Abstract

As an important small animal imaging technique, optical imaging has attracted increasing attention in recent years. However, the photon propagation process is extremely complicated for highly scattering property of the biological tissue. Furthermore, the light transport simulation in tissue has a significant influence on inverse source reconstruction. In this contribution, we present two Galerkin-based meshless methods (GBMM) to determine the light exitance on the surface of the diffusive tissue. The two methods are both based on moving least squares (MLS) approximation which requires only a series of nodes in the region of interest, so complicated meshing task can be avoided compared with the finite element method (FEM). Moreover, MLS shape functions are further modified to satisfy the delta function property in one method, which can simplify the processing of boundary conditions in comparison with the other. Finally, the performance of the proposed methods is demonstrated with numerical and physical phantom experiments.

© 2008 Optical Society of America

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2008

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

2007

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

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

2006

2005

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
[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]

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.opticsinfobase.org/abstract.cfm?URI=oe-13-18-6756.
[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]

2004

I. V. Singh, "Parallel implementation of the EFG method for heat transfer and fluid flow problems," Adv. Eng. Software 34, 453-463 (2004).

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]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

2003

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]

2002

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]

C. Contag and M. H. Bachmann, "Advances in bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235-260 (2002).
[CrossRef] [PubMed]

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=oe-10-3-159.
[PubMed]

I. V. Singh, K. Sandeep, and R. Prakash, "The element free Galerkin method in three dimensional steady state heat conduction," Int. J. Comput. Eng. Sci. 3, 291-303 (2002).
[CrossRef]

2001

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

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]

2000

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
[CrossRef] [PubMed]

J. S. Chen and H. P. Wang, "New boundary condition treatments in meshfree computation of contact problems," Comput. Methods Appl. Mech. Eng. 187, 441-468 (2000).
[CrossRef]

S. Li,W. Hao, and W. K. Liu, "Numerical simulations of large deformation of thin shell structures using meshfree methods," Comput. Mech. 25, 102-116 (2000).
[CrossRef]

1998

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5, 207-241 (1998).
[CrossRef]

1997

J. Schöberl, "Netgen an advancing front 2D/3D-mesh generator based on abstract rules," Comput. Visual.Sci. 1, 41-52 (1997).
[CrossRef]

1995

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]

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]

1994

T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin method," Int. J. Numer. Methods Eng. 37, 229-256 (1994).
[CrossRef]

T. Belytschko, L. Gu, and Y. Y. Lu, "Fracture and crack growth by element-free Galerkin methods," Modelling Simul. Mater. Sci. Eng. 2, 519-534 (1994).
[CrossRef]

1993

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]

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]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
[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. Biomed. Eng. 4, 235-260 (2002).
[CrossRef] [PubMed]

Bayford, R. H.

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

Belytschko, T.

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5, 207-241 (1998).
[CrossRef]

T. Belytschko, L. Gu, and Y. Y. Lu, "Fracture and crack growth by element-free Galerkin methods," Modelling Simul. Mater. Sci. Eng. 2, 519-534 (1994).
[CrossRef]

T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin method," Int. J. Numer. Methods Eng. 37, 229-256 (1994).
[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]

Chen, J. S.

J. S. Chen and H. P. Wang, "New boundary condition treatments in meshfree computation of contact problems," Comput. Methods Appl. Mech. Eng. 187, 441-468 (2000).
[CrossRef]

Cong, A.

Cong, W.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

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

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[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.opticsinfobase.org/abstract.cfm?URI=oe-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]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Contag, C.

C. Contag and M. H. Bachmann, "Advances in bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235-260 (2002).
[CrossRef] [PubMed]

Culver, J.

Dehghani, H.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
[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]

Dolbow, J.

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5, 207-241 (1998).
[CrossRef]

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]

Gao, F.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Gibson, A.

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

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]

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, L.

T. Belytschko, L. Gu, and Y. Y. Lu, "Fracture and crack growth by element-free Galerkin methods," Modelling Simul. Mater. Sci. Eng. 2, 519-534 (1994).
[CrossRef]

T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin method," Int. J. Numer. Methods Eng. 37, 229-256 (1994).
[CrossRef]

Hao, W.

S. Li,W. Hao, and W. K. Liu, "Numerical simulations of large deformation of thin shell structures using meshfree methods," Comput. Mech. 25, 102-116 (2000).
[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]

Henry, M.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

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.

