Abstract

Modeling light propagation in the whole body is essential and necessary for optical imaging. However, non-scattering, low-scattering and high absorption regions commonly exist in biological tissues, which lead to inaccuracy of the existing light transport models. In this paper, a novel hybrid light transport model that couples the simplified spherical harmonics approximation (SPN) with the radiosity theory (HSRM) was presented, to accurately describe light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities. In the model, the radiosity theory was used to characterize the light transport in non-scattering regions and the SPN was employed to handle the scattering problems, including subsets of low-scattering and high absorption. A Neumann source constructed by the light transport in the non-scattering region and formed at the interface between the non-scattering and scattering regions was superposed into the original light source, to couple the SPN with the radiosity theory. The accuracy and effectiveness of the HSRM was first verified with both regular and digital mouse model based simulations and a physical phantom based experiment. The feasibility and applicability of the HSRM was then investigated by a broad range of optical properties. Lastly, the influence of depth of the light source on the model was also discussed. Primary results showed that the proposed model provided high performance for light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities.

© 2013 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  34. J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett.91(10), 103901 (2003).
    [CrossRef] [PubMed]
  35. H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
    [CrossRef] [PubMed]
  36. N. Ren, J. Liang, X. Qu, J. Li, B. Lu, and J. Tian, “GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues,” Opt. Express18(7), 6811–6823 (2010).
    [CrossRef] [PubMed]
  37. B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52(3), 577–587 (2007).
    [CrossRef] [PubMed]

2013 (1)

2012 (3)

X. Chen, D. Yang, X. Qu, H. Hu, J. Liang, X. Gao, and J. Tian, “Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection,” J. Biomed. Opt.17(6), 066015 (2012).
[CrossRef] [PubMed]

D. Gorpas and S. Andersson-Engels, “Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging,” J. Biomed. Opt.17(12), 126010 (2012).
[CrossRef] [PubMed]

V. Y. Soloviev, G. Zacharakis, G. Spiliopoulos, R. Favicchio, T. Correia, S. R. Arridge, and J. Ripoll, “Tomographic imaging with polarized light,” J. Opt. Soc. Am. A29(6), 980–988 (2012).
[CrossRef] [PubMed]

2011 (2)

K. Peng, X. Gao, X. Qu, N. Ren, X. Chen, X. He, X. Wang, J. Liang, and J. Tian, “Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues,” Appl. Opt.50(21), 3808–3823 (2011).
[CrossRef] [PubMed]

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

2010 (3)

2009 (4)

Y. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman, and A. F. Chatziioannou, “Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework,” Opt. Express17(19), 16681–16695 (2009).
[CrossRef] [PubMed]

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

Z. Yuan, X.-H. Hu, and H. Jiang, “A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography,” Phys. Med. Biol.54(1), 67–88 (2009).
[CrossRef] [PubMed]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl.25(12), 123010 (2009).
[CrossRef]

2008 (2)

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov.7(7), 591–607 (2008).
[CrossRef] [PubMed]

2007 (3)

S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol.18(1), 247–260 (2007).
[CrossRef]

W. Cong, A. Cong, H. Shen, Y. Liu, and G. Wang, “Flux vector formulation for photon propagation in the biological tissue,” Opt. Lett.32(19), 2837–2839 (2007).
[CrossRef] [PubMed]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52(3), 577–587 (2007).
[CrossRef] [PubMed]

2006 (2)

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. Express14(18), 8211–8223 (2006).
[CrossRef] [PubMed]

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

2005 (7)

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(3), 313–320 (2005).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50(4), R1–R43 (2005).
[CrossRef] [PubMed]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202(1), 323–345 (2005).
[CrossRef]

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, “Hybrid radiative-transfer-diffusion model for optical tomography,” Appl. Opt.44(6), 876–886 (2005).
[CrossRef] [PubMed]

W. X. 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. Express13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

2004 (2)

