Abstract

In this paper, we propose a dual-excitation-mode methodology for three-dimensional (3D) fluorescence molecular tomography (FMT). For this modality, an effective reconstruction algorithm is developed to reconstruct fluorescent yield and lifetime using finite element techniques. In the steady state mode, a direct linear relationship is established between measured optical data on the body surface of a small animal and the unknown fluorescent yield inside the animal, and the reconstruction of fluorescent yield is formulated as a linear least square minimization problem. In the frequency domain mode, based on localization results of the fluorescent probe obtained using the first mode, the reconstruction of fluorescent lifetime is transformed into a relatively simple optimization problem. This algorithm helps overcome the ill-posedness with FMT. The effectiveness of the proposed method is numerically demonstrated using a heterogeneous mouse chest phantom, showing good accuracy, stability, noise characteristics and computational efficiency.

© 2005 Optical Society of America

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References

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Appl. Opt. (2)

J. Biomed. Opt. (1)

J. R. Mansfield, K. W. Gossage, C. C. Hoyt, and R. M. Levenson, “Autofluorescence removal, multiplexing, and automated analysis methods for in-vivo fluorescence imaging,” J. Biomed. Opt. 10, 041207 (2005).
[CrossRef]

J. Comput. Phys. (1)

A. D. Klose, V. Ntziachristos, and A. H. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323-345 (2004).
[CrossRef]

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

Med. Phys. (4)

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 conditons,” Med. Phys. 22, 1779–1792 (1995).
[CrossRef] [PubMed]

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

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] [PubMed]

A. Godavarty, E. M. Sevick-Muraca and M. J. Eppstein, “Three-dimensional fluorescence lifetime tomography,” Med. Phys. 32, 992–1000 (2005).
[CrossRef] [PubMed]

Mol. Imag. (1)

G. Choy, P. Choyke, and S. K. Libutti, “Current advances in molecular imaging: noninvasive in vivo bioluminescent and fluorescent optical Imaging in Cancer Research,” Mol. Imag. 2, 303–312 (2003).
[CrossRef]

Nature Biotech. (1)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nature Biotech. 23, 313–320 (2005).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Phys. Med. Biol. (1)

A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003).
[CrossRef] [PubMed]

Proc. SPIE (1)

W. Cong, D. Kumar, Y. Liu, A. Cong, and G.Wang, “A practical method to determine the light source distribution in bioluminescent imaging,” Proc. SPIE 5535, 679–686 (2004).
[CrossRef]

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Figures (9)

Fig. 1.
Fig. 1.

Mouse chest phantom. (a) finite element mouse chest geometrical model (each region is labeled by a letter, H for heart, L for lung, B for bone, and M for muscle), (b) a cross section of the model.

Fig. 2.
Fig. 2.

Imaging geometry. (a) excitation light source positions, (b) feasible region.

Fig. 3.
Fig. 3.

Target location reconstruction. (a) actual target position (pointed by the arrow), (b) reconstructed target position(pointed by the arrow).

Fig. 4.
Fig. 4.

Fluorescent yield reconstruction. (a) actual fluorescent yield distribution, (b) fluorescent yield reconstructed with measurement corrupted by 10% guassian noise.

Fig. 5.
Fig. 5.

Fluorescent lifetime reconstruction. (a) actual fluorescent lifetime distribution, (b) fluorescent lifetime reconstructed with measurement corrupted by 10% guassian noise.

Fig. 6.
Fig. 6.

Targets’ locations reconstruction. (a) actual target position(pointed by the arrow), (b) reconstructed target position(pointed by the arrow).

Fig. 7.
Fig. 7.

Fluorescent yield reconstruction. (a) actual fluorescent yield distribution, (b) fluorescent yield reconstructed with measurement corrupted by 10% guassian noise.

Fig. 8.
Fig. 8.

Fluorescent lifetime reconstruction. (a) actual fluorescent lifetime distribution, (b) fluorescent lifetime reconstructed with measurement corrupted by 10% guassian noise.

Fig. 9.
Fig. 9.

Comparison between the actual measurement data at different detection positions in the frequency domain mode and the corresponding profiles of surface photon density computed based on the reconstructed fluorescent yield and lifetime. (a) The actual measurement data and the corresponding fitting profiles with the first excitation light source, and (b) the counterparts with the second excitation light source.

Tables (3)

Tables Icon

Table 1. Optical parameters

Tables Icon

Table 2. Reconstruction result of a single fluorescent target.

Tables Icon

Table 3. Reconstruction results of two fluorescent targets.

Equations (18)

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· [ D x ( r ) Φ x r ω ] [ μ a x ( r ) + c ] Φ x r ω = 0
2 ρ D x ( r ) Φ x ( r ) n + Φ x ( r ) + S r ω = 0
{ · [ D m ( r ) Φ m r ω ] [ μ a m ( r ) + c ] Φ m r ω = Φ x r ω U ( r , ω , η μ a f , τ ) U ( r , ω , η μ a f , τ ) = η ( r ) μ a f ( r ) 1 + iωτ ( r ) 1 + ω 2 τ 2 ( r )
2 ρ D m ( r ) Φ m r ω n + Φ m r ω = 0
Φ x r ω k = 1 N v ϕ x k ( ω ) ψ k ( r )
( A x + C x + P x + Q x ) Φ x ( ω ) = H ( ω )
{ a x ij = Ω D x ( r ) ( ψ i ( r ) ) · ( ψ j ( r ) ) d r c x ij = Ω μ a x ( r ) ψ i ( r ) ψ j ( r ) d r p x ij = 1 c Ω ψ i ( r ) ψ j ( r ) d r q x ij = 1 2 ρ Ω ψ i ( r ) ψ j ( r ) d r h x i = 1 2 ρ Ω S r ω ψ j ( r ) d r
{ Φ m r ω k = 1 M n ϕ m k ( ω ) ψ k ( r ) U ( r , ω , η μ a f , τ ) k = 1 M n u k ( ω ) γ k ( r )
( A m + C m + P m + Q m ) Φ m ( ω ) = F m U ( ω , ημ a f , τ )
{ a m ij = Ω D x ( r ) ( ψ i ( r ) ) · ( ψ j ( r ) ) d r c m ij = Ω μ a x ( r ) ψ i ( r ) ψ j ( r ) d r p m ij = 1 c Ω ψ i ( r ) ψ j ( r ) d r q m ij = 1 2 ρ Ω ψ i ( r ) ψ j ( r ) d r f m ij = 1 2 ρ Ω Φ x ( r ) ψ i ( r ) γ j ( r ) d r
Φ x = K x 1 H ( 0 )
Φ m = K m 1 F m U ( ημ a f )
Φ m meas = B p y U p y ( ημ a f )
min 0 u k α Φ m meas B p y U p y ( ημ a f ) Λ + σβ ( U p y ( ημ a f ) )
Φ x ( ω ) = K x 1 H ( ω )
Φ m ( ω ) = K m 1 F m U ω τ
Φ m meas = B p l U p l ω τ
min 0 τ α Φ m meas B p l U p l ω τ Λ

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