## Differential diffuse optical tomography

Optics Express, Vol. 5, Issue 10, pp. 230-242 (1999)

http://dx.doi.org/10.1364/OE.5.000230

Acrobat PDF (414 KB)

### Abstract

We formulate a perturbative solution for the heterogeneous diffusion equation which demonstrates how to use differential changes in diffuse light transmission to construct images of tissue absorption changes following contrast agent administration. The analysis exposes approximations leading to an intuitive and simplified inverse algorithm, shows explicitly why transmission geometries are less susceptible to error than the remission geometries, and why differential measurements are less susceptible to surface artifacts. These ideas about differential diffuse optical tomography are not only applicable to tumor detection and characterization using contrast agents, but also to functional activation studies with or without contrast agents and multi-wavelength measurements.

© Optical Society of America

## 1. Introduction

1. B.W. Pogue, “Focus issue: Biomedical diffuse optical tomography - Introduction,” Opt Express , **4**, 230–230 (1999). http://epubs.osa.org/opticsexpress/tocv4n8.htm [CrossRef] [PubMed]

2. F. Kelcz and G. Santyr, “Gadolinium-Enhanced Breast MRI,” Critical Reviews in Diagnostic Imaging **36**, 287–338 (1995). [PubMed]

4. C. Tilcock, “Delivery of contrast agents for magnetic resonance imaging, computed tomography, nuclear medicine and ultrasound,” Adv Drug Deliver Rev **37**, 33–51 (1999). [CrossRef]

4. C. Tilcock, “Delivery of contrast agents for magnetic resonance imaging, computed tomography, nuclear medicine and ultrasound,” Adv Drug Deliver Rev **37**, 33–51 (1999). [CrossRef]

5. R.P. Kedar, D. Cosgrove, V.R. McCready, J.C. Bamber, and E.R. Carter, “Microbubble contrast agent for color Doppler US: Effect on breast masses,” Radiology **198**, 679–686 (1996). [PubMed]

6. M.L. Melany, E.G. Grant, and S. Farooki, et al. “Effect of US contrast agents on spectral velocities: In vitro evaluation”, Radiology **211**, 427–431 (1999). [PubMed]

4. C. Tilcock, “Delivery of contrast agents for magnetic resonance imaging, computed tomography, nuclear medicine and ultrasound,” Adv Drug Deliver Rev **37**, 33–51 (1999). [CrossRef]

7. S.E. Thompson, V. Raptopoulos, R.L. Sheiman, M.M.J McNicholas, and P. Prassopoulos, “Abdominal helical CT: Milk as a low-attenuation oral contrast agent,” Radiology **211**, 870–875 (1999). [PubMed]

8. R. Jain, S. Sawhney, P. Sahni, K. Taneja, and M. Berry, “CT portography by direct intrasplenic contrast injection: a new technique,” Abdominal Imaging **24**, 272–277 (1999). [CrossRef] [PubMed]

9. L.W. Nunes, M.D. Schnall, S.G. Orel, M.G. Hochman, C.P. Langlotz, C.A. Reynolds, and M.H Torosian, “Correlation of lesion appearance and histologic findings for the nodes of a breast MR imaging interpretation model,” Radiographics **19**, 79–92 (1999). [PubMed]

10. S.G. Orel, M.D. Schnall, V.A. Livolsi, and R.H. Troupin, “Suspicious Breast-Lesions - MR-Imaging With Radiologic-Pathological Correlation,” Radiology **190**, 485–493 (1994). [PubMed]

11. B.W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Express **1**, 391–403 (1997). http://www.opticsexpress.org/oearchive/source/2827.htm [CrossRef] [PubMed]

12. V. Ntziachristos, X.H. Ma, and B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instr. **69**, 4221–4233 (1998). [CrossRef]

13. V. Ntziachristos, A.G. Yodh, M.D. Schnall, and B. Chance, “Comparison between intrinsic and extrinsic contrast for malignancy detection using NIR mammography,” Proc. SPIE **3597**, 565–570 (1999). [CrossRef]

*pre-ICG breast*is used to indicate the “baseline” breast before the contrast agent injection and the term

*post-ICG breast*marks the breast following contrast agent administration.

