Abstract

Fluorescence diffuse optical tomography (FDOT) is a computationally demanding imaging problem. The discretizations of FDOT forward and inverse problems pose a trade-off between the accuracy and the computational efficiency of the image reconstruction. To address this trade-off, we analyzed the effect of discretization on the accuracy of FDOT imaging and proposed novel adaptive meshing algorithms for FDOT in a series of studies. In this Letter, we apply these new adaptive meshing algorithms to FDOT imaging using real data from a phantom experiment to demonstrate the practical advantages of our algorithms in FDOT image reconstruction.

© 2010 Optical Society of America

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References

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  1. R. Weissleder and V. Ntziachristos, Nat. Med. 9, 123 (2003).
    [CrossRef] [PubMed]
  2. M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
    [CrossRef] [PubMed]
  3. W. Bangerth and A. Joshi, Inverse Probl. 24, 034011 (2008).
    [CrossRef]
  4. J. Lee, A. Joshi, and E. Sevick-Muraca, Opt. Express 15, 6955 (2007).
    [CrossRef] [PubMed]
  5. M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
    [CrossRef]
  6. L. Zhou and B. Yazici, “Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography in the presence of measurement noise,” IEEE Trans. Image Process. (to be published).
  7. In Eqs. , Dij=[σij2+∫Ωκ(r)ϕi2(r)(gj*)2(r)dr]1/2, where σij2 is the noise variance in Γij, κ represents the variance of μ, πij is the inverse problem solution when Γij=1 and Γkl=0, for all kl≠ij, k=1,…,NS and l=1,…,ND. Note that we use ∥·∥∞,k, ∥·∥0,k, and ∥·∥1,k to denote the L∞, L2, and H1 norms of a function on the kth element, and use ∥·∥∞ and ∥·∥0 to denote the L∞ and L2 norms of a function on the domain Ω.
  8. N. Deliolanis, T. Lasser, D. Hyde, A. Soubret, J. Ripoll, and V. Ntziachristos, Opt. Lett. 32, 382 (2007).
    [CrossRef] [PubMed]

2010 (2)

M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
[CrossRef] [PubMed]

M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
[CrossRef]

2008 (1)

W. Bangerth and A. Joshi, Inverse Probl. 24, 034011 (2008).
[CrossRef]

2007 (2)

2003 (1)

R. Weissleder and V. Ntziachristos, Nat. Med. 9, 123 (2003).
[CrossRef] [PubMed]

Bangerth, W.

W. Bangerth and A. Joshi, Inverse Probl. 24, 034011 (2008).
[CrossRef]

Deliolanis, N.

Guven, M.

M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
[CrossRef]

M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
[CrossRef] [PubMed]

Hyde, D.

Joshi, A.

Lasser, T.

Lee, J.

Ntziachristos, V.

Reilly-Raska, L.

M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
[CrossRef] [PubMed]

M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
[CrossRef]

Ripoll, J.

Sevick-Muraca, E.

Soubret, A.

Weissleder, R.

R. Weissleder and V. Ntziachristos, Nat. Med. 9, 123 (2003).
[CrossRef] [PubMed]

Yazici, B.

M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
[CrossRef]

M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
[CrossRef] [PubMed]

L. Zhou and B. Yazici, “Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography in the presence of measurement noise,” IEEE Trans. Image Process. (to be published).

Zhou, L.

M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
[CrossRef] [PubMed]

M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
[CrossRef]

L. Zhou and B. Yazici, “Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography in the presence of measurement noise,” IEEE Trans. Image Process. (to be published).

IEEE Trans. Med. Imaging (2)

M. Guven, L. Reilly-Raska, L. Zhou, and B. Yazici, IEEE Trans. Med. Imaging 29, 217 (2010).
[CrossRef] [PubMed]

M. Guven, L. Zhou, L. Reilly-Raska, and B. Yazici, IEEE Trans. Med. Imaging 29, 230 (2010).
[CrossRef]

Inverse Probl. (1)

W. Bangerth and A. Joshi, Inverse Probl. 24, 034011 (2008).
[CrossRef]

Nat. Med. (1)

R. Weissleder and V. Ntziachristos, Nat. Med. 9, 123 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Other (2)

L. Zhou and B. Yazici, “Discretization error analysis and adaptive meshing algorithms for fluorescence diffuse optical tomography in the presence of measurement noise,” IEEE Trans. Image Process. (to be published).

In Eqs. , Dij=[σij2+∫Ωκ(r)ϕi2(r)(gj*)2(r)dr]1/2, where σij2 is the noise variance in Γij, κ represents the variance of μ, πij is the inverse problem solution when Γij=1 and Γkl=0, for all kl≠ij, k=1,…,NS and l=1,…,ND. Note that we use ∥·∥∞,k, ∥·∥0,k, and ∥·∥1,k to denote the L∞, L2, and H1 norms of a function on the kth element, and use ∥·∥∞ and ∥·∥0 to denote the L∞ and L2 norms of a function on the domain Ω.

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Figures (4)

Fig. 1
Fig. 1

(a) Phantom used in the experiment. (b) FDOT imaging system setup.

Fig. 2
Fig. 2

Adaptive mesh generated by our algorithm for (a) the detector at ( 0.47 , 0.88, 1.12 ), (b) the inverse problem.

Fig. 3
Fig. 3

Relationship between the average number of nodes in the forward adaptive mesh for a certain source or detector and the z coordinate of its position.

Fig. 4
Fig. 4

Fluorophore heterogeneity reconstructed using (a) uniform meshes and (b) the adaptive meshes. The blue tube indicates the true fluorophore heterogeneity.

Tables (1)

Tables Icon

Table 1 Discretization Error, Maximum Width Along x Direction, and the Volume outside the Fluorophore Heterogeneity Reconstructed by Using Different Meshes

Equations (4)

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Γ i j = Ω g j * ( r ) ϕ i ( r ) μ ( r ) d r ,
ε f i ( k ) j = 1 N D 1 σ i j 2 [ g j * ϕ i 0 [ g j * μ 0 , n i + i , j N S , N D g j * D i j π i j 0 , n i ] + [ | Γ i j | + D i j ] g j * , n i ] · ϕ i 1 , n i h n i ,
ε f j ( k ) i = 1 N S 1 σ i j 2 [ g j * ϕ i 0 [ ϕ i μ 0 , m j + i , j N S , N D ϕ i D i j π i j 0 , m j ] + [ | Γ i j | + D i j ] ϕ i , m j ] · g j * 1 , m j h m j ,
ε i ( k ) [ i , j N S , N D G j * Φ i 0 σ i j 2 G j * Φ i 0 , t + 1 κ , t ] [ μ 1 , t + i , j N S , N D D i j π i j 1 , t ] h t .

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