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

J. H. Lee, S. Kim, and Y. T. Kim, “Modeling of diffuse-diffuse photon coupling via a nonscattering region: a comparative study,” Appl. Opt.43(18), 3640–3655 (2004).
[CrossRef] [PubMed]

2003 (2)

T. Hayashi, Y. Kashio, and E. Okada, “Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region,” Appl. Opt.42(16), 2888–2896 (2003).
[CrossRef] [PubMed]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett.91(10), 103901 (2003).
[CrossRef] [PubMed]

2001 (1)

V. A. Markel and J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3), 035601 (2001).
[CrossRef] [PubMed]

2000 (3)

1999 (1)

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol.44(12), 2897–2906 (1999).
[CrossRef] [PubMed]

1996 (1)

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol.41(4), 767–783 (1996).
[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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Andersson-Engels, S.

D. Gorpas and S. Andersson-Engels, “Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging,” J. Biomed. Opt.17(12), 126010 (2012).
[CrossRef] [PubMed]

Arridge, S. R.

V. Y. Soloviev, G. Zacharakis, G. Spiliopoulos, R. Favicchio, T. Correia, S. R. Arridge, and J. Ripoll, “Tomographic imaging with polarized light,” J. Opt. Soc. Am. A29(6), 980–988 (2012).
[CrossRef] [PubMed]

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl.25(12), 123010 (2009).
[CrossRef]

S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol.18(1), 247–260 (2007).
[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50(4), R1–R43 (2005).
[CrossRef] [PubMed]

J. Riley, H. Dehghani, M. Schweiger, S. R. Arridge, J. Ripoll, and M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express7(13), 462–467 (2000).
[CrossRef] [PubMed]

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A17(9), 1659–1670 (2000).
[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(1), 252–264 (2000).
[CrossRef] [PubMed]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol.44(12), 2897–2906 (1999).
[CrossRef] [PubMed]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol.41(4), 767–783 (1996).
[CrossRef] [PubMed]

Bai, J.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

Bao, S.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

Chatziioannou, A. F.

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

Y. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman, and A. F. Chatziioannou, “Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework,” Opt. Express17(19), 16681–16695 (2009).
[CrossRef] [PubMed]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52(3), 577–587 (2007).
[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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Chen, X.

Cong, A.

Cong, W.

Cong, W. X.

W. X. 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. Express13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Correia, T.

Dehghani, H.

J. Riley, H. Dehghani, M. Schweiger, S. R. Arridge, J. Ripoll, and M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express7(13), 462–467 (2000).
[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(1), 252–264 (2000).
[CrossRef] [PubMed]

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A17(9), 1659–1670 (2000).
[CrossRef] [PubMed]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol.44(12), 2897–2906 (1999).
[CrossRef] [PubMed]

Delpy, D. T.

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A17(9), 1659–1670 (2000).
[CrossRef] [PubMed]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol.44(12), 2897–2906 (1999).
[CrossRef] [PubMed]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol.41(4), 767–783 (1996).
[CrossRef] [PubMed]

Dinkelborg, L. M.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov.7(7), 591–607 (2008).
[CrossRef] [PubMed]

Dogdas, B.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52(3), 577–587 (2007).
[CrossRef] [PubMed]

Douraghy, A.

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

Y. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman, and A. F. Chatziioannou, “Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework,” Opt. Express17(19), 16681–16695 (2009).
[CrossRef] [PubMed]

Favicchio, R.

Firbank, M.

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol.41(4), 767–783 (1996).
[CrossRef] [PubMed]

Gambhir, S. S.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov.7(7), 591–607 (2008).
[CrossRef] [PubMed]

Gao, Q.

Gao, X.

X. Chen, D. Yang, X. Qu, H. Hu, J. Liang, X. Gao, and J. Tian, “Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection,” J. Biomed. Opt.17(6), 066015 (2012).
[CrossRef] [PubMed]

K. Peng, X. Gao, X. Qu, N. Ren, X. Chen, X. He, X. Wang, J. Liang, and J. Tian, “Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues,” Appl. Opt.50(21), 3808–3823 (2011).
[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(4), R1–R43 (2005).
[CrossRef] [PubMed]

Gorpas, D.

