Abstract

We investigate the origin of fluorescent or phosphorescent signals reemitted from highly scattering media (such as tissues), using diffusion theory and probability analysis. Results show that the lifetime of a uniformly distributed phosphorescent or fluorescent optical probe will profoundly affect the volume interrogated by noninvasive reflectance measurements. When the lifetime is greater than photon migration times, the origin of the reemitted signal is confined closest to the surface. Our computations suggest that noninvasive measurements of tissue oxygen concentration may not necessarily interrogate deep tissues when systemically administered phosphorescent dyes are used.

© 1994 Optical Society of America

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  1. D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
    [PubMed]
  2. J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
    [PubMed]
  3. W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
    [PubMed]
  4. J. R. Lakowicz, H. Szmacinski, Sensors Actuators 11, 133 (1993).
    [CrossRef]
  5. W. Cui, N. Wang, B. Chance, Opt. Lett. 16, 1632 (1991).
    [CrossRef] [PubMed]
  6. M. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,”Appl. Opt. (to be published).
  7. M. S. Patterson, B. W. Pogue, Appl. Opt. 33, 1963 (1994).
    [CrossRef] [PubMed]
  8. E. M. Sevick-Muraca, L. Suddeath, C. L. Burch, “Localization of signals for phosphorescent and fluorescent lifetime sensing in tissues,”Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).
  9. M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2331 (1989).
    [CrossRef] [PubMed]
  10. E. M. Sevick, J. K. Frisoli, C. L. Burch, J. R. Lakowicz, Appl. Opt. 33, 3562 (1994).
    [CrossRef] [PubMed]
  11. G. H. Weiss, R. Nossal, R. F. Bonner, J. Mod. Opt. 36, 348 (1989).
    [CrossRef]

1994 (2)

1993 (1)

J. R. Lakowicz, H. Szmacinski, Sensors Actuators 11, 133 (1993).
[CrossRef]

1991 (2)

W. Cui, N. Wang, B. Chance, Opt. Lett. 16, 1632 (1991).
[CrossRef] [PubMed]

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

1989 (2)

G. H. Weiss, R. Nossal, R. F. Bonner, J. Mod. Opt. 36, 348 (1989).
[CrossRef]

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2331 (1989).
[CrossRef] [PubMed]

1988 (1)

D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
[PubMed]

1987 (1)

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
[PubMed]

Andersson-Engels, S.

M. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,”Appl. Opt. (to be published).

Bonner, R. F.

G. H. Weiss, R. Nossal, R. F. Bonner, J. Mod. Opt. 36, 348 (1989).
[CrossRef]

Burch, C. L.

E. M. Sevick, J. K. Frisoli, C. L. Burch, J. R. Lakowicz, Appl. Opt. 33, 3562 (1994).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, L. Suddeath, C. L. Burch, “Localization of signals for phosphorescent and fluorescent lifetime sensing in tissues,”Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

Chance, B.

Cui, W.

Frisoli, J. K.

Green, T. J.

D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
[PubMed]

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
[PubMed]

Iturriaga, R.

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

Lahiri, S.

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

Lakowicz, J. R.

Maniara, G.

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
[PubMed]

Nossal, R.

G. H. Weiss, R. Nossal, R. F. Bonner, J. Mod. Opt. 36, 348 (1989).
[CrossRef]

Osei, E. K.

M. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,”Appl. Opt. (to be published).

Patterson, M.

M. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,”Appl. Opt. (to be published).

Patterson, M. S.

Pogue, B. W.

Rumsey, W. L.

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
[PubMed]

Sevick, E. M.

Sevick-Muraca, E. M.

E. M. Sevick-Muraca, L. Suddeath, C. L. Burch, “Localization of signals for phosphorescent and fluorescent lifetime sensing in tissues,”Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

Spergel, D.

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

Suddeath, L.

