The inverse source problem based on the radiative transfer equation in optical molecular imaging

Journal of Computational Physics

Volumn 202, Issue 1, 2005, Pages 323-345

  Klose, Alexander D ^a   Ntziachristos, Vasilis ^b   Hielscher, Andreas H ^a  

^a Columbia University ^*  (United States)

^b HARVARD MEDICAL SCHOOL   (United States)

Author keywords

Adjoint differentiation; Algorithmic differentiation; Discrete ordinates method; Equation of radiative transfer; Fluorescence imaging; Fluorescence tomography; Inverse source problem; Molecular imaging; Scattering media; Tissue optics

Indexed keywords

INFRARED DEVICES; INVERSE PROBLEMS; ITERATIVE METHODS; MOLECULAR IMAGING; OPTICAL TOMOGRAPHY; RADIATIVE TRANSFER; TISSUE;

ADJOINT DIFFERENTIATION; ADJOINTS; ALGORITHMIC DIFFERENTIATIONS; DISCRETE ORDINATES METHOD; EQUATION OF RADIATIVE TRANSFER; FLUORESCENCE IMAGING; FLUORESCENCE TOMOGRAPHY; INVERSE SOURCE PROBLEM; SCATTERING MEDIUM; TISSUES OPTICS;

FLUORESCENCE IMAGING;

EID: 8744226110     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.07.008     Document Type: Article

References (101)

