F. Asllanaj and S. Fumeron, “Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation,” J. Biomed. Opt. 17, 075007 (2012).

[CrossRef]

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[CrossRef]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[CrossRef]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[CrossRef]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “Signal reconstruction for the diffusion transport equation using tensorial spline galerking approximation,” Appl. Numer. Math. 62, 1089–1108 (2012).

[CrossRef]

P. S. 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, 7364–7383 (2011).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[CrossRef]

M. Boffety, M. Allain, A. Sentenac, M. Massonneau, and R. Carminati, “Cramer–Rao analysis of steady-state and time-domain fluorescence diffuse optical imaging,” Biomed. Opt. Express 2, 1626–1636 (2011).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method,” Appl. Math. Comput. 215, 4067–4079 (2010).

[CrossRef]

D. Gorpas, D. Yova, and K. Politopoulos, “A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging,” J. Quant. Spectrosc. Radiat. Transfer 111, 553–568 (2010).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

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, 65–88(2009).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat.. Phys. 38, 149–192 (2009).

[CrossRef]

S. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

[CrossRef]

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Philos. Trans. R. Soc. A 367, 3055–3072 (2009).

[CrossRef]

Q. Zhang, H. Soon, H. Tian, S. Fernando, Y. Ha, and N. Chen, “Pseudo-random single photon counting for time-resolved optical measurement,” Opt. Express 16, 13233–13239 (2008).

[CrossRef]

T. Tarvainen, M. Vauhkonen, and S. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2767–2778 (2008).

[CrossRef]

H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 104, 24–39 (2007).

[CrossRef]

J. Selb, A. Dale, and D. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).

[CrossRef]

E. D. Aydin, “Three-dimensional photon migration through voidlike regions and channels,” Appl. Opt. 46, 8272–8277 (2007).

[CrossRef]

K. Ren, G. Bal, and A. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28, 1463–1489 (2006).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

J. Selb, D. Joseph, and D. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11, 044008 (2006).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

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

[CrossRef]

J. Boulanger and A. Charette, “Reconstruction optical spectroscopy using transient radiative transfer equation and pulsed laser: a numerical study,” J. Quant. Spectrosc. Radiat. Transfer 93, 325–336 (2005).

[CrossRef]

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

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

E. Boman, J. Tervo, and M. Vauhkonen, “Modelling the transport of ionizing radiation using the finite element method,” Phys. Med. Biol. 50, 265–280 (2005).

[CrossRef]

S. Wright, M. Schweiger, and S. Arridge, “Solutions to the transport equation using variable order angular basis,” Proc. SPIE 5859, 585914 (2005).

[CrossRef]

J. Heiskala, I. Nissilä, T. Neuvonen, S. Järvenpää, and E. Somersalo, “Modeling anisotropic light propagation in a realistic model of the human head,” Appl. Opt. 44, 2049–2057 (2005).

[CrossRef]

G. Abdoulaev and A. Hielscher, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12, 594–601 (2003).

[CrossRef]

A. Klose and A. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).

[CrossRef]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[CrossRef]

F. Gao, H. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 778–791 (2002).

[CrossRef]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).

[CrossRef]

S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat, “Radiative transfer with finite elements I. Basic method and tests,” Astron. Astrophys. 380, 776–788 (2001).

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).

[CrossRef]

H. Jiang, “Optical image reconstruction based on the third-order diffusion equations,” Opt. Express 4, 241–246 (1999).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[CrossRef]

G. Kanschat, “A robust finite element discretization for radiative transfer problems with scattering,” East-West J. Numer. Math. 6, 265–272 (1998).

S. R. Arridge and W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).

[CrossRef]

A. D. Kim and A. Ishimaru, “Optical diffusion of continuos-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. 37, 5313–5319 (1998).

[CrossRef]

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).

[CrossRef]

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

[CrossRef]

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

R. T. Ackroyd, Finite Element Methods for Particle Transport: Applications to Reactor and Radiation Physics (Research Studies, 1997).

