Abstract

We investigated the diffuse optical image errors resulting from systematic errors in the background scattering and absorption coefficients, Gaussian noise in the measurements, and the depth at which the image is reconstructed when using a 2D linear reconstruction algorithm for a 3D object. The fourth Born perturbation approach was used to generate reflectance measurements and k-space tomography was used for the reconstruction. Our simulations using both single and dual wavelengths show large systematic errors in the absolute reconstructed absorption coefficients and corresponding hemoglobin concentrations, while the errors in the relative oxy- and deoxy- hemoglobin concentrations are acceptable. The greatest difference arises from a systematic error in the depth at which an image is reconstructed. While an absolute reconstruction of the hemoglobin concentrations can deviate by 100% for a depth error of ±1 mm, the error in the relative concentrations is less than 5%. These results demonstrate that while quantitative diffuse optical tomography is difficult, images of the relative concentrations of oxy- and deoxy-hemoglobin are accurate and robust. Other results, not presented, confirm that these findings hold for other linear reconstruction techniques (i.e. SVD and SIRT) as well as for transmission through slab geometries.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]

1998 (1)

1997 (6)

1996 (1)

1995 (4)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).
[CrossRef]

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,”Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

1994 (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

1993 (3)

1992 (2)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef]

J. M. Schmitt, A. Knuttel, and J. R. Knutson, “Interference of diffusive light waves,” J.Opt.Soc.Am.A 9, 1832 (1992).
[CrossRef] [PubMed]

1991 (1)

M. Cope, “The Development of a Near-Infrared Spectroscopy System and Its Application for Noninvasive Monitoring of Cerebral Blood and Tissue Oxygenation in the Newborn Infant,” University College London (1991).

1988 (1)

S. Wray, M. Cope, and D. T. Delpy, “Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation.,” Biochim Biophys Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

1986 (1)

A. J. Devaney, “Reconstruction tomography with diffractive wave-fields,” Inverse Problems 2, 161–183 (1986).
[CrossRef]

Aarnoudse, J. G.

Arridge, S. R.

S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med.Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Boas, D. A.

Chance, B.

Cheng, X.

Cooper, C. E.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

Cope, M.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

M. Cope, “The Development of a Near-Infrared Spectroscopy System and Its Application for Noninvasive Monitoring of Cerebral Blood and Tissue Oxygenation in the Newborn Infant,” University College London (1991).

S. Wray, M. Cope, and D. T. Delpy, “Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation.,” Biochim Biophys Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Dassel, A. C. M.

de Mul, F. F. M.

Delpy, D. T.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med.Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

S. Wray, M. Cope, and D. T. Delpy, “Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation.,” Biochim Biophys Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Devaney, A. J.

A. J. Devaney, “Reconstruction tomography with diffractive wave-fields,” Inverse Problems 2, 161–183 (1986).
[CrossRef]

Durduran, T.

Elwell, C. E.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

Fishkin, J. B.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambirdge Univ. Press, New York,1988) Ch2 p52.

Furutsu, K.

K. Furutsu, “Diffusion equation derived from the space-time transport equation in anisotropic random media,” J.Math.Phys. 24, 765–777 (1997).

Graaff, R.

Gratton, E.

Hebden, J. C.

S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997).
[CrossRef] [PubMed]

Hielscher, A. H.

A. D. Klose and A. H. Hielscher, “A transport-theory based reconstruction algorithm for optical tomography,” B. Chance, R. Alfano, and B. Tromberg ed., SPIE BiOS99, San Jose, CA, (SPIE,1999).
[CrossRef]

Hiraoka, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med.Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Jacques, S. L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,”Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Jiang, H.

Kak, A. C.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York,1988).

Klose, A. D.

A. D. Klose and A. H. Hielscher, “A transport-theory based reconstruction algorithm for optical tomography,” B. Chance, R. Alfano, and B. Tromberg ed., SPIE BiOS99, San Jose, CA, (SPIE,1999).
[CrossRef]

Knutson, J. R.

