Abstract

As a new mode of molecular imaging, bioluminescence tomography (BLT) has become a hot topic over the past two years. In this paper, a multilevel adaptive finite element algorithm is developed for BLT reconstruction. In this algorithm, the mesh is adaptively refined according to a posteriori error estimation, which helps not only to improve localization and quantification of sources but also to enhance the robustness and efficiency of reconstruction. In the numerical simulation, bioluminescent signals on the body surface of a heterogeneous phantom are synthesized in a molecular optical simulation environment (MOSE) that we developed to model the photon transportation via Monte Carlo simulation. The performance of the algorithm is evaluated in numerical tests involving single and multiple sources in various arrangements. The results demonstrate the merits and potential of the multilevel adaptive approach for BLT.

© 2006 Optical Society of America

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2005 (5)

V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weisslder , “ Looking and listening to light: the evolution of whole body photonic imaging ,” Nature Biotechnology   23 (3), 313 – 320 ( 2005 ).
[Crossref] [PubMed]

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

G. Alexandrakis , F. R. Rannou , and 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 ).
[Crossref] [PubMed]

W. Cong , G. Wang , D. Kumar , Y. Liu , M. Jiang , L. V. Wang , E. A Hoffman , G. McLennan , P. B. McCray , J. Zabner , and A. Cong , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express   13 , 6756 – 6771 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 .
[Crossref] [PubMed]

A. P. Gibson , J. C. Hebden , and S. R. Arridge , “ Recent advances in diffuse optical imaging ,” Phys. Med. Biol.   50 , R1 – R43 ( 2005 ).
[Crossref] [PubMed]

2004 (6)

A. Joshi , W. Bangerth , and E. M. Sevick-Muraca , “ Adaptive finite element based tomography for fluorescence optical imaging in tissue ,” Opt. Express   12 , 5402 – 5417 ( 2004 ), www.opticsexpress.org/abstract.cfm?URI=OPEX-12-22-5402 .
[Crossref] [PubMed]

G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys.   31 , 2289 – 2299 ( 2004 ).
[Crossref] [PubMed]

M. Jiang and G. Wang , “ Image reconstruction for bioluminescence tomography ,” Proc. SPIE   5535 , 335 – 351 ( 2004 ).
[Crossref]

W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE   5535 , 679 – 686 ( 2004 ).
[Crossref]

X. Gu , Q. Zhang , L. Larcom , and H. Jiang , “ Three-dimensional bioluminescence tomography with model-based reconstruction ,” Opt. Express   12 , 3996 – 4000 ( 2004 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-17-3996 .
[Crossref] [PubMed]

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

2003 (4)

E. E. Graves , J. Ripoll , R. Weissleder , and V. Ntziachristos , “ A submillimeter resolution fluorescence molecular imaging system for small animal imaging ,” Med. Phys.   30 , 901 – 911 ( 2003 ).
[Crossref] [PubMed]

T. F. Massoud and S. S. Gambhir , “ Molecular imaging in living subjects: seeing fundamental biological processes in a new light ,” Genes Dev.   17 , 545 – 580 ( 2003 ).
[Crossref] [PubMed]

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

Z. Wu and J. M. Sullivan , “ Multiple material marching cubes algorithm ,” Int. J. Numer. Methods Eng.   58 , 189 – 207 ( 2003 ).
[Crossref]

2002 (3)

C. Contag and M. H. Bachmann , “ Advances in bioluminescence imaging of gene expression ,” Annu. Rev. Bio-med. Eng.   4 , 235 – 260 ( 2002 ).
[Crossref]

S. Bhaumik and S. S. Gambhir , “ Optical imaging of Renilla luciferase reporter gene expression in living mice ,” Proc. Natl. Acad. Sci. USA   99 , 377 – 382 ( 2002 ).
[Crossref]

D. Boas , J. Culver , J. Stott , and A. Dunn , “ Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head ,” Opt. Express   10 , 159 – 169 ( 2002 ), http://www.opticsinfobase.org/abstract.cfm?URI=OPEX-10-3-159 .
[PubMed]

2001 (1)

