Abstract

Using a set of coupled radiation transport equations, we derive image operators for luminescence optical tomography with which it is possible to reconstruct concentration and mean lifetime distribution from information obtained from dc and time-harmonic optical sources. Weight functions and detector readings were computed from analytic solutions of the diffusion equation and from numerical solutions of the transport equation by Monte Carlo methods. Detector readings were also obtained from experiments on vessels containing a balloon filled with dye embedded in an Intralipid suspension with dye in the background. Image reconstructions were performed by the conjugate gradient descent method and the simultaneous algebraic reconstruction technique with a positivity constraint. A concentration correction was developed in which the reconstructed concentration information is used in the mean-lifetime reconstruction. The results show that the target can be accurately located in both the simulated and the experimental cases, but quantitative inaccuracies are present. Observed errors include a shadowing effect in regions that have the lowest weight within the inclusion. Application of the concentration correction can significantly improve computational efficiency and reduce error in the mean-lifetime reconstructions.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. G. J. Müller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).
  2. R. R. Alfano, ed., Advances in Optical Imaging, Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994).
  3. B. Chance, R. R. Alfano, eds., Optical Tomography: Photon Migration and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389, 2–874 (1995).
  4. J. Chang, H. Graber, R. Aronson, R. L. Barbour, “Fluorescence imaging using transport-theory-based imaging operators,” in 1995 IEEE Engineering in Medicine and Biology 17th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 1995), abstract 2.3.2.14.
  5. J. Chang, R. L. Barbour, H. Graber, R. Aronson, “Fluorescence optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, M. A. Fiddy, eds., Proc. SPIE2570, 59–72 (1995).
    [CrossRef]
  6. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996).
    [CrossRef] [PubMed]
  7. Y. Paithankar, E. M. Sevick-Muraca, “Fluorescence lifetime imaging with frequency-domain photon migration measurement,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996), pp. 155–157.
  8. P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).
  9. A. H. Anderson, A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imag. 6, 81–94 (1984).
  10. A. V. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), Chap. 7, pp. 285–292.
  11. H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).
  12. H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 1, Chap. 3, pp. 16–23.
  13. J. Chang, R. Aronson, H. L. Graber, R. L. Barbour, “Imaging diffusive media using time-independent and time-harmonic sources: dependence of image quality on imaging algorithms, target volume, weight matrix, and view angles,” Ref. 3, pp. 448–464.
  14. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983), Chap. 1, pp. 1–15.
  15. H. J. van Staveren, C. J. M. Moes, J. van Marle, S. A. Prahl, M. J. C. van Gemert, “Light scattering in Intralipid-10% in the wavelength range of 400–1100 nm,” Appl. Opt. 30, 4507–4514 (1991).
    [CrossRef] [PubMed]
  16. J. Chang, H. L. Graber, R. L. Barbour, “Dependence of optical diffusion tomography image quality on image operator and noise,” in Conference Record of the 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1524–1528.
  17. J. Chang, H. L. Graber, R. L. Barbour, “Image reconstruction of dense scattering media from CW sources using constrained CGD and a matrix rescaling technique,” Ref. 3, pp. 682–691.

1996 (1)

1991 (1)

1984 (1)

A. H. Anderson, A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imag. 6, 81–94 (1984).

Alsmiller, R. G.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

Anderson, A. H.

A. H. Anderson, A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imag. 6, 81–94 (1984).

Aronson, R.

J. Chang, H. Graber, R. Aronson, R. L. Barbour, “Fluorescence imaging using transport-theory-based imaging operators,” in 1995 IEEE Engineering in Medicine and Biology 17th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 1995), abstract 2.3.2.14.

J. Chang, R. L. Barbour, H. Graber, R. Aronson, “Fluorescence optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, M. A. Fiddy, eds., Proc. SPIE2570, 59–72 (1995).
[CrossRef]

Barbour, R. L.

J. Chang, H. L. Graber, R. L. Barbour, “Dependence of optical diffusion tomography image quality on image operator and noise,” in Conference Record of the 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1524–1528.

