Skip to main content

Radiative transfer of luminescence light in biological tissue

  • Chapter
Light Scattering Reviews 4

Part of the book series: Springer Praxis Books ((ENVIRONSCI))

Abstract

Radiative transfer of light in biological tissue plays a vital part in in vivo biomedical optics. Tissue constitutes a highly scattering and absorbing medium for light at wavelengths of the visible and near-infrared spectrum, and its light-tissue interaction can be exploited not just for therapeutic but also for diagnostic purposes [13]. In biomedical optics, light sources are placed on top of the tissue surface, either in contact or non-contact, and illuminate the tissue. Optical images of the reflected or trans-illuminated light are taken, which subsequently provide valuable biomedical information about macroscopic tissue changes. These optically detected tissue changes are mostly based on the absorption contrast that is caused by intrinsic tissue chromophores. The optical contrast of the detected images is, however, relatively poor due to the multiple scattered light inside tissue. Optical imaging has already been utilized in clinical and pre-clinical practice in order to detect these macroscopic tissue changes. Advances have been made in, for example, studying brain function [4,5], optical mammography and detecting breast cancer [6,7], small animal (for example rodents) imaging [811], or in detecting the inflammatory progression of rheumatoid arthritis in finger joints [12].

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.R. Arridge: Optical tomography in medical imaging. Inv. Prob. 15, R41–R93 (1999)

    Article  Google Scholar 

  2. D.A. Boas, D.H. Brooks, E.L. Miller, C.A. DiMarzio, M. Kilmer, R.J. Gaudette, Q. Zhang: Imaging the body with diffuse optical tomography. IEEE Signal Processing Magazine, 57–75 (2001)

    Google Scholar 

  3. A.P. Gibson, J.C. Hebden, S.R. Arridge: Recent advances in diffuse optical imaging. Phys. Med. Biol. 50, R1–R43 (2005)

    Article  Google Scholar 

  4. H. Obrig, A. Villringer: Beyond the visible — imaging the human brain with light. J. Cereb. Blood Flow Metab. 23, 1–18 (2003)

    Article  Google Scholar 

  5. M.A. Franceschini, D.A. Boas: Noninvasive measurement of neuronal activity with near-infrared optical imaging. Neuroimage, 21, 372–386 (2004)

    Article  Google Scholar 

  6. B.W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, S. Srinivasan, X. Song, T.D. Tosteson, S.P. Poplack, K.D. Paulsen: Characterization of hemoglobin, water and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes. J. Biomed. Opt. 9, 541–552 (2004)

    Article  Google Scholar 

  7. D. Grosenick, H. Wabnitz, K.T. Moesta, J. Mucke, M. Möller, C. Stroszczynski, J. Strössel, B. Wassermann, P.M. Schlag, H. Rinneberg: Concentration and oxygen saturation of haemoglobin of 50 breast tumours determined by time-domain optical mammography. Phys. Med. Biol. 49, 1165–1181 (2004)

    Article  Google Scholar 

  8. A.Y. Bluestone, M. Stewart, B. Lei, I.S. Kass, J. Lasker, G.S. Abdoulaev, A.H. Hielscher: Three-dimensional optical tomographic brain imaging in small animals, Part I: Hypercapnia. J. Biomed. Opt. 9(5), 1046–1062 (2004)

    Article  Google Scholar 

  9. A.Y. Bluestone, M. Stewart, J. Lasker, G.S. Abdoulaev, A.H. Hielscher: Three-dimensional optical tomographic brain imaging in small animals, Part II: Unilateral carotid occlusion. J. Biomed. Opt. 9(5), 1063–1073 (2004)

    Article  Google Scholar 

  10. J.P. Culver, T. Durduran, D. Furuya, C. Cheung, J.H. Greenberg, A.G. Yodh: Diffuse optical tomography of cerebral blood flow, oxygenation, and metabolism in rat during focal ischemia. J. Cereb. Blood Flow Metab. 23, 911–924 (2003)

    Article  Google Scholar 

  11. A.H. Hielscher: Optical tomographic imaging of small animals. Current Opinion in Biotechnology 16(1), 79–88 (2005)

    Article  Google Scholar 

  12. A.H. Hielscher, A.D. Klose, A. Scheel, B. Moa-Anderson, M. Backhaus, U. Netz, J. Beuthan: Sagittal laser optical tomography for imaging of rheumatoid finger joints. Phys. Med. Biol. 49, 1147–1163 (2004)

    Article  Google Scholar 

  13. R. Weissleder, U. Mahmood: Molecular imaging. Radiology, 219, 316–333 (2001)

    Google Scholar 

  14. T.F. Massoud, S.S. Gambhir: Molecular imaging in living subjects: seeing fundamental biological processes in a new light. Genes Dev., 17, 545–580 (2003)

    Article  Google Scholar 

  15. R. Weissleder, V. Ntziachristos: Shedding light onto live molecular targets. Nat. Med. 9, 123–128 (2003)

    Article  Google Scholar 

  16. J.V. Frangioni: In vivo near-infrared fluorescence imaging. Curr. Opin. Chem. Biol. 7, 626–634 (2003)

    Article  Google Scholar 

  17. S. Achilefu: Lighting up tumors with receptor-specific optical molecular probes. Technol. Cancer Res. & Treat. 3(4), 393–409 (2004)