D. Gorpas and S. Andersson-Engels, “Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging,” J. Biomed. Opt.17(12), 126010 (2012).
[CrossRef] [PubMed]

Han, D.

Hayashi, T.

He, X.

Hebden, J. C.

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Herschman, H.

Y. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman, and A. F. Chatziioannou, “Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework,” Opt. Express17(19), 16681–16695 (2009).
[CrossRef] [PubMed]

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

Hielscher, A. H.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202(1), 323–345 (2005).
[CrossRef]

Hoffman, E. A.

W. X. 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. Express13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Hu, H.

X. Chen, D. Yang, X. Qu, H. Hu, J. Liang, X. Gao, and J. Tian, “Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection,” J. Biomed. Opt.17(6), 066015 (2012).
[CrossRef] [PubMed]

Hu, X.-H.

Z. Yuan, X.-H. Hu, and H. Jiang, “A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography,” Phys. Med. Biol.54(1), 67–88 (2009).
[CrossRef] [PubMed]

Jiang, H.

Z. Yuan, X.-H. Hu, and H. Jiang, “A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography,” Phys. Med. Biol.54(1), 67–88 (2009).
[CrossRef] [PubMed]

Jiang, M.

Kaipio, J. P.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, “Hybrid radiative-transfer-diffusion model for optical tomography,” Appl. Opt.44(6), 876–886 (2005).
[CrossRef] [PubMed]

Kashio, Y.

Kim, S.

Kim, Y. T.

Klose, A. D.

A. D. Klose, “The forward and inverse problem in tissue optics based on the radiative transfer equation: A brief review,” J. Quant. Spectrosc. Radiat. Transf.111(11), 1852–1853 (2010).
[CrossRef] [PubMed]

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202(1), 323–345 (2005).
[CrossRef]

Kolehmainen, V.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, “Hybrid radiative-transfer-diffusion model for optical tomography,” Appl. Opt.44(6), 876–886 (2005).
[CrossRef] [PubMed]

Kumar, D.

Larsen, E. W.

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

Leahy, R. M.

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52(3), 577–587 (2007).
[CrossRef] [PubMed]

Lee, J. H.

Li, H.

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. Express14(18), 8211–8223 (2006).
[CrossRef] [PubMed]

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Li, J.

Li, Y.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

Liang, J.

Liang, W.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

Liu, K.

Liu, Y.

Lu, B.

Lu, Y.

Luo, J.

Lv, Y.

Machado, H. B.

Y. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman, and A. F. Chatziioannou, “Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework,” Opt. Express17(19), 16681–16695 (2009).
[CrossRef] [PubMed]

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

Markel, V. A.

V. A. Markel and J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3), 035601 (2001).
[CrossRef] [PubMed]

McCray, P. B.

McLennan, G.

Nieto-Vesperinas, M.

Ntziachristos, V.

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202(1), 323–345 (2005).
[CrossRef]

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(3), 313–320 (2005).
[CrossRef] [PubMed]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett.91(10), 103901 (2003).
[CrossRef] [PubMed]

Okada, E.

T. Hayashi, Y. Kashio, and E. Okada, “Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region,” Appl. Opt.42(16), 2888–2896 (2003).
[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(1), 252–264 (2000).
[CrossRef] [PubMed]

Peng, K.

Pulkkinen, A.

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

Qin, C.

Qu, X.

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(17), 4225–4241 (2005).
[CrossRef] [PubMed]

Ren, N.

Ren, S.

Riley, J.

Ripoll, J.