W. Rice , M. D. Cable , and M. B. Nelson , “ In vivo imaging of light-emitting probes ,” J. Biomed. Opt.   6 , 432 – 440 ( 2001 ).
[Crossref] [PubMed]

1998 (1)

Thérèse and J. W. Hastings , “ Bioluminescence ,” Annu. Rev. Cell Dev. Bi.   14 , 197 – 230 ( 1998 ).
[Crossref]

1995 (3)

M. Schweiger , S. R. Arridge , M. Hiraoka , and D. T. Delpy , “ The finite element method for the propagation of light in scattering media: Boundary and source conditions ,” Med. Phys.   22 , 1779 – 1792 ( 1995 ).
[Crossref] [PubMed]

J. Bey , “ Tetrahedral grid refinement ,” Computing   55 , 355 – 378 ( 1995 ).
[Crossref]

L. H. Wang , S. L. Jacques , and L. Q. Zheng , “ MCML-Monte Carlo modeling of photon transport in multi-layered tissues ,” Comput. Meth. Prog. Biomed.   47 , 131 – 146 ( 1995 ).
[Crossref]

1993 (1)

S. R. Arridge , M. Schweiger , M. Hiraoka , and D. T. Delpy , “ A finite element approach for modeling photon transport in tissue ,” Med. Phys.   20 , 299 – 309 ( 1993 ).
[Crossref] [PubMed]

Ainsworth, M.

M. Ainsworth and J. T. Oden , A posteriori error estimation in finite element analysis , ( Wiley , 2000 ).
[Crossref]

Alexandrakis, G.

G. Alexandrakis , F. R. Rannou , and 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 ).
[Crossref] [PubMed]

Arridge, S. R.

A. P. Gibson , J. C. Hebden , and S. R. Arridge , “ Recent advances in diffuse optical imaging ,” Phys. Med. Biol.   50 , R1 – R43 ( 2005 ).
[Crossref] [PubMed]

M. Schweiger , S. R. Arridge , M. Hiraoka , and D. T. Delpy , “ The finite element method for the propagation of light in scattering media: Boundary and source conditions ,” Med. Phys.   22 , 1779 – 1792 ( 1995 ).
[Crossref] [PubMed]

S. R. Arridge , M. Schweiger , M. Hiraoka , and D. T. Delpy , “ A finite element approach for modeling photon transport in tissue ,” Med. Phys.   20 , 299 – 309 ( 1993 ).
[Crossref] [PubMed]

Bachmann, M. H.

C. Contag and M. H. Bachmann , “ Advances in bioluminescence imaging of gene expression ,” Annu. Rev. Bio-med. Eng.   4 , 235 – 260 ( 2002 ).
[Crossref]

Bading, J. R.

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

Banerjee, D.

J. Huang , X. Huang , D. Metaxes , and D. Banerjee , “ 3D tumor shape reconstruction from 2D bioluminescence images ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Bangerth, W.

Bey, J.

J. Bey , “ Tetrahedral grid refinement ,” Computing   55 , 355 – 378 ( 1995 ).
[Crossref]

Bhaumik, S.

S. Bhaumik and S. S. Gambhir , “ Optical imaging of Renilla luciferase reporter gene expression in living mice ,” Proc. Natl. Acad. Sci. USA   99 , 377 – 382 ( 2002 ).
[Crossref]

Boas, D.

Cable, M. D.

W. Rice , M. D. Cable , and M. B. Nelson , “ In vivo imaging of light-emitting probes ,” J. Biomed. Opt.   6 , 432 – 440 ( 2001 ).
[Crossref] [PubMed]

Chatziioannou, A. F.

G. Alexandrakis , F. R. Rannou , and 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 ).
[Crossref] [PubMed]

Chaudhari, A. J.

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

Cheng, J.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Cherry, S. R.

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

Cline, H. E.

W. E. Lorensen and H. E. Cline , “ Marching cubes: a high resolution 3D surface construction algorithm ,” in Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques ( ACM Press , 1987 ), pp. 163 – 169 .

Cong, A.

Cong, W.