    Google Scholar 

  18. S.R. Cherry: In vivo molecular and genomic imaging: new challenges for imaging physics. Phys. Med. Biol., 49, R13–R48 (2004)

    Article  Google Scholar 

  19. D.K. Welsh, S.A. Kay: Bioluminescence imaging in living organisms. Curr. Opin. Biotechnol., 16, 73–78 (2005)

    Article  Google Scholar 

  20. V. Ntziachristos: Fluorescence molecular imaging. Annu. Rev. Biomed. Eng., 8, 1–33 (2006)

    Article  Google Scholar 

  21. J. Rao, A. Dragulescu-Andrasi, H. Yao: Fluorescence imaging in vivo: recent advances. Curr. Opin. Biotech., 18, 17–25 (2007)

    Article  Google Scholar 

  22. F. Natterer: Mathematical models for medical imaging. In: Computational Radiology and Imaging: Therapy and Diagnostics. The IMA Volumes in Mathematics and its Applications, ed. by Ch. Boergers, F. Natterer (Springer, New York, 1999), pp. 17–32

    Google Scholar 

  23. A.J. Welch, M.J.C. van Gemert: Optical-Thermal Response of Laser-Irradiated Tissue (Plenum Press, New York, 1995)

    Google Scholar 

  24. V. Tuchin: Tissue Optics (SPIE, Bellingham, 2000)

    Google Scholar 

  25. B. Beauvoit, S.M. Evans, T.W. Jenkins, E.E. Miller, B. Chance: Correlation between the light scattering and the mitochondrial content of normal tissues and transplantable rodent tumors. Analyt. Biochem., 226, 167–174 (1995)

    Article  Google Scholar 

  26. J. Beuthan, O. Minet, J. Helfman, M. Herrig, G. Müller: The spatial variation of the refractive index in biological cells. Phys. Med. Biol. 41, 369–382 (1996)

    Article  Google Scholar 

  27. J.R. Mourant, J.P. Freyer, A.H. Hielscher, A.A. Eick, D. Shen, T.M. Johnson: Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnosis. Appl. Opt. 37(16), 3586–3593 (1998)

    Article  Google Scholar 

  28. J.R. Mourant, M. Canpolat, C. Brocker, O. Esponda-Ramos, T.M. Johnson, A. Matanock, K. Stetter, J.P. Freyer: Light scattering from cells: the contribution of the nucleus and the effects of proliferative status. J. Biomed. Opt. 5, 131–137 (2000)

    Article  Google Scholar 

  29. W.-F. Cheong, S.A. Prahl, A.J. Welch: A review of the optical properties of biological tissues. IEEE Journal of Quantum Electronics 26(12), 2166–2185 (1990)

    Article  Google Scholar 

  30. L.G. Henyey, J.L. Greenstein: Diffuse radiation in the galaxy. Astrophys. J. 90, 70–83 (1941)

    Article  Google Scholar 

  31. F.P. Bolin, L.E. Preuss, R.C. Taylor, R.J. Ference: Refractive index of some mammalian tissues using a fiber optic cladding method. Appl. Opt. 28, 2297–2303 (1989)

    Article  Google Scholar 

  32. G.J. Tearney, M.E. Brezinski, J.F. Southern, B.E. Bouma, M.R. Hee, J.G. Fujimoto: Determination of the refractive-index of highly scattering human tissue by optical coherence tomography. Opt. Lett. 20, 2258–2260 (1995)

    Article  Google Scholar 

  33. H. Li, S. Xie: Measurement method of the refractive index of biotissue by internal reflection. Appl. Opt. 35, 1793–1795 (1996)

    Article  Google Scholar 

  34. J.J.J. Dirckx, L.C. Kuypers, W.F. Decraemer: Refractive index of tissue measured. J. Biomed. Opt. 10(4), 044014 (2005)

    Article  Google Scholar 

  35. M. Keijzer, S.L. Jacques, S.A. Prahl, A.J. Welch: Light distributions in artery tissue: Monte Carlo simulations for finite-diameter laser beams. Lasers Surg. Med. 9, 148–154 (1989)

    Article  Google Scholar 

  36. W.T. Mason: Fluorescent and Luminescent Probes for Biological Activity 2nd edn (Academic Press, San Diego, 1999)

    Google Scholar 

  37. B. Yuan, N.G. Chen, Q. Zhu: Emission and absorption properties of indocyanine green in intralipid solution. J. Biomed. Opt. 9(3), 497–503 (2004)

    Article  Google Scholar 

  38. V. Ntziachristos, A.G. Yodh, M. Schnall, B. Chance: Concurrent MRI and diffuse optical tomography of breast following indocyanine green enhancement. Proc. Natl. Acad. Sci. USA 97, 2767–2772 (2000)

    Article  Google Scholar 

  39. R.Y. Tsien: The green fluorescent protein. Annu. Rev. Biochem. 67, 509–544 (1998)

    Article  Google Scholar 

  40. A. Becker, C. Hessenius, K. Licha, B. Ebert, U. Sukowski, W. Semmler, B. Wiedenmann, C. Grötzinger: Receptor targeted optical imaging of tumors with near-infrared fluorescent ligands. Nat. Biotechnol. 19, 327–331 (2001)

    Article  Google Scholar 

  41. C.J. Daly, J.C. McGrath: Fluorescent ligands, antibodies, and proteins for the study of receptors. Pharmacol. Therap. 100, 101–118 (2003)