V. Y. Soloviev, G. Zacharakis, G. Spiliopoulos, R. Favicchio, T. Correia, S. R. Arridge, and J. Ripoll, “Tomographic imaging with polarized light,” J. Opt. Soc. Am. A29(6), 980–988 (2012).
[CrossRef] [PubMed]

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(3), 313–320 (2005).
[CrossRef] [PubMed]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett.91(10), 103901 (2003).
[CrossRef] [PubMed]

J. Riley, H. Dehghani, M. Schweiger, S. R. Arridge, J. Ripoll, and M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express7(13), 462–467 (2000).
[CrossRef] [PubMed]

Schotland, J. C.

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl.25(12), 123010 (2009).
[CrossRef]

V. A. Markel and J. C. Schotland, “Inverse scattering for the diffusion equation with general boundary conditions,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys.64(3), 035601 (2001).
[CrossRef] [PubMed]

Schulz, R. B.

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiments,” Phys. Rev. Lett.91(10), 103901 (2003).
[CrossRef] [PubMed]

Schweiger, M.

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol.18(1), 247–260 (2007).
[CrossRef]

J. Riley, H. Dehghani, M. Schweiger, S. R. Arridge, J. Ripoll, and M. Nieto-Vesperinas, “3D optical tomography in the presence of void regions,” Opt. Express7(13), 462–467 (2000).
[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(1), 252–264 (2000).
[CrossRef] [PubMed]

H. Dehghani, S. R. Arridge, M. Schweiger, and D. T. Delpy, “Optical tomography in the presence of void regions,” J. Opt. Soc. Am. A17(9), 1659–1670 (2000).
[CrossRef] [PubMed]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol.41(4), 767–783 (1996).
[CrossRef] [PubMed]

Shen, H.

Soloviev, V. Y.

Spiliopoulos, G.

Stout, D.

Y. Lu, H. B. Machado, A. Douraghy, D. Stout, H. Herschman, and A. F. Chatziioannou, “Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework,” Opt. Express17(19), 16681–16695 (2009).
[CrossRef] [PubMed]

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol.52(3), 577–587 (2007).
[CrossRef] [PubMed]

Surya Mohan, P.

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

Tarvainen, T.

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, “Hybrid radiative-transfer-diffusion model for optical tomography,” Appl. Opt.44(6), 876–886 (2005).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

Tian, J.

D. Yang, X. Chen, S. Ren, X. Qu, J. Tian, and J. Liang, “Influence investigation of a void region on modeling light propagation in a heterogeneous medium,” Appl. Opt.52(3), 400–408 (2013).
[CrossRef] [PubMed]

X. Chen, D. Yang, X. Qu, H. Hu, J. Liang, X. Gao, and J. Tian, “Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection,” J. Biomed. Opt.17(6), 066015 (2012).
[CrossRef] [PubMed]

K. Peng, X. Gao, X. Qu, N. Ren, X. Chen, X. He, X. Wang, J. Liang, and J. Tian, “Graphics processing unit parallel accelerated solution of the discrete ordinates for photon transport in biological tissues,” Appl. Opt.50(21), 3808–3823 (2011).
[CrossRef] [PubMed]

N. Ren, J. Liang, X. Qu, J. Li, B. Lu, and J. Tian, “GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues,” Opt. Express18(7), 6811–6823 (2010).
[CrossRef] [PubMed]

K. Liu, Y. Lu, J. Tian, C. Qin, X. Yang, S. Zhu, X. Yang, Q. Gao, and D. Han, “Evaluation of the simplified spherical harmonics approximation in bioluminescence tomography through heterogeneous mouse models,” Opt. Express18(20), 20988–21002 (2010).
[CrossRef] [PubMed]

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[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. Express14(18), 8211–8223 (2006).
[CrossRef] [PubMed]

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

van Bruggen, N.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov.7(7), 591–607 (2008).
[CrossRef] [PubMed]

Vauhkonen, M.

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, and J. P. Kaipio, “Hybrid radiative-transfer-diffusion model for optical tomography,” Appl. Opt.44(6), 876–886 (2005).
[CrossRef] [PubMed]

Wang, G.

Wang, L. V.

W. X. 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. Express13(18), 6756–6771 (2005).
[CrossRef] [PubMed]

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(3), 313–320 (2005).
[CrossRef] [PubMed]

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Wang, X.