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.opticsinfobase.org/abstract.cfm?URI=oe-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 environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Holder, D. S.

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

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, M.

Kumar, D.

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

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.opticsinfobase.org/abstract.cfm?URI=oe-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]

Li, H.

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Li, S.

S. Li,W. Hao, and W. K. Liu, "Numerical simulations of large deformation of thin shell structures using meshfree methods," Comput. Mech. 25, 102-116 (2000).
[CrossRef]

Liu, W. K.

S. Li,W. Hao, and W. K. Liu, "Numerical simulations of large deformation of thin shell structures using meshfree methods," Comput. Mech. 25, 102-116 (2000).
[CrossRef]

Liu, Y.

Lu, Y. Y.

T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin method," Int. J. Numer. Methods Eng. 37, 229-256 (1994).
[CrossRef]

T. Belytschko, L. Gu, and Y. Y. Lu, "Fracture and crack growth by element-free Galerkin methods," Modelling Simul. Mater. Sci. Eng. 2, 519-534 (1994).
[CrossRef]

Luo, J.

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Lv, Y.

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

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

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.

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. Weissleder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23, 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]

Okada, E.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
[CrossRef] [PubMed]

Prakash, R.

I. V. Singh, K. Sandeep, and R. Prakash, "The element free Galerkin method in three dimensional steady state heat conduction," Int. J. Comput. Eng. Sci. 3, 291-303 (2002).
[CrossRef]

Qian, X.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

Qin, C.

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

Qin, D.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

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]

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. Weissleder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23, 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]

Sandeep, K.

I. V. Singh, K. Sandeep, and R. Prakash, "The element free Galerkin method in three dimensional steady state heat conduction," Int. J. Comput. Eng. Sci. 3, 291-303 (2002).
[CrossRef]

Schöberl, J.

J. Schöberl, "Netgen an advancing front 2D/3D-mesh generator based on abstract rules," Comput. Visual.Sci. 1, 41-52 (1997).
[CrossRef]

Schweiger, M.

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
[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]

Shen, H.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

Singh, I. V.

I. V. Singh, "Parallel implementation of the EFG method for heat transfer and fluid flow problems," Adv. Eng. Software 34, 453-463 (2004).

I. V. Singh, K. Sandeep, and R. Prakash, "The element free Galerkin method in three dimensional steady state heat conduction," Int. J. Comput. Eng. Sci. 3, 291-303 (2002).
[CrossRef]

Soloviev, V. Y.

Stott, J.

Tanikawa, Y.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Tian, J.

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

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Tidswell, A, T.

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

Tizzard, A.

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

Wang, G.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

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

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[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.opticsinfobase.org/abstract.cfm?URI=oe-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]

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Wang, H. P.

J. S. Chen and H. P. Wang, "New boundary condition treatments in meshfree computation of contact problems," Comput. Methods Appl. Mech. Eng. 187, 441-468 (2000).
[CrossRef]

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.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23, 313-320 (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.opticsinfobase.org/abstract.cfm?URI=oe-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 environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Wang, Y.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23, 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]

Xu, M.

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

Yang, W.

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

Y. Lv, J. Tian, W. Cong, G. Wang, J. Luo, W. Yang, and H. Li, "A multilevel adaptive finite element algorithm for bioluminescence tomography," Opt. Express 14, 8211-8223 (2006), http://www.opticsinfobase. org/abstract.cfm?URI=oe-14-18-8211.
[CrossRef] [PubMed]

Zabner, J.

Zhao, H.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

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]

Zhu, F.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Acad. Radiol.

H. Li, J. Tian, F. Zhu, W. Cong, L. V. Wang, E. A. Hoffman, and G. Wang, "A mouse optical simulation environment (MOSE) to investigate bioluminescent phenomena in the living mouse with Monte Carlo method," Acad. Radiol. 11, 1029-1038 (2004).
[CrossRef] [PubMed]

Adv. Eng. Software

I. V. Singh, "Parallel implementation of the EFG method for heat transfer and fluid flow problems," Adv. Eng. Software 34, 453-463 (2004).

Annu. Rev. Biomed. Eng.

C. Contag and M. H. Bachmann, "Advances in bioluminescence imaging of gene expression," Annu. Rev. Biomed. Eng. 4, 235-260 (2002).
[CrossRef] [PubMed]

Appl. Opt.

Arch. Comput. Methods Eng.