J. Chang, H. Graber, R. Aronson, R. L. Barbour, “Fluorescence imaging using transport-theory-based imaging operators,” in 1995 IEEE Engineering in Medicine and Biology 17th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 1995), abstract 2.3.2.14.

J. Chang, R. L. Barbour, H. Graber, R. Aronson, “Fluorescence optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, M. A. Fiddy, eds., Proc. SPIE2570, 59–72 (1995).
[CrossRef]

Berger, M. J.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

Boas, D. A.

Chance, B.

Chang, J.

J. Chang, R. L. Barbour, H. Graber, R. Aronson, “Fluorescence optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, M. A. Fiddy, eds., Proc. SPIE2570, 59–72 (1995).
[CrossRef]

J. Chang, H. L. Graber, R. L. Barbour, “Dependence of optical diffusion tomography image quality on image operator and noise,” in Conference Record of the 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1524–1528.

J. Chang, H. Graber, R. Aronson, R. L. Barbour, “Fluorescence imaging using transport-theory-based imaging operators,” in 1995 IEEE Engineering in Medicine and Biology 17th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 1995), abstract 2.3.2.14.

Gill, P. E.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

Graber, H.

J. Chang, H. Graber, R. Aronson, R. L. Barbour, “Fluorescence imaging using transport-theory-based imaging operators,” in 1995 IEEE Engineering in Medicine and Biology 17th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 1995), abstract 2.3.2.14.

J. Chang, R. L. Barbour, H. Graber, R. Aronson, “Fluorescence optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, M. A. Fiddy, eds., Proc. SPIE2570, 59–72 (1995).
[CrossRef]

Graber, H. L.

J. Chang, H. L. Graber, R. L. Barbour, “Dependence of optical diffusion tomography image quality on image operator and noise,” in Conference Record of the 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1524–1528.

Kak, A. C.

A. H. Anderson, A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imag. 6, 81–94 (1984).

Kak, A. V.

A. V. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), Chap. 7, pp. 285–292.

Kellerer, A. M.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

Lakowicz, J. R.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983), Chap. 1, pp. 1–15.

Li, X. D.

Moes, C. J. M.

Murray, W.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

O’Leary, M. A.

Paithankar, Y.

Y. Paithankar, E. M. Sevick-Muraca, “Fluorescence lifetime imaging with frequency-domain photon migration measurement,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996), pp. 155–157.

Prahl, S. A.

Roesch, W. C.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

Rossi, H. H.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

Sevick-Muraca, E. M.

Y. Paithankar, E. M. Sevick-Muraca, “Fluorescence lifetime imaging with frequency-domain photon migration measurement,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996), pp. 155–157.

Slaney, M.

A. V. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), Chap. 7, pp. 285–292.

Spencer, L. V.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

van de Hulst, H. C.

H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 1, Chap. 3, pp. 16–23.

van Gemert, M. J. C.

van Marle, J.

van Staveren, H. J.

Wright, M. H.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

Yodh, A. G.

Zaider, M. A.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

Appl. Opt. (1)

Opt. Lett. (1)

Ultrason. Imag. (1)

A. H. Anderson, A. C. Kak, “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the ART algorithm,” Ultrason. Imag. 6, 81–94 (1984).

Other (14)

A. V. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (Institute of Electrical and Electronics Engineers, New York, 1988), Chap. 7, pp. 285–292.

H. H. Rossi, R. G. Alsmiller, M. J. Berger, A. M. Kellerer, W. C. Roesch, L. V. Spencer, M. A. Zaider, Conceptual Basis for Calculations of Absorbed-Dose Distribution, , National Council for Radiation Protection, Bethsda, Md., 1991).

H. C. van de Hulst, Multiple Light Scattering: Tables, Formulas, and Applications (Academic, New York, 1980), Vol. 1, Chap. 3, pp. 16–23.

J. Chang, R. Aronson, H. L. Graber, R. L. Barbour, “Imaging diffusive media using time-independent and time-harmonic sources: dependence of image quality on imaging algorithms, target volume, weight matrix, and view angles,” Ref. 3, pp. 448–464.

