Abstract

Three-dimensional phosphorescence lifetime imaging is a novel method for the mapping of oxygen concentration in biological tissues. We present reconstruction techniques for recovering phosphorescent objects in highly scattering media based on the telegraph equation and two regularization methods, i.e., the Tikhonov—Phillips regularization and the maximum entropy method. Theoretical results are experimentally validated, and the reconstructed images of phosphorescent objects rendering oxygen maps in a layer are presented.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. Kress, Linear Integral Equations (Springer-Verlag, Berlin, 1989).
    [CrossRef]
  2. F. Natterer, F. Wubbeling, Mathematical Methods in Image Reconstruction (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
    [CrossRef]
  3. J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978).
    [CrossRef]
  4. M. Cutler, “Transillumination of the breast,” Surg. Gynecol. Obstet. 48, 721–728 (1929).
  5. U. Hampel, E. Schleicher, R. Freyer, “Volume image reconstruction for diffuse optical tomography,” Appl. Opt. 41, 3816–3826 (2002).
    [CrossRef] [PubMed]
  6. E. L. Hull, M. G. Nicholas, T. H. Foster, “Localization of luminescent inhomogeneities in turbud media with spatially resolved measurements of cw diffuse luminescent emittance,” Appl. Opt. 37, 2755–2765 (1998).
    [CrossRef]
  7. 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]
  8. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
    [CrossRef]
  9. J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
    [PubMed]
  10. W. L. Rumsey, J. M. Vanderkooi, D. F. Wilson, “Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue,” Science 241, 1649–1651 (1988).
    [CrossRef] [PubMed]
  11. S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
    [CrossRef] [PubMed]
  12. S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
    [CrossRef]
  13. M. Pawlowski, D. F. Wilson, “Monitoring of the oxygen pressure in the blood of live animals using the oxygen dependent quenching of phosphorescence,” Adv. Exp. Med. Biol. 316, 179–183 (1992).
    [CrossRef] [PubMed]
  14. R. D. Shonat, D. F. Wilson, C. E. Riva, M. Pawlowski, “Oxygen distribution in the retinal and choroidal vessels of the cat as measured by a new phosphorescence imaging method,” Appl. Opt. 31, 3711–3718 (1992).
    [CrossRef] [PubMed]
  15. D. F. Wilson, S. A. Vinogradov, “Tissue oxygen measurements using phosphorescence quenching,” in Handbook of Biomedical Fluorescence, M.-A. Mycek, B. W. Pogue, eds. (Marcel Dekker, New York, 2003), pp. 637–663.
  16. S. A. Vinogradov, D. F. Wilson, “Metallotetrabenzoporphyrins. New phosphorescent probes for oxygen measurements,” J. Chem. Soc. Perkin Trans. 2 2, 103–111 (1994).
  17. S. A. Vinogradov, D. F. Wilson, “Extended porphyrins—new IR phosphors for oxygen measurements,” Adv. Exp. Med. Biol. 411, 597–603 (1997).
    [CrossRef]
  18. O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
    [CrossRef]
  19. I. B. Rietveld, E. Kim, S. A. Vinogradov, “Dendrimers with tetrabenzoporphyrin cores: near infrared phosphors for in vivo oxygen imaging,” Tetrahedron 59, 3821–3831 (2003).
    [CrossRef]
  20. V. V. Rozhkov, M. Khajehpour, S. A. Vinogradov, “Luminescent Zn and Pd tetranaphthaloporphyrins,” Inorg. Chem. 42, 4253–4255 (2003).
    [CrossRef] [PubMed]
  21. O. S. Finikova, A. V. Cheprakov, S. A. Vinogradov, “Novel route to functionalized tetraaryl [2,3] tetranaphthaloporphyrins via oxidative aromatization,” J. Org. Chem. 68, 7517–7520 (2003).
    [CrossRef] [PubMed]
  22. V. Y. Soloviev, D. F. Wilson, S. A. Vinogradov, “Phosphorescence lifetime imaging in turbud media: the forward problem,” Appl. Opt. 42, 113–123 (2003).
    [CrossRef] [PubMed]
  23. G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
    [CrossRef]
  24. W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
    [CrossRef] [PubMed]
  25. T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
    [CrossRef] [PubMed]
  26. E. Shives, Y. Xu, H. Jiang, “Fluorescence lifetime tomography in turbid media based on an oxygen-sensitive dye,” Opt. Exp.10, 1557–1562 (2002), http://www.opticsexpress.org .
    [CrossRef]
  27. J. C. Schotland, V. A. Markel, “Inverse scattering with diffusive waves,” J. Opt. Soc. Am. A 18, 2767–2777 (2001).
    [CrossRef]
  28. V. A. Markel, J. C. Schotland, “Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas,” J. Opt. Soc. Am. A 18, 1336–1347 (2001).
    [CrossRef]
  29. V. A. Markel, J. C. Schotland, “Inverse problem in optical diffusion tomography. II. Role of boundary conditions,” J. Opt. Soc. Am. A 19, 558–565 (2002).
    [CrossRef]
  30. A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington, D.C., 1977).
  31. A. I. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).
  32. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).
  33. T. J. R. Hughes, The Finite Element Method (Dover, New York, 2000).
  34. A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Vol. 120 of Applied Mathematical Sciences (Springer, New York, 1996).
    [CrossRef]
  35. H. W. Engl, “On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems,” J. Approx. Theory 49, 55–63 (1987).
    [CrossRef]
  36. H. W. Engl, “Discrepancy principal for Tikhonov regularization of ill-posed problems leading to optimal convergence rates,” J. Optim. Theory Appl. 52, 209–215 (1987).
    [CrossRef]
  37. P. Blomgren, T. F. Chan, “Modular solvers for image restoration problems using the discrepancy principle,” Numer. Linear Algebra Appl. 9, 347–358 (2002).
    [CrossRef]
  38. S. A. Vinogradov, D. F. Wilson, “Recursive maximum entropy algorithm and its application to the luminescence lifetime distribution recovery,” Appl. Spectrosc. 54, 849–855 (2000).
    [CrossRef]
  39. H. Engl, A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 2000).
  40. H. W. Engl, G. Landl, “Convergence-rates for maximum-entropy regularization,” SIAM J. Numer. Anal. 30, 1509–1536 (1993).
    [CrossRef]
  41. G. Christakos, Modern Spatiotemporal Geostatistics (Oxford U. Press, London, UK, 2000).
  42. F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
    [CrossRef]
  43. T. L. Cornwell, K. F. Evans, “A simple maximum entropy deconvolution algorithm,” Astron. Astrophys. 143, 77–83 (1985).
  44. J. Skilling, R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Mon. Not. R. Astron. Soc. 211, 111–124 (1984).
  45. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannerly, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).
  46. V. A. Markel, J. C. Schotland, “Scanning paraxial optical tomography,” Opt. Lett. 27, 1123–1125 (2002).
    [CrossRef]
  47. V. A. Markel, J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
    [CrossRef]
  48. I. Dunphy, S. A. Vinogradov, D. F. Wilson, “Oxyphor R2 and G2: new phosphors for measuring oxygen by oxygen dependent quenching of phosphorescence,” Anal. Biochem. 310, 191–198 (2002).
    [CrossRef] [PubMed]