J. Dolbow and T. Belytschko, "An introduction to programming the meshless element free Galerkin method," Arch. Comput. Methods Eng. 5, 207-241 (1998).
[CrossRef]

Comput. Mech.

S. Li,W. Hao, and W. K. Liu, "Numerical simulations of large deformation of thin shell structures using meshfree methods," Comput. Mech. 25, 102-116 (2000).
[CrossRef]

Comput. Meth. Prog. Biomed.

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]

Comput. Methods Appl. Mech. Eng.

J. S. Chen and H. P. Wang, "New boundary condition treatments in meshfree computation of contact problems," Comput. Methods Appl. Mech. Eng. 187, 441-468 (2000).
[CrossRef]

Front. Biosci.

G. Wang, W. Cong, H. Shen, X. Qian, M. Henry, and Y. Wang, "Overview of bioluminescence tomography-a new molecular imaging modality," Front. Biosci. 13, 1281-1293 (2008).
[CrossRef]

Genes Dev.

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. Comput. Eng. Sci.

I. V. Singh, K. Sandeep, and R. Prakash, "The element free Galerkin method in three dimensional steady state heat conduction," Int. J. Comput. Eng. Sci. 3, 291-303 (2002).
[CrossRef]

Int. J. Numer. Methods Eng.

T. Belytschko, Y. Y. Lu, and L. Gu, "Element-free Galerkin method," Int. J. Numer. Methods Eng. 37, 229-256 (1994).
[CrossRef]

J. Biomed. Opt.

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.

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]

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, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model for the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).
[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]

Modelling Simul. Mater. Sci. Eng.

T. Belytschko, L. Gu, and Y. Y. Lu, "Fracture and crack growth by element-free Galerkin methods," Modelling Simul. Mater. Sci. Eng. 2, 519-534 (1994).
[CrossRef]

Nat. Biotechnol.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, "Looking and listening to light: the evolution of whole body photonic imaging," Nat. Biotechnol. 23, 313-320 (2005).
[CrossRef] [PubMed]

Opt. Express

Phys. Med. Biol.

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

Phys.Med. Biol.

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]

Physiol. Meas.

R. H. Bayford, A. Gibson, A. TizzardA, T. Tidswell, and D. S. Holder, "Solving the forward problem in electrical impedance tomography for the human head using IDEAS (integrated design engineering analysis software), a finite element modelling tool," Physiol. Meas. 22, 55-64 (2001).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA

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

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]

Y. Lv, J. Tian, H. Li, J. Luo, W. Cong, G. Wang, and D. Kumar, "Modeling the forward problem based on the adaptive FEMs framework in bioluminescence tomography," Proc. SPIE 6318, 63180I (2006).
[CrossRef]

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, "Experimental determination of optical properties in turbid medium by TCSPC technique," Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Sci.

J. Schöberl, "Netgen an advancing front 2D/3D-mesh generator based on abstract rules," Comput. Visual.Sci. 1, 41-52 (1997).
[CrossRef]

Other

X. Zhang and Y. Liu, Meshless methods, (Tsinghua University Press, Beijing, 2004).

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Figures (10)

Fig. 1.
Fig. 1.

(a) The flowchart of the proposed GBMM algorithm without modification; (b) The flowchart of the presented GBMM algorithm with modification.

Fig. 2.
Fig. 2.

Homogeneous numerical phantom. (a) A homogeneous tissue-like phantom with a series of nodes and a light source; (b) and (c) The surface light power simulated by GBMM1 and GBMM2.

Fig. 3.
Fig. 3.

FEM simulation for homogeneous phantom. (a) The volumetric mesh used in FEM simulation; (b) The photon flux density on the phantom surface calculated by FEM. (c) Comparison of the computational results by GBMM and FEM.

Fig. 4.
Fig. 4.

Heterogeneous numerical phantom. (a) A cube heterogeneous phantom with two light sources; (b) and (c) The light exitance view of the side surface using GBMM1 and GBMM2.

Fig. 5.
Fig. 5.

FEM simulation for heterogeneous phantom. (a) The discretized mesh; (b) The surface light power simulated via FEM; (c), (d) and (e) Comparison of the corresponding calculational results along the detection square on the phantom surface.

Fig. 6.
Fig. 6.

Cubic resinous phantoms. (a) and (c) Phantoms with one or two light sources; (b) and (d) The middle cross-section of the phantoms. The four degrees show the direction of the CCD camera during data acquisition.

