Abstract

Accurate depth localization and quantitative recovery of a regional activation are the major challenges in functional diffuse optical tomography (DOT). The photon density drops severely with increased depth, for which conventional DOT reconstruction yields poor depth localization and quantitative recovery. Recently we have developed a depth compensation algorithm (DCA) to improve the depth localization in DOT. In this paper, we present an approach based on the depth-compensated reconstruction to improve the quantification in DOT by forming a spatial prior. Simulative experiments are conducted to demonstrate the usefulness of this approach. Moreover, noise suppression is a key to success in DOT which also affects the depth localization and quantification. We present quantitative analysis and comparison on noise suppression in DOT with and without depth compensation. The study reveals that appropriate combination of depth-compensated reconstruction with the spatial prior can provide accurate depth localization and improved quantification at variable noise levels.

© 2010 OSA

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  1. A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
    [CrossRef] [PubMed]
  2. D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
    [CrossRef] [PubMed]
  3. C. K. Lee, C. W. Sun, P. L. Lee, H. C. Lee, C. Yang, C. P. Jiang, Y. P. Tong, T. C. Yeh, and J. C. Hsieh, “Study of photon migration with various source-detector separations in near-infrared spectroscopic brain imaging based on three-dimensional Monte Carlo modeling,” Opt. Express 13(21), 8339–8348 (2005).
    [CrossRef] [PubMed]
  4. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
    [CrossRef]
  5. H. Niu, F. Tian, Z. J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
    [CrossRef] [PubMed]
  6. H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.
  7. M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
    [PubMed]
  8. H. Dehghani, B. W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
    [CrossRef] [PubMed]
  9. G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
    [CrossRef] [PubMed]
  10. E. R. Hom, http://www.nmr.mgh.harvard.edu/PMI/toolbox/index.html
  11. L. Wu, “A parameter choice method for Tikhonov regularization,” Electron. Trans. Numer. Anal. 16, 107–128 (2003).
  12. P. C. Hansen and D. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. (USA) 14(6), 1487–1503 (1993).
    [CrossRef]
  13. B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
    [CrossRef] [PubMed]

2010

2007

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

2005

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

C. K. Lee, C. W. Sun, P. L. Lee, H. C. Lee, C. Yang, C. P. Jiang, Y. P. Tong, T. C. Yeh, and J. C. Hsieh, “Study of photon migration with various source-detector separations in near-infrared spectroscopic brain imaging based on three-dimensional Monte Carlo modeling,” Opt. Express 13(21), 8339–8348 (2005).
[CrossRef] [PubMed]

2004

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

2003

1999

R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[CrossRef]

1997

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
[CrossRef] [PubMed]

1993

P. C. Hansen and D. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. (USA) 14(6), 1487–1503 (1993).
[CrossRef]

1988

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Arridge, R.

R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[CrossRef]

Boas, D. A.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

Boverman, G.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Brooks, D. H.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Brooksby, B.

Chance, B.

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
[CrossRef] [PubMed]

Chaves, T.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Cope, M.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Culver, J. P.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

Dale, A. M.

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

Dehghani, H.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

H. Dehghani, B. W. Pogue, J. Shudong, B. Brooksby, and K. D. Paulsen, “Three-dimensional optical tomography: resolution in small-object imaging,” Appl. Opt. 42(16), 3117–3128 (2003).
[CrossRef] [PubMed]

Delpy, D. T.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Dhamne, S.

H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.

Franceschini, M. A.

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

Hansen, P. C.

P. C. Hansen and D. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. (USA) 14(6), 1487–1503 (1993).
[CrossRef]

Hsieh, J. C.

Jiang, C. P.

Lee, C. K.

Lee, H. C.

Lee, P. L.

Li, A.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Lin, Z.

H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.

Lin, Z. J.

Liu, H.

H. Niu, F. Tian, Z. J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[CrossRef] [PubMed]

H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.

Miller, E. L.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Niu, H.

H. Niu, F. Tian, Z. J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[CrossRef] [PubMed]

H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.

O’Leary, D.

P. C. Hansen and D. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. (USA) 14(6), 1487–1503 (1993).
[CrossRef]

Paulsen, K. D.

Pogue, B. W.

Reynolds, E. O.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Schlaggar, B. L.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

Shudong, J.

Sun, C. W.

Tian, F.

H. Niu, F. Tian, Z. J. Lin, and H. Liu, “Development of a compensation algorithm for accurate depth localization in diffuse optical tomography,” Opt. Lett. 35(3), 429–431 (2010).
[CrossRef] [PubMed]

H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.

Tong, Y. P.

van der Zee, P.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Villringer, A.

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
[CrossRef] [PubMed]

White, B. R.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

Wray, S.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Wu, L.

L. Wu, “A parameter choice method for Tikhonov regularization,” Electron. Trans. Numer. Anal. 16, 107–128 (2003).

Wyatt, J.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Yang, C.

Yeh, T. C.

Zeff, B. W.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

Zhang, Q.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Adv. Exp. Med. Biol.

M. Cope, D. T. Delpy, E. O. Reynolds, S. Wray, J. Wyatt, and P. van der Zee, “Methods of quantitating cerebral near infrared spectroscopy data,” Adv. Exp. Med. Biol. 222, 183–189 (1988).
[PubMed]

Appl. Opt.