2003 (6)

I. B. Rietveld, E. Kim, S. A. Vinogradov, “Dendrimers with tetrabenzoporphyrin cores: near infrared phosphors for in vivo oxygen imaging,” Tetrahedron 59, 3821–3831 (2003).
[CrossRef]

V. V. Rozhkov, M. Khajehpour, S. A. Vinogradov, “Luminescent Zn and Pd tetranaphthaloporphyrins,” Inorg. Chem. 42, 4253–4255 (2003).
[CrossRef] [PubMed]

O. S. Finikova, A. V. Cheprakov, S. A. Vinogradov, “Novel route to functionalized tetraaryl [2,3] tetranaphthaloporphyrins via oxidative aromatization,” J. Org. Chem. 68, 7517–7520 (2003).
[CrossRef] [PubMed]

V. Y. Soloviev, D. F. Wilson, S. A. Vinogradov, “Phosphorescence lifetime imaging in turbud media: the forward problem,” Appl. Opt. 42, 113–123 (2003).
[CrossRef] [PubMed]

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

2002 (7)

V. A. Markel, J. C. Schotland, “Inverse problem in optical diffusion tomography. II. Role of boundary conditions,” J. Opt. Soc. Am. A 19, 558–565 (2002).
[CrossRef]

P. Blomgren, T. F. Chan, “Modular solvers for image restoration problems using the discrepancy principle,” Numer. Linear Algebra Appl. 9, 347–358 (2002).
[CrossRef]

V. A. Markel, J. C. Schotland, “Scanning paraxial optical tomography,” Opt. Lett. 27, 1123–1125 (2002).
[CrossRef]

V. A. Markel, J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
[CrossRef]

I. Dunphy, S. A. Vinogradov, D. F. Wilson, “Oxyphor R2 and G2: new phosphors for measuring oxygen by oxygen dependent quenching of phosphorescence,” Anal. Biochem. 310, 191–198 (2002).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

U. Hampel, E. Schleicher, R. Freyer, “Volume image reconstruction for diffuse optical tomography,” Appl. Opt. 41, 3816–3826 (2002).
[CrossRef] [PubMed]

2001 (4)

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
[CrossRef]

O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
[CrossRef]

J. C. Schotland, V. A. Markel, “Inverse scattering with diffusive waves,” J. Opt. Soc. Am. A 18, 2767–2777 (2001).
[CrossRef]

