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

Journal of the Optical Society of America A: Optics and Image Science, and Vision

Volumn 27, Issue 7, 2010, Pages 1723-1742

  Sassaroli, Angelo ^a   Martelli, Fabrizio ^b   Fantini, Sergio ^a  

^a Tufts University   (United States)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ABSORPTION; APPROXIMATION ALGORITHMS; COMPUTER SIMULATION; FREQUENCY DOMAIN ANALYSIS; MONTE CARLO METHODS; NEAR INFRARED SPECTROSCOPY; OPTICAL PROPERTIES; OPTICAL TOMOGRAPHY; PARTIAL DIFFERENTIAL EQUATIONS; PERSONAL COMPUTERS; PERTURBATION TECHNIQUES;

ALTERNATING CURRENT; APPROXIMANTS; APPROXIMATE FORMULAS; COMPUTATIONAL TIME; DIFFUSE OPTICAL TOMOGRAPHY; DIFFUSION EQUATIONS; DIFFUSIVE MEDIA; FAST FORWARD; FOURTH ORDER; FREQUENCY AND TIME DOMAINS; FREQUENCY DOMAINS; HIGHER ORDER; MONTE CARLO SIMULATION; PATH LENGTH; PENTIUM; PERTURBATION THEORY; PHASE DATA; POINT-SPREAD FUNCTION; SLAB GEOMETRY; TIME DOMAIN;

TIME DOMAIN ANALYSIS;

ABSORPTION; ARTICLE; DIFFUSION; INFRARED SPECTROPHOTOMETRY; LIGHT; OPTICAL TOMOGRAPHY; THEORETICAL MODEL; TIME;

ABSORPTION; DIFFUSION; LIGHT; MODELS, THEORETICAL; SPECTROPHOTOMETRY, INFRARED; TIME FACTORS; TOMOGRAPHY, OPTICAL;

EID: 77955992900     PISSN: 10847529     EISSN: 15208532     Source Type: Journal    
DOI: 10.1364/JOSAA.27.001723     Document Type: Article

References (38)