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(3), 313–320 (2005).
[CrossRef] [PubMed]

Willmann, J. K.

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov.7(7), 591–607 (2008).
[CrossRef] [PubMed]

Wright, S.

S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol.18(1), 247–260 (2007).
[CrossRef]

Yan, X. P.

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

Yang, D.

D. Yang, X. Chen, S. Ren, X. Qu, J. Tian, and J. Liang, “Influence investigation of a void region on modeling light propagation in a heterogeneous medium,” Appl. Opt.52(3), 400–408 (2013).
[CrossRef] [PubMed]

X. Chen, D. Yang, X. Qu, H. Hu, J. Liang, X. Gao, and J. Tian, “Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection,” J. Biomed. Opt.17(6), 066015 (2012).
[CrossRef] [PubMed]

Yang, W.

Yang, X.

Yuan, Z.

Z. Yuan, X.-H. Hu, and H. Jiang, “A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography,” Phys. Med. Biol.54(1), 67–88 (2009).
[CrossRef] [PubMed]

Zabner, J.

Zacharakis, G.

Zhu, F. P.

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Zhu, S.

Acad. Radiol. (1)

H. Li, J. Tian, F. P. Zhu, W. X. 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 the Monte Carlo method,” Acad. Radiol.11(9), 1029–1038 (2004).
[CrossRef] [PubMed]

Appl. Opt. (5)

IEEE Eng. Med. Biol. Mag. (1)

J. Tian, J. Bai, X. P. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag.27(5), 48–57 (2008).
[CrossRef] [PubMed]

Inverse Probl. (1)

S. R. Arridge and J. C. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl.25(12), 123010 (2009).
[CrossRef]

J. Biomed. Opt. (2)

D. Gorpas and S. Andersson-Engels, “Evaluation of a radiative transfer equation and diffusion approximation hybrid forward solver for fluorescence molecular imaging,” J. Biomed. Opt.17(12), 126010 (2012).
[CrossRef] [PubMed]

X. Chen, D. Yang, X. Qu, H. Hu, J. Liang, X. Gao, and J. Tian, “Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection,” J. Biomed. Opt.17(6), 066015 (2012).
[CrossRef] [PubMed]

J. Comput. Phys. (3)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys.202(1), 323–345 (2005).
[CrossRef]

P. Surya Mohan, T. Tarvainen, M. Schweiger, A. Pulkkinen, and S. R. Arridge, “Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements,” J. Comput. Phys.230(19), 7364–7383 (2011).
[CrossRef]

A. D. Klose and E. W. Larsen, “Light transport in biological tissue based on the simplified spherical harmonics equations,” J. Comput. Phys.220(1), 441–470 (2006).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Quant. Spectrosc. Radiat. Transf. (1)

A. D. Klose, “The forward and inverse problem in tissue optics based on the radiative transfer equation: A brief review,” J. Quant. Spectrosc. Radiat. Transf.111(11), 1852–1853 (2010).
[CrossRef] [PubMed]

Meas. Sci. Technol. (1)

S. Wright, M. Schweiger, and S. R. Arridge, “Reconstruction in optical tomography using the PN approximations,” Meas. Sci. Technol.18(1), 247–260 (2007).
[CrossRef]

Med. Phys. (1)

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(1), 252–264 (2000).
[CrossRef] [PubMed]

Nat. Biotechnol. (1)

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(3), 313–320 (2005).
[CrossRef] [PubMed]

Nat. Rev. Drug Discov. (1)

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov.7(7), 591–607 (2008).
[CrossRef] [PubMed]

Opt. Express (6)

Opt. Lett. (1)

Phys. Med. Biol. (8)

Y. Lu, A. Douraghy, H. B. Machado, D. Stout, J. Tian, H. Herschman, and A. F. Chatziioannou, “Spectrally resolved bioluminescence tomography with the third-order simplified spherical harmonics approximation,” Phys. Med. Biol.54(21), 6477–6493 (2009).
[CrossRef] [PubMed]