    Article  Google Scholar 

  42. S. Ke, X.X. Wen, M. Gurfinkel, C. Charnsangavej, S. Wallace, et al.: Near-infrared optical imaging of epidermal growth factor receptor in breast cancer xenografts. Cancer Res. 63, 7870–7875 (2003)

    Google Scholar 

  43. D. Citrin, A.K. Lee, T. Scott, M. Sproull, C. Menard, P.J. Tofilon, K. Camphausen: In vivo tumor imaging in mice with near-infrared labeled endostatin. Mol. Cancer Ther. 3, 481–488 (2004)

    Google Scholar 

  44. S. Achilefu, S. Bloch, M.A. Markiewicz, T.X. Zhong, Y.P. Ye, et al.: Synergistic effects of light-emitting probes and peptides for targetting and monitoring integrin expression. Proc. Natl. Acad. Sci. USA 102, 7976–7981 (2005)

    Article  Google Scholar 

  45. W.T. Che, U. Mahmood, R. Weissleder, C.H. Tung: Arthritis imaging using near-infrared fluorescence folate-targeted probe. Arthritis Res. Ther. 7, R310–R317 (2005)

    Article  Google Scholar 

  46. R. Weissleder, C.H. Tung, U. Mahmood, A. Bogdanov: In vivo imaging of tumors with protease-activated near-infrared fluorescent probes. Nat. Biotechnol. 17, 375–378 (1999)

    Article  Google Scholar 

  47. C.H. Tung: Fluorescent peptide probes for in vivo diagnostic imaging. Biopolymers 76, 391–403 (2004)

    Article  Google Scholar 

  48. R.M. Hoffman: The multiple uses of fluorescent proteins to visualize cancer in vivo. Nat. Rev. Cancer 5, 796–806 (2005)

    Article  Google Scholar 

  49. X. Michalet, F.F. Pinaud, L.A. Bentolila, J.M. Tsay, S. Doose, J.J. Li, G. Sundaresan, A.M. Wu, S.S. Gambhir, S. Weiss: Quantum dots for live cells, in vivo imaging, and diagnostics. Science 307, 538–544 (2005)

    Article  Google Scholar 

  50. K. Licha: Contrast agents for optical imaging. In: Topics in Current Chemistry, vol. 222 (Springer, Heidelberg, 2002), pp. 1–29

    Google Scholar 

  51. Y. Lin, R. Weissleder, C.-H. Tung: Novel near-infrared cyanine fluorochromes: Synthesis, properties, and bioconjugation. Bioconjugate Chem. 13, 605–610 (2002)

    Article  Google Scholar 

  52. R.C. Benson, H.A. Kues: Fluorescence properties of indicyanine green as related to angiography. Phys. Med. Biol. 23(1), 159–163 (1978)

    Article  Google Scholar 

  53. Invitrogen The Handbook. A guide to fluorescent probes and labeling technologies. web. edition, datasheets.

    Google Scholar 

  54. L. Murow, I. Carmichael, G.L. Hug: Handbook of Photochemistry (Marcel Dekker, New York, 1993)

    Google Scholar 

  55. G.-J. Kremers, J. Goedhart, D.J. van den Heuvel, H.C. Gerritsen, T.W.J. Gadella: Improved green and blue fluorescent proteins for expression in bacteria and mammalian cells. Biochemistry 46(12), 3775–3783 (2007)

    Article  Google Scholar 

  56. N.C. Shaner, R.E. Campbell, P.A. Steinbach, B.N.G. Giepmans, A.E. Palmer, R.Y. Tsien: Improved monomeric red, orange and yellow fluorescent proteins derived from Discosoma sp. red fluorescent protein. Nature Biotech. 22, 1567–1572 (2004)

    Article  Google Scholar 

  57. R.E. Campbell, O. Tour, A.E. Palmer, P.A. Steinbach, G.S. Baird, D.A. Zacharias, R.Y. Tsien: A monomeric red fluorescent protein. Proc. Natl. Acad. Sci. 99, 7877–7882 (2002)

    Article  Google Scholar 

  58. B. Bowen, N. Woodbury: Single-molecule fluorescence lifetime and anisotropy measurements of the red fluorescent protein, DsRed, in solution. Photochem. & Photobiol. 77(4), 362–369 (2003)

    Article  Google Scholar 

  59. M. Peter, S.M. Ameer-Beg, M.K.Y. Hughes, M.D. Keppler, S. Prag, M. Marsh, B. Vojnovic, T. Ng: Multiphoton-FLIM quantification of the EGFP-mRFP1 FRET pair for localization of membrane receptor-kinase interactions. Biophys. J. 88, 1224–1237 (2005)

    Article  Google Scholar 

  60. G. Choy, P. Choyke, S.K. Libutti: Current advances in molecular imaging: noninvasive in vivo bioluminescent and fluorescent optical imaging of cancer. Mol. Imag. 2, 303–312 (2003)

    Article  Google Scholar 

  61. B.W. Rice, M.D. Cable, M.B. Nelson: In vivo imaging of light-emitting probes. J. Biomed. Opt. 6(4), 432–440 (2001)

    Article  Google Scholar 

  62. T. Troy, D. Jekic-McMullen, L. Sambucetti, B. Rice: Quantitative comparison of the sensitivity of detection of fluorescent and bioluminescent reporters in animal models. Molecular Imaging 3(1), 9–23 (2004)

