Abstract

Application of adjoint time domain methods to the inverse problem in 3D fluorescence imaging is a novel approach. We demonstrate the feasibility of this approach experimentally on the basis of a time gating technique completely in the time domain by using a small number of time windows. The evolution of the fluorescence energy density function inside a highly scattering cylinder was reconstructed together with optical parameters. Reconstructed energy density was used in localizing two fluorescent tubes. Relatively accurate reconstruction demonstrates the effectiveness and the potential of the proposed technique.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

2007 (3)

2006 (6)

R. B. Schulz, J. Peter, W. Semmler, C. D'Andrea, G. Valentini, and R. Cubeddu, “Comparison of noncontact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769-771 (2006).
[CrossRef] [PubMed]

A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, “Time resolved fluorescence tomography of turbid media based on lifetime contrast,” Opt. Express 14, 12255-12270 (2006), http://www.opticsexpress.org.
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

V. Y. Soloviev and L. V. Krasnosselskaia, “Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography,” Appl. Opt. 45, 2828-2837 (2006).
[CrossRef] [PubMed]

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176-4183(2006).
[CrossRef] [PubMed]

2005 (1)

2003 (3)

A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomography,” Appl. Opt. 42, 3081-3094 (2003).
[CrossRef] [PubMed]

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

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

1999 (1)

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

1997 (3)

M Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585-1605 (1997).
[CrossRef]

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

J. S. Reynolds, C. A. Thompson, K. J. Webb, F. P. LaPlant, and D. Ben-Amotz, “Frequency domain modeling of reradiation in highly scattering media,” Appl. Opt. 36, 2252-2259 (1997).
[CrossRef] [PubMed]

1996 (1)

1995 (1)

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

1994 (1)

1993 (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach to modelling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Arridge, S. R.

V. Y. Soloviev, K. B. Tahir, J. McGinty, D. S. Elson, M. A. A. Neil, P. M. W. French, and S. R. Arridge, “Fluorescence lifetime imaging by using time gated data acquisition,” Appl. Opt. 46, 7384-7391(2007).
[CrossRef] [PubMed]

V. Y. Soloviev, J. McGinty, K. B. Tahir, M. A. A. Neil, A. Sardini, J. V. Hajnal, S. R. Arridge, and P. M. W. French, “Fluorescence lifetime tomography of live cells expressing enhanced green fluorescent protein embedded in a scattering medium exhibiting background autofluorescence,” Opt. Lett. 32, 2034-2036 (2007).
[CrossRef] [PubMed]

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

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach to modelling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Bacskai, B. J.

Bangerth, W.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

Ben-Amotz, D.

Boas, D. A.

Bouman, C. A.

Boverman, G.

Chance, B.

Comelli, D.

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

Cubeddu, R.

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

R. B. Schulz, J. Peter, W. Semmler, C. D'Andrea, G. Valentini, and R. Cubeddu, “Comparison of noncontact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769-771 (2006).
[CrossRef] [PubMed]

D'Andrea, C.

R. B. Schulz, J. Peter, W. Semmler, C. D'Andrea, G. Valentini, and R. Cubeddu, “Comparison of noncontact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769-771 (2006).
[CrossRef] [PubMed]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

Delpy, D. T.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach to modelling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Dunn, A. K.

Elson, D. S.

French, P. M. W.

Graves, E. E.

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

Hajnal, J. V.

Hiraoka, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach to modelling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Hutchinson, C. L.

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

Hwan, K.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

Joshi, A.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

Krasnosselskaia, L. V.

Kumar, A. T. N.

LaPlant, F. P.

Li, X. D.

Lopez, G.

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

McGinty, J.

Millane, R. P.

Milstein, A. B.

Neil, M. A. A.

Ntziachristos, V.

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

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

Oh, S.

O'Leary, M. A.

Patterson, M. S.

Peter, J.

Pifferi, A.

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

Pogue, B. W.

Rasmussen, J. C.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

Raymond, S. B.

Reynolds, J. S.

J. S. Reynolds, C. A. Thompson, K. J. Webb, F. P. LaPlant, and D. Ben-Amotz, “Frequency domain modeling of reradiation in highly scattering media,” Appl. Opt. 36, 2252-2259 (1997).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

Ripoll, J.

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

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

Sardini, A.

Schulz, R. B.

R. B. Schulz, J. Peter, W. Semmler, C. D'Andrea, G. Valentini, and R. Cubeddu, “Comparison of noncontact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769-771 (2006).
[CrossRef] [PubMed]

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

Schweiger, M.

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach to modelling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

Semmler, W.

Sevick-Muraca, E. M.

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

Skoch, J.

Soloviev, V. Y.

Tadi, M

M Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585-1605 (1997).
[CrossRef]

Tahir, K. B.

Thompson, C. A.

Torricelli, A.

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

Troy, T. L.

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

Valentini, G.

R. B. Schulz, J. Peter, W. Semmler, C. D'Andrea, G. Valentini, and R. Cubeddu, “Comparison of noncontact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769-771 (2006).
[CrossRef] [PubMed]

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

Webb, K. J.

Weissleder, R.

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

Yodh, A. G.

Zhang, Q.

