Brain Function and Metabolism, E. Dirnagl, A. Arno, K. M. Einhapl, eds. (Plenum, New York, 1993), pp. 225–232.

B. Chance, R. R. Alfano, eds., Optical Tomography: Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389, (1995).

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Figures (7)

Fig. 1
Fig. 1

Schematic illustrating the probability for detecting a fluorescent photon at position r d and time t that is generated at position r following an excitation impulse at a point source at r s .

Fig. 2
Fig. 2

Schematic illustrating the probability of detecting a fluorescent photon at position r d that is generated at position r in response to an excitation source modulated at frequency ω at r s .

Fig. 3
Fig. 3

Schematic of the frequency-domain system for monitoring phase-shift and amplitude modulation of excitation and emission light.

Fig. 4
Fig. 4

Phase-shift θ m (ω) (filled symbols) and amplitude demodulation ratio M m (ω)/M x (0) (open symbols) as a function of frequency for reemitted fluorescent light that is generated by the excitation of DTTCI in ethanol. The symbols denote measurements for isotropic scattering coefficients that vary between 5 and 20 cm−1. Measurements are reported relative to the incident excitation light and include contributions from the instrument.

Fig. 5
Fig. 5

Phase-shift difference θ m (ω) − θ x (ω) (filled symbols) and amplitude demodulation ratio [M m (ω)/M m (0)]/[M x (ω)/M x (0)] (open symbols) as a function of frequency for reemitted fluorescent light that is generated by the excitation of DTTCI in ethanol and varying concentrations of polystyrene beads. Measurements are reported relative to the detected excitation light. The symbols denote actual measurements whereas the solid curve represents the least-squares fit to Eq. (19) (τ = 0.94 ns). A parameter estimate of 1.17 ns for the lifetime of DTTCI was obtained from referenced measurements (x symbols) of phase shift in nonscattering ethanol. The least-squares fit to Eq. (16) is denoted by the dotted curve.

Fig. 6
Fig. 6

Phase-shift θ m (ω) (open symbols) as a function of frequency for reemitted fluorescent light that is generated by the excitation of IR-125 in ethanol. The symbols denote actual measurements and the dotted curve denotes the least-squares fit to Eq. (16). A lifetime of 0.58 ns was obtained. Phase-shift difference θ m (ω) − θ x (ω) (filled symbols) as a function of frequency for reemitted fluorescent light that is generated by the excitation of IR-125 in ethanol and with polystyrene microspheres added. Measurements are reported relative to the detected excitation light, and the solid curve denotes the least-squares fit to Eq. (19). Alifetime of 0.537 ns was obtained.

Fig. 7
Fig. 7

Phase shift θ m (ω) (open symbols) as a function of frequency for reemitted fluorescent light that is generated by the excitation of IR-140 in ethanol. The symbols denote measurements and the dotted curve denotes the least-squares fit to Eq. (16). Alifetime of 0.88 ns was obtained. Phase-shift difference θ m (ω) − θ x (ω) (filled symbols) as a function of frequency for reemitted fluorescent light that is generated by the excitation of IR-140 in ethanol with polystyrene microspheres added. Measurements are reported relative to the detected excitation light, and the solid curve denotes the least-squares fit to Eq. (19). A lifetime of 0.72 ns was obtained.

Equations (21)

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I m ( t ) = α [ C ( r ) ] L τ exp ( t τ ) .
I m = 0 α [ C ( r ) ] L τ exp ( t τ ) d t = α [ C ( r ) ]
I m λ 1 I m λ 2 = α λ 1 α λ 2 f { [ C ( r ) ] } .
P ( t * , r s r ) = 1 τ t = 0 t = t * Φ x ( t , r s r ) × α [ C ( r ) ] L exp ( t * t τ ) d t .
I m ( t ) = 1 τ V t * = 0 t * = t Φ m ( t t * , r r d ) × t = 0 t = t * Φ x ( t , r s r ) α [ C ( r ) ] × exp ( t * t τ ) t t * 3 r .
I m = 1 τ t = 0 t = V t * = 0 t * = t Φ m ( t t * , r r d ) × t = 0 t = t * Φ x ( t , r s r ) α [ C ( r ) ] × exp ( t * t τ ) t t * 3 r t .
P ( ω ) = 0 α [ C ( r ) ] τ exp ( t T ) exp ( i ω t ) t = α [ C ( r ) ] 1 i ωτ = α [ C ( r ) ] exp ( i tan 1 ωτ ) 1 + ω 2 τ 2 .
θ m ( ω ) = tan 1 ( ωτ ) .
θ m s ( ω ) θ m r ( ω ) = tan 1 ( ωτ s ) tan 1 ( ωτ r ) .
M m ( ω ) = α [ C ( r ) ] 1 + { ωτ } 2
M m ( ω ) M m ( 0 ) = 1 1 + { ωτ } 2 .
M m s ( ω ) M m s ( 0 ) M m r ( ω ) M m r ( 0 ) = 1 + { ωτ r } 2 1 + { ωτ s } 2 .
τ 0 τ = 1 + K SV τ 0 [ Q ] ,
P ( ω ) = V Φ x ( ω , r s r ) Φ m ( ω , r r d ) α [ C ( r ) ] L 1 i ωτ d 3 r = α 1 i ωτ V Φ x ( ω , r s r ) Φ m ( ω , r r d ) [ C ( r ) ] d 3 r .
P s ( ω ) P r ( ω ) = α s 1 i ωτ s V Φ x s ( ω , r s r ) Φ m s ( ω , r r d ) [ C s ( r ) ] d 3 r α r 1 i ωτ r V Φ x r ( ω , r s r ) Φ m r ( ω , r r d ) [ C r ( r ) ] d 3 r .
P m s ( ω ) P m r ( ω ) = α s [ C s ] 1 + ( ωτ r ) 2 α r [ C r ] 1 + ( ωτ s ) 2 × exp  [ i ( tan 1 ωτ s tan 1 ωτ r ) ] .
θ m s ( ω ) θ m r ( ω ) = tan 1 ( ωτ s ) tan 1 ( ωτ r ) ,
M m s ( ω ) M m s ( 0 ) M m r ( ω ) M m r ( 0 ) = 1 + ( ωτ r ) 2 1 + ( ωτ s ) 2 .
P m s ( ω ) P x ( ω ) = α s [ C s ] L 1 i ωτ s V Φ x ( ω , r s r ) Φ m ( ω , r r d ) d 3 r V Φ x ( ω , r s r ) Φ x ( ω , r r d ) d 3 r α s [ C s ] L 1 i ωτ s V Φ x ( ω , r s r ) Φ x ( ω , r r d ) d 3 r V Φ x ( ω , r s r ) Φ x ( ω , r r d ) d 3 r .
θ m ( ω ) θ x ( ω ) = tan 1 ( ωτ ) ,
M m ( ω ) M m ( 0 ) M x ( ω ) M x ( 0 ) = 1 1 + ( ωτ ) 2 .

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