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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 3, Iss. 1 — Jan. 1, 2012
  • pp: 26–36

Perturbative forward solver software for small localized fluorophores in tissue

F. Martelli, S. Del Bianco, and P. Di Ninni  »View Author Affiliations


Biomedical Optics Express, Vol. 3, Issue 1, pp. 26-36 (2012)
http://dx.doi.org/10.1364/BOE.3.000026


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Abstract

In this paper a forward solver software for the time domain and the CW domain based on the Born approximation for simulating the effect of small localized fluorophores embedded in a non-fluorescent biological tissue is proposed. The fluorescence emission is treated with a mathematical model that describes the migration of photons from the source to the fluorophore and of emitted fluorescent photons from the fluorophore to the detector for all those geometries for which Green’s functions are available. Subroutines written in FORTRAN that can be used for calculating the fluorescent signal for the infinite medium and for the slab are provided with a linked file. With these subroutines, quantities such as reflectance, transmittance, and fluence rate can be calculated.

© 2011 OSA

OCIS Codes
(170.3660) Medical optics and biotechnology : Light propagation in tissues
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(170.5280) Medical optics and biotechnology : Photon migration
(170.6280) Medical optics and biotechnology : Spectroscopy, fluorescence and luminescence

ToC Category:
Optics of Tissue and Turbid Media

History
Original Manuscript: September 9, 2011
Revised Manuscript: November 7, 2011
Manuscript Accepted: November 8, 2011
Published: December 2, 2011

Citation
F. Martelli, S. Del Bianco, and P. Di Ninni, "Perturbative forward solver software for small localized fluorophores in tissue," Biomed. Opt. Express 3, 26-36 (2012)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-1-26