Appl. Opt. (6)

Inverse Probl. (2)

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

M Tadi, “Inverse heat conduction based on boundary measurement,” Inverse Probl. 13, 1585-1605 (1997).
[CrossRef]

J. Phys. D (1)

C. D'Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D 36, 1675-1681 (2006).
[CrossRef]

Med. Phys. (5)

E. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901-911 (2003).
[CrossRef] [PubMed]

M. Schweiger, S. R. Arridge, M. Hiraoka, and D. T. Delpy, “The finite element method for the propagation of light in scattering media: boundary and source conditions,” Med. Phys. 22, 1779-1792 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach to modelling photon transport in tissue,” Med. Phys. 20, 299-309 (1993).
[CrossRef] [PubMed]

A. Joshi, W. Bangerth, K. Hwan, J. C. Rasmussen, and E. M. Sevick-Muraca, “Fully adaptive FEM based fluorescence tomography from time-dependant measurements with area illumination and detection,” Med. Phys. 33, 1299-1310 (2006).
[CrossRef] [PubMed]

V. Y. Soloviev, “Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging,” Med. Phys. 33, 4176-4183(2006).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (4)

Photochem. Photobiol. (1)

E. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanism for biomedical optical imaging using frequency domain techniques,” Photochem. Photobiol. 66, 55-64 (1997).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

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

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Figures (6)

Fig. 1
Fig. 1

Experimental setup. PD, photodiode; ICCD, intensified CCD camera; Del, delay generator; RS, the rotational stage.

Fig. 2
Fig. 2

(a) phantom diagram; (b) surface mesh, and; (c) phantom cut showing interior mesh structure.

Fig. 3
Fig. 3

Reconstructed superposition of fluorescent energy density distributions 0 i < 5 u i ( t ) for five camera positions. A homogeneous medium is assumed. Each slice shows a different time window.

Fig. 4
Fig. 4

Reconstructed superposition of fluorescent energy density distributions 0 i < 5 u i ( t ) for five camera positions in the inhomogeneous medium. Slices show different time windows.

Fig. 5
Fig. 5

(a) reconstructed diffusion κ and (b) absorption μ a coefficients.

Fig. 6
Fig. 6

Localized fluorescence sources. Each slice shows a different time window.

Equations (28)

Equations on this page are rendered with MathJax. Learn more.

J α = l = 0 L 1 J α ( l ) ,
J α ( l ) = Δ t m = 0 M 1 [ u ( r m , t l ; u l 1 / 2 ) φ ( r m , t l ) ] 2 + α 0 2 Δ t u l 1 / 2 2 ,
χ ( r ) = δ n N m = 0 M 1 δ ( r r m ) ,
J α ( l ) = τ n = 1 N V χ ( r ) ( u l , n φ l ) 2 d 3 r + α 0 2 u l 1 / 2 2 ,
1 c u t · κ u + μ a u = 0 ,
( u + γ κ n · u ) | V = 0 ,
φ ( t l ) = u e ( t ) g ( t l t ) d t .
B u l , n + 1 u l , n c τ + Λ u l , n = 0 ,
Λ = · κ + μ a ,
B = I + σ c τ Λ ,
L ( l ) = J α ( l ) n = 0 N 1 V ψ l , n + 1 [ B ( u l , n + 1 u l , n ) + c τ Λ u l , n ] d 3 r ,
ψ l , N = 0.
δ L ( l ) = 2 τ n = 1 N ( δ u l , n , χ ( r ) ( u l , n φ l ) ) + α 0 ( δ u l 1 / 2 , u l 1 / 2 ) n = 0 N 1 ( ψ l , n + 1 , B ( δ u l , n + 1 δ u l , n ) + c τ Λ δ u l , n ) .
n = 0 N 1 ( ψ l , n + 1 , B δ u l , n + 1 ) = n = 1 N ( δ u l , n , B ψ l , n ) ,
n = 0 N 1 ( ψ l , n + 1 , ( c τ Λ B ) δ u l , n ) = ( δ u l 1 / 2 , ( c τ Λ B ) ψ 1 ) + n = 1 N ( δ u l , n , ( c τ Λ B ) ψ l , n + 1 ) .
B ψ l , 0 = ( B c τ Λ ) ψ l , 1
δ L ( l ) = 2 τ n = 1 N ( δ u l , n , χ ( r ) ( u l , n φ l ) ) + α 0 ( δ u l 1 / 2 , u l 1 / 2 ) + n = 1 N ( δ u l , n , B ( ψ l , n ψ l , n + 1 ) + c τ Λ ψ l , n + 1 ) + ( δ u l 1 / 2 , B ψ l , 0 ) .
B u l , n + 1 ( k ) u l , n ( k ) c τ + Λ u l , n ( k ) = 0.
B ψ l , n ψ l , n + 1 c τ + Λ ψ l , n + 1 = 2 χ ( r ) ( u l , n ( k ) φ l ) ,
u l 1 / 2 ( k + 1 ) u l 1 / 2 ( k ) λ k c τ + Λ u l 1 / 2 ( k ) = 0 ,
u l 1 / 2 ( k + 1 ) u l 1 / 2 ( k ) λ k + B u l 1 / 2 ( k ) = 1 α 0 B ψ l , 0 ,
1 2 α κ c Δ t l = 0 L 2 V ( κ l + 1 κ l c Δ t ) 2 d 3 r
c Δ t l = 0 L 2 V ψ l + 1 · κ l u l d 3 r ,
B ψ l ψ l + 1 c Δ t + Λ ψ l + 1 = 2 χ ( r ) ( u l ( k ) φ l ) ,
α κ ( δ κ 0 , κ 1 κ 0 c Δ t ) + α κ l = 1 L 2 ( δ κ l , κ l + 1 2 κ l + κ l 1 c Δ t ) + c Δ t 3 l = 0 L 2 V δ κ l κ l ψ l + 1 u l d 2 r c Δ t l = 0 L 2 ( δ κ l , ψ l + 1 · u l ) = 0.
α κ R κ κ 1 κ 0 ( c Δ t ) 2 = ψ 1 · u 0 ,
α κ R κ κ l + 1 2 κ l + κ l 1 ( c Δ t ) 2 = ψ l + 1 · u l ,
s l 1 / 2 B u l + 1 / 2 u l 1 / 2 c Δ t .

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