M. Addam, A. Bouhamidi, and K. Jbilou, “Signal reconstruction for the diffusion transport equation using tensorial spline galerking approximation,” Appl. Numer. Math. 62, 1089–1108 (2012).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method,” Appl. Math. Comput. 215, 4067–4079 (2010).

[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

S. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

[CrossRef]

T. Tarvainen, M. Vauhkonen, and S. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2767–2778 (2008).

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

S. Wright, M. Schweiger, and S. Arridge, “Solutions to the transport equation using variable order angular basis,” Proc. SPIE 5859, 585914 (2005).

[CrossRef]

P. S. 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, 7364–7383 (2011).

[CrossRef]

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

[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).

[CrossRef]

S. R. Arridge and W. R. B. Lionheart, “Nonuniqueness in diffusion-based optical tomography,” Opt. Lett. 23, 882–884 (1998).

[CrossRef]

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

[CrossRef]

F. Asllanaj and S. Fumeron, “Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation,” J. Biomed. Opt. 17, 075007 (2012).

[CrossRef]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[CrossRef]

K. Ren, G. Bal, and A. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28, 1463–1489 (2006).

[CrossRef]

K. Ren, G. Abdoulaev, G. Bal, and A. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004).

[CrossRef]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[CrossRef]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[CrossRef]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[CrossRef]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[CrossRef]

R. Koch and R. Becker, “Evaluation of quadrature schemes for the discrete ordinates method,” J. Quant. Spectrosc. Radiat. Transfer 84, 423–435 (2004).

[CrossRef]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[CrossRef]

J. Selb, A. Dale, and D. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).

[CrossRef]

J. Selb, D. Joseph, and D. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11, 044008 (2006).

[CrossRef]

E. Boman, J. Tervo, and M. Vauhkonen, “Modelling the transport of ionizing radiation using the finite element method,” Phys. Med. Biol. 50, 265–280 (2005).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “Signal reconstruction for the diffusion transport equation using tensorial spline galerking approximation,” Appl. Numer. Math. 62, 1089–1108 (2012).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method,” Appl. Math. Comput. 215, 4067–4079 (2010).

[CrossRef]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[CrossRef]

J. Boulanger and A. Charette, “Reconstruction optical spectroscopy using transient radiative transfer equation and pulsed laser: a numerical study,” J. Quant. Spectrosc. Radiat. Transfer 93, 325–336 (2005).

[CrossRef]

K. M. Case and P. F. Zweifel, Linear Transport Theory(Addison-Wesley, 1967).

C. Cercignani, The Boltzmann Equation and Its Applications (Springer-Verlag, 1988).

S. Chandrasekhar, Radiative Transfer (Oxford University, 1950).

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[CrossRef]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[CrossRef]

H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 104, 24–39 (2007).

[CrossRef]

J. Boulanger and A. Charette, “Reconstruction optical spectroscopy using transient radiative transfer equation and pulsed laser: a numerical study,” J. Quant. Spectrosc. Radiat. Transfer 93, 325–336 (2005).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[CrossRef]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[CrossRef]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[CrossRef]

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Philos. Trans. R. Soc. A 367, 3055–3072 (2009).

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

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

[CrossRef]

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).

[CrossRef]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[CrossRef]

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[CrossRef]

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, 1979).

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

F. Asllanaj and S. Fumeron, “Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation,” J. Biomed. Opt. 17, 075007 (2012).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat.. Phys. 38, 149–192 (2009).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Philos. Trans. R. Soc. A 367, 3055–3072 (2009).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

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

[CrossRef]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[CrossRef]

D. Gorpas, D. Yova, and K. Politopoulos, “A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging,” J. Quant. Spectrosc. Radiat. Transfer 111, 553–568 (2010).

[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[CrossRef]

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

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

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

K. Ren, G. Bal, and A. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28, 1463–1489 (2006).

[CrossRef]

K. Ren, G. Abdoulaev, G. Bal, and A. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004).

[CrossRef]

A. Klose and A. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).

[CrossRef]

G. Abdoulaev and A. Hielscher, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12, 594–601 (2003).

[CrossRef]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[CrossRef]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).

[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

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

[CrossRef]

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, 65–88(2009).

[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).

[CrossRef]

A. D. Kim and A. Ishimaru, “Optical diffusion of continuos-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. 37, 5313–5319 (1998).

[CrossRef]

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

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, SPIE Institute Series, Vol.5, (SPIE, 1989), pp. 102–111.

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

J. Heiskala, I. Nissilä, T. Neuvonen, S. Järvenpää, and E. Somersalo, “Modeling anisotropic light propagation in a realistic model of the human head,” Appl. Opt. 44, 2049–2057 (2005).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “Signal reconstruction for the diffusion transport equation using tensorial spline galerking approximation,” Appl. Numer. Math. 62, 1089–1108 (2012).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method,” Appl. Math. Comput. 215, 4067–4079 (2010).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[CrossRef]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[CrossRef]

J. Selb, D. Joseph, and D. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11, 044008 (2006).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

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

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat, “Radiative transfer with finite elements I. Basic method and tests,” Astron. Astrophys. 380, 776–788 (2001).

[CrossRef]

G. Kanschat, “A robust finite element discretization for radiative transfer problems with scattering,” East-West J. Numer. Math. 6, 265–272 (1998).

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, SPIE Institute Series, Vol.5, (SPIE, 1989), pp. 102–111.

H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 104, 24–39 (2007).

[CrossRef]

A. Klose and A. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).

[CrossRef]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[CrossRef]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).

[CrossRef]

R. Koch and R. Becker, “Evaluation of quadrature schemes for the discrete ordinates method,” J. Quant. Spectrosc. Radiat. Transfer 84, 423–435 (2004).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

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

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat, “Radiative transfer with finite elements I. Basic method and tests,” Astron. Astrophys. 380, 776–788 (2001).

[CrossRef]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[CrossRef]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[CrossRef]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[CrossRef]

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, 1979).

S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat, “Radiative transfer with finite elements I. Basic method and tests,” Astron. Astrophys. 380, 776–788 (2001).

[CrossRef]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.

P. S. 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, 7364–7383 (2011).

[CrossRef]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

J. Heiskala, I. Nissilä, T. Neuvonen, S. Järvenpää, and E. Somersalo, “Modeling anisotropic light propagation in a realistic model of the human head,” Appl. Opt. 44, 2049–2057 (2005).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

D. Gorpas, D. Yova, and K. Politopoulos, “A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging,” J. Quant. Spectrosc. Radiat. Transfer 111, 553–568 (2010).

[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, SPIE Institute Series, Vol.5, (SPIE, 1989), pp. 102–111.

P. S. 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, 7364–7383 (2011).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

K. Ren, G. Bal, and A. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28, 1463–1489 (2006).

[CrossRef]

K. Ren, G. Abdoulaev, G. Bal, and A. Hielscher, “Algorithm for solving the equation of radiative transfer in the frequency domain,” Opt. Lett. 29, 578–580 (2004).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat, “Radiative transfer with finite elements I. Basic method and tests,” Astron. Astrophys. 380, 776–788 (2001).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

S. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

[CrossRef]

P. S. 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, 7364–7383 (2011).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

S. Wright, M. Schweiger, and S. Arridge, “Solutions to the transport equation using variable order angular basis,” Proc. SPIE 5859, 585914 (2005).

[CrossRef]

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

[CrossRef]

J. Selb, A. Dale, and D. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).

[CrossRef]

J. Selb, D. Joseph, and D. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11, 044008 (2006).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

P. S. 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, 7364–7383 (2011).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

T. Tarvainen, M. Vauhkonen, and S. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2767–2778 (2008).

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

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

[CrossRef]

E. Boman, J. Tervo, and M. Vauhkonen, “Modelling the transport of ionizing radiation using the finite element method,” Phys. Med. Biol. 50, 265–280 (2005).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

T. Tarvainen, M. Vauhkonen, and S. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2767–2778 (2008).

[CrossRef]

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

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

E. Boman, J. Tervo, and M. Vauhkonen, “Modelling the transport of ionizing radiation using the finite element method,” Phys. Med. Biol. 50, 265–280 (2005).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, SPIE Institute Series, Vol.5, (SPIE, 1989), pp. 102–111.