E. M. Sevick-Muraca, L. Suddeath, C. L. Burch, “Localization of signals for phosphorescent and fluorescent lifetime sensing in tissues,”Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

Szmacinski, H.

J. R. Lakowicz, H. Szmacinski, Sensors Actuators 11, 133 (1993).
[CrossRef]

Vanderkooi, J. M.

D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
[PubMed]

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
[PubMed]

Wang, N.

Weiss, G. H.

G. H. Weiss, R. Nossal, R. F. Bonner, J. Mod. Opt. 36, 348 (1989).
[CrossRef]

Wilson, B. C.

M. S. Patterson, B. Chance, B. C. Wilson, Appl. Opt. 28, 2331 (1989).
[CrossRef] [PubMed]

M. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,”Appl. Opt. (to be published).

Wilson, D. F.

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
[PubMed]

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
[PubMed]

Am. J. Physiol. (1)

W. L. Rumsey, R. Iturriaga, D. Spergel, S. Lahiri, D. F. Wilson, Am. J. Physiol. 261, C614 (1991).
[PubMed]

Appl. Opt. (3)

J. Biol. Chem. (2)

D. F. Wilson, W. L. Rumsey, T. J. Green, J. M. Vanderkooi, J. Biol. Chem. 263, 2712 (1988).
[PubMed]

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, J. Biol. Chem. 262, 5476 (1987).
[PubMed]

J. Mod. Opt. (1)

G. H. Weiss, R. Nossal, R. F. Bonner, J. Mod. Opt. 36, 348 (1989).
[CrossRef]

Opt. Lett. (1)

Sensors Actuators (1)

J. R. Lakowicz, H. Szmacinski, Sensors Actuators 11, 133 (1993).
[CrossRef]

Other (2)

M. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,”Appl. Opt. (to be published).

E. M. Sevick-Muraca, L. Suddeath, C. L. Burch, “Localization of signals for phosphorescent and fluorescent lifetime sensing in tissues,”Proc. Soc. Photo-Opt. Instrum. Eng. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the processes involved in the photon migration and the generation of emission photons.

Fig. 2
Fig. 2

Probability P(0, z/l*, ct/l*) for detecting an emission photon at dimensionless time ct/l* that has been spontaneously generated (τ = 0) at dimensionless depth z/l*.

Fig. 3
Fig. 3

Probability P(0, z/l*, ct/l*) for detecting an emission photon at dimensionless time ct/l* that has been generated (τ = 10 ns) at dimensionless depth z/l*.

Fig. 4
Fig. 4

Mean depth 〈z〉/l* at which photons detected at dimensionless time ct/l* have been generated. Results are shown for lifetimes of 0, 1, and 10 ns and 1 ms.

Equations (7)

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P s ( r , z , t * ) = ϕ μ a x m τ t = 0 t = t * exp ( t t * τ ) Φ x ( r , z , t ) .
Φ x ( r , z , t ) = c ( 4 π D c t ) 3 / 2 [ exp ( z z 0 ) 2 ( r ρ / 2 ) 2 4 D c t exp ( z + z 0 ) 2 ( r ρ / 2 ) 2 4 D c t ] exp [ ( μ a x m + μ a x ) c t ] ,
D = 1 3 [ μ ax m + μ ax + ( 1 g ) μ sx ] ,
P D ( r , z , t t * ) = Φ m ( r , z , t t * ) = c [ 4 π Dc ( t t * ) ] 3 / 2 [ exp ( z z 0 ) 2 ( r + ρ / 2 ) 2 4 Dc ( t t * ) exp ( z + z 0 ) 2 ( r + ρ / 2 ) 2 4 Dc ( t t * ) ] exp [ μ am c ( t t * ) ] .
D = 1 3 [ μ am + ( 1 g ) μ s m ] .
P ( r , z , t ) = t * = 0 t * = t P S ( r , z , t * ) P D ( r , z , t t * ) .
z = P ( 0 , z , t ) z z P ( 0 , z , t ) z .

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