A fast numerical method for time-resolved photon diffusion in general stratified turbid media

Journal of Computational Physics

Volumn 201, Issue 2, 2004, Pages 771-797

  Barnett, Alex H ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Diffuse optical tomography; Diffusion; Inverse problem; Parabolic; Photon migration; Stratified; Time resolved

Indexed keywords

FINITE DIFFERENCE METHOD; HEAT CONDUCTION; INVERSE PROBLEMS; NUMERICAL METHODS; OPTICAL TOMOGRAPHY; PHOTONS;

DIFFUSE OPTICAL TOMOGRAPHY; DIFFUSION PROBLEMS; FORWARD MODELING; PARABOLICS; PHOTON DIFFUSION; PHOTON MIGRATION; STRATIFIED; TIME-RESOLVED; TIME-RESOLVED PHOTONS; TURBID MEDIA;

DIFFUSION;

EID: 8744225559     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.06.017     Document Type: Article

References (52)

1. 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 18 6 2001 57-75
2. A. Villringer B. Chance Non-invasive optical spectroscopy and imaging of human brain function Trends Neurosci. 20 1997 435-442
3. S.R. Hintz W.-F. Cheong J.P. van Houten D.K. Stevenson D.A. Benaron Bedside imaging of intracranial hemorrhage in the neonate using light: comparison with ultrasound, computed tomography, and magnetic resonance imaging Pediatr. Res. 45 1999 54-59
4. D. Grosenick K.T. Moesta H. Wabnitz J. Mucke C. Stroszczynski R. Macdonald P.M. Schlag H. Rinneberg Time-domain optical mammography: initial clinical results on detection and characterization of breast tumors Appl. Opt. 42 2003 3170-3186
5. S. Fantini M.A. Franceschini-Fantini J.S. Maier S.A. Walker B. Barbieri E. Gratton Frequency-domain multichannel optical detector for noninvasive tissue spectroscopy and oximetry Opt. Eng. 34 1995 32-42
6. A. Klose A.H. Hielscher K.M. Hanson J. Beuthan Three-dimensional optical tomography of a finger joint model for diagnostic of rheumatoid arthritis In: D.A. Benaron B. Chance M. Ferrari M. Kohl (Eds.) Photon Propagation in Tissue IV, Proc. SPIE 3566 1998 151-160
7. A. Torricelli A. Pifferi P. Taroni E. Giambattistelli R. Cubeddu In vivo optical characterization of human tissues from 610 to 1010 nm by time-resolved reflectance spectroscopy Phys. Med. Biol. 46 2001 2227-2237
8. F.E. Schmidt M.E. Fry E.M.C. Hillman J.C. Hebden D.T. Delpy A 32-channel time-resolved instrument for medical optical tomography Rev. Sci. Instruments 71 2000 256-265
9. S.R. Arridge Optical tomography in medical imaging Inverse Problems 15 1999 R41-R93
10. K.M. Hanson G.S. Cunningham S.S. Saquib Inversion based on computational simulations In: G.J. Erickson J.T. Rychert C.R. Smith (Eds.) Maximum Entropy and Bayesian Methods 1998 Kluwer Academic Dordrecht 121-135
11. A. Ishimaru Wave Propagation and Scattering in Random Media vol. 1 1978 Academic
12. J.D. Moulton, Diffusion modelling of picosecond laser pulse propagation in turbid media, Masters thesis, McMaster University, 1990
13. S.S. Saquib K.M. Hanson G.S. Cunningham Model-based image reconstruction from time-resolved diffusion data, in medical imaging: Image processing Proc. SPIE 3034 1997 369-380
14. A.H. Barnett J.P. Culver A.G. Sorensen A. Dale D.A. Boas Robust inference of baseline optical properties of the human head with 3D segmentation from magnetic resonance imaging Appl. Opt. 42 2003 3095-3108
15. S. Oh A.B. Milstein R.P. Millane C.A. Bouman K.J. Webb Source-detector calibration in three-dimensional Bayesian optical diffusion tomography J. Optical Soc. Am. A 19 2002 1983-1993
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 1998 1285-1302
17. A.H. Hielscher S.L. Jacques L. Wang F.K. Tittel The influence of boundary conditions on the accuracy of diffusion theory in time-resolved reflectance spectroscopy of biological tissues Phys. Med. Biol. 40 1995 1957-1975
18. L. Wang S.L. Jacques L. Zheng MCML-Monte Carlo modeling of light transport in multi-layered tissues Comput. Methods Programs Biomed. 47 1995 131-146
19. A.H. Hielscher H.L. Liu B. Chance F.K. Tittel S.L. Jacques Time-resolved photon emission from layered turbid media Appl. Opt. 35 1996 719-728
20. A.H. Hielscher A.D. Klose K.M. Hanson Gradient-based iterative image reconstruction scheme for time-resolved optical tomography IEEE Trans. Medical Imaging 18 1999 262-271
21. M. Firbank S.R. Arridge M. Schweiger D.T. Delpy An investigation of light transport through scattering bodies with non-scattering regions Phys. Med. Biol. 41 1996 767-783