1. R. Weissleder U. Mahmood Molecular imaging Radiology 219 2001 316
2. P.R. Contag Whole-animal cellular and molecular imaging to accelerate drug development Drug Discovery Today 7 2002 555
3. R.J. Gillies In vivo molecular imaging J. Cell. Biochem. Suppl. 39 2002 231
4. T.F. Massoud S.S. Gambhir Molecular imaging in living subjects: Seeing fundamental biological processes in a new light Genes Dev. 17 2003 545
5. R.G. Blasberg Molecular imaging and cancer Mol. Cancer Therap. 2 2003 335
6. R.G. Blasberg J.G. Tjuvajev Molecular-genetic imaging: Current and future perspectives J. Clin. Invest. 111 2003 1620
7. S.R. Cherry In vivo molecular imaging and genomic imaging: New challenges for imaging physics Phys. Med. Biol. 49 2004 R13
8. D. Piwnica-Worms D.P. Schuster J.R. Garbow Molecular imaging of host-pathogen interactions in intact small animals Cell. Microbiol. 6 2004 319
9. J. Allport R. Weissleder In vivo imaging of gene and cell therapies Exp. Hematol. 29 2001 1237
10. C. Bremer V. Ntziachristos R. Weissleder Optical-based molecular imaging: Contrast agents and potential medical applications Eur. Radiol. 13 2001 231
11. D.J. Bornhop C.H. Contag K. Licha C.J. Murphy Advances in contrast agents, reporters, and detection J. Biomed. Opt. 6 2001 106
12. K. Licha Contrast agents for optical imaging Topics in Current Chemistry vol. 222 2002 Springer Heidelberg 1-29
13. R. Weissleder V. Ntziachristos Shedding light onto live molecular targets Nat. Med. 9 2003 123
14. G. Choy P. Choyke S.K. Libutti Current advances in molecular imaging: noninvasive in vivo bioluminescent and fluorescent optical imaging in cancer research Mol. Imaging 2 2003 303
15. J.E. Bugaj S. Achilefu R.B. Dorshow R. Rajagopalan Novel fluorescent contrast agents for optical imaging of in vivo tumors based on a receptor-targeted dye-peptide conjugate platform J. Biomed. Opt. 6 2001 122
16. 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 2001 327
17. C.J. Daly J.C. McGrath Fluorescent ligands, antibodies, and proteins for the study of receptors Pharmacol. Therap. 100 2003 101
18. R. Weissleder C.-H. Tung U. Mahmood A. Bogdanov In vivo imaging of tumors with protease-activated near-infrared fluorescent probes Nat. Biotechnol. 17 1999 375
19. V. Ntziachristos C.H. Tung C. Bremer R. Weissleder Fluorescence molecular tomography resolves protease activity in vivo Nat. Med. 8 2002 757
20. V. Ntziachristos R. Bremer R. Weissleder Fluorescence imaging with near-infrared light: New technological advances that enable in vivo molecular imaging Eur. Radiol. 13 2003 195
21. P. Wunderbaldiger A. Bogdanov R. Weissleder New approaches for imaging in gene therapy Eur. J. Radiol. 34 2000 156
22. B.W. Rice M.D. Cable M.B. Nelson In vivo imaging of light-emitting probes J. Biomed. Opt. 6 2001 432
23. Y. Chen G. Zheng Z.H. Zhang D. Blessington M. Zhang H. Li Q. Liu L. Zhou X. Intes S. Achilefu B. Chance Metabolism-enhanced tumor localization by fluorescence imaging: In vivo animal studies Opt. Lett. 28 2003 2070
24. F. Natterer Mathematical models for medical imaging in: Ch. Boergers F. Natterer Computational Radiology and Imaging: Therapy and Diagnostics. The IMA Volumes in Mathematics and its Applications 1999 Springer New York 17-32
25. N.J. McCormick Inverse radiative transfer problems: A review Nucl. Sci. Eng. 112 1992 185
26. E.W. Larsen The inverse source problem in radiative transfer J. Quant. Spectrosc. Radiat. Transfer 15 1975 1
27. H.C. Yi R. Sanchez N.J. McCormick Bioluminescence estimation from ocean in situ irradiances Appl. Opt. 31 1992 822
28. C.E. Siewert An inverse source problem in radiative transfer J. Quant. Spectrosc. Radiat. Transfer 50 1993 603
29. C.E. Siewert A radiative-transfer inverse-source problem for a sphere J. Quant. Spectrosc. Radiat. Transfer 52 1994 157
30. N.J. McCormick Unified approach to analytical solutions of three inverse transport problems Prog. Nucl. Energy 34 1999 425
31. H.Y. Li M.N. Ozisik Estimation of the radiation source term with a conjugate-gradient method of inverse analysis J. Quant. Spectrosc. Radiat. Transfer 48 1992 237
32. Z. Tao N.J. McCormick R. Sanchez Ocean source and optical property estimation from explicit and implicit algorithms Appl. Opt. 33 1994 3265
33. 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. Spectrosc. Radiat. Transfer 67 2000 113
34. H.Y. Li A two-dimensional cylindrical inverse source problem in radiative transfer J. Quant. Spectrosc. Radiat. Transfer 69 2001 403