    Article  Google Scholar 

  63. V.R. Viviani, T.L. Oehlmeyer, F.G.C. Arnoldi, M.R. Brochetto-Braga: A new firefly luciferase with bimodal spectrum: identification of structural determinants of spectral pH-sensitivity in firefly luciferases. Photochem. & Photobiol. 81, 843–848 (2005)

    Article  Google Scholar 

  64. H. Zhao, T.C. Doyle, O. Coquoz, F. Kalish, B. Rice, C.H. Contag: Emission spectra of bioluminescent reporters and interaction with mammalian tissue determine the sensitivity of detection in vivo. J. Biomed: Opt. 10(4), 041210-1-9 (2005)

    Google Scholar 

  65. S. Chandrasekhar: Radiative Transfer ((xford University Press, London, 1960)

    Google Scholar 

  66. J.J. Duderstadt, W.R. Martin: Transport theory (John Wiley, New York, 1979)

    Google Scholar 

  67. K.M. Case, P.F. Zweifer: Linear Transport Theory (Addison-Wesley, Reading, MA 1967)

    Google Scholar 

  68. A. Kienle, F.K. Forster, R. Hibst: Influence of the phase function on determination of the optical properties of biological tissue by spatially resolved reflectance. Opt. Lett. 26(20), 1571–1573 (2001)

    Article  Google Scholar 

  69. S.K. Sharma, S. Banerjee: Role of approximate phase functions in Monte Carlo simulation of light propagation in tissues. J. Opt. A: Pure Appl. Opt. 5, 294–302 (2003)

    Article  Google Scholar 

  70. A.D. Klose: Transport-theory based stochastic image reconstruction of bioluminescent sources. J. Opt. Soc. Am. A 24(6), 1601–1608 (2007)

    Article  Google Scholar 

  71. H.C. Yi, R. Sanchez, N.J. McCormick: Bioluminescence estimation from ocean in situ irradiances. Appl. Opt. 31(6), 822–830 (1992)

    Article  Google Scholar 

  72. Z. Tao, N.J. McCormick, R. Sanchez: Ocean source and optical property estimation from explicit and implicit algorithms. Appl. Opt. 33(15), 3265–3275 (1994)

    Article  Google Scholar 

  73. L.K. Sundman, R. Sanchez, N.J. McCormick: Ocean optical source estimation with widely spaced irradiance measurements. Appl. Opt. 37(18), 3793–3803 (1998)

    Article  Google Scholar 

  74. S. Stephany, H.F. de Campos Velho, F.M. Ramos, C.D. Mobley: Identification of inherent optical properties and bioluminescence source term in a hydrologic optics problem. J. Quant. Spetrosc. Radiat. Transfer 67, 113–123 (2000)

    Article  Google Scholar 

  75. H.Y. Li, M.N. Ozisik: Estimation of the radiation source term with conjugate-gradient method of inverse analysis. J. Quant. Spectrosc. Radiat. Transfer 48(3), 237–244 (1992)

    Article  Google Scholar 

  76. L.H. Liu: Simultaneous identification of temperature profile and absorption coefficient in one-dimensional semitransparent medium by inverse radiation analysis. Int. Comm. Heat Mass Transfer 27(5), 635–643 (2000)

    Article  Google Scholar 

  77. H.-Y. Li: A two-dimensional cylindrical inverse source problem in radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 69, 403–414 (2001)

    Article  Google Scholar 

  78. L.H. Liu, H.P. Tan, Q.Z. Yu: Inverse radiation problem of sources and emissivities in one-dimensional semitransparent media. Int. J. of Heat and Mass Transfer 44, 63–72 (2001)

    Article  Google Scholar 

  79. J. Su, A.J.S. Neto: Two-dimensional inverse heat conduction problem of source strength estimation in cylindrical rods. Appl. Math. Modelling 25, 861–872 (2001)

    Article  Google Scholar 

  80. H.M. Park, D.H. Yoo: A multidimensional inverse radiation problem of estimating the strength of a heat source in participating media. Int. J. Heat Mass Transfer 44, 2949–2956 (2001)

    Article  Google Scholar 

  81. J.R. Lakowicz: Principles of Fluorescence Spectroscopy (Springer, New York, 2004)

    Google Scholar 

  82. E.M. Sevick-Muraca, C.L. Burch: Origin of phosphorescence signals reemitted from tissues. Opt. Lett. 19(23), 1928–1930 (1994)

    Article  Google Scholar 

  83. C.L. Hutchinson, J.R. Lakowicz, E.M. Sevick-Muraca: Fluorescence lifetime-based sensing in tissues: a computational study. Biophys. Journal 68, 1574–1582 (1995)

    Article  Google Scholar 

  84. C.L. Hutchinson, T.L. Troy, E.M. Sevick-Muraca: Fluorescence-lifetime determination in tissues or other scattering media from measurement of excitation and emission kinetics. Appl. Opt. 35(13), 2325–2332 (1996)

    Article  Google Scholar 

  85. J. Chang, R.L. Barbour, H.L. Graber, R. Aronson: Fluorescence optical tomography. Proc. SPIE 2570, 59–72 (1997)

    Article  Google Scholar 

  86. J. Chang, H.L. Graber, R.L. Barbour: Luminescence optical tomography of dense scattering media. J. Opt. Soc. Am. A 14(1), 288–299 (1997)

