Abstract

We show that a two-step reconstruction method can be adapted to improve the quantitative accuracy of the refractive index reconstruction in phase-contrast diffuse optical tomography (PCDOT). We also describe the possibility of imaging tissue glucose concentration with PCDOT. In this two-step method, we first use our existing finite-element reconstruction algorithm to recover the position and shape of a target. We then use the position and size of the target as a priori information to reconstruct a single value of the refractive index within the target and background regions using a region reconstruction method. Due to the extremely low contrast available in the refractive index reconstruction, we incorporate a data normalization scheme into the two-step reconstruction to combat the associated low signal-to-noise ratio. Through a series of phantom experiments we find that this two-step reconstruction method can considerably improve the quantitative accuracy of the refractive index reconstruction. The results show that the relative error of the reconstructed refractive index is reduced from 20% to within 1.5%. We also demonstrate the possibility of PCDOT for recovering glucose concentration using these phantom experiments.

© 2006 Optical Society of America

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References

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  1. A. H. Bennett, H. Osterberg, H. Jupnik, and O. Richards, Phase Microscope: Principles and Applications (Wiley, 1951).
  2. G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
    [CrossRef] [PubMed]
  3. T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
    [PubMed]
  4. J. F. Greenleaf, S. Johnson, and A. Lent, "Measurement of spatial distribution of refractive index in tissues by ultrasonic computer assisted tomography," Ultrasound Med. Biol. 3, 327-339 (1978).
    [CrossRef] [PubMed]
  5. H. Jiang and Y. Xu, "Phase-contrast imaging of tissue using near-infrared diffusing light," Med. Phys. 30, 1048-1051 (2003).
    [CrossRef] [PubMed]
  6. J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
    [PubMed]
  7. H. Jiang, "The diffusion approximation for turbid media with a spatially varying refractive index," in Proceedings of Advances in Optical Imaging and Photon Migration (Optical Society of America, 2000), pp. 366-368.
  8. T. Khan and H. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive index," J. Opt. A , Pure Appl. Opt. 5, 137-141 (2003).
    [CrossRef]
  9. H. Jiang, "Optical image reconstruction based on the third-order diffusion equations," Opt. Express 4, 241-246 (1999).
    [CrossRef] [PubMed]
  10. K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-702 (1995).
    [CrossRef] [PubMed]
  11. H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, "Simultaneous reconstruction of absorption and scattering maps in turbid media from near-infrared frequency-domain data," Opt. Lett. 20, 2128-2130 (1995).
    [CrossRef] [PubMed]
  12. M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-2722 (1999).
    [CrossRef] [PubMed]
  13. H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, "Three-dimensional optical tomography: resolution in small-object imaging," Appl. Opt. 42, 3117-3128 (2003).
    [CrossRef] [PubMed]
  14. C. Li and H. Jiang, "A calibration method in diffuse optical tomography," J. Opt. A , Pure Appl. Opt. 6, 844-852 (2004).
    [CrossRef]

2004 (1)

C. Li and H. Jiang, "A calibration method in diffuse optical tomography," J. Opt. A , Pure Appl. Opt. 6, 844-852 (2004).
[CrossRef]

2003 (3)

H. Dehghani, B. W. Pogue, S. Jiang, B. Brooksby, and K. D. Paulsen, "Three-dimensional optical tomography: resolution in small-object imaging," Appl. Opt. 42, 3117-3128 (2003).
[CrossRef] [PubMed]

H. Jiang and Y. Xu, "Phase-contrast imaging of tissue using near-infrared diffusing light," Med. Phys. 30, 1048-1051 (2003).
[CrossRef] [PubMed]

T. Khan and H. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive index," J. Opt. A , Pure Appl. Opt. 5, 137-141 (2003).
[CrossRef]

2000 (2)

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

1999 (2)

H. Jiang, "Optical image reconstruction based on the third-order diffusion equations," Opt. Express 4, 241-246 (1999).
[CrossRef] [PubMed]

M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-2722 (1999).
[CrossRef] [PubMed]

1995 (3)

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-702 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, "Simultaneous reconstruction of absorption and scattering maps in turbid media from near-infrared frequency-domain data," Opt. Lett. 20, 2128-2130 (1995).
[CrossRef] [PubMed]

1978 (1)

J. F. Greenleaf, S. Johnson, and A. Lent, "Measurement of spatial distribution of refractive index in tissues by ultrasonic computer assisted tomography," Ultrasound Med. Biol. 3, 327-339 (1978).
[CrossRef] [PubMed]

Arridge, S. R.

M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-2722 (1999).
[CrossRef] [PubMed]

Bennett, A. H.

A. H. Bennett, H. Osterberg, H. Jupnik, and O. Richards, Phase Microscope: Principles and Applications (Wiley, 1951).

Bouma, B.

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Brezinski, M. E.

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Brooksby, B.