W. Cong , G. Wang , D. Kumar , Y. Liu , M. Jiang , L. V. Wang , E. A Hoffman , G. McLennan , P. B. McCray , J. Zabner , and A. Cong , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express   13 , 6756 – 6771 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 .
[Crossref] [PubMed]

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE   5535 , 679 – 686 ( 2004 ).
[Crossref]

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Contag, C.

C. Contag and M. H. Bachmann , “ Advances in bioluminescence imaging of gene expression ,” Annu. Rev. Bio-med. Eng.   4 , 235 – 260 ( 2002 ).
[Crossref]

Conti, P. S.

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

Coquoz, O.

C. Kuo , O. Coquoz , D. G. Stearns , and B. W. Rice , “ Diffuse luminescence tomography of in vivo bioluminescence markers using multi-spetral data ,” in Proceedings of the 3rd International Meeting of the Society ( MIT Press , 2004 ), p. 227 .

Culver, J.

Darvas, F.

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

Delpy, D. T.

M. Schweiger , S. R. Arridge , M. Hiraoka , and D. T. Delpy , “ The finite element method for the propagation of light in scattering media: Boundary and source conditions ,” Med. Phys.   22 , 1779 – 1792 ( 1995 ).
[Crossref] [PubMed]

S. R. Arridge , M. Schweiger , M. Hiraoka , and D. T. Delpy , “ A finite element approach for modeling photon transport in tissue ,” Med. Phys.   20 , 299 – 309 ( 1993 ).
[Crossref] [PubMed]

Dunn, A.

Gambhir, S. S.

T. F. Massoud and S. S. Gambhir , “ Molecular imaging in living subjects: seeing fundamental biological processes in a new light ,” Genes Dev.   17 , 545 – 580 ( 2003 ).
[Crossref] [PubMed]

S. Bhaumik and S. S. Gambhir , “ Optical imaging of Renilla luciferase reporter gene expression in living mice ,” Proc. Natl. Acad. Sci. USA   99 , 377 – 382 ( 2002 ).
[Crossref]

Garland, M.

M. Garland and P. S. Heckbert , “ Surface simplification using quadric error metrics ,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques ( ACM Press , 1997 ), pp. 209 – 216 .

Gibson, A. P.

A. P. Gibson , J. C. Hebden , and S. R. Arridge , “ Recent advances in diffuse optical imaging ,” Phys. Med. Biol.   50 , R1 – R43 ( 2005 ).
[Crossref] [PubMed]

Gill, P. E.

P. E. Gill , W. Murray , and M. Wright , Practical optimization , ( Academic Press, New York , 1981 ).

Graves, E. E.

E. E. Graves , J. Ripoll , R. Weissleder , and V. Ntziachristos , “ A submillimeter resolution fluorescence molecular imaging system for small animal imaging ,” Med. Phys.   30 , 901 – 911 ( 2003 ).
[Crossref] [PubMed]

Gu, X.

Han, W.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Hastings, J. W.

Thérèse and J. W. Hastings , “ Bioluminescence ,” Annu. Rev. Cell Dev. Bi.   14 , 197 – 230 ( 1998 ).
[Crossref]

Hebden, J. C.

A. P. Gibson , J. C. Hebden , and S. R. Arridge , “ Recent advances in diffuse optical imaging ,” Phys. Med. Biol.   50 , R1 – R43 ( 2005 ).
[Crossref] [PubMed]

Heckbert, P. S.

M. Garland and P. S. Heckbert , “ Surface simplification using quadric error metrics ,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques ( ACM Press , 1997 ), pp. 209 – 216 .

Hiraoka, M.

M. Schweiger , S. R. Arridge , M. Hiraoka , and D. T. Delpy , “ The finite element method for the propagation of light in scattering media: Boundary and source conditions ,” Med. Phys.   22 , 1779 – 1792 ( 1995 ).
[Crossref] [PubMed]

S. R. Arridge , M. Schweiger , M. Hiraoka , and D. T. Delpy , “ A finite element approach for modeling photon transport in tissue ,” Med. Phys.   20 , 299 – 309 ( 1993 ).
[Crossref] [PubMed]

Hoffman, E. A

Hoffman, E. A.

