OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 44, Iss. 6 — Feb. 20, 2005
  • pp: 876–886

Hybrid radiative-transfer–diffusion model for optical tomography

Tanja Tarvainen, Marko Vauhkonen, Ville Kolehmainen, and Jari P. Kaipio  »View Author Affiliations

Applied Optics, Vol. 44, Issue 6, pp. 876-886 (2005)

View Full Text Article

Enhanced HTML    Acrobat PDF (189 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A hybrid radiative-transfer–diffusion model for optical tomography is proposed. The light propagation is modeled with the radiative-transfer equation in the vicinity of the laser sources, and the diffusion approximation is used elsewhere in the domain. The solution of the radiative-transfer equation is used to construct a Dirichlet boundary condition for the diffusion approximation on a fictitious interface within the object. This boundary condition constitutes an approximative distributed source model for the diffusion approximation in the remaining area. The results from the proposed approach are compared with finite-element solutions of the radiative-transfer equation and the diffusion approximation and Monte Carlo simulation. The results show that the method improves the accuracy of the forward model compared with the conventional diffusion model.

© 2005 Optical Society of America

OCIS Codes
(100.3190) Image processing : Inverse problems
(170.5280) Medical optics and biotechnology : Photon migration
(170.6960) Medical optics and biotechnology : Tomography

Original Manuscript: December 11, 2003
Revised Manuscript: September 3, 2004
Manuscript Accepted: October 13, 2004
Published: February 20, 2005