S. Wright, M. Schweiger, and S. Arridge, “Solutions to the transport equation using variable order angular basis,” Proc. SPIE 5859, 585914 (2005).

[CrossRef]

F. Gao, H. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 778–791 (2002).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[CrossRef]

D. Gorpas, D. Yova, and K. Politopoulos, “A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging,” J. Quant. Spectrosc. Radiat. Transfer 111, 553–568 (2010).

[CrossRef]

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, 65–88(2009).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat.. Phys. 38, 149–192 (2009).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).

[CrossRef]

F. Gao, H. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 778–791 (2002).

[CrossRef]

K. M. Case and P. F. Zweifel, Linear Transport Theory(Addison-Wesley, 1967).

W. Martin, C. Yehnert, L. Lorence, and J. Duderstadt, “Phase-space finite element methods applied to the first order form of the transport equation,” Ann. Nucl. Energy 8, 633–646 (1981).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “A numerical method for one-dimensional diffusion problem using Fourier transform and the B-spline Galerkin method,” Appl. Math. Comput. 215, 4067–4079 (2010).

[CrossRef]

M. Addam, A. Bouhamidi, and K. Jbilou, “Signal reconstruction for the diffusion transport equation using tensorial spline galerking approximation,” Appl. Numer. Math. 62, 1089–1108 (2012).

[CrossRef]

A. D. Kim and A. Ishimaru, “Optical diffusion of continuos-wave, pulsed, and density waves in scattering media and comparisons with radiative transfer,” Appl. Opt. 37, 5313–5319 (1998).

[CrossRef]

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

[CrossRef]

J. Heiskala, I. Nissilä, T. Neuvonen, S. Järvenpää, and E. Somersalo, “Modeling anisotropic light propagation in a realistic model of the human head,” Appl. Opt. 44, 2049–2057 (2005).

[CrossRef]

E. D. Aydin, “Three-dimensional photon migration through voidlike regions and channels,” Appl. Opt. 46, 8272–8277 (2007).

[CrossRef]

A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “Polarized pulse waves in random discrete scatterers,” Appl. Opt. 40, 5495–5502 (2001).

[CrossRef]

F. Gao, H. Zhao, and Y. Yamada, “Improvement of image quality in diffuse optical tomography by use of full time-resolved data,” Appl. Opt. 41, 778–791 (2002).

[CrossRef]

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, 3808–3823 (2011).

[CrossRef]

S. Richling, E. Meinköhn, N. Kryzhevoi, and G. Kanschat, “Radiative transfer with finite elements I. Basic method and tests,” Astron. Astrophys. 380, 776–788 (2001).

[CrossRef]

L. G. Henyey and J. L. Greenstein, “Diffuse radiation in the galaxy,” Astrophys. J. 93, 70–83 (1941).

[CrossRef]

G. Kanschat, “A robust finite element discretization for radiative transfer problems with scattering,” East-West J. Numer. Math. 6, 265–272 (1998).

D. Contini, A. Torricelli, A. Pifferi, L. Spinelli, P. Taroni, V. Quaresima, M. Ferrari, and R. Cubeddu, “Multichannel time-resolved tissue oximeter for functional imaging of the brain,” IEEE Trans. Instrum. Meas. 55, 85–90 (2006).

[CrossRef]

S. Arridge and J. Schotland, “Optical tomography: forward and inverse problems,” Inverse Probl. 25, 123010 (2009).

[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).

[CrossRef]

O. Dorn, “A transport–backtransport method for optical tomography,” Inverse Probl. 14, 1107–1130 (1998).

[CrossRef]

A. Klose and A. Hielscher, “Quasi-Newton methods in optical tomographic image reconstruction,” Inverse Probl. 19, 387–409 (2003).

[CrossRef]

J. Tervo, P. Kolmonen, M. Vauhkonen, L. Heikkinen, and J. Kaipio, “A finite-element model of electron transport in radiation therapy and a related inverse problem,” Inverse Probl. 15, 1345–1361 (1999).

[CrossRef]

T. Tarvainen, V. Kolehmainen, A. Pulkkinen, M. Vauhkonen, M. Schweiger, S. Arridge, and J. Kaipio, “Approximation error approach for compensating for modelling errors between the radiative transfer equation and the diffusion approximation in diffuse optical tomography,” Inverse Probl. 26, 015005 (2010).

[CrossRef]

N. Ducros, C. D’Andrea, A. Bassi, and F. Peyrin, “Fluorescence diffuse optical tomography: time-resolved versus continuous-wave in the reflectance configuration,” IRBM 32, 243–250 (2011).

[CrossRef]

J. Selb, D. Joseph, and D. Boas, “Time-gated optical system for depth-resolved functional brain imaging,” J. Biomed. Opt. 11, 044008 (2006).

[CrossRef]

I. Nissilä, J. Hebden, D. Jennions, J. Heino, M. Schweiger, K. Kotilahti, T. Noponen, A. Gibson, S. Järvenpää, L. Lipiäinen, and T. Katila, “Comparison between a time-domain and a frequency-domain system for optical tomography,” J. Biomed. Opt. 11, 064015 (2006).

[CrossRef]

F. Asllanaj and S. Fumeron, “Applying a new computational method for biological tissue optics based on the time-dependent two-dimensional radiative transfer equation,” J. Biomed. Opt. 17, 075007 (2012).

[CrossRef]

M. Charest, C. Groth, and Ö. Gülder, “Solution of the equation of radiative transfer using a Newton–Krylov approach and adaptive mesh refinement,” J. Comput. Phys. 231, 3023–3040 (2012).

[CrossRef]

P. S. 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, 7364–7383 (2011).

[CrossRef]

G. Abdoulaev and A. Hielscher, “Three-dimensional optical tomography with the equation of radiative transfer,” J. Electron. Imaging 12, 594–601 (2003).

[CrossRef]

A. Jha, M. Kupinski, T. Masumura, E. Clarkson, A. Maslov, and H. Barrett, “Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach,” J. Opt. Soc. Am. A 29, 1741–1756 (2012).

[CrossRef]

A. Jha, M. Kupinski, H. Barrett, E. Clarkson, and J. Hartman, “Three-dimensional Neumann-series approach to model light transport in nonuniform media,” J. Opt. Soc. Am. A 29, 1885–1898 (2012).

[CrossRef]

T. Tarvainen, M. Vauhkonen, and S. Arridge, “Gauss–Newton reconstruction method for optical tomography using the finite element solution of the radiative transfer equation,” J. Quant. Spectrosc. Radiat. Transfer 109, 2767–2778 (2008).

[CrossRef]

D. Gorpas, D. Yova, and K. Politopoulos, “A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging,” J. Quant. Spectrosc. Radiat. Transfer 111, 553–568 (2010).

[CrossRef]

O. Balima, Y. Favennec, J. Boulanger, and A. Charette, “Optical tomography with the discontinuous Galerkin forumulation of the radiative transfer equation in frequency domain,” J. Quant. Spectrosc. Radiat. Transfer 113, 805–814 (2012).

[CrossRef]

R. Koch and R. Becker, “Evaluation of quadrature schemes for the discrete ordinates method,” J. Quant. Spectrosc. Radiat. Transfer 84, 423–435 (2004).

[CrossRef]

J. Boulanger and A. Charette, “Reconstruction optical spectroscopy using transient radiative transfer equation and pulsed laser: a numerical study,” J. Quant. Spectrosc. Radiat. Transfer 93, 325–336 (2005).

[CrossRef]

H. K. Kim and A. Charette, “A sensitivity function-based conjugate gradient method for optical tomography with the frequency-domain equation of radiative transfer,” J. Quant. Spectrosc. Radiat. Transfer 104, 24–39 (2007).

[CrossRef]

A. Klose, U. Netz, J. Beuthan, and A. Hielscher, “Optical tomography using the time-independent equation of radiative transfer—Part 1: forward model,” J. Quant. Spectrosc. Radiat. Transfer 72, 691–713 (2002).

[CrossRef]

A. D. Klose and A. H. Hielscher, “Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer,” Med. Phys. 26, 1698–1707 (1999).

