OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 31, Iss. 3 — Mar. 1, 2014
  • pp: 460–469

Forward solvers for photon migration in the presence of highly and totally absorbing objects embedded inside diffusive media

Angelo Sassaroli, Antonio Pifferi, Davide Contini, Alessandro Torricelli, Lorenzo Spinelli, Heidrun Wabnitz, Paola Di Ninni, Giovanni Zaccanti, and Fabrizio Martelli  »View Author Affiliations


JOSA A, Vol. 31, Issue 3, pp. 460-469 (2014)
http://dx.doi.org/10.1364/JOSAA.31.000460


View Full Text Article

Enhanced HTML    Acrobat PDF (1510 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

In this paper, after a critical review of the literature, we present two forward solvers and a new methodology for description of photon migration in the presence of totally absorbing inclusions embedded in diffusive media in both time and CW domains. The first forward solver is a heuristic approach based on a higher order perturbation theory applied to the diffusion equation (DE) [denoted eighth-order perturbation theory (EOPT)]. The second forward solver [denoted eighth-order perturbation theory with the equivalence relation (EOPTER) ] is obtained by combining the EOPT solver with the adoption of the equivalence relation (ER) [J. Biomed. Opt. 18, 066014 (2013)]. These forward solvers can possibly overcome some evident limitations of previous approaches like the theory behind the so-called banana-shape regions or exact analytical solutions of the DE in the presence of highly or totally absorbing inclusions. We also propose the ER to reformulate the problem of a totally absorbing inclusion in terms of another inclusion having a finite absorption contrast and a re-scaled volume. For instance, we have shown how this approach can indeed be used to simulate black inclusions with the Born approximation. By means of comparisons with the results of Monte Carlo simulations, we have shown that the EOPTER solver can model totally absorbing inclusions with an error smaller than about 10%, whereas the EOPT solver shows an error smaller than about 20%, showing a performance largely better than that observed with solvers proposed previously.

© 2014 Optical Society of America

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
(290.1990) Scattering : Diffusion
(290.7050) Scattering : Turbid media
(300.1030) Spectroscopy : Absorption

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: October 4, 2013
Revised Manuscript: December 13, 2013
Manuscript Accepted: December 13, 2013
Published: February 5, 2014

Virtual Issues
Vol. 9, Iss. 5 Virtual Journal for Biomedical Optics

Citation
Angelo Sassaroli, Antonio Pifferi, Davide Contini, Alessandro Torricelli, Lorenzo Spinelli, Heidrun Wabnitz, Paola Di Ninni, Giovanni Zaccanti, and Fabrizio Martelli, "Forward solvers for photon migration in the presence of highly and totally absorbing objects embedded inside diffusive media," J. Opt. Soc. Am. A 31, 460-469 (2014)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-3-460


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. 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]
  2. A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, R. Cubeddu, and G. Danesini, “Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multiwavelength time-resolved optical mammography,” Opt. Express 11, 853–867 (2003). [CrossRef]
  3. R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, “Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI,” Breast Cancer Res. Treat. 32, 1128–1139 (2005).
  4. M. R. Stankovic, D. Maulik, W. Rosenfeld, P. G. Stubblefield, A. D. Kofinas, E. Gratton, M. A. Franceschini, S. Fantini, and D. M. Hueber, “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage—a newborn piglet study,” J. Matern. Fetal Med. 9, 142–149 (2000).
  5. A. Amelink, T. Christiaanse, and H. J. C. M. Sterenborg, “Effect of hemoglobin extinction spectra on optical spectroscopic measurements of blood oxygen saturation,” Opt. Lett. 34, 1525–1527 (2009). [CrossRef]
  6. S. Feng, F. Zeng, and B. Chance, “Photon migration in the presence of a single defect: a perturbation analysis,” Appl. Opt. 34, 3826–3837 (1995). [CrossRef]
  7. X. D. Zhu, S. Wei, S. C. Feng, and B. Chance, “Analysis of a diffuse-photon-density wave in multiple-scattering media in the presence of a small spherical object,” J. Opt. Soc. Am. A 13, 494–499 (1996). [CrossRef]
  8. F. Martelli, A. Pifferi, D. Contini, L. Spinelli, A. Torricelli, H. Wabnitz, R. Macdonald, A. Sassaroli, and G. Zaccanti, “Phantoms for diffuse optical imaging based on totally absorbing objects. Part I: basic concepts,” J. Biomed. Opt. 18, 066014 (2013). [CrossRef]
  9. A. Wabnitz, A. Jelzow, M. Mazurenka, O. Steinkellner, R. Macdonald, A. Pifferi, A. Torricelli, D. Contini, L. Zucchelli, R. Cubeddu, L. Spinelli, D. Milej, N. Zolek, M. Kacprzak, P. Sawosz, A. Liebert, S. Magazov, J. Hebden, F. Martelli, P. Di Ninni, and G. Zaccanti, “Performance assessment of time-domain optical brain imagers: a multi-laboratory study,” Proc. SPIE 8583, 85830L (2013). [CrossRef]
  10. D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994). [CrossRef]
  11. M. R. Ostermeyer and S. L. Jacques, “Perturbation theory for diffuse light transport in complex biological tissues,” J. Opt. Soc. Am. A 14, 255–261 (1997). [CrossRef]
  12. S. Carraresi, T. S. M. Shatir, F. Martelli, and G. Zaccanti, “Accuracy of a perturbation model to predict the effect of scattering and absorbing inhomogeneities on photon migration,” Appl. Opt. 40, 4622–4632 (2001). [CrossRef]
  13. L. Spinelli, A. Torricelli, A. Pifferi, P. Taroni, and R. Cubeddu, “Experimental test of a perturbation model for time-resolved imaging in diffusive media,” Appl. Opt. 42, 3145–3153 (2003). [CrossRef]
  14. J. C. J. Paasschens and G. W. ’t Hooft, “Influence of boundaries on the imaging of objects in turbid media,” J. Opt. Soc. Am. A 15, 1797–1812 (1998). [CrossRef]
  15. F. Martelli, S. Del Bianco, A. Ismaelli, and G. Zaccanti, Light Propagation through Biological Tissue and Other Diffusive Media (SPIE, 2010).
  16. 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. A 23, 2105–2118 (2006). [CrossRef]
  17. 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. II. Continuous-wave results,” J. Opt. Soc. Am. A 23, 2119–2131 (2006). [CrossRef]
  18. 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]
  19. 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. A 27, 1723–1742 (2010). [CrossRef]
  20. R. Graaff and K. Rinzema, “Practical improvements on photon diffusion theory: application to isotropic scattering,” Phys. Med. Biol. 46, 3043–3050 (2001). [CrossRef]
  21. J. D. Jackson, Classical Electrodynamics (Wiley, 1962).
  22. J. C. J. Paasschens, “Solution of the time-dependent Boltzmann equation,” Phys. Rev. E 56, 1135–1141 (1997). [CrossRef]
  23. 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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited