Abstract

Time domain fluorescence molecular tomography (TD-FMT) provides a unique dataset for enhanced quantification and spatial resolution. The time-gate dataset can be divided into two temporal groups around the maximum counts gate, which are early gates and late gates. It is well established that early gates allow for improved spatial resolution and late gates are essential for fluorophore unmixing and concentration quantification. However, the inverse problem of FMT is ill-posed and typically underdetermined, which makes image reconstruction highly susceptible to data noise. More specifically, photon counts are inherently very low at early gates due to high absorption and scattering of tissue, resulting in a low signal-to-noise ratio and unstable reconstructions. In this work, an Lp regularization-based reconstruction algorithm was developed and tested with our wide-field mesh-based Monte Carlo simulation strategy. We compared the early time-gate reconstructions obtained with the different p (p{1/16,1/8,1/4,1/3,1/2,1,2}) from a synthetic murine model simulating the fluorophore uptake in the kidneys and preclinical data. The results from a 3D mouse atlas and a mouse experiment show that our L1/4 regularization methods give the best performance for early time gates reconstructions.

© 2014 Optical Society of America

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2014

C. Darne, Y. Lu, and E. M. Sevick-Muraca, Phys. Med. Biol. 59, R1 (2014).
[CrossRef]

2013

V. Venugopal, J. Chen, and X. Intes, Proc. SPIE 8578, 857827 (2013).
[CrossRef]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

2012

M. Pimpalkhare, J. Chen, V. Venugopal, and X. Intes, Int. J. Biomed. Imag. 2012, 942326 (2012).

V. Venugopal, J. Chen, M. Barroso, and X. Intes, Biomed. Opt. Express 3, 3161 (2012).
[CrossRef]

V. C. Kavuri, Z. J. Lin, F. Tian, and H. Liu, Biomed. Opt. Express 3, 943 (2012).
[CrossRef]

J. Chen, Q. Fang, and X. Intes, J. Biomed. Opt. 17, 106009 (2012).

W. Mo, D. Rohrbach, and U. Sunar, J. Biomed. Opt. 17, 071306 (2012).
[CrossRef]

2011

2010

M. Niedre and V. Ntziachristos, Opt. Lett. 35, 369 (2010).
[CrossRef]

V. Venugopal, J. Chen, and X. Intes, Biomed. Opt. Express 1, 143 (2010).
[CrossRef]

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

H. Egger and M. Schlottbom, SIAM J. Math. Anal. 42, 1934 (2010).
[CrossRef]

M. Suzen, A. Giannoula, and T. Durduran, Opt. Express 18, 23676 (2010).
[CrossRef]

V. Venugopal, J. Chen, F. Lesage, and X. Intes, Opt. Lett. 35, 3189 (2010).
[CrossRef]

M. Y. Berezin and S. Achilefu, Chem. Rev. 110, 2641 (2010).
[CrossRef]

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, Photochem. Photobiol. B 98, 77 (2010).

2009

J. Chen and X. Intes, Opt. Express 17, 19566 (2009).
[CrossRef]

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, Philos. Transact. Ser. A. Math. Phys. Eng. Sci. 367, 3073 (2009).

A. Beck and M. Teboulle, SIAM J. Imaging Sci. 2, 183 (2009).

2008

2007

2005

A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
[CrossRef]

1997

J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, Proc. Natl. Acad. Sci. USA 94, 8783 (1997).
[CrossRef]

Abe, K.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

Achilefu, S.

M. Y. Berezin and S. Achilefu, Chem. Rev. 110, 2641 (2010).
[CrossRef]

Arridge, S. R.

Bacskai, B. J.

Barroso, M.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

V. Venugopal, J. Chen, M. Barroso, and X. Intes, Biomed. Opt. Express 3, 3161 (2012).
[CrossRef]

Beck, A.

A. Beck and M. Teboulle, SIAM J. Imaging Sci. 2, 183 (2009).

Berezin, M. Y.

M. Y. Berezin and S. Achilefu, Chem. Rev. 110, 2641 (2010).
[CrossRef]

Boas, D. A.

Chang, X.

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

Chen, D.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Chen, J.

Darne, C.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, Phys. Med. Biol. 59, R1 (2014).
[CrossRef]

Dasari, R. R.

J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, Proc. Natl. Acad. Sci. USA 94, 8783 (1997).
[CrossRef]

Davis, S. C.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, Photochem. Photobiol. B 98, 77 (2010).

Dehghani, H.

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, Philos. Transact. Ser. A. Math. Phys. Eng. Sci. 367, 3073 (2009).

Durduran, T.

Egger, H.

H. Egger and M. Schlottbom, SIAM J. Math. Anal. 42, 1934 (2010).
[CrossRef]

Elson, D. S.

Fang, Q.

J. Chen, Q. Fang, and X. Intes, J. Biomed. Opt. 17, 106009 (2012).

Feld, M. S.

J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, Proc. Natl. Acad. Sci. USA 94, 8783 (1997).
[CrossRef]

French, P. M.

Giannoula, A.

Gibson, A.

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, Philos. Transact. Ser. A. Math. Phys. Eng. Sci. 367, 3073 (2009).

Hielscher, A. H.

A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
[CrossRef]

Hoshi, Y.

Intes, X.

V. Venugopal, J. Chen, and X. Intes, Proc. SPIE 8578, 857827 (2013).
[CrossRef]

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

M. Pimpalkhare, J. Chen, V. Venugopal, and X. Intes, Int. J. Biomed. Imag. 2012, 942326 (2012).

V. Venugopal, J. Chen, M. Barroso, and X. Intes, Biomed. Opt. Express 3, 3161 (2012).
[CrossRef]

J. Chen, Q. Fang, and X. Intes, J. Biomed. Opt. 17, 106009 (2012).

J. Chen and X. Intes, Med. Phys. 38, 5788 (2011).
[CrossRef]

J. Chen, V. Venugopal, and X. Intes, Biomed. Opt. Express 2, 871 (2011).
[CrossRef]

V. Venugopal, J. Chen, F. Lesage, and X. Intes, Opt. Lett. 35, 3189 (2010).
[CrossRef]

V. Venugopal, J. Chen, and X. Intes, Biomed. Opt. Express 1, 143 (2010).
[CrossRef]

J. Chen and X. Intes, Opt. Express 17, 19566 (2009).
[CrossRef]

Kavuri, V. C.

Kumar, A. T.

Leblond, F.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, Photochem. Photobiol. B 98, 77 (2010).

Lesage, F.

Li, W.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Liang, J.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Liang, Y.

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

Lin, Z. J.

Liu, H.

Lu, Y.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, Phys. Med. Biol. 59, R1 (2014).
[CrossRef]

McGinty, J.

Mo, W.

W. Mo, D. Rohrbach, and U. Sunar, J. Biomed. Opt. 17, 071306 (2012).
[CrossRef]

Neil, M. A.

Niedre, M.

Ntziachristos, V.

Okawa, S.

Perelman, L.

J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, Proc. Natl. Acad. Sci. USA 94, 8783 (1997).
[CrossRef]

Periasamy, A.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

Pimpalkhare, M.

M. Pimpalkhare, J. Chen, V. Venugopal, and X. Intes, Int. J. Biomed. Imag. 2012, 942326 (2012).

Pogue, B. W.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, Photochem. Photobiol. B 98, 77 (2010).

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, Philos. Transact. Ser. A. Math. Phys. Eng. Sci. 367, 3073 (2009).

Raymond, S. B.

Rohrbach, D.

W. Mo, D. Rohrbach, and U. Sunar, J. Biomed. Opt. 17, 071306 (2012).
[CrossRef]

Schlottbom, M.

H. Egger and M. Schlottbom, SIAM J. Math. Anal. 42, 1934 (2010).
[CrossRef]

Sevick-Muraca, E. M.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, Phys. Med. Biol. 59, R1 (2014).
[CrossRef]

Soloviev, V. Y.

Srinivasan, S.

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, Philos. Transact. Ser. A. Math. Phys. Eng. Sci. 367, 3073 (2009).

Sunar, U.

W. Mo, D. Rohrbach, and U. Sunar, J. Biomed. Opt. 17, 071306 (2012).
[CrossRef]

Suzen, M.

Tahir, K. B.

Teboulle, M.

A. Beck and M. Teboulle, SIAM J. Imaging Sci. 2, 183 (2009).

Tian, F.

Tian, J.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Valdes, P. A.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, Photochem. Photobiol. B 98, 77 (2010).

Venugopal, V.

Wang, X.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Wang, Y.

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

Wu, J.

J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, Proc. Natl. Acad. Sci. USA 94, 8783 (1997).
[CrossRef]

Xu, Z.

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

Yamada, Y.

Yi, H.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Zhang, H.

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

Zhao, L.

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

Zhu, S.

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

Appl. Opt.

Biomed. Opt. Express

Chem. Rev.