[CrossRef]

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

[CrossRef]

E. Aydin, C. de Oliveira, and A. Goddard, “A comparison between transport and diffusion calculations using a finite element-spherical harmonics radiation transport method,” Med. Phys. 29, 2013–2023 (2002).

[CrossRef]

J. Selb, A. Dale, and D. Boas, “Linear 3D reconstruction of time-domain diffuse optical imaging differential data: improved depth localization and lateral resolution,” Opt. Express 15, 16400–16412 (2007).

[CrossRef]

Q. Zhang, H. Soon, H. Tian, S. Fernando, Y. Ha, and N. Chen, “Pseudo-random single photon counting for time-resolved optical measurement,” Opt. Express 16, 13233–13239 (2008).

[CrossRef]

H. Jiang, “Optical image reconstruction based on the third-order diffusion equations,” Opt. Express 4, 241–246 (1999).

[CrossRef]

A. Gibson and H. Dehghani, “Diffuse optical imaging,” Philos. Trans. R. Soc. A 367, 3055–3072 (2009).

[CrossRef]

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

[CrossRef]

A. H. Hielscher, R. E. Alcouffe, and R. L. Barbour, “Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues,” Phys. Med. Biol. 43, 1285–1302 (1998).

[CrossRef]

E. Boman, J. Tervo, and M. Vauhkonen, “Modelling the transport of ionizing radiation using the finite element method,” Phys. Med. Biol. 50, 265–280 (2005).

[CrossRef]

T. Tarvainen, M. Vauhkonen, V. Kolehmainen, S. Arridge, and J. 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, 4913–4930 (2005).

[CrossRef]

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, 65–88(2009).

[CrossRef]

S. Wright, M. Schweiger, and S. Arridge, “Solutions to the transport equation using variable order angular basis,” Proc. SPIE 5859, 585914 (2005).

[CrossRef]

H. Eda, I. Oda, Y. Ito, Y. Wada, Y. Oikawa, Y. Tsunazawa, M. Takada, Y. Tsuchiya, Y. Yamashita, M. Oda, A. Sassaroli, Y. Yamada, and M. Tamura, “Multichannel time-resolved optical tomographic imaging system,” Rev. Sci. Instrum. 70, 3595–3602 (1999).

[CrossRef]

F. E. W. Schmidt, M. E. Fry, E. M. C. Hillman, J. C. Hebden, and D. T. Delby, “A 32-channel time-resolved instrument for medical optical tomography,” Rev. Sci. Instrum. 71, 256–265 (2000).

[CrossRef]

K. Ren, G. Bal, and A. Hielscher, “Frequency domain optical tomography based on the equation of radiative transfer,” SIAM J. Sci. Comput. 28, 1463–1489 (2006).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat. Phys. 38, 149–192 (2009).

[CrossRef]

H. Gao and H. Zhao, “A fast-forward solver of radiative transfer equation,” Transp. Theory Stat.. Phys. 38, 149–192 (2009).

[CrossRef]

S. A. Prahl, M. Keijzer, S. L. Jacques, and A. J. Welch, “A Monte Carlo model of light propagation in tissue,” in Dosimetry of Laser Radiation in Medicine and Biology, SPIE Institute Series, Vol.5, (SPIE, 1989), pp. 102–111.

J. J. Duderstadt and W. R. Martin, Transport Theory (Wiley, 1979).

K. M. Case and P. F. Zweifel, Linear Transport Theory(Addison-Wesley, 1967).

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

S. Chandrasekhar, Radiative Transfer (Oxford University, 1950).

C. Cercignani, The Boltzmann Equation and Its Applications (Springer-Verlag, 1988).

R. T. Ackroyd, Finite Element Methods for Particle Transport: Applications to Reactor and Radiation Physics (Research Studies, 1997).

H. Wabnitz, M. Moeller, A. Liebert, H. Obrig, J. Steinbrink, and R. Macdonald, “Time-resolved near-infrared spectroscopy and imaging of the adult human brain,” in Oxygen Transport to Tissue XXXI, E. Takahashi and D. Bruley, eds. (Springer, 2010), Vol. 662, pp. 143–148.