Abstract

The dependence of the sensitivity function in fluorescence tomography on the geometry of the excitation source and detection locations can severely influence an imaging system’s ability to recover fluorescent distributions. Here a methodology for choosing imaging configuration based on the uniformity of the sensitivity function is presented. The uniformity of detection sensitivity is correlated with reconstruction accuracy in silico, and reconstructions in a murine head model show that a detector configuration optimized using Nelder–Mead minimization improves recovery over uniformly sampled tomography.

© 2013 Optical Society of America

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  1. F. Leblond, K. M. Tichauer, and B. W. Pogue, “Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography,” Biomed. Opt. Express 1, 1514–1531 (2010).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  16. R. P. Jagannath and P. K. Yalavarthy, “Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography,” J. Biomed. Opt. 18, 030503 (2013).
    [CrossRef]
  17. C. Vinegoni, D. Razansky, J. L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. 34, 319–321 (2009).
    [CrossRef]

2013 (1)

R. P. Jagannath and P. K. Yalavarthy, “Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography,” J. Biomed. Opt. 18, 030503 (2013).
[CrossRef]

2012 (2)

R. W. Holt, K. M. Tichauer, H. Dehghani, B. W. Pogue, and F. Leblond, “Multiple-gate time domain diffuse fluorescence tomography allows more sparse tissue sampling without compromising image quality,” Opt. Lett. 37, 2559–2561 (2012).
[CrossRef]

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Med. Phys. 39, 4715–4725 (2012).
[CrossRef]

2011 (1)

2010 (4)

J. Chen, V. Venugopal, F. Lesage, and X. Intes, “Time-resolved diffuse optical tomography with patterned-light illumination and detection,” Opt. Lett. 35, 2121–2123 (2010).
[CrossRef]

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

F. Leblond, K. M. Tichauer, and B. W. Pogue, “Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography,” Biomed. Opt. Express 1, 1514–1531 (2010).
[CrossRef]

2009 (2)

C. Vinegoni, D. Razansky, J. L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. 34, 319–321 (2009).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

2004 (1)

2001 (1)

1998 (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

1992 (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. Rev. D 60, 259–268 (1992).

1973 (1)

M. J. D. Powell, “On search directions for minimization algorithms,” Math. Program. 4, 193–201 (1973).
[CrossRef]

1965 (1)

J. A. Nelder and R. Mead, “A simplex-method for function minimization,” Comput. J. 7, 308–313 (1965).

Abran, M.

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

Bai, J.

Z. Xu, X. Song, and J. Bai, “Singular value decomposition-based analysis on fluorescence molecular tomography in the mouse atlas,” in Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2009 (Institute of Electrical and Electronics Engineers, 2009), pp. 3739–3742.

Belanger, S.

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Casanova, C.

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

Chen, J.

Culver, J. P.

Davis, S. C.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Dehghani, H.

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

El-Ghussein, F.

Fatemi, E.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. Rev. D 60, 259–268 (1992).

Figueiredo, J. L.

Graves, E. E.

Holboke, M. J.

Holt, R. W.

Intes, X.

J. Chen, V. Venugopal, F. Lesage, and X. Intes, “Time-resolved diffuse optical tomography with patterned-light illumination and detection,” Opt. Lett. 35, 2121–2123 (2010).
[CrossRef]

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

Jagannath, R. P.

R. P. Jagannath and P. K. Yalavarthy, “Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography,” J. Biomed. Opt. 18, 030503 (2013).
[CrossRef]

Karkala, D.

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Med. Phys. 39, 4715–4725 (2012).
[CrossRef]

Lagarias, J. C.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Leblond, F.

Lesage, F.

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

J. Chen, V. Venugopal, F. Lesage, and X. Intes, “Time-resolved diffuse optical tomography with patterned-light illumination and detection,” Opt. Lett. 35, 2121–2123 (2010).
[CrossRef]

Mead, R.

J. A. Nelder and R. Mead, “A simplex-method for function minimization,” Comput. J. 7, 308–313 (1965).

Nahrendorf, M.

Nelder, J. A.

J. A. Nelder and R. Mead, “A simplex-method for function minimization,” Comput. J. 7, 308–313 (1965).

Ntziachristos, V.

Osher, S.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. Rev. D 60, 259–268 (1992).

Paulsen, K. D.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Pogue, B. W.

R. W. Holt, K. M. Tichauer, H. Dehghani, B. W. Pogue, and F. Leblond, “Multiple-gate time domain diffuse fluorescence tomography allows more sparse tissue sampling without compromising image quality,” Opt. Lett. 37, 2559–2561 (2012).
[CrossRef]

K. M. Tichauer, R. W. Holt, F. El-Ghussein, Q. Zhu, H. Dehghani, F. Leblond, and B. W. Pogue, “Imaging workflow and calibration for CT-guided time-domain fluorescence tomography,” Biomed. Opt. Express 2, 3021–3036 (2011).
[CrossRef]

F. Leblond, K. M. Tichauer, and B. W. Pogue, “Singular value decomposition metrics show limitations of detector design in diffuse fluorescence tomography,” Biomed. Opt. Express 1, 1514–1531 (2010).
[CrossRef]

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Powell, M. J. D.

M. J. D. Powell, “On search directions for minimization algorithms,” Math. Program. 4, 193–201 (1973).
[CrossRef]

Razansky, D.

Reeds, J. A.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Ripoll, J.

Rudin, L. I.

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. Rev. D 60, 259–268 (1992).

Song, X.