## 2. Theory

15. J.B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” Opt. Soc. Am. A **10**, 127–140 (1993). [CrossRef]

*U*(

*r⃗*) is the photon fluence [W·cm

^{-2}],

*ω*is the source modulation frequency,

*c*is the speed of light in the medium [cm·s

^{-1}],

*D*(

*r⃗*)≈

*c*/3

*µ*′

_{s}(

*r⃗*) is the medium diffusion coefficient [cm

^{2}·s

^{-1}],

*µ*′

_{s}(

*r⃗*) the medium reduced scattering coefficient [cm

^{-1}],

*µ*′

_{a}(

*r⃗*) the medium absorption coefficient [cm

^{-1}] and

*S*(

*r⃗*) the source term [W·cm

^{-3}]. In this work we consider solutions of the heterogeneous diffusion equation in the frequency domain employing the perturbation approach [16,17

17. S.R. Arridge, P. van der Zee, M. Cope, and D.T. Delpy, “Reconstruction methods for infra-red absorption imaging,” Proc. SPIE **1431**, 204–215 (1991) [CrossRef]

*µ*′

_{a}(

*r⃗*)) and diffusion (

*D*′(

*r⃗*)) coefficients of the pre-ICG breast into spatially varying (

*δµ*′

_{a}(

*r⃗*),

*δD*′(

*r⃗*)) and background components (

*µ*′

_{a0},

*D*′

_{0}), i.e.

*µ*′

_{a}(

*r⃗*)=

*µ*′

_{a0}+

*δµ*′

_{a}(

*r⃗*) and

*D*′(

*r⃗*)=

*D*′

_{0}+

*δD*′(

*r⃗*). Throughout this paper a single ′ denotes pre-ICG tissue volumes. In the Rytov approximation [16] the total photon density wave measured at position

*r⃗*

_{d}due to a source at position

*r⃗*

_{s}is written as the product of two components, i.e.

*scattered field ϕ*′

_{sc}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*), is produced by heterogeneities (

*δµ*′

_{a}(

*r⃗*),

*δD*′(

*r⃗*) and the

*incident field U*′

_{0}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*), is the field that would have been detected from the same medium if these heterogeneities were not present. These terms are incorporated into the diffusion equation, whose formal solution can be expressed as an integral equation using the appropriate Green’s function for the geometry implemented. For simplicity we present this analysis for an infinite medium. This theory however can be easily extended to other simple geometries such as semi-infinite or slab, using weights derived with the method of image sources [18

18. M.S. Patterson, B. Chance, and B.C. Wilson, “Time Resolved Reflectance and Transmittance for the Noninvasive Measurement of Tissue Optical Properties,” J. Appl. Opt. **28**, 2331–2336 (1989). [CrossRef]

19. T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the non-invasive determination of tissue optical properties in-vivo,” Med. Phys. **19**, 879–888 (1992). [CrossRef] [PubMed]

20. R.C. Haskell, L.O. Svaasand, T.T. Tsay, T.C. Feng, M.S. McAdams, and B.J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A **11**, 2727–2741 (1994). [CrossRef]

21. R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A **12**, 2532–2539 (1995). [CrossRef]

*W*′

_{a},(

*W*′

_{s}) represents the absorption (scattering) weight of the voxel at position

*r⃗*, due to a source at

*r⃗*

_{s}and a detector at

*r⃗*

_{d}. In the infinite medium these weights are:

*post-ICG*, total field can be written in a similar form:

*ϕ*″

_{sc}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) is the field component scattered from the post-ICG heterogeneities (i.e.

*δµ*″

_{a}(

*r⃗*),

*δD*″(

*r⃗*) with respect to the new background optical properties

*µ*″

_{a0},

*D*″

_{0}) and

*U*″

_{0}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) is the incident field obtained from the homogeneous background medium with

*µ*″

_{a0}

*D*″

_{0}. The first order perturbative solution of the heterogeneous diffusion equation yields

_{a}(W

_{s}) represents the absorption (scattering) weight of voxels at position

*r⃗*, due to a source at

*r⃗*

_{s}and for a detector at

*r⃗*

_{d}:

*ϕ*

_{sc}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) can be attributed primarily to

*perturbations created by the contrast agent injection*.

*U*′(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) and

*U*″(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) are the actual measurements on the pre- and post- ICG breast respectively, and

*U*′

_{0}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*),

*U*″

_{0}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) can be determined from the average optical properties of the pre-and post- ICG breast (

*see discussion section*).