M. Y. Berezin and S. Achilefu, Chem. Rev. 110, 2641 (2010).
[CrossRef]

Curr. Opin. Biotechnol.

A. H. Hielscher, Curr. Opin. Biotechnol. 16, 79 (2005).
[CrossRef]

Int. J. Biomed. Imag.

M. Pimpalkhare, J. Chen, V. Venugopal, and X. Intes, Int. J. Biomed. Imag. 2012, 942326 (2012).

J. Biomed. Opt.

W. Mo, D. Rohrbach, and U. Sunar, J. Biomed. Opt. 17, 071306 (2012).
[CrossRef]

H. Yi, D. Chen, W. Li, S. Zhu, X. Wang, J. Liang, and J. Tian, J. Biomed. Opt. 18, 56013 (2013).
[CrossRef]

J. Chen, Q. Fang, and X. Intes, J. Biomed. Opt. 17, 106009 (2012).

Med. Phys.

J. Chen and X. Intes, Med. Phys. 38, 5788 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Philos. Transact. Ser. A. Math. Phys. Eng. Sci.

H. Dehghani, S. Srinivasan, B. W. Pogue, and A. Gibson, Philos. Transact. Ser. A. Math. Phys. Eng. Sci. 367, 3073 (2009).

Photochem. Photobiol. B

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, Photochem. Photobiol. B 98, 77 (2010).

Phys. Med. Biol.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, Phys. Med. Biol. 59, R1 (2014).
[CrossRef]

PLoS One

K. Abe, L. Zhao, A. Periasamy, X. Intes, and M. Barroso, PLoS One 8, e80269 (2013).
[CrossRef]

Proc. Natl. Acad. Sci. USA

J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, Proc. Natl. Acad. Sci. USA 94, 8783 (1997).
[CrossRef]

Proc. SPIE

V. Venugopal, J. Chen, and X. Intes, Proc. SPIE 8578, 857827 (2013).
[CrossRef]

Sci. China Inf. Sci.

Z. Xu, H. Zhang, Y. Wang, X. Chang, and Y. Liang, Sci. China Inf. Sci. 53, 1159 (2010).

SIAM J. Imaging Sci.

A. Beck and M. Teboulle, SIAM J. Imaging Sci. 2, 183 (2009).

SIAM J. Math. Anal.

H. Egger and M. Schlottbom, SIAM J. Math. Anal. 42, 1934 (2010).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

(a) L-curve analysis (log–log) to select λ=μλi(0) for L1/4 regularization. (b) Total errors for reconstructed kidneys and small inclusions with different Lp regularizations, p{1/16,1/8,1/4,1/3,1/2}.

Fig. 2.
Fig. 2.

3D visualizations for in silico reconstructions. (a) The 3D reconstructions for kidneys using Lp regularization with p{1/16,1/4,1,2}. (b) 3D reconstructions for small inclusions using Lp regularization with p{1/16,1/4,1,2}. A 50% threshold was used for visualizing L2, L1, L1/4, and L1/16 regularization-based reconstructions. Here the red regions denote the ground truth, and the blue regions are the reconstructed results.

Fig. 3.
Fig. 3.

Total errors for the experimental data for Lp regularizations p{1/16,1/8,1/4,1/3,1/2,1}. TE for L2 (TE=577) is not shown in the curve.

Fig. 4.
Fig. 4.

50% isovolume of 3D reconstructions based on L2, L1, and L1/4 regularizations using experimental data. The coronal plane at y=21.5mm and the axial plane at z=6.5mm were used for cross-section validation.

Tables (1)

Tables Icon

Table 1. Summary of All Objective Metrics Derived from Simulated Kidneys (Kd) and Small Inclusions (SI) with all Lp Considered

Equations (8)

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

Ax=b,
min{Axb22+λxpp},xp=(i=1n|xi|p)1/p,
min{Axb22+λi=1n|xi||xi|1p+ε},
x(k)=minx{Axb22+i=1nλi(k)|xi|},λi(k)=λi(k1)|xi(k1)|1p+ε,
xi(k)=shrink((x(k)+2μAT(bAx(k)))i,μλi(k)),μ<1/ATA2,
RMSE=i=1K(Xrecon(i)Xtrue-shift(i))2/i=1K(Xtrue-shift(i))2,
CNR=(XreconNOIXreconNOB)/WNOIσNOI2+WNOBσNOB2,
Totalerror=e(RMSE+absolute(VE)+LE)/CNR.

Metrics