35. 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 2001 2949
36. J. Su A.J. Silva Neto Two-dimensional inverse heat conduction problem of source strength estimation in cylindrical rods Appl. Math. Modeling 25 2001 861
37. 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 1997 2260
38. J. Chang H.L. Graber R.L. Barbour Imaging of fluorescence in highly scattering media IEEE Trans. Biomed. Eng. 44 1997 810
39. H. Jiang Frequency-domain fluorescent diffusion tomography: A finite-element-based algorithm and simulations Appl. Opt. 37 1998 5337
40. J. Chang H.L. Graber R.L. Barbour Luminescence optical tomography of dense scattering media J. Opt. Soc. Am. A 14 1997 288
41. R. Roy E.M. Sevick-Muraca A numerical study of gradient-based nonlinear optimization methods for contrast enhanced optical tomography Opt. Exp. 9 2001 49
42. J. Lee E.M. Sevick-Muraca Fluorescence-enhanced absorption imaging using frequency-domain photon migration: Tolerance to measurement error J. Biomed. Opt. 6 2001 58
43. M.A. O'Leary D.A. Boas X.D. Li B. Chance A.G. Yodh Fluorescence lifetime imaging in turbid media Opt. Lett. 21 1996 158
44. V. Ntziachristos R. Weissleder Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation Opt. Lett. 26 2001 893
45. 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 2002 759
46. M.J. Eppstein D.J. Hawrysz A. Godavarty E.M. SevickMuraca Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: Near-infrared fluorescence tomography PNAS 99 2002 9619
47. V. Ntziachristos R. Weissleder Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media Med. Phys. 29 2002 803
48. 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 2003 3081
49. 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 1998 5313
50. R. Aronson N. Corngold Photon diffusion coefficient in an absorbing medium J. Opt. Soc. Am. A 16 1999 1066
51. B. Chen K. Stamnes J.J. Stamnes Validity of the diffusion approximation in bio-optical imaging Appl. Opt. 40 2001 6356
52. R. Elaloufi R. Carminati J.-J. Greffet Time-dependent transport through scattering media: From radiative transfer to diffusion J. Opt. A 4 2002 S103
53. A.H. Hielscher A.D. Klose K.M. Hanson Gradient-based iterative image reconstruction scheme for time-resolved optical tomography IEEE Trans. Med. Imaging 18 1999 262
54. A.D. Klose A.H. Hielscher Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer Med. Phys. 26 1999 1698
55. 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 2002 715
56. A.D. Klose A.H. Hielscher Quasi-Newton methods in optical tomographic image reconstruction Inverse Problems 19 2003 387
57. A.D. Klose A.H. Hielscher Fluorescence tomography with simulated data based on the equation of radiative transfer Opt. Lett. 28 2003 1019
58. R.A.J. Groenhuis H.A. Ferwerda J.J. Ten Bosch Scattering and absorption of turbid materials determined from reflection measurements. 1: Theory Appl. Opt. 22 1983 2456
59. W.F. Cheong S.A. Prahl A.J. Welch A review of the optical properties of biological tissues IEEE J. Quantum Electron. 26 1990 2166
60. S.A. Prahl M.J.C. van Gemert A.J. Welch Determining the optical properties of turbid media by using the adding-doubling method Appl. Opt. 32 1993 559
61. M. Born E. Wolf Principles of Optics 1999 Cambridge University Press Cambridge, MA
62. J.J. Duderstadt W.R. Martin Transport Theory 1979 Wiley New York
63. S. Chandrasekhar Radiative Transfer 1960 Oxford University Press London
64. K.M. Case P.F. Zweifel Linear Transport Theory 1967 Addison-Wesley Massachusetts
65. E.E. Lewis W.F. Miller Computational Methods of Neutron Transport 1984 Wiley New York
66. B.G. Carlson K.D. Lathrop Transport theory - the method of discrete ordinates in: H. Greenspan (Ed.) Computing Methods in Reactor Physics 1968 Gordon and Breach New York 166-266
67. R. Sanchez N.J. McCormick A review of neutron transport approximations Nucl. Sci. Eng. 80 1982 481
68. M.L. Adams E.W. Larsen Fast iterative methods for discrete-ordinates particle transport calculations Prog. Nucl. Energy 40 2002 3
69. S.T Thynell Discrete-ordinates method in radiative heat transfer Int. J. Eng. Sci. 36 1998 1651
70. M.A. Ramankutty A.L. Crosbie Modified discrete ordinates solution of radiative transfer in two-dimensional rectangular enclosures J. Quant. Spectrosc. Radiat. Transfer 57 1997 107
