C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).

[CrossRef]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

H. Erkol and M. B. Unlu, “Virtual source method for diffuse optical imaging,” Appl. Opt. 52, 4933–4970 (2013).

[CrossRef]
[PubMed]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

W. Han, J. A. Eichholz, and G. Wang, “On a family of differential approximations of the radiative transfer equation,” J. Math. Chem. 50, 689–702 (2011).

[CrossRef]

A. Liemert and A. Kienle, “Light diffusion in N-layered turbid media: frequency and time domains,” J. Biomed. Opt. 15, 025002 (2010).

[CrossRef]
[PubMed]

A. Zhang, D. Piao, C. F. Bunting, and B. W. Pogue, “Photon diffusion in a homogeneous medium bounded externally or internally by an infinetely long circular cylindrical applicator. I. Steady-state theory,” J. Opt. Soc. Am. A 27, 648–662 (2010).

[CrossRef]

A. Liemert and A. Kienle, ‘Light diffusion in a turbid cylinder. II. Layered case,” Opt. Express 18, 9266–9279 (2010).

[CrossRef]
[PubMed]

A. Liemert and A. Kienle, “Light diffusion in a turbid cylinder. I. Homogeneous case,” Opt. Express 18, 9456–9473 (2010).

[CrossRef]
[PubMed]

M. A. Naser and M. S. Patterson, “Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties,” Biomed. Opt. Express 1, 512–526 (2010).

[CrossRef]

H. Gao, H. Zhao, W. Cong, and G. Wang, “Bioluminescence tomography in Gaussian prior,” Biomed. Opt. Express 1, 1259–1277 (2010).

[CrossRef]

Q. Zhang, L. Yin, Y. Tan, Z. Yuan, and H. Jiang, “Quantitative bioluminescence tomography guided by diffuse optical tomography,” Opt. Express 16, 1481–1486 (2008).

[CrossRef]
[PubMed]

H. Dehghani and B. W. Pogue, “Spectrally resolved bioluminescence optical tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).

[CrossRef]
[PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Rivière, “Application of inverse source concepts to photoacoustic tomography,” Inverse Problems 23, 21–35 (2007).

[CrossRef]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).

[CrossRef]
[PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

H. Dehghani, B. A. Brooksby, P. W. Pogue, and K. D. Paulsen, “Effects of refractive index on near-infrared tomography of the breast,” Appl. Opt. 44, 1870–1878 (2005).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

A. Kienle, “Light diffusion through a turbid parallelepiped,” J. Opt. Soc. Am. A 22, 1883–1888 (2005).

[CrossRef]

M. Shendeleva, “Radiative transfer in a turbid medium with a varying refractive index: comment,” J. Opt. Soc. Am. A 21, 2464–2467 (2004).

[CrossRef]

W. Cong, L. V. Wang, and G. Wang, “Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium,” Biomed. Eng. Online 3, 1–6 (2004).

[CrossRef]

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).

[CrossRef]
[PubMed]

E. Demiralp and H. Beker, “Properties of bound states of the Schrödinger equation with attractive Dirac delta potentials,” J. Phys. A 36, 7449–7459 (2003).

[CrossRef]

T. J. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

T. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Österberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).

[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999).

[CrossRef]
[PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44, 2689–2702 (1999).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “Optical tomographic reconstructon in a complex head model using a priori region boundary condition,” Phys. Med. Biol. 44, 2703–2721 (1999).

[CrossRef]
[PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).

[CrossRef]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation I. Theory,” Appl. Opt. 36, 4587–4599 (1997).

[CrossRef]
[PubMed]

E. Okada, M. Firbank, M. Schwiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).

[CrossRef]
[PubMed]

A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).

[CrossRef]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).

[CrossRef]
[PubMed]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).

[CrossRef]
[PubMed]

S. R. Arridge, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).

[CrossRef]
[PubMed]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).

[CrossRef]

I. Dayan, S. Havlin, and G. H. Weiss, “Photon migration in a two-layer turbid medium A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).

[CrossRef]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).