Electron. Trans. Numer. Anal.

L. Wu, “A parameter choice method for Tikhonov regularization,” Electron. Trans. Numer. Anal. 16, 107–128 (2003).

Inverse Probl.

R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15(2), R41–R93 (1999).
[CrossRef]

J. Biomed. Opt.

H. Niu, Z. Lin, F. Tian, S. Dhamne, and H. Liu, “Comprehensive Investigation of three-dimensional diffuse optical tomography with depth compensation algorithm,” J. Biomed. Opt. in press.

Neuroimage

D. A. Boas, A. M. Dale, and M. A. Franceschini, “Diffuse optical imaging of brain activation: approaches to optimizing image sensitivity, resolution, and accuracy,” Neuroimage 23(Suppl 1), S275–S288 (2004).
[CrossRef] [PubMed]

Opt. Express

Opt. Lett.

Phys. Med. Biol.

G. Boverman, E. L. Miller, A. Li, Q. Zhang, T. Chaves, D. H. Brooks, and D. A. Boas, “Quantitative spectroscopic diffuse optical tomography of the breast guided by imperfect a priori structural information,” Phys. Med. Biol. 50(17), 3941–3956 (2005).
[CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

B. W. Zeff, B. R. White, H. Dehghani, B. L. Schlaggar, and J. P. Culver, “Retinotopic mapping of adult human visual cortex with high-density diffuse optical tomography,” Proc. Natl. Acad. Sci. U.S.A. 104(29), 12169–12174 (2007).
[CrossRef] [PubMed]

SIAM J. Sci. Comput. (USA)

P. C. Hansen and D. O’Leary, “The use of the L-curve in the regularization of discrete ill-posed problems,” SIAM J. Sci. Comput. (USA) 14(6), 1487–1503 (1993).
[CrossRef]

Trends Neurosci.

A. Villringer and B. Chance, “Non-invasive optical spectroscopy and imaging of human brain function,” Trends Neurosci. 20(10), 435–442 (1997).
[CrossRef] [PubMed]

Other

E. R. Hom, http://www.nmr.mgh.harvard.edu/PMI/toolbox/index.html

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Figures (7)

Fig. 1
Fig. 1

Setups of simulative experiments: (a) experiment I, (b) experiment II, and (c) experiment III.

Fig. 2
Fig. 2

For experiment I, a depth cross section (y-z plane, x = 0) of the (a) actual absorber, (b) reconstructed DOT image without depth compensation, and (c) reconstructed DOT image with depth compensation. The dash circles in (b) and (c) mark the ROIs with half-maximum threshold.

Fig. 3
Fig. 3

For experiment II: Figs. 3(a), 3(c), 3(e) are depth cross sections along the diagonal plane at y = x, which is marked by the dash line in (b), of the (a) actual and reconstructed absorbers (c) without and (e) with depth compensation being utilized. Figures 3(b), 3(d), 3(f) are lateral cross sections in the x-y plane of the (b) actual and recovered absorbers (d) without and (f) with depth compensation applied, respectively.

Fig. 4
Fig. 4

For experiment III: a depth cross section along the diagonal plane at y = x of the (a) actual absorbers, (b) reconstructed DOT image without depth compensation, and (c) reconstructed DOT image with depth compensation.

Fig. 5
Fig. 5

Reconstructed depths of the absorber, using the setup of Experiment I in Fig. 1(a), with variable α and γ values when data were (a) noise-free and (b) with 1% random noise. Conventional DOT without depth compensation is equivalent to γ = 0. In (b) the reconstructed depths become divergent roughly after α = 10−3, which is attributed to the 1% random noise. The expected depth of the absorber is at z = −2 cm.

Fig. 6
Fig. 6

Quantified (a) Δµa_max , (b) Δµa_ROI and (c) VROI values of the absorber, with the given setup in Experiment I, when α and γ values are varied. The expected Δµa value is 0.2 cm−1. The expected volume of the absorber is 1.7 cm3. Conventional DOT without depth compensation is equivalent to γ = 0.

Fig. 7
Fig. 7

For phantom experiment, a depth cross section (y-z plane, x = 0) of the reconstructed DOT image (a) without depth compensation, and (b) with depth compensation. The cylindrical absorber was located at z = −2.0 cm which had an actual Δµa of 0.15 cm−1.

Tables (1)

Tables Icon

Table 1 Actual absorption perturbation, Δµa , maximum absorption perturbation recovered without ROI, Δµa_max , and absorption perturbation recovered with ROI, Δµa_ROI , for each absorber in experiments I to III. Unit: cm−1

Equations (7)

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

Δ O D ( λ , t ) = j = 1 N v o x Δ μ a , j ( λ , t ) L j ( λ )
y = A x
x ^ D O T = A T ( A A T + α s max I ) 1 y
M = [ s max , N l a y e r I s max , N l a y e r 1 I ... s max , 1 I ] γ
x ^ D C A = ( A M ) T [ ( A M ) ( A M ) T + α s max I ] 1 y
y = K A x ^ D C A
y = Δ μ a _ R O I j R O I L i , j

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