    Article  Google Scholar 

  87. O. Dorn: A transport-backtransport method for optical tomography. Inv. Prob. 14, 1107–1130 (1998)

    Article  Google Scholar 

  88. K. Mitra, S. Kumar: Development and comparison of models for light-pulse transport through scattering-absorbing media. Appl. Opt. 38(1), 188–196 (1999)

    Article  Google Scholar 

  89. Z. Guo, S. Kumar: Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media. Appl. Opt. 40(19), 3156–3163 (2001)

    Article  Google Scholar 

  90. R. Elaloufi, R. Carminati, J.-J. Greffet: Time-dependent transport through scattering media: from radiative transfer to diffusion. J. Opt. A: Pure Appl. Opt. 4, S103–S108 (2002)

    Article  Google Scholar 

  91. M. Sakami, K. Mitra, T. Vo-Dinh: Analysis of short-pulse laser photon transport through tissues for optical tomography. Opt. Lett. 27(5), 336–338 (2002)

    Article  Google Scholar 

  92. C. Das, A. Trivedi, K. Mitra, T. Vo-Dinh: Experimental and numerical analysis of short-pulse laser interaction with tissue phantoms containing inhomogeneities. Appl. Opt. 42(25), 5173–5180 (2003)

    Article  Google Scholar 

  93. Z. Guo, K. Kim: Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method. Appl. Opt. 42(16), 2897–2905 (2003)

    Article  Google Scholar 

  94. J. Boulanger, A. Charette: Numerical developments for short-pulsed near-infrared spectroscopy. Part II: Inverse treatment. J. Quant. Spectrosc. Radiat. Transfer 91, 297–318 (2005)

    Article  Google Scholar 

  95. K. Ren, G.S. Abdoulaev, G. Bal, A.H. Hielscher: Algorithm for solving the equation of radiative transfer in the frequency domain. Opt. Lett. 29, 578–580 (2004)

    Article  Google Scholar 

  96. G.S. Abdoulaev, K. Ren, A.H. Hielscher: Optical tomography as a PDE-constrained optimization problem. Inv. Prob. 21, 1507–1530 (2005)

    Article  Google Scholar 

  97. K. Ren, G. Bal, A.H. Hielscher: Frequency domain optical tomography based on the equation of radiative transfer. SIAM J. Sci. Comput. 28(4), 1463–1489 (2006)

    Article  Google Scholar 

  98. J.C. Rasmussen, A. Joshi, T. Pan, T. Wareing, J. McGhee, E.M. Sevick-Muraca: Radiative transport in fluorescence-enhanced frequency domain photon migration. Med. Phys. 33(12), 4685–4700 (2006)

    Article  Google Scholar 

  99. A. Joshi, J.C. Rasmussen, E.M. Sevick-Muraca, T.A. Wareing, J. McGhee: Radiative transport-based frequency domain fluorescence tomography. Phys. Med. Biol. 53, 2069–2088 (2008)

    Article  Google Scholar 

  100. X. Gu, K. Ren, A.H. Hielscher: Frequency-domain sensitivity analysis for small imaging domains using the equation of radiative transfer. Appl. Opt. 46(10), 1624–1632 (2007)

    Article  Google Scholar 

  101. H.K. Kim, A. Charette: A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 104, 24–39 (2007)

    Article  Google Scholar 

  102. S. Wright, M. Schweiger, S.R. Arridge: Reconstruction in optical tomography using the P N approximations. Meas. Sci. Technol. 18, 79–86 (2007)

    Article  Google Scholar 

  103. A.D. Klose, A.H. Hielscher: Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer. Med. Phys. 26, 1698–1707 (1999)

    Article  Google Scholar 

  104. E.D. Aydin, C.R.E. de Oliveira, and A.J.H. Goddard: A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method. Med. Phys. 29(9), 2013–2023 (2002)

    Article  Google Scholar 

  105. G.S. Abdoulaev, A.H. Hielscher: Three-dimensional optical tomography with the equation of radiative transfer. Journal of Electronic Imaging 12(4), 594–601 (2003)

    Article  Google Scholar 

  106. A. D. Klose, U. Netz, J. Beuthan, A. H. Hielscher: Optical tomography using the time-independent equation of radiative transfer. Part I: Forward model. J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002)

    Article  Google Scholar 

  107. A. D. Klose, A. H. Hielscher: Optical tomography using the time-independent equation of radiative transfer. Part II: Inverse model. J. Quant. Spectrosc. Radiat. Transfer 72, 715–732 (2002)

    Article  Google Scholar 

  108. A. D. Klose, A. H. Hielscher: Fluorescence tomography with simulated data based on the equation of radiative transfer. Opt. Lett. 28, 1019–1021 (2003)

    Article  Google Scholar 

  109. A.D. Klose, V. Ntziachristos, A.H. Hielscher: The inverse source problem based on the radiative transfer equation in optical molecular imaging. J. Comp. Phys. 202, 323–345 (2005)

    Article  Google Scholar 

  110. A. Kim, M. Moscoso: Radiative transport theory for optical molecular imaging. Inv. Prob. 22, 23–42 (2006)

    Article  Google Scholar 

  111. B. G. Carlson, K. D. Lathrop: Transport theory — the method of discrete ordinates. In: Computing Methods in Reactor Physics, ed. by H. Greenspan et al. (Gordon and Breach, New York, 1968) pp. 166–266