Fig. 7.
Fig. 7.

The photon energy distribution on the phantom surface detected by the CCD camera or computed using GBMM method. (a) and (e) 0°, (b) and (f) 90°, (c) and (g) 180°, (d) and (h) 270°.

Fig. 8.
Fig. 8.

Comparison between measured and computational photon density on the phantom surface at height 10mm from the bottom of the physical model. (a) 0°, (b) 90°, (c) 180°, and (d) 270°.

Fig. 9.
Fig. 9.

The surface light power distribution measured using the CCD camera or solved by GBMM in four directions 90° apart. (a) and (e) 0°, (b) and (f) 90°, (c) and (g) 180°, (d) and (h) 270°.

Fig. 10.
Fig. 10.

Comparison of experimental and computational surface photon flux density at height 10mm from the phantom top. (a) 0°, (b) 90°, (c) 180°, and (d) 270°.

Tables (3)

Tables Icon

Table 1. Photon flux (nanoWatts) simulation for homogeneous phantom.

Tables Icon

Table 2. Optical parameters of the heterogeneous phantom.

Tables Icon

Table 3. Photon flux (nanoWatts) simulation for heterogeneous phantom.

Equations (30)

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( 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 )
Φ ( x ) Φ h ( x ) = j = 1 m p j ( x ) a j ( x ) = p T ( x ) a ( x )
J ( x ) = i = 1 N n w ( x x i ) [ p T ( x i ) a ( x ) Φ i ] 2
A ( x ) a ( x ) = B ( x ) Φ
A ( x ) = i = 1 N n w ( x x i ) p ( x i ) p T ( x i )
B ( x ) = [ w ( x x 1 ) p ( x 1 ) , w ( x x 2 ) p ( x 2 ) , , w ( x x N n ) p ( x N n ) ]
Φ = ( Φ 1 , Φ 2 , , Φ N n ) T
Φ h ( x ) = i = 1 N n N i ( x ) Φ i
N i ( x ) = p T ( x ) A 1 ( x ) B i ( x )
N i , s ( x ) = p , s T A 1 B i + p T [ A 1 ( B i , s A , s A 1 B i ) ]
p T ( x ) = [ 1 , x , y , z , x 2 , xy , y 2 , yz , z 2 , zx ] , m = 10
w ( r ) = { 1 6 r 2 + 8 r 3 3 r 4 0 r 1 0 r > 1
Φ h ( x k ) = i = 1 N n N i ( x k ) Φ i = N k T Φ
Φ ̂ = Λ Φ
Φ ̂ = [ Φ h ( x 1 ) , Φ h ( x 2 ) , , Φ h ( x N n ) ] T
Λ = [ N 1 ( x 1 ) N 2 ( x 1 ) N N n ( x 1 ) N 1 ( x 2 ) N 2 ( x 2 ) N N n ( x 2 ) N 1 ( x N n ) N 2 ( x N n ) N N n ( x N n ) ]
Φ = Λ 1 Φ ̂
Φ i = l = 1 N n N l ( x i ) 1 Φ ̂ l
Φ h ( x ) = i = 1 N n N i ( x ) l = 1 N n N l ( x i ) 1 Φ ̂ l = l = 1 N n M l ( x ) Φ ̂ l
M l ( x k ) = i = 1 N n N i ( x k ) N l ( x i ) 1 = δ lk
Ω ( D ( x ) ( Φ ( x ) ) · ( Ψ ( x ) ) + μ a ( x ) Φ ( x ) Ψ ( x ) ) d x
+ Ω 1 2 A ( x ; n , n ' ) Φ ( x ) Ψ ( x ) d x = Ω S ( x ) Ψ ( x ) d x
Φ h ( x ) = l = 1 N n Υ l ( x ) Γ l
( K + C + F ) Γ = G Γ = S
{ K kl = Ω D ( x ) ( Υ k ( x ) ) · ( Υ l ( x ) ) d Ω C kl = Ω μ a ( x ) Υ k ( x ) Υ l ( x ) d Ω F kl = Ω Υ k ( x ) Υ l ( x ) / ( 2 A ( x ; n , n ) ) d Ω S k = Ω S ( x ) Υ k ( x ) d Ω
Γ = G 1 S
Φ ̂ k = [ N 1 ( x k ) , N 2 ( x k ) , , N N n ( x k ) ] [ Φ 1 , Φ 2 , , Φ n ] T

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