Tanja Tarvainen, Marko Vauhkonen, Ville Kolehmainen, and Jari P. Kaipio, "Hybrid radiative-transfer–diffusion model for optical tomography," Appl. Opt. 44, 876-886 (2005)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. K. T. Moesta, S. Fantini, H. Jess, S. Totkas, M. A. Franceschini, M. Kaschke, P. M. Schlag, “Contrast features of breast cancer in frequency-domain laser scanning mammography,” J. Biomed. Opt. 3, 129–136 (1998). [CrossRef] [PubMed]
  2. H. Jess, H. Erdl, K. T. Moesta, S. Fantini, M. A. Franceschini, E. Gratton, “Intensity modulated breast imaging: technology and clinical pilot study results,” in Advances in Optical Imaging and Photon Migration, R. R. Alfano, J. G. Fujimoto, eds., Vol. 2 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 126–129.
  3. S. R. Arridge, M. Schweiger, “A general framework for iterative reconstruction algorithms in optical tomography, using a finite-element method,” in Computational Radiology and Imaging: Therapy and Diagnosis, C. Borgers, F. Natterer, eds., IMA Volumes in Mathematics and its Applications, Vol. 110 (Springer-Verlag, Berlin, 1998), pp. 45–70. [CrossRef]
  4. J. P. van Houten, D. A. Benaron, S. Splilman, D. K. Stevenson, “Imaging brain injury using time-resolved near-infrared light scanning,” Pediatr. Res. 39, 470–476 (1996). [CrossRef] [PubMed]
  5. J. S. Wyatt, M. Cope, D. T. Delpy, C. E. Richardson, A. D. Edwards, S. C. Wray, E. O. R. Reynolds, “Quantitation of cerebral blood volume in newborn infants by near-infrared spectroscopy,” J. Appl. Physiol. 68, 1086–1091 (1990).
  6. A. Villringer, B. Chance, “Noninvasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20, 435–442 (1997). [CrossRef] [PubMed]
  7. C. Hirth, H. Obrig, K. Villringer, A. Thiel, J. Bernarding, W. Muhhlnickel, H. Flor, U. Dirnagl, A. Villringer, “Noninvasive functional mapping of the human motor cortex using near-infrared spectroscopy,” NeuroReport7, 1977–1981 (1996). [CrossRef] [PubMed]
  8. K. R. Heereken, H. Obrig, R. Wenzel, K. Eberle, J. Ruben, K. Villringer, R. Kurth, A. Villringer, “Cerebral haemoglobin oxygenation during sustained visual stimulation—a near-infrared spectroscopy study,” Philos. Trans. R. Soc. London Ser. B 352, 743–750 (1997). [CrossRef]
  9. S. Prince, V. Kolehmainen, J. Kaipio, M. Franceschini, D. Boas, S. Arridge, “Time-series estimation of biological factors in optical diffusion tomography,” Phys. Med. Biol. 48, 1491–1504 (2003). [CrossRef] [PubMed]
  10. R. Williams, M. Beck, eds., Process Tomography, Principles, Techniques and Applications, (Butterworth-Heinemann, Oxford, 1995).
  11. V. Kolehmainen, S. Prince, S. Arridge, J. Kaipio, “State-estimation approach to the nonstationary optical tomography problem,” J. Opt. Soc. Am. A 20, 876–889 (2003). [CrossRef]
  12. S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999). [CrossRef]
  13. M. C. Case, P. F. Zweifel, Linear Transport Theory (Addison-Wesley, Reading, Mass., 1967).
  14. A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, New York, 1978), Vol. 1.
  15. J. P. Kaltenbach, M. Kaschke, “Frequency- and time-domain modeling of light transport in random media,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. Muller, B. Chance, R. Alfano, S. Arridge, J. Beuthan, E. Gratton, M. Kaschke, B. Masters, S. Svanberg, P. van der Zee, eds. (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1993), pp. 65–86.
  16. A. H. Hielscher, R. E. Alcouffe, R. L. Barbour, “Comparison of finite difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998). [CrossRef] [PubMed]
  17. L. Wang, S. L. Jacques, “Hybrid model of Monte Carlo simulation diffusion theory for light reflectance by turbid media,” J. Opt. Soc. Am. A 10, 1746–1752 (1993). [CrossRef]
  18. G. Alexandrakis, T. Farrell, M. Patterson, “Monte Carlo diffusion hybrid model for photon migration in a two-layer medium in the frequency domain,” Appl. Opt. 39, 2235–2244 (2000). [CrossRef]
  19. W. G. Tam, A. Zardecki, “Off-axis propagation of a laser beam in low visibility weather conditions,” Appl. Opt. 19, 2822–2827 (1980). [CrossRef] [PubMed]
  20. D. A. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1996).
  21. V. Kolehmainen, “Novel approaches to image reconstruction in diffusion tomography,” Ph.D. dissertation (University of Kuopio, Kuopio, Finland, 2001).
  22. O. Dorn, “A transport-back transport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998). [CrossRef]
  23. J. Heino, E. Somersalo, “Estimation of optical absorption in anisotropic background,” Inverse Probl. 18, 559–573 (2002). [CrossRef]
  24. L. G. Henyey, J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941). [CrossRef]
  25. J. Heino, S. R. Arridge, J. Sikora, E. Somersalo, “Anisotropic effects in highly scattering media,” Phys. Rev. E 68, 031908: 1–8, (2003). [CrossRef]
  26. J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999). [CrossRef]
  27. E. Amaldi, “The production and slowing down of neutrons,” in Encyclopedia of Physics, S. Flügge, ed., Vol. 38/2Neutrons and Related Gamma Ray Problems (Springer-Verlag, Berlin, 1959), pp. 1–659.
  28. R. A. J. Groenhuis, H. A. Ferwerda, J. J. T. Bosch, “Scattering and absorption of turbid materials determined from reflection measurements. Part 1: theory,” Appl. Opt. 22, 2456–2462 (1983). [CrossRef] [PubMed]
  29. M. Keijzer, W. M. Star, P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988). [CrossRef] [PubMed]
  30. M. Schweiger, S. R. Arridge, M. Hiraoka, D. T. Delpy, “The finite-element model for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779–1792 (1995). [CrossRef] [PubMed]
  31. S. R. Arridge, M. Schweiger, M. Hiraoka, D. T. Delpy, “A finite-element approach for modeling photon transport in tissue,” Med. Phys. 20, 299–309 (1993). [CrossRef] [PubMed]
  32. M. Kalos, P. Whitlock, Monte Carlo Methods (Wiley, New York, 1986). [CrossRef]
  33. H. Dehghani, S. R. Arridge, M. Schweiger, D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A 17, 1659–1667 (2000). [CrossRef]
  34. S. R. Arridge, H. Dehghani, M. Schweiger, E. Okada, “The finite-element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions,” Med. Phys. 27, 252–264 (2000). [CrossRef] [PubMed]
  35. J. Riley, H. Dehghani, M. Schweiger, S. R. Arridge, J. Ripoll, M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express 7, 462–467 (2000). [CrossRef] [PubMed]
  36. T. Hayashi, Y. Kashio, E. Okada, “Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region,” Appl. Opt. 42, 2888–2896 (2003). [CrossRef] [PubMed]
  37. G. Arfken, Mathematical Methods for Physicists (Academic, San Diego, 1985).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited