Abstract

A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
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2008 (2)

C. C. Handapangoda, M. Premaratne, D. M. Paganin, and P. R. D. S. Hendahewa, "Technique for handling wave propagation specific effects in biological tissue: Mapping of the photon transport equation to Maxwell’s equations," Opt. Express 16, 17792-17807 (2008).
[CrossRef] [PubMed]

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008).
[CrossRef]

2005 (1)

C. J. Rivero-Moreno, and S. Bres, "Video spatio-temporal signatures using polynomial transforms," Lect. Notes Compt. Sci. 3736, 50-59 (2005).
[CrossRef]

2004 (1)

J. C. Chai, P. F. Hsu, and Y. C. Lam, "Three-dimensional transient radiative transfer modeling using the finite volume method," J. Quantum Spectrosc. Radiat. Transfer 86, 299-313 (2004).
[CrossRef]

2003 (1)

2002 (3)

J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002).
[CrossRef]

Z. M. Tan, and P. F. Hsu, "Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media," J. Quantum Spectrosc. Radiat. Transfer 73, 181-194 (2002).
[CrossRef]

Z. Guo, and S. Kumar, "Three-dimensional discrete ordinates method in transient radiative transfer," J. Thermophys. Heat Transfer 16, 289-296 (2002).
[CrossRef]

1998 (1)

K. F. Evans, "The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer," J. Atmos. Sci. 55, 429-446 (1998).
[CrossRef]

1993 (1)

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

1992 (2)

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

1988 (2)

G. L. Stephens, "Radiative transfer through arbitrarily shaped optical media. part I: A general method of solution," J. Atmos. Sci. 45, 1818-1836 (1988).
[CrossRef]

W. A. Fiveland, "Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method," J. Thermophys. Heat Transfer 2, 309-316 (1988).
[CrossRef]

1968 (1)

K. D. Lathrop, "Spatial differencing of the transport equation: positive vs accuracy," J. Comput. Phys. 4, 475-498 (1968).
[CrossRef]

Allen, D. J.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Andrew, C. C.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Barros, R. C.

J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002).
[CrossRef]

Bindra, D. S.

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Bres, S.

C. J. Rivero-Moreno, and S. Bres, "Video spatio-temporal signatures using polynomial transforms," Lect. Notes Compt. Sci. 3736, 50-59 (2005).
[CrossRef]

Brunelle, R. L.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Bryan, N. A.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Burden-Brady, P. L.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Capron, F.

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Cardona, A. V.

J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002).
[CrossRef]

Chai, J. C.

J. C. Chai, P. F. Hsu, and Y. C. Lam, "Three-dimensional transient radiative transfer modeling using the finite volume method," J. Quantum Spectrosc. Radiat. Transfer 86, 299-313 (2004).
[CrossRef]

de Oliveira, J. V. P.

J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002).
[CrossRef]

Evans, K. F.

K. F. Evans, "The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer," J. Atmos. Sci. 55, 429-446 (1998).
[CrossRef]

Fiveland, W. A.

W. A. Fiveland, "Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method," J. Thermophys. Heat Transfer 2, 309-316 (1988).
[CrossRef]

Friend, J.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008).
[CrossRef]

Guo, Z.

Z. Guo, and K. Kim, "Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method," Appl. Opt. 42, 2897-2905 (2003).
[CrossRef] [PubMed]

Z. Guo, and S. Kumar, "Three-dimensional discrete ordinates method in transient radiative transfer," J. Thermophys. Heat Transfer 16, 289-296 (2002).
[CrossRef]

Handapangoda, C. C.

C. C. Handapangoda, M. Premaratne, D. M. Paganin, and P. R. D. S. Hendahewa, "Technique for handling wave propagation specific effects in biological tissue: Mapping of the photon transport equation to Maxwell’s equations," Opt. Express 16, 17792-17807 (2008).
[CrossRef] [PubMed]

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008).
[CrossRef]

Hendahewa, P. R. D. S.

Howey, D. C.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Hsu, P. F.

J. C. Chai, P. F. Hsu, and Y. C. Lam, "Three-dimensional transient radiative transfer modeling using the finite volume method," J. Quantum Spectrosc. Radiat. Transfer 86, 299-313 (2004).
[CrossRef]

Z. M. Tan, and P. F. Hsu, "Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media," J. Quantum Spectrosc. Radiat. Transfer 73, 181-194 (2002).
[CrossRef]

Johnson, K. W.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Kim, K.

Klein, J. C.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

Kumar, S.

Z. Guo, and S. Kumar, "Three-dimensional discrete ordinates method in transient radiative transfer," J. Thermophys. Heat Transfer 16, 289-296 (2002).
[CrossRef]

Lam, Y. C.

J. C. Chai, P. F. Hsu, and Y. C. Lam, "Three-dimensional transient radiative transfer modeling using the finite volume method," J. Quantum Spectrosc. Radiat. Transfer 86, 299-313 (2004).
[CrossRef]

Lathrop, K. D.

K. D. Lathrop, "Spatial differencing of the transport equation: positive vs accuracy," J. Comput. Phys. 4, 475-498 (1968).
[CrossRef]

Lemonnier, F.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

Lipson, D.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Mastrototaro, J. J.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

McMahan, W. C.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Moatti-Sirat, D.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Morff, R. J.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Nevin, R. S.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Noffke, B. W.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Paganin, D. M.

Poitout, V.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Premaratne, M.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008).
[CrossRef]

C. C. Handapangoda, M. Premaratne, D. M. Paganin, and P. R. D. S. Hendahewa, "Technique for handling wave propagation specific effects in biological tissue: Mapping of the photon transport equation to Maxwell’s equations," Opt. Express 16, 17792-17807 (2008).
[CrossRef] [PubMed]

Reach, G.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Rivero-Moreno, C. J.

C. J. Rivero-Moreno, and S. Bres, "Video spatio-temporal signatures using polynomial transforms," Lect. Notes Compt. Sci. 3736, 50-59 (2005).
[CrossRef]

Rowe, H. M.

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Stephens, G. L.

G. L. Stephens, "Radiative transfer through arbitrarily shaped optical media. part I: A general method of solution," J. Atmos. Sci. 45, 1818-1836 (1988).
[CrossRef]

Tan, Z. M.

Z. M. Tan, and P. F. Hsu, "Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media," J. Quantum Spectrosc. Radiat. Transfer 73, 181-194 (2002).
[CrossRef]

Thevenot, D. R.

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Vilhena, M. T.

J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002).
[CrossRef]

Wilson, G. S.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Yeo, L.

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008).
[CrossRef]

Zhang, Y.

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biosens. Bioelectron. (1)

K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992).
[CrossRef] [PubMed]

Diabetologia (2)

D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992).
[CrossRef] [PubMed]

V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993).
[CrossRef] [PubMed]

IEEE J. Sel. Top. Quantum Electron. (1)

C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008).
[CrossRef]

J. Atmos. Sci. (2)

K. F. Evans, "The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer," J. Atmos. Sci. 55, 429-446 (1998).
[CrossRef]

G. L. Stephens, "Radiative transfer through arbitrarily shaped optical media. part I: A general method of solution," J. Atmos. Sci. 45, 1818-1836 (1988).
[CrossRef]

J. Comput. Phys. (1)

K. D. Lathrop, "Spatial differencing of the transport equation: positive vs accuracy," J. Comput. Phys. 4, 475-498 (1968).
[CrossRef]

J. Quantum Spectrosc. Radiat. Transfer (3)

Z. M. Tan, and P. F. Hsu, "Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media," J. Quantum Spectrosc. Radiat. Transfer 73, 181-194 (2002).
[CrossRef]

J. C. Chai, P. F. Hsu, and Y. C. Lam, "Three-dimensional transient radiative transfer modeling using the finite volume method," J. Quantum Spectrosc. Radiat. Transfer 86, 299-313 (2004).
[CrossRef]

J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002).
[CrossRef]

J. Thermophys. Heat Transfer (2)

Z. Guo, and S. Kumar, "Three-dimensional discrete ordinates method in transient radiative transfer," J. Thermophys. Heat Transfer 16, 289-296 (2002).
[CrossRef]

W. A. Fiveland, "Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method," J. Thermophys. Heat Transfer 2, 309-316 (1988).
[CrossRef]

Lect. Notes Compt. Sci. (1)

C. J. Rivero-Moreno, and S. Bres, "Video spatio-temporal signatures using polynomial transforms," Lect. Notes Compt. Sci. 3736, 50-59 (2005).
[CrossRef]

Opt. Express (1)

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S. C. Chapra, and R. P. Canale, "Runge-Kutta methods" in Numerical Methods for Engineers, 4th ed., (McGraw-Hill, New York,2002), pp. 719-720.

G. A. Korn, and T. M. Korn, "Special functions" in Mathematical handbook for scientists and engineers: definitions, theorems and formulas for reference and review, 2nd ed., (Dover, New York, 2000), pp. 848-856.

S. Chandrasekhar, "Quadrature formulae" in Radiative Transfer, (Dover, New York, 1960), pp. 54-60.

M. F. Modest, "The method of discrete ordinates" in Radiative Heat Transfer, 2nd ed. (Academic Press, Boston, 2003), pp. 513-522.

M. Abramomitz, and I. A. Stegun, "Orthogonal polynomials" in Handbook of mathematical functions with formulas, graphs and mathematical tables, (Dover, New York, 1965), pp. 773-784.

G. A. Korn, and T. M. Korn, "Tensor analysis" in Mathematical handbook for scientists and engineers: definitions, theorems and formulas for reference and review, 2nd ed., (Dover, New York, 2000), pp. 544.

A. Sawetprawichkul, P. F. Hsu, and K. Mitra, "Parallel computing of three-dimensional monte carlo simulation of transient radiative transfer in participating media," in Proceedings of the 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conferece, (American Institute of Aeronautics and Astronautics, St. Louse, Missouri, 2002), pp. 1-10.

C. C. Handapangoda, M. Premaratne, and D. M. Paganin, "Simulation of a device concept for noninvasive sensing of blood glucose levels," in Information and Automation for Sustainability, 2007. ICIAFS 2007. Third International Conference, (Melbourne, Australia, December 2007), pp. 31-34.

C. C. Handapangoda, M. Premaratne, and D. M. Paganin, "Simulation of embedded photonic crystal structures for blood glucose measurement using Raman spectroscopy," 2008 International conference on Nanoscience and Nanotechnology, (Melbourne, Australia, February 2008).

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Figures (18)

Fig. 1.
Fig. 1.

Illustration of the incident direction, scattered direction and the scattering angle.

Fig. 2.
Fig. 2.

Relationship between Cartesian and spherical coordinates.

Fig. 3.
Fig. 3.

Incident Gaussian pulse (with I 0=1 in Eq. (27)).

Fig. 4.
Fig. 4.

(Color online) Short laser pulse incident on the biological tissue layer

Fig. 5.
Fig. 5.

Comparison of Laguerre fitting, without scaling, with the exact plot of the corresponding Gaussian function.

Fig. 6.
Fig. 6.

Comparison of Laguerre fitting, after scaling with the factor Ts , with the exact plot of the corresponding Gaussian function.

Fig. 7.
Fig. 7.

Variation of radiance with time, along the incident angle, at z̄=2 without any scattering or absorption.

Fig. 8.
Fig. 8.

(Color online) Variation of radiance with time and µ, at z̄=2 with absorption but no scattering.

Fig. 9.
Fig. 9.

(Color online) Variation of radiance with time and µ, at z̄=2 with scattering and absorption.

Fig. 10.
Fig. 10.

(Color online) Comparison: Variation of irradiance with time for 1D PTE.

Fig. 11.
Fig. 11.

(Color online) Variation of irradiance with time and x coordinate at z̄=2 for 2D PTE, using Laguerre DOM.

Fig. 12.
Fig. 12.

(Color online) Variation of irradiance with time and x coordinate at z̄=2 for 2D PTE, using Transient DOM.

Fig. 13.
Fig. 13.

(Color online) Variation of irradiance with time, x coordinate and y coordinate at z̄=2 for 3D PTE, using Laguerre DOM (Slice plane at ȳ=0, z̄=2).

Fig. 14.
Fig. 14.

(Color online) Variation of irradiance with time, x coordinate and y coordinate at z̄=2 for 3D PTE, using Laguerre DOM (Slice plane at z̄=2, t̄=6).

Fig. 15.
Fig. 15.

(Color online) Variation of irradiance with time, x coordinate and y coordinate at z̄=2 for 3D PTE, using Laguerre DOM.

Fig. 16.
Fig. 16.

(Color online) Variation of irradiance with time, x coordinate and y coordinate at z̄=2 for 3D PTE, using Laguerre DOM.

Fig. 17.
Fig. 17.

(Color online) Variation of irradiance with time, x coordinate and y coordinate at z̄=2 for 3D PTE, using Transient DOM (Slice plane at ȳ=0, z̄=2).

Fig. 18.
Fig. 18.

(Color online) Variation of irradiance with time, x coordinate and y coordinate at z̄=2 for 3D PTE, using Transient DOM (Slice plane at z̄=2, t̄=6).

Equations (33)

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1 v t I ( x , y , z , s , t ) + ξ x I ( x , y , z , s , t ) + η y I ( x , y , z , s , t ) + μ z I ( x , y , z , s , t )
σ s ( x , y , z ) 4 π 4 π P ( s ; s ) I ( x , y , s , t ) d s + σ t ( x , y , z ) I ( x , y , z , s , t ) = F ( x , y , z , s , t ) ,
τ = t x 3 v ξ y 3 v η z 3 v μ .
1 v τ I ( x , y , z , s , τ ) ξ 3 v ξ τ I ( x , y , z , s , τ ) + ξ x I ( x , y , z , s , τ ) η 3 v η τ I ( x , y , z , s , τ ) + η y I ( x , y , s , τ ) μ 3 v μ τ I ( x , y , z , s , τ ) + μ z I ( x , y , z , s , τ ) σ s ( x , y , z ) 4 π 4 π P ( s ; s ) I ( x , y , z , s , t ) d s + σ t ( x , y , z ) I ( x , y , z , s , τ ) = 0 .
ξ x I ( x , y , z , s , τ ) + η y I ( x , y , z , s , τ ) + μ z I ( x , y , z , s , τ ) σ s ( x , y , z ) 4 π 4 π P ( s ; s ) I ( x , y , z , s , τ ) d s + σ t ( x , y , z ) I ( x , y , z , s , τ ) = 0 .
xy + ( 1 x ) y + ny = 0 ,
L n ( x ) = e x n ! d n d x n ( e x x n ) .
0 L n ( x ) L m ( x ) e x d x = δ n m ,
I ( x , y , z , s , τ ) = k = 0 N B k ( x , y , z , s ) L k ( τ ) ,
ξ x B n ( x , y , z , s ) + η y B n ( x , y , z , s ) + μ z B n ( x , y , z , s ) σ s ( x , y , z ) 4 π 4 π P ( s ; s ) B n ( x , y , z , s ) d s + σ t ( x , y , z ) B n ( x , y , z , s ) = 0 ,
ξ i x B n ( x , y , z , s i ) + η i y B n ( x , y , z , s i ) + μ i z B n ( x , y , z , s i ) σ s ( x , y , z ) 4 π j = 1 L w j P ( s j ; s i ) B n ( x , y , z , s j ) + σ t ( x , y , z ) B n ( x , y , z , s i ) = 0 ,
V B n i x dV = ( B n i ) xu A xu ( B n i ) xd A xd ,
V B n i y dV = ( B n i ) yu A yu ( B n i ) yd A yd ,
V B n i y dV = ( B n i ) zu A zu ( B n i ) zd A zd .
ξ i ( ( B n i ) xu A xu ( B n i ) xd A xd ) + η i ( ( B n i ) yu A yu ( B n i ) yd A yd ) + μ i ( ( B n i ) zu A zu ( B n i ) zd A zd )
σ s ( x , y , z ) 4 π V j = 1 L w j P ( s j ; s i ) ( B n j ) p + σ t ( x , y , z ) V ( B n i ) p = 0 ,
( B n i ) p = ( γ i ) x ( B n i ) xd + ( 1 ( γ i ) x ) ( B n i ) xu ,
= ( γ i ) y ( B n i ) yd + ( 1 ( γ i ) y ) ( B n i ) yu ,
= ( γ i ) z ( B n i ) zd + ( 1 ( γ i ) z ) ( B n i ) zu .
( B n i ) p = V ( S i ) p + ξ i A xu ( B n i ) x u / ( γ i ) x + η i A yu ( B n i ) y u / ( γ i ) y + μ i A zu ( B n i ) z u / ( γ i ) z σ t V + ξ i A xu / ( γ i ) x + η i A yu / ( γ i ) y + μ i A zu / ( γ i ) z ,
( S i ) p = σ s ( x , y , z ) 4 π j = 1 L w j P ( s j ; s j ) ( B n j ) p .
( B n i ) p = ( S i ) p + ( ξ i / ( ( γ i ) x Δ x ) ) ( B n i ) x u + ( η i / ( ( γ i ) y Δ y ) ) ( B n i ) y u + ( μ i / ( ( γ i ) z Δ z ) ) ( B n i ) z u σ t + ξ i / ( ( γ i ) x Δ x ) + η i / ( ( γ i ) y Δ y ) + μ i / ( ( γ i ) z Δ z ) .
1 v t I ( x , z , s , t ) + ξ x I ( x , z , s , t ) + μ x I ( x , z , s , t )
σ s ( x , z ) 4 π 4 π P ( s ; s ) I ( x , z , s , t ) d s + σ t ( x , z ) I ( x , z , s , t ) = 0 ,
τ = t x 2 z 2 ,
ξ x B n ( x , z , s ) + μ z B n ( x , z , s ) σ s ( x , z ) 4 π 4 π P ( s : s ) B n ( x , z , s ) d s + σ t ( x , z ) B n ( x , z , s ) = 0.
1 v t I ( z , s , t ) + μ z I ( z , s , t ) σ s ( z ) 4 π 4 π P ( s ; s ) I ( z , s , t ) d s + σ t ( z ) I ( z , s , t ) = 0 .
τ = t z .
μ z B n ( z , s ) σ s ( z ) 4 π 4 π P ( s ; s ) B n ( z , s ) d s + σ t ( z ) B n ( z , s ) = 0 ,
μ i z B n ( z , s i ) σ s ( z ) 4 π j = 1 L w j P ( s j ; s i ) B n ( z , s j ) + σ t ( z ) B n ( z , s i ) = 0 ,
z AB n + σ t B n σ s 4 π PWB n = 0 ,
z B n = YB n ,
f ( t ) = I 0 e ( ( t t 0 ) T ) 2 ,

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