[CrossRef]
[PubMed]

T. J. Farrel, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of specially resolved steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).

[CrossRef]

M. S. Patterson and S. J. Madsen, “Diffusion equation representation of photon migration in tissue,” IEEE MTT-S Digest 2, 905–908 (1991).

S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. 26, 656–664 (1979).

[CrossRef]
[PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Rivière, “Application of inverse source concepts to photoacoustic tomography,” Inverse Problems 23, 21–35 (2007).

[CrossRef]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “Optical tomographic reconstructon in a complex head model using a priori region boundary condition,” Phys. Med. Biol. 44, 2703–2721 (1999).

[CrossRef]
[PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).

[CrossRef]

E. Okada, M. Firbank, M. Schwiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).

[CrossRef]
[PubMed]

S. R. Arridge, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).

[CrossRef]
[PubMed]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).

[CrossRef]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).

[CrossRef]
[PubMed]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

E. Demiralp and H. Beker, “Properties of bound states of the Schrödinger equation with attractive Dirac delta potentials,” J. Phys. A 36, 7449–7459 (2003).

[CrossRef]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).

[CrossRef]
[PubMed]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998).

[CrossRef]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).

[CrossRef]
[PubMed]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

H. Gao, H. Zhao, W. Cong, and G. Wang, “Bioluminescence tomography in Gaussian prior,” Biomed. Opt. Express 1, 1259–1277 (2010).

[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

W. Cong, L. V. Wang, and G. Wang, “Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium,” Biomed. Eng. Online 3, 1–6 (2004).

[CrossRef]

E. Okada, M. Firbank, M. Schwiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).

[CrossRef]
[PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).

[CrossRef]

I. Dayan, S. Havlin, and G. H. Weiss, “Photon migration in a two-layer turbid medium A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).

[CrossRef]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

H. Dehghani and B. W. Pogue, “Spectrally resolved bioluminescence optical tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).

[CrossRef]
[PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).

[CrossRef]
[PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).

[CrossRef]
[PubMed]

H. Dehghani, B. A. Brooksby, P. W. Pogue, and K. D. Paulsen, “Effects of refractive index on near-infrared tomography of the breast,” Appl. Opt. 44, 1870–1878 (2005).

[CrossRef]
[PubMed]

H. Dehghani and D. T. Delpy, “Near-infrared spectroscopy of the adult head: effect of scattering and absorbing obstructions in the cerebrospinal fluid layer on light distribution in the tissue,” Appl. Opt. 39, 4721–4729 (2000).

[CrossRef]

H. Dehghani and D. T. Delpy, “Near-infrared spectroscopy of the adult head: effect of scattering and absorbing obstructions in the cerebrospinal fluid layer on light distribution in the tissue,” Appl. Opt. 39, 4721–4729 (2000).

[CrossRef]

E. Okada, M. Firbank, M. Schwiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).

[CrossRef]
[PubMed]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).

[CrossRef]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).

[CrossRef]
[PubMed]

E. Demiralp and H. Beker, “Properties of bound states of the Schrödinger equation with attractive Dirac delta potentials,” J. Phys. A 36, 7449–7459 (2003).

[CrossRef]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

Y. V. Egorov and M. A. Shubin, Partial Differential Equations (Springer, 1992).

W. Han, J. A. Eichholz, and G. Wang, “On a family of differential approximations of the radiative transfer equation,” J. Math. Chem. 50, 689–702 (2011).

[CrossRef]

T. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

T. J. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

T. J. Farrel, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of specially resolved steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).

[CrossRef]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44, 2689–2702 (1999).

[CrossRef]
[PubMed]

S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. 26, 656–664 (1979).

[CrossRef]
[PubMed]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

W. Han, J. A. Eichholz, and G. Wang, “On a family of differential approximations of the radiative transfer equation,” J. Math. Chem. 50, 689–702 (2011).

[CrossRef]

I. Dayan, S. Havlin, and G. H. Weiss, “Photon migration in a two-layer turbid medium A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).

[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol 1.

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).

[CrossRef]
[PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).