Coleman, R. E.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Crain, B.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Dehghani, H.

Earl, N.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Fujimoto, J.

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Greenleaf, J. F.

J. F. Greenleaf, S. Johnson, and A. Lent, "Measurement of spatial distribution of refractive index in tissues by ultrasonic computer assisted tomography," Ultrasound Med. Biol. 3, 327-339 (1978).
[CrossRef] [PubMed]

Hanson, M.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Haraoka, S.

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Hee, M.

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Hirano, K.

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Hoffman, J. M.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Hulette, C.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Itai, Y.

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Jiang, H.

C. Li and H. Jiang, "A calibration method in diffuse optical tomography," J. Opt. A , Pure Appl. Opt. 6, 844-852 (2004).
[CrossRef]

H. Jiang and Y. Xu, "Phase-contrast imaging of tissue using near-infrared diffusing light," Med. Phys. 30, 1048-1051 (2003).
[CrossRef] [PubMed]

T. Khan and H. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive index," J. Opt. A , Pure Appl. Opt. 5, 137-141 (2003).
[CrossRef]

H. Jiang, "Optical image reconstruction based on the third-order diffusion equations," Opt. Express 4, 241-246 (1999).
[CrossRef] [PubMed]

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-702 (1995).
[CrossRef] [PubMed]

H. Jiang, K. D. Paulsen, U. L. Osterberg, B. W. Pogue, and M. S. Patterson, "Simultaneous reconstruction of absorption and scattering maps in turbid media from near-infrared frequency-domain data," Opt. Lett. 20, 2128-2130 (1995).
[CrossRef] [PubMed]

H. Jiang, "The diffusion approximation for turbid media with a spatially varying refractive index," in Proceedings of Advances in Optical Imaging and Photon Migration (Optical Society of America, 2000), pp. 366-368.

Jiang, S.

Johnson, S.

J. F. Greenleaf, S. Johnson, and A. Lent, "Measurement of spatial distribution of refractive index in tissues by ultrasonic computer assisted tomography," Ultrasound Med. Biol. 3, 327-339 (1978).
[CrossRef] [PubMed]

Jupnik, H.

A. H. Bennett, H. Osterberg, H. Jupnik, and O. Richards, Phase Microscope: Principles and Applications (Wiley, 1951).

Khan, T.

T. Khan and H. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive index," J. Opt. A , Pure Appl. Opt. 5, 137-141 (2003).
[CrossRef]

Lent, A.

J. F. Greenleaf, S. Johnson, and A. Lent, "Measurement of spatial distribution of refractive index in tissues by ultrasonic computer assisted tomography," Ultrasound Med. Biol. 3, 327-339 (1978).
[CrossRef] [PubMed]

Li, C.

C. Li and H. Jiang, "A calibration method in diffuse optical tomography," J. Opt. A , Pure Appl. Opt. 6, 844-852 (2004).
[CrossRef]

Mornse, A.

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Osterberg, H.

A. H. Bennett, H. Osterberg, H. Jupnik, and O. Richards, Phase Microscope: Principles and Applications (Wiley, 1951).

Osterberg, U. L.

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Richards, O.

A. H. Bennett, H. Osterberg, H. Jupnik, and O. Richards, Phase Microscope: Principles and Applications (Wiley, 1951).

Schweiger, M.

M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-2722 (1999).
[CrossRef] [PubMed]

Southern, J.

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Takeda, T.

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Tearney, G. J.

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Watanabe, T.

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Welsh-Bohmer, K. A.

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

Xu, Y.

H. Jiang and Y. Xu, "Phase-contrast imaging of tissue using near-infrared diffusing light," Med. Phys. 30, 1048-1051 (2003).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Nucl. Med. (1)

J. M. Hoffman, K. A. Welsh-Bohmer, M. Hanson, B. Crain, C. Hulette, N. Earl, and R. E. Coleman, "FDG PET imaging in patients with pathologically verified dementia," J. Nucl. Med. 41, 1920-1928 (2000).
[PubMed]

J. Opt. A (2)

T. Khan and H. Jiang, "A new diffusion approximation to the radiative transfer equation for scattering media with spatially varying refractive index," J. Opt. A , Pure Appl. Opt. 5, 137-141 (2003).
[CrossRef]

C. Li and H. Jiang, "A calibration method in diffuse optical tomography," J. Opt. A , Pure Appl. Opt. 6, 844-852 (2004).
[CrossRef]

Med. Phys. (2)

K. D. Paulsen and H. Jiang, "Spatially-varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-702 (1995).
[CrossRef] [PubMed]

H. Jiang and Y. Xu, "Phase-contrast imaging of tissue using near-infrared diffusing light," Med. Phys. 30, 1048-1051 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett (1)

G. J. Tearney, M. E. Brezinski, J. Southern, B. Bouma, M. Hee, and J. Fujimoto, "Determination of the refractive index of highly scattering human tissue by optical coherence tomography," Opt. Lett . 20, 2258-2260 (1995).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Med. Biol. (1)