71. R. Koch W. Krebs S. Wittig R. Viskanta Discrete ordinates quadrature schemes for multidimensional radiative transfer J. Quant. Spectrosc. Radiat. Transfer 53 1995 353
72. P.N. Brown B. Chang U.R. Hanebutte Spherical harmonic solutions of the boltzmann transport equation via discrete ordinates Prog. Nucl. Energy 39 2001 263
73. L.G. Stenholm H. Stoerzer R. Wehrse An efficient method for the solution of 3-D radiative transfer problems J. Quant. Spectrosc. Radiat. Transfer 45 1991 47
74. S.J. Wilson T.S. Tan Radiative transfer in a two-dimensional rectangular annulus medium Math. Comput. Modeling 24 1996 29
75. A.D. Klose A.H. Hielscher Modeling photon propagation in anisotropically scattering media with the equation of radiative transfer in: B. Chance R.R. Alfano B.J. Tromberg M. Tamura E.M. Sevick-Muraca (Eds.) Optical Tomography and Spectroscopy of Tissue V, Proc. 4955, SPIE 2003 The International Society for Optical Engineering Bellingham, WA 624-633
76. W.J. Wiscombe The Delta-M method: Rapid yet accurate radiative flux calculations for strongly asymmetric phase functions J. Atmos. Sci. 34 1977 1408
77. A.J. Welch M.J.C. van Gemert Optical-Thermal Response of Laser-Irradiated Tissue 1995 Plenum Press London
78. S.R. Arridge Optical tomography in medical imaging Inverse Problems 15 1999 R41
79. S.G. Nash Linear and Nonlinear Programming 1996 McGraw-Hill New York
80. J. Nocedal S.J. Wright Numerical Optimization 1999 Springer New York
81. D.G. Luenberger Linear and Nonlinear Programming 1984 Addison-Wesley Reading, MA
82. Ch.M. Bishop Neural Networks for Pattern Recognition 1997 Clarendon Press Oxford
83. G.I. Marchuk Adjoint Equations and Analysis of Complex Systems 1995 Kluwer Academic Publishers Dordrecht
84. M.E. Errico What is an adjoint model? Bull. Am. Meteorol. Soc. 78 1997 2577
85. R.E. Wengert A simple automatic derivative evaluation program Commun. ACM 7 1964 463
86. L.B. Rall Automatic Differentiation: Techniques and Applications Lecture Notes in Computer Science 120 1981 Springer Berlin
87. L.B. Rall G.F. Corliss An introduction to automatic differentiation in: A. Griewank G.F. Corliss (Ed.) Automatic Differentiation of Algorithms: Theory, Implementation, and Application 1991 SIAM Philadelphia 1-18
88. O. Talagrand The use of adjoint equations in numerical modeling of atmospheric circulation in: A. Griewank G.F. Corliss (Eds.) Automatic Differentiation of Algorithms: Theory, Implementations, and Application 1991 SIAM Philadelphia 169-180
89. T. Beck Automatic differentiation of iterative processes J. Comput. Appl. Math. 50 1994 109
90. R. Giering T. Kaminski Recipes of adjoint code construction ACM Trans. Math. Software 24 1998 437
91. 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 Publishers Dordrecht 121-135
92. T. Kaminski M. Heimann R. Giering A coarse grid three-dimensional global inverse model of atmospheric transport. 1. Adjoint model and Jacobian matrix J. Geophys. Res. 104 1999 18535
93. S.J. Norton Iterative inverse scattering algorithms: Methods of computing Frechet derivatives J. Acoust. Soc. Am. 106 1999 2653
94. T.F. Coleman F. Santosa A. Verma Efficient calculation of Jacobian and adjoint vector products in the wave propagational inverse problem using automatic differentiation J. Comput. Phys. 157 2000 234
95. E.A. Ustinov Adjoint sensitivity analysis of radiative transfer equation: Temperature and gas mixing ratio weighting functions for remote sensing of scattering atmospheres in thermal IR J. Quantum Spectrosc. Radiat. Transfer 68 2001 195
96. I.N. Polonsky M.A. Box A.B. Davis Radiative transfer through inhomogeneous turbid media: Implementation of the adjoint perturbation approach at the first order J. Quant. Spectrosc. Transfer 78 2003 85
97. E.E. Graves J. Ripoll R. Weissleder V. Ntziachristos Sub-millimeter resolution molecular imaging system for small animal imaging Med. Phys. 30 2003 901
98. R. Roy A. Godavarty E.M. SevickMuraca Fluorescence-enhanced optical tomography using referenced measurements of heterogeneous media IEEE Trans. Med. Imaging 22 2003 824
99. A. Godavarty M.J. Eppstein C. Zhang S. Theru A.B. Thompson M. Gurfinkel E.M. Sevick-Muraca Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera Phys. Med. Biol. 48 2003 1701
100. J.C. Chai H.S. Lee S.V. Patankar Ray effect and false scattering in the discrete ordinates method Numer. Heat Transfer B 24 1993 373
101. 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