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

Holder, S.

S. Holder , Electrical Impedance Tomography , ( Institute of Physics Publishing, Bristol and Philadelphia , 2005 ).

Huang, J.

J. Huang , X. Huang , D. Metaxes , and D. Banerjee , “ 3D tumor shape reconstruction from 2D bioluminescence images ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Huang, X.

J. Huang , X. Huang , D. Metaxes , and D. Banerjee , “ 3D tumor shape reconstruction from 2D bioluminescence images ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Jacques, S. L.

L. H. Wang , S. L. Jacques , and L. Q. Zheng , “ MCML-Monte Carlo modeling of photon transport in multi-layered tissues ,” Comput. Meth. Prog. Biomed.   47 , 131 – 146 ( 1995 ).
[Crossref]

Jiang, H.

Jiang, M.

W. Cong , G. Wang , D. Kumar , Y. Liu , M. Jiang , L. V. Wang , E. A Hoffman , G. McLennan , P. B. McCray , J. Zabner , and A. Cong , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express   13 , 6756 – 6771 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 .
[Crossref] [PubMed]

G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys.   31 , 2289 – 2299 ( 2004 ).
[Crossref] [PubMed]

M. Jiang and G. Wang , “ Image reconstruction for bioluminescence tomography ,” Proc. SPIE   5535 , 335 – 351 ( 2004 ).
[Crossref]

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Joshi, A.

Kumar, D.

W. Cong , G. Wang , D. Kumar , Y. Liu , M. Jiang , L. V. Wang , E. A Hoffman , G. McLennan , P. B. McCray , J. Zabner , and A. Cong , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express   13 , 6756 – 6771 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 .
[Crossref] [PubMed]

W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE   5535 , 679 – 686 ( 2004 ).
[Crossref]

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Kuo, C.

C. Kuo , O. Coquoz , D. G. Stearns , and B. W. Rice , “ Diffuse luminescence tomography of in vivo bioluminescence markers using multi-spetral data ,” in Proceedings of the 3rd International Meeting of the Society ( MIT Press , 2004 ), p. 227 .

Larcom, L.

Leahy, R. M.

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

Li, H.

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Li, Y.

G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys.   31 , 2289 – 2299 ( 2004 ).
[Crossref] [PubMed]

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Liu, Y.

Lorensen, W. E.

W. E. Lorensen and H. E. Cline , “ Marching cubes: a high resolution 3D surface construction algorithm ,” in Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques ( ACM Press , 1987 ), pp. 163 – 169 .

Luo, J.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Lv, Y.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Massoud, T. F.

T. F. Massoud and S. S. Gambhir , “ Molecular imaging in living subjects: seeing fundamental biological processes in a new light ,” Genes Dev.   17 , 545 – 580 ( 2003 ).
[Crossref] [PubMed]

McCray, P. B.

McLennan, G.

Meinel, J. F.

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

Metaxes, D.

J. Huang , X. Huang , D. Metaxes , and D. Banerjee , “ 3D tumor shape reconstruction from 2D bioluminescence images ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Moats, R. A.

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

Murray, W.

P. E. Gill , W. Murray , and M. Wright , Practical optimization , ( Academic Press, New York , 1981 ).

Nelson, M. B.

W. Rice , M. D. Cable , and M. B. Nelson , “ In vivo imaging of light-emitting probes ,” J. Biomed. Opt.   6 , 432 – 440 ( 2001 ).
[Crossref] [PubMed]

Ntziachristos, V.

V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weisslder , “ Looking and listening to light: the evolution of whole body photonic imaging ,” Nature Biotechnology   23 (3), 313 – 320 ( 2005 ).
[Crossref] [PubMed]

E. E. Graves , J. Ripoll , R. Weissleder , and V. Ntziachristos , “ A submillimeter resolution fluorescence molecular imaging system for small animal imaging ,” Med. Phys.   30 , 901 – 911 ( 2003 ).
[Crossref] [PubMed]

Oden, J. T.

M. Ainsworth and J. T. Oden , A posteriori error estimation in finite element analysis , ( Wiley , 2000 ).
[Crossref]

Qian, X.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Rannacher, R.

W. Bangerth and R. Rannacher , Adaptive finite element methods for differential equations , ( Birkhäuser Verlag , 2003 ).

Rannou, F. R.

G. Alexandrakis , F. R. Rannou , and 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 ).
[Crossref] [PubMed]

Rao, S. S.

S. S. Rao , The finite element method in engineering , ( Butterworth-Heinemann, Boston , 1999 ).

Rice, B. W.

C. Kuo , O. Coquoz , D. G. Stearns , and B. W. Rice , “ Diffuse luminescence tomography of in vivo bioluminescence markers using multi-spetral data ,” in Proceedings of the 3rd International Meeting of the Society ( MIT Press , 2004 ), p. 227 .

Rice, W.

W. Rice , M. D. Cable , and M. B. Nelson , “ In vivo imaging of light-emitting probes ,” J. Biomed. Opt.   6 , 432 – 440 ( 2001 ).
[Crossref] [PubMed]

Ripoll, J.

V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weisslder , “ Looking and listening to light: the evolution of whole body photonic imaging ,” Nature Biotechnology   23 (3), 313 – 320 ( 2005 ).
[Crossref] [PubMed]

E. E. Graves , J. Ripoll , R. Weissleder , and V. Ntziachristos , “ A submillimeter resolution fluorescence molecular imaging system for small animal imaging ,” Med. Phys.   30 , 901 – 911 ( 2003 ).
[Crossref] [PubMed]

Schweiger, M.

M. Schweiger , S. R. Arridge , M. Hiraoka , and D. T. Delpy , “ The finite element method for the propagation of light in scattering media: Boundary and source conditions ,” Med. Phys.   22 , 1779 – 1792 ( 1995 ).
[Crossref] [PubMed]

S. R. Arridge , M. Schweiger , M. Hiraoka , and D. T. Delpy , “ A finite element approach for modeling photon transport in tissue ,” Med. Phys.   20 , 299 – 309 ( 1993 ).
[Crossref] [PubMed]

Sevick-Muraca, E. M.

Shen, H.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Smith, D. J.

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

Stearns, D. G.

C. Kuo , O. Coquoz , D. G. Stearns , and B. W. Rice , “ Diffuse luminescence tomography of in vivo bioluminescence markers using multi-spetral data ,” in Proceedings of the 3rd International Meeting of the Society ( MIT Press , 2004 ), p. 227 .

Stott, J.

Sullivan, J. M.

Z. Wu and J. M. Sullivan , “ Multiple material marching cubes algorithm ,” Int. J. Numer. Methods Eng.   58 , 189 – 207 ( 2003 ).
[Crossref]

Suter, M.

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

Thérèse,

Thérèse and J. W. Hastings , “ Bioluminescence ,” Annu. Rev. Cell Dev. Bi.   14 , 197 – 230 ( 1998 ).
[Crossref]

Tian, J.

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Wang, G.

W. Cong , G. Wang , D. Kumar , Y. Liu , M. Jiang , L. V. Wang , E. A Hoffman , G. McLennan , P. B. McCray , J. Zabner , and A. Cong , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express   13 , 6756 – 6771 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 .
[Crossref] [PubMed]

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

M. Jiang and G. Wang , “ Image reconstruction for bioluminescence tomography ,” Proc. SPIE   5535 , 335 – 351 ( 2004 ).
[Crossref]

W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE   5535 , 679 – 686 ( 2004 ).
[Crossref]

G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys.   31 , 2289 – 2299 ( 2004 ).
[Crossref] [PubMed]

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Wang, L. H.

L. H. Wang , S. L. Jacques , and L. Q. Zheng , “ MCML-Monte Carlo modeling of photon transport in multi-layered tissues ,” Comput. Meth. Prog. Biomed.   47 , 131 – 146 ( 1995 ).
[Crossref]

Wang, L. V.

W. Cong , G. Wang , D. Kumar , Y. Liu , M. Jiang , L. V. Wang , E. A Hoffman , G. McLennan , P. B. McCray , J. Zabner , and A. Cong , “ Practical reconstruction method for bioluminescence tomography ,” Opt. Express   13 , 6756 – 6771 ( 2005 ), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-13-18-6756 .
[Crossref] [PubMed]

V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weisslder , “ Looking and listening to light: the evolution of whole body photonic imaging ,” Nature Biotechnology   23 (3), 313 – 320 ( 2005 ).
[Crossref] [PubMed]

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

Weisslder, R.

V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weisslder , “ Looking and listening to light: the evolution of whole body photonic imaging ,” Nature Biotechnology   23 (3), 313 – 320 ( 2005 ).
[Crossref] [PubMed]

Weissleder, R.

E. E. Graves , J. Ripoll , R. Weissleder , and V. Ntziachristos , “ A submillimeter resolution fluorescence molecular imaging system for small animal imaging ,” Med. Phys.   30 , 901 – 911 ( 2003 ).
[Crossref] [PubMed]

Wright, M.

P. E. Gill , W. Murray , and M. Wright , Practical optimization , ( Academic Press, New York , 1981 ).

Wu, Z.

Z. Wu and J. M. Sullivan , “ Multiple material marching cubes algorithm ,” Int. J. Numer. Methods Eng.   58 , 189 – 207 ( 2003 ).
[Crossref]

Zabner, J.

Zhang, Q.

Zheng, L. Q.

L. H. Wang , S. L. Jacques , and L. Q. Zheng , “ MCML-Monte Carlo modeling of photon transport in multi-layered tissues ,” Comput. Meth. Prog. Biomed.   47 , 131 – 146 ( 1995 ).
[Crossref]

Zhou, T.

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

Zhu, F.

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

Acad. Radiol. (1)

H. Li , J. Tian , F. Zhu , W. Cong , L. V. Wang , E. A. Hoffman , and G. Wang , “ A mouse optical simulation enviroment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo Method ,” Acad. Radiol.   11 , 1029 – 1038 ( 2004 ).
[Crossref] [PubMed]

Annu. Rev. Bio-med. Eng. (1)

C. Contag and M. H. Bachmann , “ Advances in bioluminescence imaging of gene expression ,” Annu. Rev. Bio-med. Eng.   4 , 235 – 260 ( 2002 ).
[Crossref]

Annu. Rev. Cell Dev. Bi. (1)

Thérèse and J. W. Hastings , “ Bioluminescence ,” Annu. Rev. Cell Dev. Bi.   14 , 197 – 230 ( 1998 ).
[Crossref]

Comput. Meth. Prog. Biomed. (1)

L. H. Wang , S. L. Jacques , and L. Q. Zheng , “ MCML-Monte Carlo modeling of photon transport in multi-layered tissues ,” Comput. Meth. Prog. Biomed.   47 , 131 – 146 ( 1995 ).
[Crossref]

Computing (1)

J. Bey , “ Tetrahedral grid refinement ,” Computing   55 , 355 – 378 ( 1995 ).
[Crossref]

Genes Dev. (1)

T. F. Massoud and S. S. Gambhir , “ Molecular imaging in living subjects: seeing fundamental biological processes in a new light ,” Genes Dev.   17 , 545 – 580 ( 2003 ).
[Crossref] [PubMed]

Int. J. Numer. Methods Eng. (1)

Z. Wu and J. M. Sullivan , “ Multiple material marching cubes algorithm ,” Int. J. Numer. Methods Eng.   58 , 189 – 207 ( 2003 ).
[Crossref]

J. Biomed. Opt. (1)

W. Rice , M. D. Cable , and M. B. Nelson , “ In vivo imaging of light-emitting probes ,” J. Biomed. Opt.   6 , 432 – 440 ( 2001 ).
[Crossref] [PubMed]

Med. Phys. (4)

G. Wang , Y. Li , and M. Jiang , “ Uniqueness theorems in bioluminescence tomography ,” Med. Phys.   31 , 2289 – 2299 ( 2004 ).
[Crossref] [PubMed]