J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Plenum, New York, 1983), Chap. 1, pp. 1–15.

G. J. Müller, B. Chance, R. R. Alfano, S. R. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. R. Masters, S. Svanberg, P. van der Zee, eds., Medical Optical Tomography: Functional Imaging and Monitoring, Vol. IS11 of Institute Series of SPIE Optical Engineering (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993).

R. R. Alfano, ed., Advances in Optical Imaging, Vol. 21 of OSA Proceedings Series (Optical Society of America, Washington, D.C., 1994).

B. Chance, R. R. Alfano, eds., Optical Tomography: Photon Migration and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, Proc. SPIE2389, 2–874 (1995).

J. Chang, H. Graber, R. Aronson, R. L. Barbour, “Fluorescence imaging using transport-theory-based imaging operators,” in 1995 IEEE Engineering in Medicine and Biology 17th Annual Conference (Institute of Electrical and Electronics Engineers, New York, 1995), abstract 2.3.2.14.

J. Chang, R. L. Barbour, H. Graber, R. Aronson, “Fluorescence optical tomography,” in Experimental and Numerical Methods for Solving Ill-Posed Inverse Problems: Medical and Nonmedical Applications, R. L. Barbour, M. J. Carvlin, M. A. Fiddy, eds., Proc. SPIE2570, 59–72 (1995).
[CrossRef]

Y. Paithankar, E. M. Sevick-Muraca, “Fluorescence lifetime imaging with frequency-domain photon migration measurement,” in Biomedical Optical Spectroscopy and Diagnostics, Vol. 3 of Trends in Optics and Photonics (Optical Society of America, Washington, D.C., 1996), pp. 155–157.

P. E. Gill, W. Murray, M. H. Wright, Practical Optimization (Academic, New York, 1981).

J. Chang, H. L. Graber, R. L. Barbour, “Dependence of optical diffusion tomography image quality on image operator and noise,” in Conference Record of the 1995 IEEE Nuclear Science Symposium and Medical Imaging Conference (Institute of Electrical and Electronics Engineers, New York, 1996), pp. 1524–1528.

J. Chang, H. L. Graber, R. L. Barbour, “Image reconstruction of dense scattering media from CW sources using constrained CGD and a matrix rescaling technique,” Ref. 3, pp. 682–691.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (7)

Fig. 1
Fig. 1

Sketches of (A) the source–detector ring and (B) the phantom structure used for the diffusion computations.

Fig. 2
Fig. 2

(A) Tissue phantom for the experiment; one balloon was suspended in the cylinder. (B) Source and detector configurations.

Fig. 3
Fig. 3

(A) Schematic of two-dimensional reconstruction with translational invariance assumed along the z axis. The cylindrical coordinate system used to discretize the phantom is shown in (B).

Fig. 4
Fig. 4

(A) γμT,12 images reconstructed from the first set of computed data at the dc frequency. (B)–(D) Reconstructed images of the mean lifetime derived from the parts of the unknowns in Eq. (11) from the first set of computed data as labeled, after 10, 100, and 1000 iterations. The reconstruction algorithm used was CGD, the modulation frequency was 100 MHz, and concentration correction was used.

Fig. 5
Fig. 5

(A) γμT,12 images reconstructed from the second set of computed data at the dc frequency. (B)–(D) reconstructed images of the mean lifetime derived from parts of the unknowns in Eq. (11) from the second set of computed data as labeled, after 10, 100, and 1000 iterations. The reconstruction algorithm used was CGD, the modulation frequency was 100 MHz, and concentration correction was used.

Fig. 6
Fig. 6

Reconstructed images of the mean lifetime derived, without the concentration correction, from the parts of unknowns in Eq. (11) as labeled, from the second set of computed data, after 10, 100, and 1000 iterations. The reconstruction algorithm used was CGD, and the modulation frequency was 100 MHz.

Fig. 7
Fig. 7

Reconstruction results obtained from the experimental dc data by the SART after the number of iterations shown. The target is also shown.

