Abstract

We introduce a methodology to determine quantitatively the depth resolution limit in luminescence diffuse optical imaging. The approach is based on a Cramer–Rao statistical analysis, a noise model, and calculations of photon transport in tissues. We illustrate the method in the case of luminescence imaging in a brain–skull model, showing its potential applications in molecular imaging on small animals.

© 2008 Optical Society of America

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  1. B. Chance, Annu. Rev. Biophys. Biophys. Chem. 20, 1 (1991).
    [CrossRef] [PubMed]
  2. V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Nat. Biotechnol. 23, 313 (2005).
    [CrossRef] [PubMed]
  3. G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).
  4. A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
    [CrossRef] [PubMed]
  5. V. Ntziachristos and R. Weissleder, Opt. Lett. 26, 893 (2001).
    [CrossRef]
  6. Z. M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, Opt. Lett. 30, 3338 (2005).
    [CrossRef]
  7. A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
    [CrossRef] [PubMed]
  8. B. Pogue and K. D. Paulsen, Opt. Lett. 23, 1716 (1998).
    [CrossRef]
  9. M. Johns, C. A. Giller, D. C. German, and H. Liu, Opt. Express 13, 4828 (2005).
    [CrossRef] [PubMed]
  10. W. F. Cheong, S. A. Prahl, and A. J. Welch, IEEE J. Quant. Electron. 26, 2166 (1990).
    [CrossRef]
  11. E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
    [CrossRef]
  12. P. Refregier, Noise Theory and Application to Physics: From Fluctuation to Information (Springer, 2004).
  13. A. Sentenac, C.-A. Guérin, P. C. Chaumet, F. Drsek, H. Giovannini, N. Bertaux, and M. Holschneider, Opt. Express 15, 1340 (2008).
    [CrossRef]
  14. M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
    [CrossRef] [PubMed]
  15. G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).
    [CrossRef]
  16. R. Elaloufi, R. Carminati, and J.-J. Greffet, J. Opt. Soc. Am. A 21, 1430 (2004).
    [CrossRef]
  17. A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
    [CrossRef]
  18. R. Elaloufi, S. Arridge, R. Pierrat, and R. Carminati, Appl. Opt. 46, 2528 (2007).
    [CrossRef] [PubMed]
  19. J. Ripoll, R. B. Schulz, and V. Ntziachristos, Phys. Rev. Lett. 91, 103901 (2003).
    [CrossRef] [PubMed]
  20. V. Ntziachristos, J. Ripoll, and R. Weissleder, Opt. Lett. 27, 333 (2002).
    [CrossRef]
  21. A. D. Klose, V. Ntziachristos, and A. H. Hielscher, J. Comput. Phys. 202, 323 (2005).
    [CrossRef]

2008

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

A. Sentenac, C.-A. Guérin, P. C. Chaumet, F. Drsek, H. Giovannini, N. Bertaux, and M. Holschneider, Opt. Express 15, 1340 (2008).
[CrossRef]

2007

R. Elaloufi, S. Arridge, R. Pierrat, and R. Carminati, Appl. Opt. 46, 2528 (2007).
[CrossRef] [PubMed]

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

2005

M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Nat. Biotechnol. 23, 313 (2005).
[CrossRef] [PubMed]

A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, J. Comput. Phys. 202, 323 (2005).
[CrossRef]

M. Johns, C. A. Giller, D. C. German, and H. Liu, Opt. Express 13, 4828 (2005).
[CrossRef] [PubMed]

Z. M. Wang, G. Y. Panasyuk, V. A. Markel, and J. C. Schotland, Opt. Lett. 30, 3338 (2005).
[CrossRef]

2004

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

R. Elaloufi, R. Carminati, and J.-J. Greffet, J. Opt. Soc. Am. A 21, 1430 (2004).
[CrossRef]

2003

J. Ripoll, R. B. Schulz, and V. Ntziachristos, Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

2002

2001

1998

1991

B. Chance, Annu. Rev. Biophys. Biophys. Chem. 20, 1 (1991).
[CrossRef] [PubMed]

1990

W. F. Cheong, S. A. Prahl, and A. J. Welch, IEEE J. Quant. Electron. 26, 2166 (1990).
[CrossRef]

Andraud, C.

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

Arridge, S.

Barrera, R. G.

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

Berger, M.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Bertaux, N.

Blanco, S.

M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
[CrossRef] [PubMed]

Boutet, J.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Carminati, R.

Chan, E.

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

Chance, B.

B. Chance, Annu. Rev. Biophys. Biophys. Chem. 20, 1 (1991).
[CrossRef] [PubMed]

Chaumet, P. C.

Cheong, W. F.

W. F. Cheong, S. A. Prahl, and A. J. Welch, IEEE J. Quant. Electron. 26, 2166 (1990).
[CrossRef]

Da Silva, A.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

Dinten, J.-M.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Drsek, F.

El Hafi, M.

M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
[CrossRef] [PubMed]

Elaloufi, R.

Fournier, R.

M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
[CrossRef] [PubMed]

German, D. C.

Giller, C. A.

Giovannini, H.

Greffet, J.-J.

Guérin, C.-A.

Henderson, J. T.

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

Henkelman, R. M.

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

Hervé, L.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Hielscher, A. H.

A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, J. Comput. Phys. 202, 323 (2005).
[CrossRef]

Ho, S. K. Y.