[CrossRef]
[PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Österberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).

[CrossRef]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

A. Liemert and A. Kienle, “Light diffusion in N-layered turbid media: frequency and time domains,” J. Biomed. Opt. 15, 025002 (2010).

[CrossRef]
[PubMed]

A. Liemert and A. Kienle, ‘Light diffusion in a turbid cylinder. II. Layered case,” Opt. Express 18, 9266–9279 (2010).

[CrossRef]
[PubMed]

A. Liemert and A. Kienle, “Light diffusion in a turbid cylinder. I. Homogeneous case,” Opt. Express 18, 9456–9473 (2010).

[CrossRef]
[PubMed]

A. Kienle, “Light diffusion through a turbid parallelepiped,” J. Opt. Soc. Am. A 22, 1883–1888 (2005).

[CrossRef]

A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44, 2689–2702 (1999).

[CrossRef]
[PubMed]

A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).

[CrossRef]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).

[CrossRef]

M. S. Patterson and S. J. Madsen, “Diffusion equation representation of photon migration in tissue,” IEEE MTT-S Digest 2, 905–908 (1991).

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Analytical approximate solutions of the timedomain diffusion equation in layered slabs,” J. Opt. Soc. Am. A. 19, 71–80 (2002).

[CrossRef]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation I. Theory,” Appl. Opt. 36, 4587–4599 (1997).

[CrossRef]
[PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Österberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).

[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Rivière, “Application of inverse source concepts to photoacoustic tomography,” Inverse Problems 23, 21–35 (2007).

[CrossRef]

S. G. Mykhlin, Mathematical Physics: An Advanced Course (North-Holland, 1970).

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).

[CrossRef]
[PubMed]

M. A. Naser and M. S. Patterson, “Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties,” Biomed. Opt. Express 1, 512–526 (2010).

[CrossRef]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).

[CrossRef]
[PubMed]

T. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

T. J. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).

[CrossRef]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).

[CrossRef]
[PubMed]

T. J. Farrel, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of specially resolved steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).

[CrossRef]

M. S. Patterson and S. J. Madsen, “Diffusion equation representation of photon migration in tissue,” IEEE MTT-S Digest 2, 905–908 (1991).

M. S. Patterson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).

[CrossRef]
[PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).

[CrossRef]
[PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).

[CrossRef]
[PubMed]

H. Dehghani, B. A. Brooksby, P. W. Pogue, and K. D. Paulsen, “Effects of refractive index on near-infrared tomography of the breast,” Appl. Opt. 44, 1870–1878 (2005).

[CrossRef]
[PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Österberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).

[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999).

[CrossRef]
[PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

A. Zhang, D. Piao, C. F. Bunting, and B. W. Pogue, “Photon diffusion in a homogeneous medium bounded externally or internally by an infinetely long circular cylindrical applicator. I. Steady-state theory,” J. Opt. Soc. Am. A 27, 648–662 (2010).

[CrossRef]

H. Dehghani and B. W. Pogue, “Spectrally resolved bioluminescence optical tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).

[CrossRef]
[PubMed]

H. Dehghani, S. C. Davis, S. Jiang, B. W. Pogue, K. D. Paulsen, and M. S. Patterson, “Spectrally resolved bioluminescence optical tomography,” Opt. Lett. 31, 365–367 (2006).

[CrossRef]
[PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).

[CrossRef]
[PubMed]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Österberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).

[CrossRef]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999).

[CrossRef]
[PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Rivière, “Application of inverse source concepts to photoacoustic tomography,” Inverse Problems 23, 21–35 (2007).

[CrossRef]

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Analytical approximate solutions of the timedomain diffusion equation in layered slabs,” J. Opt. Soc. Am. A. 19, 71–80 (2002).

[CrossRef]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “Optical tomographic reconstructon in a complex head model using a priori region boundary condition,” Phys. Med. Biol. 44, 2703–2721 (1999).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).

[CrossRef]
[PubMed]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).

[CrossRef]

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).