Equations (26)

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

1cdϕ1dt+Ω·ϕ1+(μT,1+μT,12)ϕ1=q1+4π μs,1(Ω·Ω)ϕ1dΩ,
1cdϕ2dt+Ω·ϕ2+μT,2ϕ2=q2+4π μs,2(Ω·Ω)ϕ2dΩ,
dNgdt=-ΣT,12 ϕ¯1Ng+1τNe,
q2=γ4πτNe,
R=v4π r2v 4π q2G2(r, Ω; r, Ω; t)dΩd3rdΩd3r=14πvγτNeϕ¯2+d3r,
R˜=14πvγτN˜ϕ¯˜2+d3r,
(1+jωτ)N˜g+τΣT,122πϕ¯˜1N˜g=2πN0δ(ω),
N˜e=2πN0δ(ω)-N˜g,
N˜g(0)=2πN0(1-τΣT,12ϕ¯10)δ(0),
N˜g(ω0)=-N˜e(ω0)=-2πτΣT,12N0ϕ¯10η1+jω0τδ(0).
N˜g(0)=2πN01+τΣT,12ϕ¯10δ(0)×2(1+τΣT,12ϕ¯10)2+2(ω0τ)22(1+τΣT,12ϕ¯10)2+2(ω0τ)2-(τΣT,12ηϕ¯10)2,
N˜g(ω0)=-N˜s(ω0)=2πN01+τΣT,12ϕ¯10δ(0)×-2τΣT,12ϕ¯10η(1+τΣT,12ϕ¯10-jω0τ)2(1+τΣT,12ϕ¯10)2+2(ω0τ)2-(τΣT,12ηϕ¯10)2.
N˜e=τΣT,12N01+τΣT,12ϕ¯10ϕ¯˜1=τΣT,12Ngϕ¯˜1.
R˜=14πv ϕ¯˜1ϕ¯˜2+(γΣT,12Ng)d3r=v w(γΣT,12Ng)d3r=v wγτΣT,12N01+τΣT,12ϕ¯10d3r,
R˜=v w1-jω0τ1+ω02τ2d3r,
R˜=vw[2η(1+τΣT,12ϕ¯10-jω0τ)]d3r2(1+τΣT,12ϕ¯10)2+2(ω0τ)2-(τΣT,12ϕ¯10η)2,
dNgdt=-ΣT,12ϕ¯1(Ng-Ne2)+1τNe1-(Ng-Ne1)ωΣT,2ϕ¯2dω,
dNe1dt=1τNe2-1τNe1+(Ng-Ne1)ωΣT,2ϕ¯2dω,
dNe2dt=ΣT,12ϕ¯1(Ng-Ne2)-1τNe2,
ddtNgNe1=-2ΣT,12ϕ¯1(τ-1-ΣT,12ϕ¯1)-τ-1-(τ-1+τ-1)NgNe1+ΣT,12ϕ¯1N0τ-1N0.
2πN0δ(ω)=τΣT,12ϕ¯10[ηN˜g(ω-ω0)+ηN˜g(ω+ω0)]+(1+τΣT,12ϕ¯10+jωτ)N˜g(ω).
2πN0δ(0)=(1+τΣT,12ϕ¯10)N˜g(0)+τΣT,12ϕ¯10[ηN˜g(-ω0)+ηN˜g(ω0)].
R[ηN˜g(ω0)]=2πN0δ(0)+(1+τΣT,12ϕ¯10)N˜g(0)2τΣT,12ϕ¯10.
(1+τΣT,12ϕ¯10+jω0τ)N˜g(ω0)+τΣT,12ϕ¯10[ηN˜g(0)+ηN˜g(2ω0)]=0.
N˜g(ω0)-τΣT,12ϕ¯10ηN˜g(0)1+τΣT,12ϕ¯10+jω0τ,
R[ηN˜g(ω0)]-τΣT,12ϕ¯10(η/2)2(1+τΣT,12ϕ¯10)N˜g(0)(1+τΣT,12ϕ¯10)2+(ω0τ)2.

Metrics