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

Hoffman, E. A.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Holschneider, M.

Johns, M.

Josserand, V.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Klose, A. D.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, J. Comput. Phys. 202, 323 (2005).
[CrossRef]

Koenig, A.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Kovacevic, N.

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

Lafait, J.

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

Liu, H.

Markel, V. A.

McLennan, G.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Meinel, J.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Ntziachristos, V.

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Nat. Biotechnol. 23, 313 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, J. Comput. Phys. 202, 323 (2005).
[CrossRef]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, and R. Weissleder, Opt. Lett. 27, 333 (2002).
[CrossRef]

V. Ntziachristos and R. Weissleder, Opt. Lett. 26, 893 (2001).
[CrossRef]

Panasyuk, G. Y.

Paulsen, K. D.

Peltié, P.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

Pierrat, R.

Pogue, B.

Prahl, S. A.

W. F. Cheong, S. A. Prahl, and A. J. Welch, IEEE J. Quant. Electron. 26, 2166 (1990).
[CrossRef]

Refregier, P.

P. Refregier, Noise Theory and Application to Physics: From Fluctuation to Information (Springer, 2004).

Ripoll, J.

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Nat. Biotechnol. 23, 313 (2005).
[CrossRef] [PubMed]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, and R. Weissleder, Opt. Lett. 27, 333 (2002).
[CrossRef]

Robin, T.

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

Roger, M.

M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
[CrossRef] [PubMed]

Schotland, J. C.

Schulz, R. B.

J. Ripoll, R. B. Schulz, and V. Ntziachristos, Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

Sentenac, A.

Stamnes, K.

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).
[CrossRef]

Suter, M.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Thomas, G. E.

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).
[CrossRef]

Wang, G.

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Nat. Biotechnol. 23, 313 (2005).
[CrossRef] [PubMed]

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Wang, Z. M.

Weissleder, R.

Welch, A. J.

W. F. Cheong, S. A. Prahl, and A. J. Welch, IEEE J. Quant. Electron. 26, 2166 (1990).
[CrossRef]

Annu. Rev. Biophys. Biophys. Chem.

B. Chance, Annu. Rev. Biophys. Biophys. Chem. 20, 1 (1991).
[CrossRef] [PubMed]

Appl. Opt.

Curr. Opin. Biotechnol.

A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
[CrossRef] [PubMed]

J. Biomed. Opt.

A. Koenig, L. Hervé, V. Josserand, M. Berger, J. Boutet, A. Da Silva, J.-M. Dinten, and P. Peltié, J. Biomed. Opt. 13, 011008 (2008).
[CrossRef] [PubMed]

J. Comput. Phys.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, J. Comput. Phys. 202, 323 (2005).
[CrossRef]

J. Mod. Opt.

A. Da Silva, C. Andraud, J. Lafait, T. Robin, and R. G. Barrera, J. Mod. Opt. 51, 313 (2004).
[CrossRef]

J. Opt. Soc. Am. A

J. Quant. Electron.

W. F. Cheong, S. A. Prahl, and A. J. Welch, IEEE J. Quant. Electron. 26, 2166 (1990).
[CrossRef]

Nat. Biotechnol.

V. Ntziachristos, J. Ripoll, L. V. Wang and R. Weissleder, Nat. Biotechnol. 23, 313 (2005).
[CrossRef] [PubMed]

Neuroscience

E. Chan, N. Kovacevic, S. K. Y. Ho, R. M. Henkelman, and J. T. Henderson, Neuroscience 144, 604 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. Lett.

J. Ripoll, R. B. Schulz, and V. Ntziachristos, Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

M. Roger, S. Blanco, M. El Hafi, and R. Fournier, Phys. Rev. Lett. 95, 180601 (2005).
[CrossRef] [PubMed]

Radiology

G. Wang, E. A. Hoffman, G. McLennan, L. V. Wang, M. Suter, and J. Meinel, Radiology 229, 566 (2003).

Other

G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean (Cambridge U. Press, 1999).
[CrossRef]

P. Refregier, Noise Theory and Application to Physics: From Fluctuation to Information (Springer, 2004).

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Figures (3)

Fig. 1
Fig. 1

One-dimensional model of a mouse brain–skull system. The inset shows a cross section of a real system. The parameters of each layer are given in Table 1.

Fig. 2
Fig. 2

PDP g ( L ) for the multilayer brain–skull model in Fig. 1 (squares) and for a homogeneous slab with effective optical parameters (circles). The vertical line locates the interface between grey and white matters.

Fig. 3
Fig. 3

Normalized resolution Δ L norm . (a) Multilayer brain–skull model. (b) Homogeneous slab with effective optical parameters.

Tables (1)

Tables Icon

Table 1 Parameters of the Brain–Skull Model

Equations (7)

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

m k , p = T V g k , p ( r ) n ( r ) d 3 r ,
P ( m ) = p = 1 N k = 1 M m k , p m k , p m k , p ! exp [ m k , p ] ,
CRB = [ L ln P ( m ) ] 2 1 ,
CRB = { η T p = 1 N k = 1 M 1 g k , p ( L ) [ L g k , p ( L ) ] 2 } 1 .
CRB = g ( L ) η T [ L g ( L ) ] 2
Δ L = 1 η T g ( L ) L g ( L ) .
Δ L norm = η T Δ L = g ( L ) L g ( L ) .

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