    Google Scholar 

  112. C.-Y. Wu, B.-T. Liou: Discrete-ordinate solutions for radiative transfer in a cylindrical enclosure with Fresnel boundaries. Int. J. Heat Mass Transfer 40(10), 2467–2475 (1997)

    Article  Google Scholar 

  113. S.T. Thynell: Discrete-ordinates method in radiative heat transfer. Int. J. Eng. Sci. 36, 1651–1675 (1998)

    Article  Google Scholar 

  114. M.A. Ramankutty, A.L. Crosbie: Modified discrete ordinates solution of radiative transfer in two-dimensional rectangular enclosures. J. Quant. Spectrosc. Radiat. Transfer 57, 107–140 (1997)

    Article  Google Scholar 

  115. R. Koch, W. Krebs, S. Wittig, R. Viskanta: Discrete ordinates quadrature schemes for multidimensional radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 53, 353–372 (1995)

    Article  Google Scholar 

  116. M.F. Modest: Radiative Heat Transfer 2nd edn (Academic Press, New York, 2003)

    Google Scholar 

  117. W.J. Minkowycz, E.M. Sparrow, J.Y. Murthy: Handbook of Numerical Heat Transfer 2nd edn (John Wiley, Hoboken, NJ, 2006)

    Google Scholar 

  118. J.K. Fletcher: The solution of the multigroup neutron transport equation using spherical harmonics. Nucl. Sci. Eng. 84, 33–46 (1983)

    Google Scholar 

  119. K. Kobayashi, H. Oigawa, H. Yamagata: The spherical harmonics method for the multigroup transport equations in x−y geometry. Ann. Nucl. Energy 13(12), 663–678 (1986)

    Article  Google Scholar 

  120. R. Sanchez, N.J. McCormick: A review of neutron transport approximations. Nucl. Sci. Eng. 80, 481–535 (1982)

    Google Scholar 

  121. E.E. Lewis, W.F. Miller: Computational Methods of Neutron Transport (John Wiley, New York, 1984)

    Google Scholar 

  122. M.L. Adams, E.W. Larsen: Fast iterative methods for discrete-ordinates particle transport calculations. Prog. Nucl. Energy 40(1), 3–159 (2002)

    Article  Google Scholar 

  123. A.D. Klose, E.W. Larsen: Light transport in biological tissue based on the simplified spherical harmonics equations. J. Comp. Phys. 220, 441–470 (2006)

    Article  Google Scholar 

  124. 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)

    Article  Google Scholar 

  125. J.C. Chai, H.S. Lee, S.V. Patankar: Ray effect and false scattering in the discrete ordinates method. Numerical Heat Transfer Part B 24, 373–389 (1993)

    Article  Google Scholar 

  126. W.J. Wiscombe: The Delta-M method: rapid yet accurate radiative flux calculations for strongly asymmetric phase functions. J. Atmos. Sci. 34, 1408–1422 (1977)

    Article  Google Scholar 

  127. T. Khan, A. Thomas: Comparison of P N or spherical harmonics approximation for scattering media with spatially varying and spatially constant refractive indices. Optics Communications 255, 130–166 (2005)

    Article  Google Scholar 

  128. R.E. Marshak: Note on the spherical harmonic method as applied to the Milne problem for a sphere. Phys. Rev. 71(7), 443–446 (1947)

    Article  Google Scholar 

  129. D.I. Tomasevic, E.W. Larsen: The simplified P 2 approximation. Nucl. Sci. Eng. 122, 309–325 (1996)

    Google Scholar 

  130. E.W. Larsen, J.E. Morel, J.M. McGhee: Asymptotic derivation of the multigroup P1 and simplified P N equations with anisotropic scattering. Nucl. Sci. Eng. 123, 328–342 (1996)

    Google Scholar 

  131. R.T. Ackroyd, C.R.E. de Oliveira, A. Zolfaghari, A.J.H. Goddard: On a rigorous resolution of the transport equation into a system of diffusion-like equations. Prog. Nucl. Energy 35(1), 1–64 (1999)

    Article  Google Scholar 

  132. P.S. Brantley, E.W. Larsen: The simplified P3 approximation. Nucl. Sci. Eng. 134, 1–21 (2000)

    Google Scholar 

  133. J.E. Morel, J.M. McGhee, E.W. Larsen: A three-dimensional time-dependent unstructured tetrahedral-mesh SP N method. Nucl. Sci. Eng. 123, 319–327 (1996)

    Google Scholar 

  134. P. Kotiluoto: Fast tree multigrid transport application for the simplified P 3 approximation. Nucl. Sci. Eng. 138, 269–278 (2001)

    Google Scholar 

  135. P. Kotiluoto, P. Hiismáki: Application of the new MultiTrans SP 3 radiation transport code in BNCT dose planning. Med. Phys. 28(9), 1905–1910 (2001)

    Article  Google Scholar 

  136. R. Ciolini, G.G.M. Coppa, B. Montagnini, P. Ravetto: Simplified P N and A N methods in neutron transport. Prog. Nucl. Energy 40(2), 237–264 (2002)

    Article  Google Scholar 

  137. M. Lemanska: On the simplified P n method in the 2-D diffusion code EXTERMINATOR. Atomkernenergie 37, 173–175 (1981)