E. E. Graves , J. Ripoll , R. Weissleder , and V. Ntziachristos , “ A submillimeter resolution fluorescence molecular imaging system for small animal imaging ,” Med. Phys.   30 , 901 – 911 ( 2003 ).
[Crossref] [PubMed]

S. R. Arridge , M. Schweiger , M. Hiraoka , and D. T. Delpy , “ A finite element approach for modeling photon transport in tissue ,” Med. Phys.   20 , 299 – 309 ( 1993 ).
[Crossref] [PubMed]

M. Schweiger , S. R. Arridge , M. Hiraoka , and D. T. Delpy , “ The finite element method for the propagation of light in scattering media: Boundary and source conditions ,” Med. Phys.   22 , 1779 – 1792 ( 1995 ).
[Crossref] [PubMed]

Nature Biotechnology (1)

V. Ntziachristos , J. Ripoll , L. V. Wang , and R. Weisslder , “ Looking and listening to light: the evolution of whole body photonic imaging ,” Nature Biotechnology   23 (3), 313 – 320 ( 2005 ).
[Crossref] [PubMed]

Opt. Express (4)

Phys. Med. Biol. (3)

A. P. Gibson , J. C. Hebden , and S. R. Arridge , “ Recent advances in diffuse optical imaging ,” Phys. Med. Biol.   50 , R1 – R43 ( 2005 ).
[Crossref] [PubMed]

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

G. Alexandrakis , F. R. Rannou , and 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 ).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

S. Bhaumik and S. S. Gambhir , “ Optical imaging of Renilla luciferase reporter gene expression in living mice ,” Proc. Natl. Acad. Sci. USA   99 , 377 – 382 ( 2002 ).
[Crossref]

Proc. SPIE (2)

M. Jiang and G. Wang , “ Image reconstruction for bioluminescence tomography ,” Proc. SPIE   5535 , 335 – 351 ( 2004 ).
[Crossref]

W. Cong , D. Kumar , Y. Liu , A. Cong , and G. Wang , “ A practical method to determine the light source distribution in bioluminescent imaging ,” Proc. SPIE   5535 , 679 – 686 ( 2004 ).
[Crossref]

Radiology (1)

G. Wang , E. A. Hoffman , G. McLennan , L. V. Wang , M. Suter , and J. F. Meinel , “ Development of the first bioluminescence ct scanner ,” Radiology   229(P) , 566 ( 2003 ).

Other (11)

S. Holder , Electrical Impedance Tomography , ( Institute of Physics Publishing, Bristol and Philadelphia , 2005 ).

C. Kuo , O. Coquoz , D. G. Stearns , and B. W. Rice , “ Diffuse luminescence tomography of in vivo bioluminescence markers using multi-spetral data ,” in Proceedings of the 3rd International Meeting of the Society ( MIT Press , 2004 ), p. 227 .

User’s Manual (release 3.0) of TracePro (Software for Opto-Mechanical Modeling), Lambda Research Corporation, Littleton, MA.

J. Huang , X. Huang , D. Metaxes , and D. Banerjee , “ 3D tumor shape reconstruction from 2D bioluminescence images ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

M. Garland and P. S. Heckbert , “ Surface simplification using quadric error metrics ,” in Proceedings of the 24th Annual Conference on Computer Graphics and Interactive Techniques ( ACM Press , 1997 ), pp. 209 – 216 .

S. S. Rao , The finite element method in engineering , ( Butterworth-Heinemann, Boston , 1999 ).

G. Wang , M. Jiang , J. Tian , W. Cong , Y. Li , W. Han , D. Kumar , X. Qian , H. Shen , T. Zhou , J. Cheng , Y. Lv , H. Li , and J. Luo , “ Recent development in bioluminescence tomography ,” presented in the third IEEE International Symposium on Biomedical Imaging (ISBI 2006), Virginia, USA , 6–9 Apr. 2006 .

W. Bangerth and R. Rannacher , Adaptive finite element methods for differential equations , ( Birkhäuser Verlag , 2003 ).