*D*′

_{0}=

*D*″

_{0}=

*D*

_{0}and

*δD*′(

*r⃗*)=

*δD*″(

*r⃗*). Substitution of Eq.3 and Eq.8 into Eq.12 yields:

*W*″

_{s}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,r⃗,µ*″

_{a0},

*D*

_{0},

*ω*)≈

*W*′

_{s}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,r⃗,µ*′

_{a0},

*D*

_{0},

*ω*). This is a very good approximation when the

*average absorption change*due to the contrast agent is small or in the transmission geometry (

*see Appendix and discussion for absorption variations below*).

*r⃗*) be the total absorption perturbation due to the ICG injection that includes both position-independent and position-dependent contributions. Then

*µ*″

_{a}(

*r⃗*) can be written

*r⃗*)=

*µ*′

_{a0}-

*µ*″

_{a0}+

*r⃗*) represents the position-dependent absorption heterogeneities induced by the contrast agent. The relative scattered field is computed by substitution of Eq. 15 into Eq.13. It depends on contrast agent induced absorption heterogeneities and on pre-ICG tissue absorption heterogeneities.

*W*″

_{a}-

*W*′

_{a}the influence of this term can be quite small. Using the analytical forms of the weights (Eq.4 and Eq. 9) we can write out Eq.17 explicitly, i.e.

*e*

^{i(k′-k″)R(r⃗)}in Eq.18 is approximately unity and S≈0 when the average absorption increase due to the ICG injection is very small (i.e.

*k*′≈

*k*″). Usually however

*k*′≠

*k*″. For example the recommended ICG dosage for humans (0.25mg/kg) introduces an average

*µ*

_{a}increase within the interval [0.005–0.015] cm

^{-1}depending on breast vascularization [13

13. V. Ntziachristos, A.G. Yodh, M.D. Schnall, and B. Chance, “Comparison between intrinsic and extrinsic contrast for malignancy detection using NIR mammography,” Proc. SPIE **3597**, 565–570 (1999). [CrossRef]

*e*

^{i(k′-k″)R(r⃗)}respectively, for different

*R*(

*r⃗*), as a function of the post-ICG breast absorption coefficient for a source detector separation |

*r⃗*

_{d}-

*r⃗*

_{s}|=6cm, using the geometry of Figure 1c. The background

*µ*

_{a}=0.05 cm

^{-1}and the background

*µ*’

_{s}=10cm

^{-1}.

*e*

^{i(k′-k″)R(r⃗)}from unity increases for perturbations farther from the line adjoining source and detector (i.e. as |

*r⃗*

_{d}-

*r⃗*|+|

*r⃗*

_{s}-

*r⃗*| grows larger than |

*r⃗*

_{d}-

*r⃗*

_{s}| when a increases). However, the probability for photons to pass through these “distant” perturbations decreases exponentially via the weight

*W*″

_{a}in the integrand of Eq.18. Hence accumulated contributions of the heterogeneities at large a are small. Figure 2 plots the deviations introduced into

*ϕ*

_{sc}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,ω*) by taking S=0. Figure 2a depicts the ratio of the amplitude detected with no approximation to the amplitude detected assuming S=0. Similarly Fig. 2b depicts the phase shift between the phase detected with no approximation and the phase detected assuming S=0. The error is plotted for a single perturbation at different positions a for the geometry depicted in Fig. 1c. The values assumed in Eq. 16 were

*δµ*′

_{a}(

*r⃗*)=0.05 cm

^{-1},

*r⃗*)=0.05 cm

^{-1}and the background optical properties

*µ*′

_{a0}=0.05cm

^{-1},

*µ*″

_{a0}=0.05cm

^{-1}and

*µ*′

_{s}=10cm

^{-1}.

*δµ*′

_{a}(

*r⃗*)) provide the most probable photon paths. The same behavior is exhibited for the scattering weights as shown in the Appendix. Eq.16 thus becomes

*e*

^{i(k′-k″)R(r⃗)}will appear in all the terms corresponding to image sources. Note however that the assumption that S≈0 is best suited for slab geometry where |

*r⃗*

_{d}

*-r⃗*|+|

*r⃗*

_{s}

*-r⃗*|≈|

*r⃗*

_{d}

*-r⃗*

_{s}| for the most probable photon paths. This condition is not always true for reflectance geometry.

*δµ*′

_{a}(

*r⃗*) in Eq.18 could be used to approximate surface heterogeneities by taking

*r⃗*to be close to medium surface, near to the corresponding source or detector. The influence of such terms is virtually zero since in such a geometry

*R*(

*r⃗*)≅0 and subsequently S=0.