1. N. Shah, A. Cerussi, C. Eker, J. Espinoza, J. Butler, J. Fish-kin, R. Hornung, and B. Tromberg, "Noninvasive functional optical spectroscopy of human breast tissue", Proc. Natl. Acad. Sci. U. S. A. 98, 4420-4425 (2001).
2. T. O. McBride, B. W. Pogue, S. Poplack, S. Soho, W. A. Wells, S. Jiang, U. L. Osterberg, and K. D. Paulsen, "Mul-tispectral near-infrared tomography: a case study in compensating for water and lipid content in hemoglobin imaging of the breast", J. Biomed. Opt. 7, 72-79 (2002).
3. Y. Yu, N. Liu, A. Sassaroli, and S. Fantini, "Near-infrared spectral imaging of the female breast for quantitative oxim-etry in optical tomography", Appl. Opt. 48, D225-D235 (2009).
4. G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, "Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information", Phys. Med. Biol. 50, 3941-3956 (2005).
5. M. A. Franceschini, D. K. Joseph, T. J. Huppert, S. G. Diamond, and D. A. Boas, "Diffuse optical imaging of the whole head", J. Biomed. Opt. 11, 054007 (2006).
6. A. Y. Bluestone, G. Abdoulaev, C. H. Schmitz, R. L. Bar-bour, and A. H. Hielscher, "Three-dimensional optical tomography of hemodynamics in the human head", Opt. Express 9, 272-286 (2001).
7. V. Toronov, A. Webb, J. H. Choi, M. Wolf, U. Wolf, and E. Gratton, "Study of local cerebral hemodynamics by frequency-domain near-infrared spectroscopy and correlation with simultaneously acquired functional magnetic resonance imaging", Opt. Express 9, 417-427 (2001).
8. T. Durduran, C. Zhou, B. L. Edlow, G. Yu, R. Choe, M. N. Kim, B. L. Cucchiara, M. E. Putt, Q. Shah, S. E. Kasner, J. H. Greenberg, A. G. Yodh, and J. A. Detre, "Transcranial optical monitoring of cerebrovascular hemodynamics in acute stroke patients", Opt. Express 17, 3884-3902 (2009).
9. B. Chance, E. Anday, S. Nioka, S. Zhou, H. Long, K. Worden, C. Li, T. Turray, Y. Ovetsky, D. Pidikiti, and R. Thomas, "A novel method for fast imaging of brain function, non-invasively, with light", Opt. Express 2, 411-423 (1998).
10. J. Steinbrink, A. Villringer, F. Kempf, D. Haux, S. Boden, and H. Obrig, "Illuminating the BOLD signal: combined fMRI-fNIRS studies", Magn. Reson. Imaging 24, 495-505 (2006).
11. M. S. Patterson, B. Chance, and B. C. Wilson, "Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties", Appl. Opt. 28, 2331-2336 (1989).
12. K. Ren, G. Abdoulaev, G. Bal, and A. H. Hielscher, "Frequency-domain optical tomography based on the equation of radiative transfer", SIAM J. Sci. Comput. (USA) 28, 1463-1489 (2006).
13. E. L. Hull and T. H. Foster, "Steady-state reflectance spec-troscopy in the P3 approximation", J. Opt. Soc. Am. A 18, 584-599 (2001).
14. K. G. Phillips and S. L. Jacques, "Solution of transport equations in layered media with refractive index mismatch using the PN-method", J. Opt. Soc. Am. A 26, 2147-2162 (2009).
15. B. Wassermann, "Limits of high-order perturbation theory in time-domain optical mammography", Phys. Rev. E 74, 031908 (2006).
16. F. Martelli, A. Sassaroli, S. Del Bianco, Y. Yamada, and G. Zaccanti, "Solution of the time-dependent diffusion equation for layered diffusive media by the eigenfunction method", Phys. Rev. E 67, 056623 (2003).
17. V. A. Markel and J. C. Schotland, "Inverse problem in optical diffusion tomography. I. Fourier-Laplace inversion formulas", J. Opt. Soc. Am. A 18, 1336-1347 (2001).
18. D. A. Boas, M. A. O'Leary, B. Chance, and A. G. Yodh, "Scattering of diffuse photon density waves by spherical in-homogeneities within turbid media: Analytical solution and applications", Proc. Natl. Acad. Sci. U. S. A. 91, 4887-4891 (1994).
19. A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer", Med. Phys. 26, 1698-1707 (1999).
20. S. R. Arridge and J. C. Hebden, "Optical imaging in medicine: II. Modeling and reconstruction", Phys. Med. Biol. 42, 841-853 (1997).
21. S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, "A finite element approach for modelling photon transport in tissue", Med. Phys. 20, 299-309 (1993).
22. W. Bangerth and A. Joshi, "Adaptive finite element methods for the solution of inverse problems in optical tomography", Inverse Probl. 24, 034011 (2008).
23. H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, "Near infrared optical tomography using NIR-FAST: Algorithm for numerical model and image reconstruction", Commun. Numer. Methods Eng. 25, 711-732 (2009).
24. Q. Fang and D. A. Boas, "Monte Carlo simulation of photon migration in 3D turbid media accelerated by graphics processing units", Opt. Express 17, 20178-20190 (2009).
25. V. Chernomordik, D. W. Hattery, D. Grosenick, H. Wabnitz, H. Rinneberg, K. T. Moesta, P. M. Schlag, and A. Gandjba-khche, "Quantification of optical properties of a breast tumor using random walk theory", J. Biomed. Opt. 7, 80-87 (2002).
26. D. A. Boas, "A fundamental limitation of linearized algorithms for diffuse optical tomography", Opt. Express 1, 404-413 (1997).
27. 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).
28. 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. E 76, 061908 (2007).
29. 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).
30. 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).
31. A. Sassaroli, F. Martelli, S. Fantini, "Fourth order perturbation theory for the diffusion equation: continuous wave results for absorbing defects", Proc. SPIE 7174, 717402 (2009).
32. 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).
33. R. Graaff and K. Rinzema, "Practical improvements on photon diffusion theory: application to isotropic scattering", Phys. Med. Biol. 46, 3043-3050 (2001).
34. J. C. J. Paasschens, "Solution of the time-dependent Boltz-mann equation", Phys. Rev. E 56, 1135-1141 (1997).
35. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes, 2nd ed. (Cambridge U. Press, 1992).
36. D. Contini, F. Martelli, and G. Zaccanti, "Photon migration through a turbid slab described by a model based on diffusion approximation. I. Theory", Appl. Opt. 36, 4587-4599 (1997).
37. A. Torricelli, L. Spinelli, A. Pifferi, P. Taroni, and R. Cu-beddu, "Use of a nonlinear perturbation approach for in vivo breast lesion characterization by multi-wavelength time-resolved optical mammography", Opt. Express 11, 853-867 (2003).
38. G. A. Baker and P. Graves-Morris, Padé Approximants, 2nd ed. (Cambridge U. Press, 1996).