H. Dehghani, D. T. Delpy, and S. R. Arridge, “Photon migration in non-scattering tissue and the effects on image reconstruction,” Phys. Med. Biol.44(12), 2897–2906 (1999).
[CrossRef] [PubMed]

A. P. Gibson, J. C. Hebden, and S. R. Arridge, “Recent advances in diffuse optical imaging,” Phys. Med. Biol.50(4), R1–R43 (2005).
[CrossRef] [PubMed]

Z. Yuan, X.-H. Hu, and H. Jiang, “A higher order diffusion model for three-dimensional photon migration and image reconstruction in optical tomography,” Phys. Med. Biol.54(1), 67–88 (2009).
[CrossRef] [PubMed]

M. Firbank, S. R. Arridge, M. Schweiger, and D. T. Delpy, “An investigation of light transport through scattering bodies with non-scattering regions,” Phys. Med. Biol.41(4), 767–783 (1996).
[CrossRef] [PubMed]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. R. Arridge, and J. P. Kaipio, “Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions,” Phys. Med. Biol.50(20), 4913–4930 (2005).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Experimental geometries employed in the accuracy verification experiments. (a)-(b) Two types of regular models; (c) Digital mouse model, where the torso of the digital mouse atlas was used; (d) Cubic phantom.

Fig. 2
Fig. 2

Comparisons among the HSRM, HRDM and MOSE in the regular model based simulations at the heights of z = 0, 3.5, 7 mm. (a)-(c) Comparisons for Model NO.1 ; (d)-(f) Comparisons for Model NO.2.

Fig. 3
Fig. 3

Comparisons among the HSRM, HRDM and MOSE in the digital mouse-based simulation. (a)-(c) Distribution of the photon density obtained by HSRM, HRDM and MOSE respectively. (d)-(e) Profiles at the height of z = 26.5mm and 34.5mm respectively.

Fig. 4
Fig. 4

Comparisons among the HSRM, HRDM and CCD mapped in the physical phantom-based experiment. (a)-(c) Distribution of the photon density obtained by the HSRM, HRDM and CCD system on surface 1 and 2 respectively. (d)-(e) Profiles at the height of z = 15 mm and z = 11 mm respectively.

Fig. 5
Fig. 5

Geometry used in the investigation experiments of the optical properties and the depth of the light source (a) Experimental geometry employed in the investigation of the optical propriety; (b) Experimental geometry employed in investigation of the depth of the light source, where the dotted lines represent the other two depths of the light source.

Fig. 6
Fig. 6

Comparisons of profiles for MOSE, HSRM and HRDM with different optical properties. (a)-(c) show the comparison profile of the first three experiments with the HSHA optical property at the height of z = 0 mm; (d)-(f) are the second three experiments with the HSLA optical property at the height of z = 0 mm; (g)-(i) and (j)-(l) are the third three experiments with the LSHA optical property and the fourth three with the LSLA optical property at the height of z = 0 mm respectively.

Fig. 7
Fig. 7

Comparisons of results of HSRM, HRDM and MOSE for the experiments with different depths of the light source. (a) The depth of the light source is 7mm; (b) The depth of the light source is 5.5mm; (c) The depth of the light source is 4mm.

Tables (6)

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Table 1 Geometrical parameters and the related optical properties for the regular geometry based simulations

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Table 2 Optical properties of the main organs of the digital mouse

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Table 3 Relative errors between the results of the HSRM or HRDM and MOSE

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Table 4 Geometrical parameters for the model employed in the investigation of the optical proprieties (mm)

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Table 5 Average relative error of the HSRM vs MOSE and the HRDM vs MOSE

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Table 6 Quantitative comparisons among the HSRM, HRDM and MOSE for all of the experiments with different depths of the light source.