J. M. Schmitt, A. Knuttel, and J. R. Knutson, “Interference of diffusive light waves,” J.Opt.Soc.Am.A 9, 1832 (1992).
[CrossRef] [PubMed]

Knuttel, A.

J. M. Schmitt, A. Knuttel, and J. R. Knutson, “Interference of diffusive light waves,” J.Opt.Soc.Am.A 9, 1832 (1992).
[CrossRef] [PubMed]

Koelink, M. H.

Li, X. D.

Matcher, S. J.

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

Matson, C. L.

O’Leary, M. A.

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Experimental images of heterogeneous turbid media by frequency-domain diffusing-photon tomography,” Opt. Lett. 20, 426–428 (1995).
[CrossRef]

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef]

Osterberg, U. L.

Pattanayak, D. N.

Patterson, M. S.

Paulsen, K. D.

Pogue, B. W.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambirdge Univ. Press, New York,1988) Ch2 p52.

Schmitt, J. M.

J. M. Schmitt, A. Knuttel, and J. R. Knutson, “Interference of diffusive light waves,” J.Opt.Soc.Am.A 9, 1832 (1992).
[CrossRef] [PubMed]

Schweiger, M.

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med.Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Slaney, M.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York,1988).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambirdge Univ. Press, New York,1988) Ch2 p52.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambirdge Univ. Press, New York,1988) Ch2 p52.

Wang, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,”Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Wray, S.

S. Wray, M. Cope, and D. T. Delpy, “Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation.,” Biochim Biophys Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Yodh, A.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Yodh, A. G.

Zheng, L.

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,”Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Zijlstra, W. G.

Anal. Biochem. (1)

S. J. Matcher, C. E. Elwell, C. E. Cooper, M. Cope, and D. T. Delpy, “Performance comparison of several published tissue near-infrared spectroscopy algorithms,” Anal. Biochem. 227, 54–68 (1995).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biochim Biophys Acta (1)

S. Wray, M. Cope, and D. T. Delpy, “Characteristics of the near infrared absorption spectra of cytochrome aa3 and hemoglobin for the noninvasive monitoring of cerebral oxygenation.,” Biochim Biophys Acta 933, 184–192 (1988).
[CrossRef] [PubMed]

Comput. Methods Programs Biomed. (1)

L. Wang, S. L. Jacques, and L. Zheng, “MCML-Monte Carlo modeling of light transport in multi-layered tissues,”Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Inverse Problems (1)

A. J. Devaney, “Reconstruction tomography with diffractive wave-fields,” Inverse Problems 2, 161–183 (1986).
[CrossRef]

J. Opt. Soc. Am. A (3)

J.Math.Phys. (1)

K. Furutsu, “Diffusion equation derived from the space-time transport equation in anisotropic random media,” J.Math.Phys. 24, 765–777 (1997).

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

J. M. Schmitt, A. Knuttel, and J. R. Knutson, “Interference of diffusive light waves,” J.Opt.Soc.Am.A 9, 1832 (1992).
[CrossRef] [PubMed]

Med.Phys. (1)

S. R. Arridge, M. Schweiger, M. Hiraoka, and D. T. Delpy, “A finite element approach for modeling photon transport in tissue,” Med.Phys. 20, 299–309 (1993).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Med. Biol. (1)

S. R. Arridge and J. C. Hebden, “Optical Imaging in Medicine: II. Modelling and reconstruction,” Phys. Med. Biol. 42, 841–854 (1997).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Refraction of diffuse photon density waves,” Phys. Rev. Lett. 69, 2658–2661 (1992).
[CrossRef]

Phys. Today (1)

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 48, 34–40 (1995).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

D. A. Boas, M. A. O’Leary, B. Chance, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneties within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. USA 91, 4887–4891 (1994).
[CrossRef] [PubMed]

Other (6)

A. D. Klose and A. H. Hielscher, “A transport-theory based reconstruction algorithm for optical tomography,” B. Chance, R. Alfano, and B. Tromberg ed., SPIE BiOS99, San Jose, CA, (SPIE,1999).
[CrossRef]

M. Cope, “The Development of a Near-Infrared Spectroscopy System and Its Application for Noninvasive Monitoring of Cerebral Blood and Tissue Oxygenation in the Newborn Infant,” University College London (1991).