    Google Scholar 

  138. E.E. Lewis, G. Palmiotti: Simplified spherical harmonics in the variational nodal method. Nucl. Sci. Eng. 126, 48–58 (1997)

    Google Scholar 

  139. M.A. O’Leary, D.A. Boas, X.D. Li, B. Chance, A.G. Yodh: Fluorescence lifetime imaging in turbid media. Opt. Lett. 21(2), 158–160 (1996)

    Article  Google Scholar 

  140. X.D. Li, M.A. O’Leary, D.A. Boas, B. Chance, A.G. Yodh: Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications. Appl. Opt. 35(19), 3746–3758 (1996)

    Article  Google Scholar 

  141. D.Y. Paithankar, A.U. Chen, B.W. Pogue, M.S. Patterson, E.M. Sevick-Muraca: Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media. Appl. Opt. 36, 2260–2272 (1997)

    Article  Google Scholar 

  142. J. Chang, H.L. Graber, R.L. Barbour: Imaging of fluorescence in highly scattering media. IEEE Trans. Biomed. Eng. 44, 810–822 (1997)

    Article  Google Scholar 

  143. H. Jiang: Frequency-domain fluorescent diffusion tomography: a finite-element-based algorithm and simulations. Appl. Opt. 37, 5337–5343 (1998)

    Article  Google Scholar 

  144. V. Ntziachristos, R. Weissleder: Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation. Opt. Lett. 26, 893–895 (2001)

    Article  Google Scholar 

  145. J. Lee, E.M. Sevick-Muraca: Three-dimensional fluorescence enhanced optical tomography using referenced frequency-domain photon migration measurements at emission and excitation wavelengths. J. Opt. Soc. Am. A 19, 759–771 (2002)

    Article  Google Scholar 

  146. A.B. Milstein, S. Oh, K.J. Webb, C.A. Bouman, Q. Zhang, D.A. Boas, R.P. Millane: Fluorescence optical diffusion tomography. Appl. Opt. 42, 3081–3094 (2003)

    Article  Google Scholar 

  147. L. Herve, A. Koenig, A. Da Silva, M. Berger, J. Boutet, J.M. Dinten, P. Peltie, P. Rizo: Noncontact fluorescence diffuse optical tomography of heterogeneous media. Appl. Opt. 46(22), 4896–4906 (2007)

    Article  Google Scholar 

  148. G. Wang, Y. Li, M. Jiang: Uniqueness theorems in bioluminescence tomography. Med. Phys. 31, 2289–2299 (2004)

    Article  Google Scholar 

  149. W. Cong, G. Wang, D. Kumar, Y. Liu, M. Jiang, L.V. Wang, E.A. Hoffman, G. McLennan, P.B. McCray, J. Zabner, A. Cong: Practical reconstruction method for bioluminescence tomography. Opt. Exp. 13(18), 6756–6771 (2005)

    Article  Google Scholar 

  150. G. Alexandrakis, F.R. Rannou, A.F. Chatziioannou: Tomographic bioluminescence imaging by use of a combined optical-PET (OPET) system: a computer simulation feasibility study. Phys. Med. Biol. 50, 4225–4241 (2005)

    Article  Google Scholar 

  151. A.J. Chaudhari, F. Darvas, J.R. Bading, R.A. Moats, P.S. Conti, D.J. Smith, S.R. Cherry, R.M. Leahy: Hyperspectral and multispectral bioluminescence optical tomography for small animal imaging. Phys. Med. Biol. 50, 5421–5441 (2005)

    Article  Google Scholar 

  152. H. Dehghani, S.C. Davis, S. Jiang, B.W. Pogue, K.D. Paulsen: Spectrally resolved bioluminescence optical tomography. Opt. Lett. 31(3), 365–367 (2006)

    Article  Google Scholar 

  153. C. Kuo, O. Coquoz, T.L. Troy, H. Xu, B.W. Rice: Three-dimensional reconstruction of in vivo bioluminescent sources based on multispectral imaging. J. Biomed. Opt. 12(2), 024007-1-12 (2007)

    Google Scholar 

  154. W. Cong, K. Durairaj, L.V. Wang, G. Wang: A Born-type approximation method for bioluminescence tomography. Med. Phys. 33(3), 679–686 (2006)

    Article  Google Scholar 

  155. W. Han, W. Cong, and G. Wang: Mathematical theory and numerical analysis of bioluminescence tomography. Inv. Prob. 22, 1659–1675 (2006)

    Article  Google Scholar 

  156. Y. Lv, J. Tian, W. Cong, G. Wang, W. Yang, C. Qin, M. Xu: Spectrally resolved bioluminescence tomography with adaptive finite element analysis: methodology and simulation. Phys. Med. Biol. 52, 4497–4512 (2007)

    Article  Google Scholar 

  157. K.M. Yoo, F. Liu, R.R. Alfano: When does the diffusion approximation fail to describe photon transport in random media? Phys. Rev. Lett. 64(22), 2647–2650 (1990)

    Article  Google Scholar 

  158. A.D. Kim, A. Ishimaru: Optical diffusion of continuous-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer. Appl. Opt. 37, 5313–5319 (1998)

    Article  Google Scholar 

  159. B. Chen, K. Stamnes, J.J. Stamnes: Validity of the diffusion approximation in biooptical imaging. Appl. Opt. 40, 6356–6366 (2001)