Equations (14)

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- ξ i, φ i φ i (r)+ j=1 (N+1)/2 ξ i, φ j φ j (r)= ξ i, S S(r),rΩ
j=1 (N+1)/2 ξ i, φ j b ν φ j (r)= j=1 (N+1)/2 ξ i, φ j b φ j (r) ,rΩ
J + (r)= j=1 (N+1)/2 ξ j, φ j e ν φ j (r)+ j=1 (N+1)/2 ξ j, φ j e φ j (r),rΩ
q(r)= B ¯ h(r, r ) J + ( r )cosθcos θ π|r r | 2 e μ a |r r | d B ¯ ,r B ¯
q(r)= j=1 (N+1)/2 B ¯ h(r, r ) β j φ j ( r )cosθcos θ π|r r | 2 e μ a |r r | d B ¯ ,r B ¯
{ β 1 = ξ 2, φ 2 b ξ 1, φ 1 b ξ 1, φ 2 b ξ 2, φ 1 b ξ 1, φ 1 b ξ 2, φ 2 b ξ 1, φ 2 b ξ 2, φ 1 b ξ 1, φ 1 e + ξ 1, φ 1 b ξ 2, φ 1 b ξ 2, φ 1 b ξ 1, φ 1 b ξ 1, φ 1 b ξ 2, φ 2 b ξ 1, φ 2 b ξ 2, φ 1 b ξ 2, φ 2 e + ξ 1, φ 1 e β 2 = ξ 2, φ 2 b ξ 1, φ 2 b ξ 1, φ 2 b ξ 2, φ 2 b ξ 1, φ 1 b ξ 2, φ 2 b ξ 1, φ 2 b ξ 2, φ 1 b ξ 1, φ 1 e + ξ 1, φ 1 b ξ 2, φ 2 b ξ 2, φ 1 b ξ 1, φ 2 b ξ 1, φ 1 b ξ 2, φ 2 b ξ 1, φ 2 b ξ 2, φ 1 b ξ 2, φ 2 e + ξ 2, φ 2 e .
Q=S+q,
{ - ξ i, φ i φ i (r)+ j=1 (N+1)/2 ξ i, φ j φ j (r)= ξ i,S S(r) + j=1 (N+1)/2 B ¯ ξ i,S h(t, r ) β j φ j ( r )cosθcos θ π|t r | 2 e μ a |t r | d B ¯ , rΩ; t, r B ¯ j=1 (N+1)/2 ξ i, φ j b ν φ j (r)= j=1 (N+1)/2 ξ i, φ j b φ j (r) , rΩ .
φ i (r) k=1 N ϕ i,k ψ k (r) ,
S(r) k=1 N s i,k ψ k (r) ,
Ω ( ξ i, φ i ψ m (r) ψ n (r) + j=1 (N+1)/2 ξ i, φ j ψ m (r) ψ n (r) )dΩ B ( j=1 (N+1)/2 ξ i, φ j B ψ m (s) ψ n (s) )dB = Ω ξ i,S ψ m (r) ψ n (r)dΩ + B ¯ B ¯ ( j=1 (N+1)/2 ξ i,S h(t, r ) β j ψ m ( r ) ψ n (t)cosθcos θ π|t r | 2 e μ a |t r | )d B ¯ d B ¯ , rΩ;sB; r ,t B ¯
(MΞ)φ=Fs,
{ M m,n i,j = Ω ( ξ i, φ i ψ m (r) ψ n (r) + j=1 (N+1)/2 ξ i, φ j ψ m (r) ψ n (r) )dΩ B ( j=1 (N+1)/2 ξ i, φ j B ψ m (s) ψ n (s) )dB, rΩ,sB Ξ m,n i,j = B ¯ B ¯ ( j=1 (N+1)/2 ξ i,S h(t, r ) β j ψ m ( r ) ψ n (t)cosθcos θ π|t r | 2 e μ a |t r | )d B ¯ d B ¯ , r ,t B ¯ F m,n i,j = Ω ξ i,S ψ m (r) ψ n (r)dΩ, rΩ .
ARE= i=1 N (abs( f i std f i cal )/max( f i std ) N

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