22. 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]

*n*voxels and

*m*=

*o×p×q*measurements, where

*o*is the number of sources,

*p*is the number of detectors and

*q*is the number of frequencies employed, the discretization yields a set of coupled linear equations

## 3.Results and Discussion

*r⃗*)=

*µ*′

_{a0}-

*µ*″

_{a0}+

*r⃗*). Secondly, the relative scattered field

*ϕ*

_{sc}depends both on the ratio,

*U*″/

*U*′, of the actual pre-ICG and post-ICG measurements, and the multiplicative term

*U*′

_{0}/

*U*″

_{0}=exp(

*i*(

*k*′-

*k*″)·|

*r*⃗

_{s}-

*r*⃗

_{d}|). This term expresses the change in the incident field due to the average absorption coefficient increase of the post-ICG breast. Its use in Eq.12 leads to significant reconstruction improvements [23

23. V. Ntziachristos, A. Hielscher, A.G. Yodh, and B. Chance, “Performance of perturbation tomography with highly heterogeneous media under the P1 approximation,” in *Biomedical Optics* : Advances in Optical Imaging, Photon Migration and Tissue Optics, OSA Technical Digest CLEO/Europe AMB3-1 : 211–213 (1999).

*U*′

_{0}/

*U*″

_{0}depends on |

*r⃗*

_{s}

*-r*⃗| and not on

*R*(

*r⃗*). Therefore the arguments that led on the elimination of S from Eq.16 cannot be applied to this term since |

*r⃗*

_{s}

*-r⃗*|≫

*R*(

*r⃗*). The term

*U*′

_{0}/

*U*″

_{0}can be analytically calculated for simple geometries such as infinite, semi-infinite or slab or calculated numerically for more complicated geometries if we know the average optical properties of the pre- and post- ICG breast.

*µ*′

_{a0}=0.03cm

^{-1}and

*µ*′

_{s0}=8cm

^{-1}.

_{1}-weighted MR image. This image depicts structure. White regions correspond primarily to adipose (fatty) tissue while dark regions correspond to parenchymal (glandular) tissue. Figure 3b depicts the signal enhancement of the same T1-weighted image due to injection of the MRI contrast agent Gd-DTPA. The Gd-DTPA enhancement is superimposed in color. An infiltrating ductal carcinoma (shown in yellow) demonstrated the highest signal enhancement. Gd-DTPA and ICG have similar distribution patterns. Here we assume that the Gd-DTPA distribution reflects the ICG distribution.

13. V. Ntziachristos, A.G. Yodh, M.D. Schnall, and B. Chance, “Comparison between intrinsic and extrinsic contrast for malignancy detection using NIR mammography,” Proc. SPIE **3597**, 565–570 (1999). [CrossRef]

*µ*

_{a}=0.30cm

^{-1}

*µ*

_{s}’=8cm

^{-1}). The average absorption of the pre- and post- ICG breast were found to be

*µ*′

_{a0}=0.0473 cm

^{-1}and

*µ*″

_{a0}=0.0589 cm

^{-1}so that average absorption increase due to the ICG is

*µ*″

_{a0}-

*µ*′

_{a0}=0.0116 cm

^{-1}.

*r⃗*) for the three cases examined are shown in Figure 6.

*weaker*perturbations introduced by the ICG injection, relative to the average absorption increase. Since by construction the perturbation method works especially well for weak perturbations [16], it is expected that the use of Eq. 20 will more accurately image the heterogeneous medium. The same behavior is expected for a Born-type [16] perturbative formulation. We note that Fig.6b images the

*r⃗*) and not the

*r⃗*) as in Fig, 6a and 6c. Therefore it is reasonable that the reconstructed value for cancer in Fig. 6b is higher than the value reconstructed in Fig.6a and 6c. The difference in reconstructed values equals approximately the average absorption increase in the post-ICG breast (

*µ*″

_{a0}-

*µ*′

_{a0}=0.0116 cm

^{-1}).

*r⃗*) is imaged. The magnitude of the cancer is slightly overestimated and its size is significantly overestimated. Similarly to Fig. 6b, strong artifacts appear close to the boundary. A distributed absorption is also reconstructed which does not correspond to the ICG distribution and is also an artifact. Compared to the other approaches the subtraction yields the most artifacts.