V. A. Markel, J. C. Schotland, “Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas,” J. Opt. Soc. Am. A 18, 1336–1347 (2001).
[CrossRef]

2000 (1)

1999 (2)

F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

1998 (1)

1997 (1)

S. A. Vinogradov, D. F. Wilson, “Extended porphyrins—new IR phosphors for oxygen measurements,” Adv. Exp. Med. Biol. 411, 597–603 (1997).
[CrossRef]

1996 (2)

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]

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

1994 (1)

S. A. Vinogradov, D. F. Wilson, “Metallotetrabenzoporphyrins. New phosphorescent probes for oxygen measurements,” J. Chem. Soc. Perkin Trans. 2 2, 103–111 (1994).

1993 (1)

H. W. Engl, G. Landl, “Convergence-rates for maximum-entropy regularization,” SIAM J. Numer. Anal. 30, 1509–1536 (1993).
[CrossRef]

1992 (2)

M. Pawlowski, D. F. Wilson, “Monitoring of the oxygen pressure in the blood of live animals using the oxygen dependent quenching of phosphorescence,” Adv. Exp. Med. Biol. 316, 179–183 (1992).
[CrossRef] [PubMed]

R. D. Shonat, D. F. Wilson, C. E. Riva, M. Pawlowski, “Oxygen distribution in the retinal and choroidal vessels of the cat as measured by a new phosphorescence imaging method,” Appl. Opt. 31, 3711–3718 (1992).
[CrossRef] [PubMed]

1988 (1)

W. L. Rumsey, J. M. Vanderkooi, D. F. Wilson, “Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue,” Science 241, 1649–1651 (1988).
[CrossRef] [PubMed]

1987 (3)

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
[PubMed]

H. W. Engl, “On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems,” J. Approx. Theory 49, 55–63 (1987).
[CrossRef]

H. W. Engl, “Discrepancy principal for Tikhonov regularization of ill-posed problems leading to optimal convergence rates,” J. Optim. Theory Appl. 52, 209–215 (1987).
[CrossRef]

1985 (1)

T. L. Cornwell, K. F. Evans, “A simple maximum entropy deconvolution algorithm,” Astron. Astrophys. 143, 77–83 (1985).

1984 (1)

J. Skilling, R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Mon. Not. R. Astron. Soc. 211, 111–124 (1984).

1978 (1)

J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978).
[CrossRef]

1929 (1)

M. Cutler, “Transillumination of the breast,” Surg. Gynecol. Obstet. 48, 721–728 (1929).

Arridge, S. R.

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

Arsenin, V. Y.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington, D.C., 1977).

Beletskaya, I. P.

O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
[CrossRef]

Blomgren, P.

P. Blomgren, T. F. Chan, “Modular solvers for image restoration problems using the discrepancy principle,” Numer. Linear Algebra Appl. 9, 347–358 (2002).
[CrossRef]

Boas, D. A.

Bryan, R. K.

J. Skilling, R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Mon. Not. R. Astron. Soc. 211, 111–124 (1984).

Campos Velho, H. F.

F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
[CrossRef]

Carvalho, J. C.

F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
[CrossRef]

Chan, T. F.

P. Blomgren, T. F. Chan, “Modular solvers for image restoration problems using the discrepancy principle,” Numer. Linear Algebra Appl. 9, 347–358 (2002).
[CrossRef]

Chance, B.

Cheprakov, A. V.

O. S. Finikova, A. V. Cheprakov, S. A. Vinogradov, “Novel route to functionalized tetraaryl [2,3] tetranaphthaloporphyrins via oxidative aromatization,” J. Org. Chem. 68, 7517–7520 (2003).
[CrossRef] [PubMed]

O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
[CrossRef]

Christakos, G.

G. Christakos, Modern Spatiotemporal Geostatistics (Oxford U. Press, London, UK, 2000).

Cornwell, T. L.

T. L. Cornwell, K. F. Evans, “A simple maximum entropy deconvolution algorithm,” Astron. Astrophys. 143, 77–83 (1985).

Creed, J.

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

Cutler, M.

M. Cutler, “Transillumination of the breast,” Surg. Gynecol. Obstet. 48, 721–728 (1929).

DeCampli, W. M.

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

Dugan, B. W.

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
[CrossRef]

Dunphy, I.

I. Dunphy, S. A. Vinogradov, D. F. Wilson, “Oxyphor R2 and G2: new phosphors for measuring oxygen by oxygen dependent quenching of phosphorescence,” Anal. Biochem. 310, 191–198 (2002).
[CrossRef] [PubMed]

Engl, H.