Z. Xu, X. Song, and J. Bai, “Singular value decomposition-based analysis on fluorescence molecular tomography in the mouse atlas,” in Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2009 (Institute of Electrical and Electronics Engineers, 2009), pp. 3739–3742.

Srinivasan, S.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Tichauer, K. M.

Valdes, P. A.

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

Venugopal, V.

Vinegoni, C.

Weissleder, R.

Wright, M. H.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Wright, P. E.

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Xu, Z.

Z. Xu, X. Song, and J. Bai, “Singular value decomposition-based analysis on fluorescence molecular tomography in the mouse atlas,” in Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2009 (Institute of Electrical and Electronics Engineers, 2009), pp. 3739–3742.

Yalavarthy, P. K.

R. P. Jagannath and P. K. Yalavarthy, “Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography,” J. Biomed. Opt. 18, 030503 (2013).
[CrossRef]

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Med. Phys. 39, 4715–4725 (2012).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Yodh, A. G.

Zhu, Q.

Biomed. Opt. Express (2)

Commun. Numer. Methods Eng. (1)

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

Comput. J. (1)

J. A. Nelder and R. Mead, “A simplex-method for function minimization,” Comput. J. 7, 308–313 (1965).

J. Biomed. Opt. (2)

R. P. Jagannath and P. K. Yalavarthy, “Efficient gradient-free simplex method for estimation of optical properties in image-guided diffuse optical tomography,” J. Biomed. Opt. 18, 030503 (2013).
[CrossRef]

S. Belanger, M. Abran, X. Intes, C. Casanova, and F. Lesage, “Real-time diffuse optical tomography based on structured illumination,” J. Biomed. Opt. 15, 016006 (2010).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Photochem. Photobiol. B (1)

F. Leblond, S. C. Davis, P. A. Valdes, and B. W. Pogue, “Pre-clinical whole-body fluorescence imaging: review of instruments, methods and applications,” J. Photochem. Photobiol. B 98, 77–94 (2010).
[CrossRef]

Math. Program. (1)

M. J. D. Powell, “On search directions for minimization algorithms,” Math. Program. 4, 193–201 (1973).
[CrossRef]

Med. Phys. (1)

D. Karkala and P. K. Yalavarthy, “Data-resolution based optimization of the data-collection strategy for near infrared diffuse optical tomography,” Med. Phys. 39, 4715–4725 (2012).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. D (1)

L. I. Rudin, S. Osher, and E. Fatemi, “Nonlinear total variation based noise removal algorithms,” Phys. Rev. D 60, 259–268 (1992).

SIAM J. Optim. (1)

J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder–Mead simplex method in low dimensions,” SIAM J. Optim. 9, 112–147 (1998).
[CrossRef]

Other (1)

Z. Xu, X. Song, and J. Bai, “Singular value decomposition-based analysis on fluorescence molecular tomography in the mouse atlas,” in Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2009 (Institute of Electrical and Electronics Engineers, 2009), pp. 3739–3742.

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Figures (9)

Fig. 1.
Fig. 1.

Diagrammatic representation of a “banana-shaped” sensitivity function from source to detector is shown. Each line of the Jacobian matrix represents the intensity values from such an image. (a) Function overlay on a representative x-ray CT. (b) Function with corresponding source location and detector location.

Fig. 2.
Fig. 2.

Sample sensitivity functions. (a) The optical projection connection between an excitation source and detection location for full tomographic imaging scheme. (b) The summed sensitivity function for a full tomographic imaging scheme. (c) The optical projection connection between an excitation source and detector location for a transmission imaging scheme [9]. (d) The summed sensitivity function for a transmission imaging scheme.

Fig. 3.
Fig. 3.

(a) Characteristic imaging domain from x-ray CT of a mouse cranium showing the skull and brain regions at top center. (b) Finite element method nodal discretization (blue) and source placement (red). (c) Fluorescent target location encoding depth dependence.

Fig. 4.
Fig. 4.

Process of randomly assigning an imaging scheme. (a) Assign the source locations. (b) Randomly distribute detection locations and force to center of 2.8° bins. (c) Enforce that the detection is symmetric with respect to the source location. (d) Assign the same angular detection distribution to all sources.

Fig. 5.
Fig. 5.

Sample reconstructions comparing various u and AUC. (a) The fluorescent target map. (b) The fluorescent recovery and (c) summed sensitivity function for the imaging scheme with the lowest measured curvature parameter. (d) The fluorescent recovery and (e) the summed sensitivity for a less favorable imaging scheme.

Fig. 6.
Fig. 6.

Log-scale bin plot of the relationship between the accuracy of the reconstruction as measured by AUC and (a) curvature parameter or (b) total variation for a series of imaging schemes.

Fig. 7.
Fig. 7.

(a) Average AUC for a ROC analysis for imaging schemes as a function of detection angle with respect to source. (b) Relative angular detection importance density based on (a).

Fig. 8.
Fig. 8.

Representative geometric results of minimized curvature using the Nelder–Meade routine compared to the imaging scheme with full tomographic geometry. (a)–(d) Comparison of imaging geometry for the two schemes for a given subset of excitation locations.

Fig. 9.
Fig. 9.

Image reconstructions based on (a) imaging scheme with minimized curvature parameter and (b) full tomographic imaging scheme with the same number of optical projections. (c) Ideal target map.

Equations (5)

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

J i j = φ i μ j = η G x ( r s i , | r r j | ) G m ( | r r j | , r d i ) d r ,
L i j = { 1 , if i = j 1 n 1 , otherwise ,
S j = i = 1 m J i j ,
u = L S .
L r , i j = { 1 , if i = j and in region r , 1 n r 1 , if i j and in region r , 0 , otherwise ,

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