M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-2722 (1999).
[CrossRef] [PubMed]

Radiology (1)

T. Takeda, A. Mornse, K. Hirano, S. Haraoka, T. Watanabe, and Y. Itai, "Human carcinoma: early experience with phase-contrast x-ray CT with synchrotron radiation: comparative specimen study with optical microscope," Radiology 214, 298-301 (2000).
[PubMed]

Ultrasound Med. Biol. (1)

J. F. Greenleaf, S. Johnson, and A. Lent, "Measurement of spatial distribution of refractive index in tissues by ultrasonic computer assisted tomography," Ultrasound Med. Biol. 3, 327-339 (1978).
[CrossRef] [PubMed]

Other (2)

A. H. Bennett, H. Osterberg, H. Jupnik, and O. Richards, Phase Microscope: Principles and Applications (Wiley, 1951).

H. Jiang, "The diffusion approximation for turbid media with a spatially varying refractive index," in Proceedings of Advances in Optical Imaging and Photon Migration (Optical Society of America, 2000), pp. 366-368.

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Figures (6)

Fig. 1
Fig. 1

Schematic of the diffuse optical imaging system. Light from ten laser modules with wavelengths from 673 to 965   nm was delivered to 16 excitation positions through a 1 × 10 optical switch. Diffused light is received by 16 detection optical fiber bundles and sent to 16 silicon photodiodes controlled by a homemade circuit board, and data are recorded by a 16-bit analog-to-digital (A/D) board coupled with a personal computer (PC). Note that 16 source and 16 detector fibers are alternately attached to the surface of the phantom with equal spacing (filled circles, source fibers bundles; empty circles, detector fibers).

Fig. 2
Fig. 2

Schematic of the phantom geometry under study. R 1 = 50   mm ; R 2 = 10 or 5   mm ; d = 14 or 18   mm .

Fig. 3
Fig. 3

(Color online) Refractive index images reconstructed from the measurements on tissue-mimicking phantoms where the scattering and absorption coefficients were μ a = 0.007 mm - 1 and μ s = 1.0 mm - 1 for both the background and the target ( 10   mm in diameter) containing different glucose concentrations: (a) 1 % glucose concentration ( n = 1.3312 ) , (b) 2 % glucose concentration ( n = 1.3332 ) , (c) 3 % glucose concentration ( n = 1.3353 ) , (d) 5 % glucose concentration ( n = 1.3393 ) .

Fig. 4
Fig. 4

(Color online) Refractive index images recovered with the region reconstruction method. The optical properties of the phantom were the same as those for the images shown in Fig. 2. (a) 1 % glucose concentration ( n = 1.3312 ) . (b) 2 % glucose concentration ( n = 1.3332 ) . (c) 3 % glucose concentration ( n = 1.3353 ) . (d) 5 % glucose concentration ( n = 1.3393 ) . Note that the target shape is not round because of the limited number of finite-element nodes used.

Fig. 5
Fig. 5

(Color online) (a) Comparison of ideal and calculated absolute values of glucose concentration for all four cases. (b) Comparison of ideal and calculated relative values of glucose concentration for all four cases.

Fig. 6
Fig. 6

(Color online) Refractive index images reconstructed (a), (b) without and (c), (d) with the region reconstruction method for the 5 mm diameter target experiments. The absorption and scattering coefficients of the background and target were μ a = 0.007 mm - 1 and μ s = 1.0 mm - 1 . The target contained (a), (c) 3 % and (b), (d) 5 % glucose concentration.

Tables (2)

Tables Icon

Table 1 Values of the Refractive Index Corresponding to Glucose Concentration

Tables Icon

Table 2 Comparison of Ideal and Reconstructed Values of the Refractive Index and Glucose Concentration

Equations (12)

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

· D Φ ( r ) + 2 D n n · Φ ( r ) μ a Φ ( r ) = S 0 δ ( r r 0 ) ,
D Φ · n ^ = α Φ ,
[ A ] { Φ } = { b } ,
[ A ] { Φ n } = { b n } [ A n ] { Φ } ,
( T + λ I ) Δ n = T ( Φ ( m ) Φ ( c ) ) ,
D i ,max = max ( D i , j ) , j = 1 , 2 ,   …   ,   16 .
D ˜ i , j = D i , j / D i ,max .
˜ = K ,
K = [ R 1 R 2 R n k 1 , 1 k 1 , 2 k 1 , n k 2 , 1 k 2 , 2 k 2 , n k j , 1 k j , 2 k j , n ] , where k ξ , η = { 1 , ξ R η 0 , ξ R η } .
( ˜ T ˜ ) Δ n ˜ = ˜ T ( Φ ( m ) Φ ( c ) ) .
Δ n = Δ n ˜ K 1 .
n = 0.2015 [ C ] + 1.3292 ,

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