“Trends in Optics and Photonics Series,” R. Alfano ed., Advances in Optical Imaging and Photon Migration,Orlando, FLA, (OSA,1996).

S. R. Arridge, J. P. Kaltenbach, R. L. Barbour, and G. Muller ed., Bellingham, Wa, (Proc. SPIE,1993).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C: The Art of Scientific Computing (Cambirdge Univ. Press, New York,1988) Ch2 p52.

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York,1988).

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Figures (6)

Figure 1.
Figure 1.

Images reconstructed at various depths. Each image is 6 × 6 cm.

Figure 2.
Figure 2.

Absorption coefficients of hemoglobin (50 μmole/liter) and H2O.

Figure 3.
Figure 3.

Systematic errors in the reconstructed image values of the object resulting from the errors in the depth at which the image is reconstructed.

Figure 4.
Figure 4.

Systematic errors in the reconstructed image values of the object resulting from the errors in the background absorption (red line) and scattering coefficient (black line).

Figure 5.
Figure 5.

Uncertainties in the image value caused by Gaussian measurement noise. In (a) the depth of the object is 2 cm and the noise is varied. In (b) the depth is varied while the noise is held constant at 3×10-5 percent.

Figure 6.
Figure 6.

Systematic errors in the reconstructed Δ[Hb], Δ[HbO], and Δ[Hb]/Δ[HbO] resulting from errors in the depth of the image reconstruction.

Tables (2)

Tables Icon

Table 1. Errors and uncertainties in the images values resulting from the systematic errors of background optical properties, the depth position of the image and random system noise in one-wavelength simulation.

Tables Icon

Table 2. Image errors in the absolute and ratio reconstruction resulting from the systematic errors of background optical properties, the depth position of the image in two-wavelength simulation

Equations (9)

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

ϕ sc 1 ( r d ) = d r ϕ inc ( r s , r ) v δ μ a ( r ) D G ( r , r d ) .
ϕ sc 2 ( r d ) = d r ( ϕ inc ( r s , r ) + ϕ sc 1 ( r ) ) v δ μ a ( r ) D G ( r , r d )
ϕ sc n ( r d ) = d r ( ϕ inc ( r s , r ) + ϕ sc n 1 ( r ) ) v δ μ a ( r ) D G ( r , r d ) .
ϕ ˜ sc n ( ω x , ω y ) = G ˜ ( ω x , ω y , z ) A ( ω x , ω y , z ) dz ,
A ( ω x , ω y , z ) = d x d y ϕ inc ( r s , x , y , z ) v δ μ a ( x , y , z ) D exp ( i ω x x + i ω y y )
δ μ a ( x , y , z ) = D h ϕ inc ( x , y , z ) FT 1 [ ϕ ˜ sc n ( ω x , ω y ) G ˜ ( ω x , ω y , z ) ]
μ a ( λ ) = ε Hbo ( λ ) [ HbO ] + ε Hb ( λ ) [ Hb ]
Δ [ Hb ] = ε Hbo λ 2 δ μ a λ 1 ε Hbo λ 1 δ μ a λ 2 ε Hb λ 1 ε Hbo λ 2 ε Hb λ 2 ε Hbo λ 1
Δ [ HbO ] = ε Hbo λ 1 δ μ a λ 2 ε Hbo λ 2 δ μ a λ 1 ε Hb λ 1 ε Hbo λ 2 ε Hb λ 2 ε Hbo λ 1

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