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References

  1. S. Andersson-Engels and B. C. Wilson, “In vivo fluorescence in clinical oncology: fundamental and practical issues,” J. Cell. Pharmacol.3, 66–79 (1992).
  2. D. R. Braichotte, J. F. Savary, P. Monnier, and H. E. van den Bergh, “Optimizing light dosimetry in photodynamic theraphy of early stage carcinomas of the esophagus using fluorescence spectroscopy,” Laser Surg. Med.19, 340–346 (1996). [CrossRef]
  3. I. J. Bigio and J. R. Mourant, “Ultraviolet and visible spectroscopies for tissue diagnostics: fluorescence spectroscopy and elastic-scattering spectroscopy,” Phys. Med. Biol.42, 803–814 (1997). [CrossRef] [PubMed]
  4. G. A. Wagnieres, W. M. Star, and B. C. Wilson, “In vivo fluorescence spectroscopy and imaging for oncological applications,” Photochem. Photobiol.68, 603–632 (1998). [PubMed]
  5. A. Liebert, H. Wabnitz, H. Obrig, R. Erdmann, M. Möller, R. Macdonald, H. Rinneberg, A. Villinger, and J. Steinbrink, “Non-invasive detection of fluorescence from exogeneous chromophores in the adult human brain,” NeuroImage31, 600–608 (2006). [CrossRef] [PubMed]
  6. R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D: Appl. Phys.35, R61–R76 (2002). [CrossRef]
  7. V. Ntziachristos, C. Bremer, and R. Weissleder, “Fluorescence imaging with near-infrared light: new technological advances that enable in vivo molecular imaging,” Eur. Radiol.13, 195–208 (2002).
  8. J. R. Lakowicz, Principles of Fluorescence Spectroscopy (Springer, New York, 2006). [CrossRef]
  9. M. Patterson and B. Pogue, “Mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissues,” Appl. Opt.33, 1963–1974 (1994). [CrossRef] [PubMed]
  10. C. L. Hutchinson, J. R. Lakowicz, and E. Sevick-Muraca, “Fluorescence lifetime-based sensing in tissues: A computational study,” NeuroImage68, 1574–1582 (1995).
  11. D. E. Hyde, T. J. Farrel, M. Patterson, and B. Wilson, “A diffusion theory model of spatially resolved fluorescence from depth-dependent fluorophore concentrations,” Phys. Med. Biol.46, 369–383 (2001). [CrossRef] [PubMed]
  12. M. Sadoqi, P. Riseborough, and S. Kumar, “Analytical models of time resolved fluorescence spectroscopy in tissues,” Phys. Med. Biol.46, 2725–2743 (2001). [CrossRef] [PubMed]
  13. D. Hattery, V. Chernomordik, M. Loew, I. Gannot, and A. Gandjbakhche, “Analytical solutions for time-resolved imaging in a turbid medium such as tissue,” Opt. Express16, 13188–13202 (2001).
  14. Y. Lu, B. Zhu, H. Shen, J. C. Rasmussen, G. Wang, and E. M. Sevick-Muraca, “A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging,” Phys. Med. Biol.55, 4625–4645 (2010). [CrossRef] [PubMed]
  15. J. Swartling, A. Pifferi, A. M. K. Enejder, and S. Andersson-Engels, “Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues,” J. Opt. Soc. Am. A20, 714–727 (2003). [CrossRef]
  16. A. Liebert, H. Wabnitz, N. Żołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express16, 13188–13202 (2008). [CrossRef] [PubMed]
  17. A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202, 323–345 (2005). [CrossRef]
  18. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett.21, 158–160 (1996). [CrossRef]
  19. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett.26, 893–895 (2001). [CrossRef]
  20. X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Fluorescent diffuse photon density waves in homogeneous and heterogenous turbid media: analytic solutions and applications,” Appl. Opt.35, 3746–3758 (1996). [CrossRef] [PubMed]
  21. F. Martelli, S. Del Bianco, A. Ismaelli, and G. ZaccantiLight Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Software (SPIE, Bellingham, 2010). [CrossRef] [PubMed]
  22. A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomography,” Appl. Opt.42, 3081–3094 (2003). [CrossRef] [PubMed]
  23. H. Jiang, “Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations,” Appl. Opt.37, 5337–5343 (1998). [CrossRef]
  24. L. Zhang, G. Gao, H. He, and H. Zhao, “Three-dimentional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express16, 7214–7222 (2008). [CrossRef] [PubMed]
  25. A. D. Klose and A. H. Hielscher, “Fluorescence tomography with simulated data based on the equation of radiative tranfer,” Opt. Lett.28, 1019–1021 (2003). [CrossRef] [PubMed]
  26. B. Wassermann, “Limits of high-order perturbation theory in time-domain optical mammography,” Phys. Rev. E74, 031908 (2006). [CrossRef]
  27. D. Grosenick, A. Kummrow, R. Macdonald, P. M. Schlag, and H. Rinneberg, “Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast equivalent phantoms and optical mammograms,” Phys. Rev. E76, 061908 (2007). [CrossRef]
  28. A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. I. Theory,” J. Opt. Soc. Am. A48, 2105–2118 (2006). [CrossRef]
  29. T. Durduran, R. Choe, W. B. Baker, and A. G. Yodh, “Diffuse optics for tissue monitoring and tomography,” Rep. Prog. Phys.73, 076701 (2010). [CrossRef]
  30. A. Kienle and M. S. Patterson, “Improved solution of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A14, 246–524 (1997). [CrossRef]
  31. V. Venugopalan, J. S. You, and B. J. Tromberg, “Radiative transport in the diffusion approximation: An extention for highly absorbing media and small source-detector separations,” Phys. Rev. E58, 2395–2407 (1998). [CrossRef]
  32. R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol.46, 3043–3050 (2001). [CrossRef] [PubMed]
  33. M. Chu, K. Vishwanath, A. D. Klose, and H. Dehghani, “Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations,” Phys. Med. Biol.54, 2493–2509 (2009). [CrossRef] [PubMed]
  34. A. Liemert and A. Kienle, “Analytical solutions of the simplified spherical harmonics equations,” Opt. Lett.35, 3507–3509 (2010). [CrossRef] [PubMed]
  35. P. N. Reinersman and K. L. Carder, “Hybrid numerical method for solution of the radiative transfer equation in one, two, or three dimensions,” Appl. Opt.43, 2734–2743 (2004). [CrossRef] [PubMed]
  36. T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50, 4913–4930 (2005). [CrossRef] [PubMed]
  37. F. Martelli, A. Sassaroli, A. Pifferi, A. Torricelli, L. Spinelli, and G. Zaccanti, “Heuristic Green’s function of the time dependent radiative transfer equation for a semi-infinite medium,” Opt. Express15, 18168–18175 (2007). [CrossRef] [PubMed]
  38. J. C. J. Paasschens, “Solution of the time-dependent Boltzmann equation,” Phys. Rev. E56, 1135–1141 (1997). [CrossRef]
  39. M. Machida, G. Y. Panasyuk, J. C. Schotland, and V. A. Markel, “The Greens function for the radiative transport equation in the slab geometry,” J. Phys. A: Math. Theor.43, 065402 (2010). [CrossRef]
  40. A. Liemert and A. Kienle, “Analytical solution of the radiative transfer equation for the infinite-space fluence,” Phys. Rev. A83, 015804 (2011). [CrossRef]
  41. A. Sassaroli, F. Martelli, and S. Fantini, “Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries,” Appl. Opt.48, D62–D73 (2009). [CrossRef] [PubMed]
  42. A. Sassaroli, F. Martelli, and S. Fantini, “Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results,” J. Opt. Soc. Am. A27, 1723–1742 (2010). [CrossRef]
  43. A. Sassaroli, C. Blumetti, F. Martelli, L. Alianelli, D. Contini, A. Ismaelli, and G. Zaccanti, “Monte Carlo procedure for investigating light propagation and imaging of highly scattering media,” Appl. Opt.37, 7392–7400 (1998). [CrossRef]

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