22. E. Okada D.T. Delpy Near-infrared light propagation in an adult head model. I. Modeling of low-level scattering in the cerebrospinal fluid layer Appl. Opt. 42 2003 2906-2914
23. V. Ntziachristos B. Chance Accuracy limits in the determination of absolute optical properties using time-resolved NIR spectroscopy Med. Phys. 28 2001 1115-1124
24. V. Ntziachristos A.H. Hielscher A.G. Yodh B. Chance Diffuse optical tomography of highly heterogeneous media IEEE Trans. Med. Imaging 20 2001 470-478
25. R.C. Haskell L.O. Svaasand T.-T. Tsay T.-C. Feng M.S. McAdams B.J. Tromberg Boundary conditions for the diffusion equation in radiative transfer J. Opt. Soc. Am. A 11 1994 2727-2741
26. R.J. LeVeque, Finite Difference Methods for Differential Equations, notes available at http://www.amath.washington.edu/~rjl/booksnotes.html
27. R.D. Richtmeyer K.W. Morton Difference Methods for Initial-Value Problems 1967 John Wiley & Sons NY
28. S. Takatani M.D. Graham Theoretical analysis of diffuse reflectance from a two-layer tissue model IEEE Trans. Biomed. Eng. 26 1979 656-664
29. J.M. Schmitt G.X. Zhou E.C. Walker R.T. Wall Multilayer model of photon diffusion in skin J. Opt. Soc. Am. A 7 1990 2141-2153
30. I. Dayan S. Havlin G.H. Weiss Photon migration in a two-layer turbid medium. A diffusion analysis J. Mod. Opt. 39 1992 1567-1582
31. A. Kienle M.S. Patterson Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium J. Opt. Soc. Am. A 14 1997 246-254
32. A. Kienle M.S. Patterson N. Dögnitz R. Bays G. Wagnières H. van den Bergh Noninvasive determination of the optical properties of two-layered media Appl. Opt. 37 1998 779-791
33. J.-M. Tualle J. Prat E. Tinet S. Avrillier Real-space Green's function calculation for the solution of the diffusion equation in stratified turbid media J. Opt. Soc. Am. A 17 2000 2046-2055
34. F. Martelli A. Sassaroli Y. Yamada G. Zaccanti Analytical approximate solutions of the time-domain diffusion equation in layered slabs J. Opt. Soc. Am. A 19 2002 71-80
35. F. Martelli A. Sassaroli S. Del Bianco Y. Yamada G. Zaccanti Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method Phys. Rev. E 67 2003 056623
36. F. Martelli S. Del Bianco G. Zaccanti Procedure for retrieving the optical properties of a two-layered medium from time-resolved reflectance measurements Opt. Lett. 28 2003 1236-1238
37. F. Martelli A. Sassaroli G. Zaccanti Y. Yamada Properties of the light emerging from a diffusive medium: Angular dependence and flux at the external boundary Phys. Med. Biol. 44 1999 1257-1275
38. M.S. Patterson B. Chance B.C. Wilson Time-resolved reflectance and transmittance for the non-invasive measurement of tissue optical properties Appl. Opt. 28 1989 2331-2336
39. 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 1990 2647
40. G. Bal Transport through diffusive and non-diffusive regions, embedded objects, and clear layers SIAM J. Appl. Math. 62 5 2002 1677-1697
41. 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 1995 2258-2260
42. F. Bevilacqua D. Piguet P. Marquet J.D. Gross B.J. Tromberg C. Depeursinge In vivo local determination of tissue optical properties: applications to human brain Appl. Opt. 38 1999 4939-4950
43. min.
44. -1 used by Okada [22] since it is a whole order of magnitude larger than any in vivo literature value. Disagreements remain about in vivo baseline properties of the scalp, skull, grey and white matter [16,42,14,22].
45. This simple picture is complicated by the fact that time-correlation in the forward signals I(R,t) can effectively average statisticallyindependent measurement errors, forcing us to make the forward model more accurate. Ultimately we plan an error analysis of the full (linearized) inverse problem in order to determine what types and sizes of forward errors have negligible effect on answers to the inverse problem.
46. J.D. Jackson Classical Electrodynamics 1975 Wiley New York
47. L. Greengard J.A. Strain A fast algorithm for evaluating heat potentials Comm. Pure Appl. Math XLIII 1990 949-963
48. L. Greengard P. Lin Spectral approximation of the free-space heat kernel Appl. Computat. Harmonic Anal. 9 2000 83-97
49. J.R. Kuttler V.G. Sigillito Eigenvalues of the laplacian in two dimensions SIAM Rev. 26 1984 163-193
50. LAPACK, available at http://www.netlib.org/lapack
51. W.H. Press, B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambridge University Press, 1992), p. 848, available at http://lib-www.lanl.gov/numerical/bookcpdf.html
52. J.-M. Tualle, private communication