H. Engl, A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Engl, H. W.

H. W. Engl, G. Landl, “Convergence-rates for maximum-entropy regularization,” SIAM J. Numer. Anal. 30, 1509–1536 (1993).
[CrossRef]

H. W. Engl, “On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems,” J. Approx. Theory 49, 55–63 (1987).
[CrossRef]

H. W. Engl, “Discrepancy principal for Tikhonov regularization of ill-posed problems leading to optimal convergence rates,” J. Optim. Theory Appl. 52, 209–215 (1987).
[CrossRef]

Evans, K. F.

T. L. Cornwell, K. F. Evans, “A simple maximum entropy deconvolution algorithm,” Astron. Astrophys. 143, 77–83 (1985).

Evans, S. M.

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

Fernandez-Seara, M. A.

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
[CrossRef]

Ferreira, N. J.

F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
[CrossRef]

Finikova, O. S.

O. S. Finikova, A. V. Cheprakov, S. A. Vinogradov, “Novel route to functionalized tetraaryl [2,3] tetranaphthaloporphyrins via oxidative aromatization,” J. Org. Chem. 68, 7517–7520 (2003).
[CrossRef] [PubMed]

O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
[CrossRef]

Flannerly, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannerly, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Foster, T. H.

Freyer, R.

Greeley, W. J.

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

Green, T. J.

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
[PubMed]

Hampel, U.

Hughes, T. J. R.

T. J. R. Hughes, The Finite Element Method (Dover, New York, 2000).

Hull, E. L.

Ishimaru, A.

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

Jenkins, W. T.

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

Khajehpour, M.

V. V. Rozhkov, M. Khajehpour, S. A. Vinogradov, “Luminescent Zn and Pd tetranaphthaloporphyrins,” Inorg. Chem. 42, 4253–4255 (2003).
[CrossRef] [PubMed]

Khinchin, A. I.

A. I. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).

Kim, E.

I. B. Rietveld, E. Kim, S. A. Vinogradov, “Dendrimers with tetrabenzoporphyrin cores: near infrared phosphors for in vivo oxygen imaging,” Tetrahedron 59, 3821–3831 (2003).
[CrossRef]

Kirsch, A.

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Vol. 120 of Applied Mathematical Sciences (Springer, New York, 1996).
[CrossRef]

Knight, K.

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

Koch, C.

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

Kress, R.

R. Kress, Linear Integral Equations (Springer-Verlag, Berlin, 1989).
[CrossRef]

Landl, G.

H. W. Engl, G. Landl, “Convergence-rates for maximum-entropy regularization,” SIAM J. Numer. Anal. 30, 1509–1536 (1993).
[CrossRef]

Li, X. D.

Lo, L.-W.

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

Maniara, G.

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
[PubMed]

Markel, V. A.

McWhirter, J. G.

J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978).
[CrossRef]

Myung, R.

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

Natterer, F.

F. Natterer, F. Wubbeling, Mathematical Methods in Image Reconstruction (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

Neubauer, A.

H. Engl, A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 2000).

Nicholas, M. G.

O’Leary, M. A.

Pastuszko, A.

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

Pawlowski, M.

R. D. Shonat, D. F. Wilson, C. E. Riva, M. Pawlowski, “Oxygen distribution in the retinal and choroidal vessels of the cat as measured by a new phosphorescence imaging method,” Appl. Opt. 31, 3711–3718 (1992).
[CrossRef] [PubMed]

M. Pawlowski, D. F. Wilson, “Monitoring of the oxygen pressure in the blood of live animals using the oxygen dependent quenching of phosphorescence,” Adv. Exp. Med. Biol. 316, 179–183 (1992).
[CrossRef] [PubMed]

Pike, E. R.

J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978).
[CrossRef]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannerly, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Ramost, F. M.

F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
[CrossRef]

Rietveld, I. B.

I. B. Rietveld, E. Kim, S. A. Vinogradov, “Dendrimers with tetrabenzoporphyrin cores: near infrared phosphors for in vivo oxygen imaging,” Tetrahedron 59, 3821–3831 (2003).
[CrossRef]

Riva, C. E.

Rozhkov, V. V.

V. V. Rozhkov, M. Khajehpour, S. A. Vinogradov, “Luminescent Zn and Pd tetranaphthaloporphyrins,” Inorg. Chem. 42, 4253–4255 (2003).
[CrossRef] [PubMed]

Rumsey, W. L.

W. L. Rumsey, J. M. Vanderkooi, D. F. Wilson, “Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue,” Science 241, 1649–1651 (1988).
[CrossRef] [PubMed]

Schears, G.

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

Schleicher, E.

Schotland, J. C.

Schultz, S.

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

Shen, J.

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

Shonat, R. D.

Skilling, J.

J. Skilling, R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Mon. Not. R. Astron. Soc. 211, 111–124 (1984).

Soloviev, V. Y.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannerly, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Tikhonov, A. N.

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington, D.C., 1977).

Vanderkooi, J. M.