P. E. Gill , W. Murray , and M. Wright , Practical optimization , ( Academic Press, New York , 1981 ).

M. Ainsworth and J. T. Oden , A posteriori error estimation in finite element analysis , ( Wiley , 2000 ).
[Crossref]

W. E. Lorensen and H. E. Cline , “ Marching cubes: a high resolution 3D surface construction algorithm ,” in Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques ( ACM Press , 1987 ), pp. 163 – 169 .

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Figures (7)

Fig. 1.
Fig. 1.

Irregular refinements for the green closure in 3D.

Fig. 2.
Fig. 2.

Heterogeneous phantom. (a) A heterogeneous phantom with a single light source, composed of muscle (green), lungs (blue), heart (carmine), bone (white), liver (pink) and source (red); (b) The discretized mesh of the phantom used in MOSE; (c) The initial mesh used in the adaptive reconstruction; (d) The middle cross-section, including muscle, lungs and bone.

Fig. 3.
Fig. 3.

Four views of the phantom surface with an angular increment of 90 degrees. Red lines denote the isoline of the surface light power.

Fig. 4.
Fig. 4.

Comparison between the actual and reconstructed sources. (a) BLT reconstruction in the case of a single light source, and (b) BLT reconstruction in the case of four light sources.

Fig. 5.
Fig. 5.

Mesh evolution for the permissible source region in the single light source case. The green mesh denotes the permissible source region; The red sphere is the actual source. (a) The first-level reconstruction, (b) and (c) The second- and third-level results, respectively.

Fig. 6.
Fig. 6.

BLT reconstruction in the fixed mesh of different descretized scales. The green mesh denotes the permissible source region; The red sphere is the actual source. (a) and (b) The average element diameter of the mesh is about 2mm and 1mm respectively.

Fig. 7.
Fig. 7.

Numerical study on the spatial resolution of the multilevel adaptive algorithm. (a) The BLT reconstruction in the case of 1.5mm separation; (b) The counterpart in the case of 1.0mm separation; and (c) That in the case of 0.5mm separation.

Tables (4)

Tables Icon

Table 1. Optical parameters of the heterogeneous phantom.

Tables Icon

Table 2. Comparison between the fixed mesh of three different discretized scales and the adaptive mesh. Mesh size denotes the average element diameter of reconstructed results.

Tables Icon

Table 3. Comparison between the actual and reconstructed sources in the four-source case.

Tables Icon

Table 4. Comparison between the actual and reconstructed source centers and energy densities.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

( D ( x ) Φ ( x ) ) + μ a ( x ) Φ ( x ) = S ( x ) ( x Ω )
Φ ( x ) + 2 A x n n ( D ( x ) ( v ( x ) Φ ( x ) ) = 0 ( x Ω )
A x n n 1 + R ( x ) 1 R ( x )
Q ( x ) = D ( x ) ( v Φ ( x ) ) = Φ ( x ) 2 A x n n ( x Ω )
Ω ( D ( x ) ( Φ ( x ) ) ( Ψ ( x ) ) + μ a ( x ) Φ ( x ) Ψ ( x ) ) d x
+ Ω 1 2 A n ( x ) Φ ( x ) Ψ ( x ) d x = Ω S ( x ) Ψ ( x ) d x ( Ψ ( x ) H 1 ( Ω ) )
Φ ( S λ ) Φ h ( S λ h ) L 2 ( Ω ) 2 + λ S λ S λ h L 2 ( Ω ) 2 c h 3 4
Φ k ( x ) = i = 1 N P k ϕ i k ( x ) ψ i k ( x )
S k ( x ) = i = 1 N S k s i k ( x ) γ i k ( x )
( i = 1 N P k ( τ i ( D ( ψ m k ) ( ψ n k ) + μ a ψ m k ψ n k ) d x + τ i ψ m k ψ n k 2 A n d x ) ) Φ k = ( i = 1 N P k τ i ψ m k ψ n k d x ) S k
M k Φ k = F k S k
A k S k p = Φ k m
min S inf k S k p S sup k = Θ k ( S k p ) = { A k S k p Φ k m Λ + λ k η k ( S k p ) }
S k + 1 0 = I k k + 1 S k r
e ˜ V k W k = D k 1 r k
P s = { x y z 13.0 < z < 17.0 , x y z Right lung }

Metrics