[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

Y. V. Egorov and M. A. Shubin, Partial Differential Equations (Springer, 1992).

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. 26, 656–664 (1979).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

H. Erkol and M. B. Unlu, “Virtual source method for diffuse optical imaging,” Appl. Opt. 52, 4933–4970 (2013).

[CrossRef]
[PubMed]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

W. Han, J. A. Eichholz, and G. Wang, “On a family of differential approximations of the radiative transfer equation,” J. Math. Chem. 50, 689–702 (2011).

[CrossRef]

H. Gao, H. Zhao, W. Cong, and G. Wang, “Bioluminescence tomography in Gaussian prior,” Biomed. Opt. Express 1, 1259–1277 (2010).

[CrossRef]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

W. Cong, L. V. Wang, and G. Wang, “Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium,” Biomed. Eng. Online 3, 1–6 (2004).

[CrossRef]

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).

[CrossRef]
[PubMed]

L. H. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging Hoboken (Wiley, 2007).

W. Cong, L. V. Wang, and G. Wang, “Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium,” Biomed. Eng. Online 3, 1–6 (2004).

[CrossRef]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

I. Dayan, S. Havlin, and G. H. Weiss, “Photon migration in a two-layer turbid medium A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).

[CrossRef]

T. J. Farrel, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of specially resolved steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).

[CrossRef]

L. H. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging Hoboken (Wiley, 2007).

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Analytical approximate solutions of the timedomain diffusion equation in layered slabs,” J. Opt. Soc. Am. A. 19, 71–80 (2002).

[CrossRef]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Analytical approximate solutions of the timedomain diffusion equation in layered slabs,” J. Opt. Soc. Am. A. 19, 71–80 (2002).

[CrossRef]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation I. Theory,” Appl. Opt. 36, 4587–4599 (1997).

[CrossRef]
[PubMed]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Rivière, “Application of inverse source concepts to photoacoustic tomography,” Inverse Problems 23, 21–35 (2007).

[CrossRef]

M. S. Patterson, “Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties,” Appl. Opt. 28, 2331–2336 (1989).

[CrossRef]
[PubMed]

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation I. Theory,” Appl. Opt. 36, 4587–4599 (1997).

[CrossRef]
[PubMed]

E. Okada, M. Firbank, M. Schwiger, S. R. Arridge, M. Cope, and D. T. Delpy, “Theoretical and experimental investigation of near-infrared light propagation in a model of the adult head,” Appl. Opt. 36, 21–31 (1997).

[CrossRef]
[PubMed]

S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998).

[CrossRef]

H. Dehghani and D. T. Delpy, “Near-infrared spectroscopy of the adult head: effect of scattering and absorbing obstructions in the cerebrospinal fluid layer on light distribution in the tissue,” Appl. Opt. 39, 4721–4729 (2000).

[CrossRef]

B. W. Pogue, S. Geimer, T. O. McBride, S. Jiang, U. L. Österberg, and K. D. Paulsen, “Three-dimensional simulation of near-infrared diffusion in tissue: boundary condition and geometry analysis for finite-element image reconstruction,” Appl. Opt. 40, 588–600 (2001).

[CrossRef]

H. Dehghani, B. A. Brooksby, P. W. Pogue, and K. D. Paulsen, “Effects of refractive index on near-infrared tomography of the breast,” Appl. Opt. 44, 1870–1878 (2005).

[CrossRef]
[PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, and A. G. Yodh, “Diffuse optical tomography with spectral constraints and wavelength optimization,” Appl. Opt. 44(11), 2082–2093 (2005).

[CrossRef]
[PubMed]

H. Erkol and M. B. Unlu, “Virtual source method for diffuse optical imaging,” Appl. Opt. 52, 4933–4970 (2013).

[CrossRef]
[PubMed]

W. Cong, L. V. Wang, and G. Wang, “Formulation of photon diffusion from spherical bioluminescent sources in an infinite homogeneous medium,” Biomed. Eng. Online 3, 1–6 (2004).