W. L. Rumsey, J. M. Vanderkooi, D. F. Wilson, “Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue,” Science 241, 1649–1651 (1988).
[CrossRef] [PubMed]

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
[PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannerly, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

Vinogradov, S. A.

O. S. Finikova, A. V. Cheprakov, S. A. Vinogradov, “Novel route to functionalized tetraaryl [2,3] tetranaphthaloporphyrins via oxidative aromatization,” J. Org. Chem. 68, 7517–7520 (2003).
[CrossRef] [PubMed]

V. V. Rozhkov, M. Khajehpour, S. A. Vinogradov, “Luminescent Zn and Pd tetranaphthaloporphyrins,” Inorg. Chem. 42, 4253–4255 (2003).
[CrossRef] [PubMed]

V. Y. Soloviev, D. F. Wilson, S. A. Vinogradov, “Phosphorescence lifetime imaging in turbud media: the forward problem,” Appl. Opt. 42, 113–123 (2003).
[CrossRef] [PubMed]

I. B. Rietveld, E. Kim, S. A. Vinogradov, “Dendrimers with tetrabenzoporphyrin cores: near infrared phosphors for in vivo oxygen imaging,” Tetrahedron 59, 3821–3831 (2003).
[CrossRef]

I. Dunphy, S. A. Vinogradov, D. F. Wilson, “Oxyphor R2 and G2: new phosphors for measuring oxygen by oxygen dependent quenching of phosphorescence,” Anal. Biochem. 310, 191–198 (2002).
[CrossRef] [PubMed]

O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
[CrossRef]

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
[CrossRef]

S. A. Vinogradov, D. F. Wilson, “Recursive maximum entropy algorithm and its application to the luminescence lifetime distribution recovery,” Appl. Spectrosc. 54, 849–855 (2000).
[CrossRef]

S. A. Vinogradov, D. F. Wilson, “Extended porphyrins—new IR phosphors for oxygen measurements,” Adv. Exp. Med. Biol. 411, 597–603 (1997).
[CrossRef]

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

S. A. Vinogradov, D. F. Wilson, “Metallotetrabenzoporphyrins. New phosphorescent probes for oxygen measurements,” J. Chem. Soc. Perkin Trans. 2 2, 103–111 (1994).

D. F. Wilson, S. A. Vinogradov, “Tissue oxygen measurements using phosphorescence quenching,” in Handbook of Biomedical Fluorescence, M.-A. Mycek, B. W. Pogue, eds. (Marcel Dekker, New York, 2003), pp. 637–663.

Wilson, D. F.

V. Y. Soloviev, D. F. Wilson, S. A. Vinogradov, “Phosphorescence lifetime imaging in turbud media: the forward problem,” Appl. Opt. 42, 113–123 (2003).
[CrossRef] [PubMed]

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

I. Dunphy, S. A. Vinogradov, D. F. Wilson, “Oxyphor R2 and G2: new phosphors for measuring oxygen by oxygen dependent quenching of phosphorescence,” Anal. Biochem. 310, 191–198 (2002).
[CrossRef] [PubMed]

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
[CrossRef]

S. A. Vinogradov, D. F. Wilson, “Recursive maximum entropy algorithm and its application to the luminescence lifetime distribution recovery,” Appl. Spectrosc. 54, 849–855 (2000).
[CrossRef]

S. A. Vinogradov, D. F. Wilson, “Extended porphyrins—new IR phosphors for oxygen measurements,” Adv. Exp. Med. Biol. 411, 597–603 (1997).
[CrossRef]

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

S. A. Vinogradov, D. F. Wilson, “Metallotetrabenzoporphyrins. New phosphorescent probes for oxygen measurements,” J. Chem. Soc. Perkin Trans. 2 2, 103–111 (1994).

R. D. Shonat, D. F. Wilson, C. E. Riva, M. Pawlowski, “Oxygen distribution in the retinal and choroidal vessels of the cat as measured by a new phosphorescence imaging method,” Appl. Opt. 31, 3711–3718 (1992).
[CrossRef] [PubMed]

M. Pawlowski, D. F. Wilson, “Monitoring of the oxygen pressure in the blood of live animals using the oxygen dependent quenching of phosphorescence,” Adv. Exp. Med. Biol. 316, 179–183 (1992).
[CrossRef] [PubMed]

W. L. Rumsey, J. M. Vanderkooi, D. F. Wilson, “Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue,” Science 241, 1649–1651 (1988).
[CrossRef] [PubMed]

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
[PubMed]

D. F. Wilson, S. A. Vinogradov, “Tissue oxygen measurements using phosphorescence quenching,” in Handbook of Biomedical Fluorescence, M.-A. Mycek, B. W. Pogue, eds. (Marcel Dekker, New York, 2003), pp. 637–663.

Wubbeling, F.

F. Natterer, F. Wubbeling, Mathematical Methods in Image Reconstruction (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

Yodh, A. G.

