Abstract

Model based image reconstruction in Diffuse Optical Tomography relies on both the numerical accuracy of the forward model as well as the computational speed and efficiency of the inverse model. Most model based image reconstruction algorithms rely on Newton type inversion methods, whereby the inverse of a large Jacobian is approximated. In this work we present an efficient Jacobian reduction method which takes into account the total sensitivity of the imaging domain to the measured boundary data. It is shown using numerical and phantom data that by removing regions within the inverse model whose contribution to the measured data is less than 1%, it has no significant effect upon the estimated inverse problem, but does provide up to a 14 fold improvement in computational time.

© 2007 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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2007

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, "Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography," Med. Phys. 34, 2085-2098 (2007).
[CrossRef] [PubMed]

M. Guven, B. Yazici, K. Kwon, E. Giladi, and X. Intes, "Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging," Inverse Probl. 23, 1135-1160 (2007).
[CrossRef]

H. Dehghani and M , Soleimani, "Numerical modelling errors in electrical impedance tomography," Physiol Meas 28, S45-S55 (2007).
[CrossRef]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, C. M. Carpenter, S. Jiang, and K. D. Paulsen, "Structural information within regularization matrices improves near infrared diffuse optical tomography," Opt. Express 15, 8043-8058 (2007).
[CrossRef] [PubMed]

2006

2005

A. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction," Technol. Cancer Res. Treat. 5, 513-526 (2005).

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, "Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: A case study with comparison to MRI," Med. Phys. 32, 1128-1139 (2005).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, and K. D. Paulsen, "Spectrally constrained Chromophore and Scattering NIR Tomography provides quantitative and robust reconstruction," Appl. Opt. 44, 1858-1869 (2005).
[CrossRef] [PubMed]

A. Corlu, R. Choe, T. Durduran, K. Lee, M. Schweiger, S. R. Arridge, E. M. C. Hillman, A. G. Yodh, "Diffuse optical tomography with spectral constraints and wavelength optimization," Appl. Opt. 44, 2082-2093 (2005).
[CrossRef] [PubMed]

2004

2003

2002

M. Molinari, B. H. Blott, S. J. Cox, G. J. Daniell, "Optimal imaging with adaptive mesh refinement in electrical impedance tomography," Physiol. Meas. 23, 121-128 (2002).
[CrossRef] [PubMed]

2000

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).

1999

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative image reconstruction scheme for time- resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

A. D. Klose, and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

1998

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

S. R. Arridge and M. Schwieger, "Gradient-based optimisation scheme for optical tomography," Opt. Express. 2, 212-226 (1998).
[CrossRef]

1996

1995

K. D. Paulsen, and H. Jiang "Spatially varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-701 (1995).
[CrossRef] [PubMed]

1963

D. W. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," Appl. Math 11, 431-441 (1963).
[CrossRef]

Appl. Math

D. W. Marquardt, "An algorithm for least squares estimation of nonlinear parameters," Appl. Math 11, 431-441 (1963).
[CrossRef]

Appl. Opt.

IEEE Trans. Med. Imaging

A. H. Hielscher, A. D. Klose, and K. M. Hanson, "Gradient-based iterative image reconstruction scheme for time- resolved optical tomography," IEEE Trans. Med. Imaging 18, 262-271 (1999).
[CrossRef] [PubMed]

Inverse Probl.

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Probl. 14, 1107-1130 (1998).
[CrossRef]

M. Guven, B. Yazici, K. Kwon, E. Giladi, and X. Intes, "Effect of discretization error and adaptive mesh generation in diffuse optical absorption imaging," Inverse Probl. 23, 1135-1160 (2007).
[CrossRef]

S. R. Arridge, "Optical tomography in medical imaging," Inverse Probl. 15, R41-R93 (1999).
[CrossRef]

A. D. Klose and A. H. Hielscher, "Quasi Newton methods in optical tomographic image reconstruction," Inverse Probl. 19, 387-409 (2003).
[CrossRef]

J. Comput. Phys.

A. D. Klose and E. W. Larsen, "Light transport in biological tissue based on the simplified spherical harmonics equations," J. Comput. Phys. 220, 441-470 (2006).
[CrossRef]

Med. Phys.

R. Choe, A. Corlu, K. Lee, T. Durduran, S. D. Konecky, M. Grosicka-Koptyra, S. R. Arridge, B. J. Czerniecki, D. L. Fraker, A. DeMichele, B. Chance, M. A. Rosen, and A. G. Yodh, "Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: A case study with comparison to MRI," Med. Phys. 32, 1128-1139 (2005).
[CrossRef] [PubMed]

P. K. Yalavarthy, B. W. Pogue, H. Dehghani, and K. D. Paulsen, "Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography," Med. Phys. 34, 2085-2098 (2007).
[CrossRef] [PubMed]

A. D. Klose, and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-1707 (1999).
[CrossRef] [PubMed]

K. D. Paulsen, and H. Jiang "Spatially varying optical property reconstruction using a finite element diffusion equation approximation," Med. Phys. 22, 691-701 (1995).
[CrossRef] [PubMed]

S. R. Arridge, H. Dehghani, M. Schweiger, and E. Okada, "The finite element model of the propagation of light in scattering media: A direct method for domains with nonscattering regions," Med. Phys. 27, 252-264 (2000).

Opt. Express

Opt. Express.

S. R. Arridge and M. Schwieger, "Gradient-based optimisation scheme for optical tomography," Opt. Express. 2, 212-226 (1998).
[CrossRef]

Phys. Med. Biol.

A. Gibson, J. C. Hebden, and S. R. Arridge, "Recent advances in diffuse optical imaging," Phys. Med. Biol. 50, R1-R43 (2005).
[CrossRef] [PubMed]

Physiol Meas

H. Dehghani and M , Soleimani, "Numerical modelling errors in electrical impedance tomography," Physiol Meas 28, S45-S55 (2007).
[CrossRef]

Physiol. Meas.

M. Molinari, B. H. Blott, S. J. Cox, G. J. Daniell, "Optimal imaging with adaptive mesh refinement in electrical impedance tomography," Physiol. Meas. 23, 121-128 (2002).
[CrossRef] [PubMed]

Technol. Cancer Res. Treat.

S. Srinivasan, B. W. Pogue, B. Brooksby, S. Jiang, H. Dehghani, C. Kogel, S. P. Poplack, and K. D. Paulsen, "Near-infrared characterization of breast tumors in vivo using spectrally-constrained reconstruction," Technol. Cancer Res. Treat. 5, 513-526 (2005).

Other

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, 12169-12174 (2007).
[CrossRef] [PubMed]

S. Srinivasan, B. W. Pogue, S. Jiang, H. Dehghani, C. Kogel, S. Soho, J. J. Gibson, T. D. Tosteson, S. P. Poplack, K. D. Paulsen, "Interpreting hemoglobin and water concentration, oxygen saturation and scattering measured in Vivo by near-infrared breast tomography," Proc. Natl. Acad. Sci. U. S.A. 100, 12349-12354 (2003).
[CrossRef] [PubMed]

J. R. Westlake, A handbook of numerical matrix inversion and solution of linear equations (John Wiley & Sons Inc, New York, 1968).

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Figures (6)

Fig. 1.
Fig. 1.

The normalized sensitivity for a circular model with a single source and detector. In each case, the contour line shows the threshold of the sensitivity as a percentage of total sensitivity throughout the model.

Fig. 2.
Fig. 2.

The female breast mesh used for generation of simulated data. The indentation represents the modelling of the optical fiber source and detectors.

Fig. 3.
Fig. 3.

A sagittal cross-section of the breast model shown in Fig. 2 illustrating the truest fields of optical absorption used at 785 nm.

Fig. 4.
Fig. 4.

The sagittal plot of the normalized total sensitivity for a breast model. In each case, the contour line shows the threshold of the sensitivity as a percentage of total sensitivity throughout the model.

Fig. 5.
Fig. 5.

The sagittal and coronal cross-section of the reconstructed images of the breast model using the reduced and non-reduced (0% threshold) Jacobian.

Fig. 6.
Fig. 6.

The coronal cross-section of the reconstructed images for µa and µs ’ of the cylindrical phantom using the reduced and non-reduced (0% threshold) Jacobian.

Tables (3)

Tables Icon

Table 1. The chromophore concentration of different regions within the 3D breast model, and the corresponding optical properties at 785 nm are listed.

Tables Icon

Table 2. The details of each method used for the calculation of the forward model and the reconstruction of the breast mesh model.

Tables Icon

Table 3. The details of each method used for the calculation of the forward model and the reconstruction of the phantom.

Equations (7)

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

· κ ( r ) Φ ( r , ω ) + ( μ a ( r ) + i ω c m ( r ) ) Φ ( r , ω ) = q 0 ( r , ω ) ,
κ = 1 3 ( μ a + μ ' s ) ,
Φ ( ξ ) + 2 A n ̂ · κ ( ξ ) Φ ( ξ ) = 0 ,
Ω = { i = 1 NM ( Φ i M Φ i C ) 2 } , μ min
( J T J + λ I ) 1 J T δ Φ = δ μ ,
J = [ δ ln I 1 δ μ a 1 δ ln I 1 δ μ a 2 δ ln I 1 δ μ aNN δ ln I 2 δ μ a 1 δ ln I 2 δ μ a 2 δ ln I 2 δ μ aNN δ ln I 3 δ μ a 1 δ ln I 3 δ μ a 2 δ ln I 3 δ μ aNN δ ln I NM δ μ a 1 δ ln I NM δ μ a 2 δ ln I NM δ μ aNN ] .
J ˜ ij = { J ij if i = 1 NM J ij > = threshold 0 if i = 1 NM J ij < threshold ,

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