[CrossRef]

J. Zhang, D. Chen, J. Liang, H. Xue, J. Lei, Q. Wang, D. Chen, M. Meng, Z. Jin, and J. Tian, “Incorporating MRI structural information into bioluminescence tomography: system, heterogeneous reconstruction and in vivo quantification,” Biomed. Opt. Express 5, 1861–1876 (2014).

[CrossRef]
[PubMed]

M. A. Naser and M. S. Patterson, “Algorithms for bioluminescence tomography incorporating anatomical information and reconstruction of tissue optical properties,” Biomed. Opt. Express 1, 512–526 (2010).

[CrossRef]

H. Gao, H. Zhao, W. Cong, and G. Wang, “Bioluminescence tomography in Gaussian prior,” Biomed. Opt. Express 1, 1259–1277 (2010).

[CrossRef]

M. S. Patterson and S. J. Madsen, “Diffusion equation representation of photon migration in tissue,” IEEE MTT-S Digest 2, 905–908 (1991).

S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng. 26, 656–664 (1979).

[CrossRef]
[PubMed]

M. A. Anastasio, J. Zhang, D. Modgil, and P. J. L. Rivière, “Application of inverse source concepts to photoacoustic tomography,” Inverse Problems 23, 21–35 (2007).

[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).

[CrossRef]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcıoğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).

[CrossRef]

T. J. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

T. Farrel and M. S. Patterson, “Experimental verification of the effect of refractive index mismatch on the light fluence in a turbid medium,” J. Biomed. Opt. 6, 468–473 (2001).

[CrossRef]

A. Liemert and A. Kienle, “Light diffusion in N-layered turbid media: frequency and time domains,” J. Biomed. Opt. 15, 025002 (2010).

[CrossRef]
[PubMed]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).

[CrossRef]

W. Han, J. A. Eichholz, and G. Wang, “On a family of differential approximations of the radiative transfer equation,” J. Math. Chem. 50, 689–702 (2011).

[CrossRef]

I. Dayan, S. Havlin, and G. H. Weiss, “Photon migration in a two-layer turbid medium A diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).

[CrossRef]

A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A 14, 246–254 (1997).

[CrossRef]

J. M. Schmitt, G. X. Zhou, E. C. Walker, and R. T. Wall, “Multilayer model of photon diffusion in skin,” J. Opt. Soc. Am. A 7, 2141–2153 (1990).

[CrossRef]
[PubMed]

A. Kienle, “Light diffusion through a turbid parallelepiped,” J. Opt. Soc. Am. A 22, 1883–1888 (2005).

[CrossRef]

A. Zhang, D. Piao, C. F. Bunting, and B. W. Pogue, “Photon diffusion in a homogeneous medium bounded externally or internally by an infinetely long circular cylindrical applicator. I. Steady-state theory,” J. Opt. Soc. Am. A 27, 648–662 (2010).

[CrossRef]

G. W. Faris, “Diffusion equation boundary conditions for the interface between turbid media: a comment,” J. Opt. Soc. Am. A 19, 519–520 (2002).

[CrossRef]

R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A 12, 2532–2539 (1995).

[CrossRef]

M. Shendeleva, “Radiative transfer in a turbid medium with a varying refractive index: comment,” J. Opt. Soc. Am. A 21, 2464–2467 (2004).

[CrossRef]

J. M. Tualle, J. Prat, E. Tinet, and S. Avrillier, “Real-space Greens function calculation for the solution of the diffusion equation in stratified turbid media,” J. Opt. Soc. Am. A 17, 2046–2055 (2000).

[CrossRef]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Analytical approximate solutions of the timedomain diffusion equation in layered slabs,” J. Opt. Soc. Am. A. 19, 71–80 (2002).

[CrossRef]

E. Demiralp and H. Beker, “Properties of bound states of the Schrödinger equation with attractive Dirac delta potentials,” J. Phys. A 36, 7449–7459 (2003).

[CrossRef]

J. A. Guggenheim, H. R. A. Basevi, J. Frampton, I. B. Styles, and H. Dehghani, “Multi-modal molecular diffuse optical tomography system for small animal imaging,” Meas. Sci. Technol. 24, 105405 (2013).