    Article  Google Scholar 

  160. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery: Numerical Recipes in C: The Art of Scientific Computing, 2nd edn (Cambridge University Press, Cambridge, 1994)

    Google Scholar 

  161. K.W. Morton, D.F. Mayers: Numerical Solution of Partial Differential Equations (Cambridge University Press, Cambridge, 1994)

    Google Scholar 

  162. K.D. Lathrop: Spatial differencing of the transport equation: positivity vs. accuracy. J. Comp. Phys. 4, 475–498 (1969)

    Article  Google Scholar 

  163. Y. Saad: GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems. SIAM Journal of Scientific and Statistical Computing 7, 856–869 (1986)

    Article  Google Scholar 

  164. W.L. Briggs, V.E. Henson, S.F. McCormick: A Multigrid Tutorial, 2nd edn (SIAM, Philadelphia, PA, 2000)

    Google Scholar 

  165. P. Wesseling: An Introduction to Multigrid Methods (R. T. Edwards Inc., Philadelphia, PA, 2004)

    Google Scholar 

  166. B.W. Patton, J.P. Holloway: Application of preconditioned GMRES to the numerical solution of neutron transport equation. Annals of Nuclear Energy 29, 109–136 (2002)

    Article  Google Scholar 

  167. S. Oliveira, Y. Deng: Preconditioned Krylov subspace methods for transport equations. Prog. Nucl. Energy 33, 155–174 (1998)

    Article  Google Scholar 

  168. W. Hackbusch: Multi-Grid Methods and Applications (Springer, Berlin New York, 1985)

    Google Scholar 

  169. S.F. McCormick: Multilevel Adaptive Methods for Partial Differential Equations (SIAM, Philadelphia, 1989)

    Google Scholar 

  170. N.J. McCormick: Inverse radiative transfer problems: A review. Nucl. Sci. Eng. 112, 185–198 (1992)

    Google Scholar 

  171. E.W. Larsen: The inverse source problem in radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 15, 1–5 (1975)

    Article  Google Scholar 

  172. C.E. Siewert: An inverse source problem in radiative transfer. J. Quant. Spectrosc. Radiat. Transfer 50(6), 603–609 (1993)

    Article  Google Scholar 

  173. C.E. Siewert: A radiative-transfer inverse-source problem for a sphere. J. Quant. Spectrosc. Radiat. Transfer 52(2), 157–160 (1994)

    Article  Google Scholar 

  174. S.G. Nash: Linear and Nonlinear Programming (McGraw-Hill, New York, 1996)

    Google Scholar 

  175. J. Nocedal, S.J. Wright: Numerical Optimization (Springer, New York, 1999)

    Book  Google Scholar 

  176. O.M. Alifanov: Inverse Heat Transfer Problems (Springer, Berlin, 1994)

    Google Scholar 

  177. G.I. Marchuk: Adjoint Equations and Analysis of Complex Systems (Kluwer Academic Publishers, Dordrecht, 1995)

    Google Scholar 

  178. I.N. Polonsky, M.A. Box, A.B. Davis, Radiative transfer through inhomogeneous turbid media: implementation of the adjoint perturbation approach at the 1st order. J. Quant. Spectrosc. Radiat. Transfer 78, 85–98 (2003)

    Article  Google Scholar 

  179. R.E. Wengert: A simple automatic derivative evaluation program. Communications of the ACM 7, 463–464 (1964)

    Article  Google Scholar 

  180. L.B. Rall: Automatic Differentiation: Techniques and Applications. Lecture Notes in Computer Science, Vol. 120 (Springer, Berlin, 1981)

    Google Scholar 

  181. L.B. Rall, G.F. Corliss: An introduction to automatic differentiation. In: Automatic Differentiation of Algorithms: Theory, Implementation, and Application, ed. by A. Griewank, G.E. Corliss (SIAM, Philadelphia, PA, 1991) pp.1–18

    Google Scholar 

  182. T. Beck: Automatic differentiation of iterative processes. J. Comp. Appl. Math. 50, 109–118 (1994)

    Article  Google Scholar 

  183. K.M. Hanson, G.S. Cunningham, S.S. Saquib: Inversion based on computational simulations. In: Maximum Entropy and Bayesian Methods, ed. by G.J. Erickson, J.T. Rychert, C.R. Smith (Kluwer Academic Publishers, Dordrecht, 1998) pp. 121–135

    Google Scholar 

  184. R. Giering, T. Kaminski: Recipes for adjoint code construction. ACM Trans. Math. Software 24, 437–474 (1998)

    Article  Google Scholar 

  185. H.M. Bücker, G.F. Corliss, P.D. Hovland, U. Naumann, B. Norris: Automatic Differentiation: Applications, Theory, and Implementations (Springer, Berlin, 2005)

    Google Scholar 

  186. S.S. Saquib, K.M. Hanson, G.S. Cunningham: Model-based image reconstruction from time-resolved diffusion data. Proc. SPIE 3034, 369–380 (1997)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Praxis Publishing Ltd, Chichester, UK

About this chapter

Cite this chapter

Klose, A.D. (2009). Radiative transfer of luminescence light in biological tissue. In: Kokhanovsky, A.A. (eds) Light Scattering Reviews 4. Springer Praxis Books. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74276-0_6

Download citation

Publish with us

Policies and ethics