Zaitseva, T. S.

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

Adv. Exp. Med. Biol. (4)

M. Pawlowski, D. F. Wilson, “Monitoring of the oxygen pressure in the blood of live animals using the oxygen dependent quenching of phosphorescence,” Adv. Exp. Med. Biol. 316, 179–183 (1992).
[CrossRef] [PubMed]

S. A. Vinogradov, D. F. Wilson, “Extended porphyrins—new IR phosphors for oxygen measurements,” Adv. Exp. Med. Biol. 411, 597–603 (1997).
[CrossRef]

G. Schears, J. Shen, J. Creed, T. S. Zaitseva, D. F. Wilson, W. J. Greeley, A. Pastuszko, “Brain oxygenation during cardiopulmonary bypass and circulatory arrest,” Adv. Exp. Med. Biol. 510, 325–330 (2002).
[CrossRef]

T. S. Zaitseva, J. Creed, G. Schears, J. Shen, K. Knight, D. F. Wilson, A. Pastuszko, “Effect of hypoxia and ischemia on expression of selected genes in brain of newborn piglets,” Adv. Exp. Med. Biol. 510, 319–324 (2003).
[CrossRef] [PubMed]

Anal. Biochem. (1)

I. Dunphy, S. A. Vinogradov, D. F. Wilson, “Oxyphor R2 and G2: new phosphors for measuring oxygen by oxygen dependent quenching of phosphorescence,” Anal. Biochem. 310, 191–198 (2002).
[CrossRef] [PubMed]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

V. A. Markel, J. C. Schotland, “Effects of sampling and limited data in optical tomography,” Appl. Phys. Lett. 81, 1180–1182 (2002).
[CrossRef]

Appl. Spectrosc. (1)

Astron. Astrophys. (1)

T. L. Cornwell, K. F. Evans, “A simple maximum entropy deconvolution algorithm,” Astron. Astrophys. 143, 77–83 (1985).

Biophys. J. (1)

S. A. Vinogradov, L.-W. Lo, W. T. Jenkins, S. M. Evans, C. Koch, D. F. Wilson, “Noninvasive imaging of the distribution in oxygen in tissue in vivo using near-infrared phosphors,” Biophys. J. 70, 1609–1617 (1996).
[CrossRef] [PubMed]

Chem. Commun. (1)

O. S. Finikova, A. V. Cheprakov, I. P. Beletskaya, S. A. Vinogradov, “An expedient synthesis of substituted tetraaryltetrabenzoporphyrins,” Chem. Commun. 3, 261–262 (2001).
[CrossRef]

Inorg. Chem. (1)

V. V. Rozhkov, M. Khajehpour, S. A. Vinogradov, “Luminescent Zn and Pd tetranaphthaloporphyrins,” Inorg. Chem. 42, 4253–4255 (2003).
[CrossRef] [PubMed]

Inverse Probl. (2)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

F. M. Ramost, H. F. Campos Velho, J. C. Carvalho, N. J. Ferreira, “Novel approach to entropic regularization,” Inverse Probl. 15, 1139–1148 (1999).
[CrossRef]

J. Approx. Theory (1)

H. W. Engl, “On the choice of the regularization parameter for iterated Tikhonov regularization of ill-posed problems,” J. Approx. Theory 49, 55–63 (1987).
[CrossRef]

J. Biol. Chem. (1)

J. M. Vanderkooi, G. Maniara, T. J. Green, D. F. Wilson, “An optical method for measurement of dioxygen concentration based on quenching of phosphorescence,” J. Biol. Chem. 262, 5476–5482 (1987).
[PubMed]

J. Chem. Soc. Perkin Trans. 2 (1)

S. A. Vinogradov, D. F. Wilson, “Metallotetrabenzoporphyrins. New phosphorescent probes for oxygen measurements,” J. Chem. Soc. Perkin Trans. 2 2, 103–111 (1994).

J. Opt. Soc. Am. A (3)

J. Optim. Theory Appl. (1)

H. W. Engl, “Discrepancy principal for Tikhonov regularization of ill-posed problems leading to optimal convergence rates,” J. Optim. Theory Appl. 52, 209–215 (1987).
[CrossRef]

J. Org. Chem. (1)

O. S. Finikova, A. V. Cheprakov, S. A. Vinogradov, “Novel route to functionalized tetraaryl [2,3] tetranaphthaloporphyrins via oxidative aromatization,” J. Org. Chem. 68, 7517–7520 (2003).
[CrossRef] [PubMed]

J. Phys. A (1)

J. G. McWhirter, E. R. Pike, “On the numerical inversion of the Laplace transform and similar Fredholm integral equations of the first kind,” J. Phys. A 11, 1729–1745 (1978).
[CrossRef]

J. Thorac. Cardiovasc. Surg. (1)

W. M. DeCampli, G. Schears, R. Myung, S. Schultz, J. Creed, A. Pastuszko, D. F. Wilson, “Tissue oxygen tension during regional low flow perfusion in neonates,” J. Thorac. Cardiovasc. Surg. 125, 472–480 (2003).
[CrossRef] [PubMed]

Mon. Not. R. Astron. Soc. (1)

J. Skilling, R. K. Bryan, “Maximum entropy image reconstruction: general algorithm,” Mon. Not. R. Astron. Soc. 211, 111–124 (1984).

Numer. Linear Algebra Appl. (1)

P. Blomgren, T. F. Chan, “Modular solvers for image restoration problems using the discrepancy principle,” Numer. Linear Algebra Appl. 9, 347–358 (2002).
[CrossRef]

Opt. Lett. (2)

Rev. Sci. Instrum. (1)

S. A. Vinogradov, M. A. Fernandez-Seara, B. W. Dugan, D. F. Wilson, “Frequency domain instrument for measuring phosphorescence lifetime distributions in heterogeneous samples,” Rev. Sci. Instrum. 72, 3396–3406 (2001).
[CrossRef]

Science (1)

W. L. Rumsey, J. M. Vanderkooi, D. F. Wilson, “Imaging of phosphorescence: a novel method for measuring the distribution of oxygen in perfused tissue,” Science 241, 1649–1651 (1988).
[CrossRef] [PubMed]

SIAM J. Numer. Anal. (1)

H. W. Engl, G. Landl, “Convergence-rates for maximum-entropy regularization,” SIAM J. Numer. Anal. 30, 1509–1536 (1993).
[CrossRef]

Surg. Gynecol. Obstet. (1)

M. Cutler, “Transillumination of the breast,” Surg. Gynecol. Obstet. 48, 721–728 (1929).

Tetrahedron (1)

I. B. Rietveld, E. Kim, S. A. Vinogradov, “Dendrimers with tetrabenzoporphyrin cores: near infrared phosphors for in vivo oxygen imaging,” Tetrahedron 59, 3821–3831 (2003).
[CrossRef]

Other (12)

D. F. Wilson, S. A. Vinogradov, “Tissue oxygen measurements using phosphorescence quenching,” in Handbook of Biomedical Fluorescence, M.-A. Mycek, B. W. Pogue, eds. (Marcel Dekker, New York, 2003), pp. 637–663.

R. Kress, Linear Integral Equations (Springer-Verlag, Berlin, 1989).
[CrossRef]

F. Natterer, F. Wubbeling, Mathematical Methods in Image Reconstruction (Society for Industrial and Applied Mathematics, Philadelphia, Pa., 2001).
[CrossRef]

E. Shives, Y. Xu, H. Jiang, “Fluorescence lifetime tomography in turbid media based on an oxygen-sensitive dye,” Opt. Exp.10, 1557–1562 (2002), http://www.opticsexpress.org .
[CrossRef]

A. N. Tikhonov, V. Y. Arsenin, Solution of Ill-Posed Problems (Winston, Washington, D.C., 1977).

A. I. Khinchin, Mathematical Foundations of Information Theory (Dover, New York, 1957).

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978).

T. J. R. Hughes, The Finite Element Method (Dover, New York, 2000).

A. Kirsch, An Introduction to the Mathematical Theory of Inverse Problems, Vol. 120 of Applied Mathematical Sciences (Springer, New York, 1996).
[CrossRef]

G. Christakos, Modern Spatiotemporal Geostatistics (Oxford U. Press, London, UK, 2000).

H. Engl, A. Neubauer, Regularization of Inverse Problems (Kluwer Academic, Dordrecht, The Netherlands, 2000).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannerly, Numerical Recipes in C. The Art of Scientific Computing (Cambridge U. Press, Cambridge, UK, 1992).

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 (6)

Fig. 1
Fig. 1

Simulated tomographic images of the phosphorescent point source in a 10-mm-thick layer. The coordinates of the source are (1, 1, 5). The sampling steps for the excitation source and the detector are 0.5 mm.

Fig. 2
Fig. 2

Simulated tomographic images of the phosphorescent point source in a 10-mm-thick layer. The coordinates of the source are (1, 1, 5). The sampling steps for the excitation source and the detector are 5 mm.

Fig. 3
Fig. 3

Schematic diagram of the experimental design used in this study.

Fig. 4
Fig. 4

Experimental images of a single hypoxic capsule hidden in the solution of the Intralipid. The image was reconstructed by CG implementation of the Tikhonov—Phillips regularization algorithm. The convergence was achieved after 190 iterations. The marks on the axes indicate real dimensions in millimeters. The black contour lines show the real shape of the capsule cross section in the slice.

Fig. 5
Fig. 5

Experimental images of a single hypoxic capsule hidden in the solution of the Intralipid. The image was reconstructed by CG implementation of the MEM. The convergence was achieved after seven iterations. The marks on the axes indicate real dimensions in millimeters. The black contour lines show the real shape of the capsule cross section in the slice.

Fig. 6
Fig. 6

Experimental images of two hypoxic capsules hidden in the solution of the Intralipid. The marks on the axes indicate real dimensions in millimeters. The black contour lines show the real shape of the capsules’ cross sections in the slice.

Equations (53)

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

I0/I=τ0/τ=1+KSVO2.
U=3λP0γ exp-iωt0G,
Gexp-χ|r-r0|4π|r-r0|+14πm0n=14 Fnmexp-χRnmRnm,
Fnm=1-2γRnmχZnm+γRnm2m+2, n=1, 3,Fnm=1-2γRnmχZnm+γRnm2m+1, n=2, 4,Z1m=2m+2zd-z+z0,Z2m=2m+2zd-z-z0,Z3m=2m+2zd+z-z0,Z4m=2mzd+z+z0,Rnm=x-x02+y-y02+Znm21/2,γ=α1+i ωαv,
χ=3γγ-αλ1/2.
1-λλv Ur, r0; t-t0
qτr, t-t=prθt-texp-t-t/τr,
Nr, r0; t=1-λλvhνdtd3rt0t Ur, r0; t-t0×qτr, t-tdt
λ2hν2Nr, r0; tU2r, r; t-t
Ur, r0, t-t0=Vd3r -tdt -tdt×Kr, r0, r; t, t0, t, t×qτr, t-t,
Kr, r0, r; t, t0, t, t=C0λ1λ2U1r, r0, t-t0U2r, r; t-t,
C0=1-λ1λ1v1 N0hν2.
Ur, r0; ω=exp-iωt0Vd3r×Kr, r0, r; ωqr; ω,
qr; ω=q0r1+iωτr,
U1r0, r; t-t0=U01r0, r1+a sinω0t-t0,
Ur, r0; ω0, t-t0=Vd3rK0r, r0, rq0r+aC0λ1λ2Vd3r×U01r, r0q0r×Imexpiω0t-t01+iω0τr×U2r, r; ω0,
K0r, r0, r=C0λ1λ2U01r0, rU02r, r.
ω0αv  1.
Ur, r0; ω0, t-t0=Vd3rK0r, r0, r×qr; ω0,t-t0,
qr; ω0, t-t0=q0rfω0,
fω0=1+a1+ω02τ2r1/2×sinω0t-t0-arctanω0τr.
Nijk=181+ξx1+ζy1+ηz,
ξx=2x-xi-1-xi/h:xxi-1, xi-2x-xi-xi+1/h:xxi, xi+10:xxi-1, xi+1,ζy=2y-yj-1-yj/h:yyj-1, yj-2y-yj-yj+1/h:yyj, yj+10:yyj-1, yj+1,ηz=2z-zk-1-zk/h:zzk-1, zk-2z-zk-zk+1/h:zzk, zk+10:zzk-1, zk+1.
Kr, r0, rijkrijkV Nijkξ, ζ, ηKr, r0, rijk,
qrrijkV\V Nijkξ, ζ, ηqrijk.
Ur, r0=rijkV\V Aijkr, r0qrijk
Aijkr, r0=h63rijkvertices Kr, r0, rijk+4 rijkedges Kr, r0, rijk+16 rijkfaces Kr, r0, rijk+64Kr, r0, rijk.
Um=n=0N-1 Amnqn,
AKL,
KqL=Vd3rVd3r0Vd3rKr, r0, r; ω0qr
4C0 maxl1 maxl2|q|L,
A4C0 maxl1 maxl2.
minqβ,δAqβ,δ-uδ2+βΩqβ,δ,
qβ,δ0; β,
Aqβ,δ-uδδ; β0.
minqβ,δAqβ,δ-uδ2+βqβ,δ2.
ATA+βIqβ,δ=ATuδ.
ϕβ=Aqβ,δ-uδ2-δ2.
βδAuδ-δ4C0δ maxl1 maxl2uδ-δ.
u=1Mm=0M-1 Ume,
an=1Mm=0M-1 Amn.
u=a, qβ,δ.
qnuan.
minqβ,δAqβ,δ-uδ2+βHqβ,δ.
H=-n=0N-1 qn lnqnqβ,δ1,
qβ,δ1=n=0N-1 qn.
ATAqβ,δ+βHqβ,δ=ATuδ.
ATA+βEqβ,δqβ,δ=ATuδ,
Enmqβ,δ=-δnm1qnlnqnqβ,δ1.
qi+1β,δ=ATA+βEqiβ,δ-1ATuδ.
qn,i+1=kvnkσkσk2+βEkkqk,im smkum,
qβ,δ=Bq,
Bnm=δnm-β kvnkvmkσk2+β.

Metrics