[CrossRef]
[PubMed]

H. Dehghani and B. W. Pogue, “Spectrally resolved bioluminescence optical tomography using the reciprocity approach,” Med. Phys. 35, 4863–4871 (2008).

[CrossRef]
[PubMed]

T. J. Farrel, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of specially resolved steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).

[CrossRef]

G. Wang, Y. Li, and M. Jiang, “Uniqueness theorems in bioluminescence tomography,” Med. Phys. 31(8), 2289–2299 (2004).

[CrossRef]
[PubMed]

S. R. Arridge, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).

[CrossRef]
[PubMed]

M. Schweiger and S. R. Arridge, “The finite-element method for the propagation of light in scattering media: frequency domain case,” Med. Phys. 24, 895–902 (1997).

[CrossRef]
[PubMed]

B. W. Pogue, T. O. McBride, U. L. Osterberg, and K. D. Paulsen, “Comparison of imaging geometries for diffuse optical tomography of tissue,” Opt. Express 4, 270–286 (1999).

[CrossRef]
[PubMed]

A. Liemert and A. Kienle, ‘Light diffusion in a turbid cylinder. II. Layered case,” Opt. Express 18, 9266–9279 (2010).

[CrossRef]
[PubMed]

A. Liemert and A. Kienle, “Light diffusion in a turbid cylinder. I. Homogeneous case,” Opt. Express 18, 9456–9473 (2010).

[CrossRef]
[PubMed]

P. K. Yalavarthy, H. Dehghani, B. W. Pogue, and K. D. Paulsen, “Critical computational aspects of near infrared circular tomographic imaging: Analysis of measurement number, mesh resolution and reconstruction basis,” Opt. Express 14, 6113–6127 (2006).

[CrossRef]
[PubMed]

G. Wang, W. Cong, K. Durairaj, X. Qian, H. Shen, P. Sinn, E. Hoffman, G. Mclennan, and M. Henry, “In vivo mouse studies with bioluminescence tomography,” Opt. Express 14, 7801–7809 (2006).

[CrossRef]
[PubMed]

Q. Zhang, L. Yin, Y. Tan, Z. Yuan, and H. Jiang, “Quantitative bioluminescence tomography guided by diffuse optical tomography,” Opt. Express 16, 1481–1486 (2008).

[CrossRef]
[PubMed]

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).

[CrossRef]
[PubMed]

L. O. Svaasand, T. Spott, J. B. Fishkin, T. Pham, B. J. Tromberg, and M. W. Berns, “Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions,” Phys. Med. Biol. 44, 801–813 (1999).

[CrossRef]
[PubMed]

A. Kienle and T. Glanzmann, “In vivo determination of the optical properties of muscle with time-resolved reflectance using a layered model,” Phys. Med. Biol. 44, 2689–2702 (1999).

[CrossRef]
[PubMed]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).

[CrossRef]
[PubMed]

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59, R1–R64 (2014).

[CrossRef]

M. Schweiger and S. R. Arridge, “Optical tomographic reconstructon in a complex head model using a priori region boundary condition,” Phys. Med. Biol. 44, 2703–2721 (1999).

[CrossRef]
[PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).

[CrossRef]
[PubMed]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).

[CrossRef]
[PubMed]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: Analytic solution and applications,” Proc. Natl. Acad. Sci. U.S.A. 91, 4887–4891 (1994).

[CrossRef]
[PubMed]

H. Yan, Y. Lin, W. C. Barber, M. B. Unlu, and G. Gulsen, “A gantry-based tri-modality system for bioluminescence tomography,” Rev. Sci. Instrum. 83, 043708 (2012).

[CrossRef]
[PubMed]

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic, 1978), Vol 1.

L. H. V. Wang and H. Wu, Biomedical Optics: Principles and Imaging Hoboken (Wiley, 2007).

S. G. Mykhlin, Mathematical Physics: An Advanced Course (North-Holland, 1970).

Y. V. Egorov and M. A. Shubin, Partial Differential Equations (Springer, 1992).