**3597**, 565–570 (1999). [CrossRef]

24. V. Ntziachristos, X.H. Ma, A.G. Yodh, and B. Chance, “Multichannel photon counting instrument for spatially resolved near infrared spectroscopy,” Rev. Sci. Instr. **70**, 193–201 (1999). [CrossRef]

*µ*′

_{a0}-

*µ*″

_{a0}, (necessary to calculate both

*U*′

_{0}/

*U*″

_{0}and

*r⃗*)) with an accuracy of the order of 10

^{-3}cm

^{-1}.

## APPENDIX

*W*″

_{s}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,r⃗,µ*″

_{a0},

*D*

_{0},

*ω*) to

*W*′

_{s}(

*r⃗*

_{s}

*,r⃗*

_{d}

*,r⃗,µ*′

_{a0},

*D*

_{0},

*ω*) is sufficiently small so that when subtracting Eq.3 from Eq.8 to produce Eq.13, the scattering terms cancel out. Instead of expressing all the terms analytically, we plot the ratio

*δD*′(

*r⃗*)=

*δD*″(

*r⃗*) the scattering terms can be ignored when reconstructing the absorption perturbation only due to contrast agent injection. When introducing boundaries, the assumption of small a compared to the source-detector distance for the most probable photon paths works better for transmittance geometry.

## Acknowledgements

## References and links

1. | B.W. Pogue, “Focus issue: Biomedical diffuse optical tomography - Introduction,” Opt Express , |

2. | F. Kelcz and G. Santyr, “Gadolinium-Enhanced Breast MRI,” Critical Reviews in Diagnostic Imaging |

3. | F. Barkhof, J. Valk, O.R. Hommes, and P. Scheltens, “Meningeal Gd-DTPA enhancement in multiple-sclerosis,” Am. J. Neuroradiology |

4. | C. Tilcock, “Delivery of contrast agents for magnetic resonance imaging, computed tomography, nuclear medicine and ultrasound,” Adv Drug Deliver Rev |

5. | R.P. Kedar, D. Cosgrove, V.R. McCready, J.C. Bamber, and E.R. Carter, “Microbubble contrast agent for color Doppler US: Effect on breast masses,” Radiology |

6. | M.L. Melany, E.G. Grant, and S. Farooki, et al. “Effect of US contrast agents on spectral velocities: In vitro evaluation”, Radiology |

7. | S.E. Thompson, V. Raptopoulos, R.L. Sheiman, M.M.J McNicholas, and P. Prassopoulos, “Abdominal helical CT: Milk as a low-attenuation oral contrast agent,” Radiology |

8. | R. Jain, S. Sawhney, P. Sahni, K. Taneja, and M. Berry, “CT portography by direct intrasplenic contrast injection: a new technique,” Abdominal Imaging |

9. | L.W. Nunes, M.D. Schnall, S.G. Orel, M.G. Hochman, C.P. Langlotz, C.A. Reynolds, and M.H Torosian, “Correlation of lesion appearance and histologic findings for the nodes of a breast MR imaging interpretation model,” Radiographics |

10. | S.G. Orel, M.D. Schnall, V.A. Livolsi, and R.H. Troupin, “Suspicious Breast-Lesions - MR-Imaging With Radiologic-Pathological Correlation,” Radiology |

11. | B.W. Pogue, M. Testorf, T. McBride, U. Osterberg, and K. Paulsen, “Instrumentation and design of a frequency-domain diffuse optical tomography imager for breast cancer detection,” Opt. Express |

12. | V. Ntziachristos, X.H. Ma, and B. Chance, “Time-correlated single photon counting imager for simultaneous magnetic resonance and near-infrared mammography,” Rev. Sci. Instr. |

13. | V. Ntziachristos, A.G. Yodh, M.D. Schnall, and B. Chance, “Comparison between intrinsic and extrinsic contrast for malignancy detection using NIR mammography,” Proc. SPIE |

14. | A. Ishimaru, |

15. | J.B. Fishkin and E. Gratton, “Propagation of photon-density waves in strongly scattering media containing an absorbing semi-infinite plane bounded by a straight edge,” Opt. Soc. Am. A |

16. | A.C. Kak and M. Slaney, |

17. | S.R. Arridge, P. van der Zee, M. Cope, and D.T. Delpy, “Reconstruction methods for infra-red absorption imaging,” Proc. SPIE |

18. | M.S. Patterson, B. Chance, and B.C. Wilson, “Time Resolved Reflectance and Transmittance for the Noninvasive Measurement of Tissue Optical Properties,” J. Appl. Opt. |

19. | T.J. Farrell, M.S. Patterson, and B. Wilson, “A diffusion-theory model of spatially resolved, steady-state diffuse reflectance for the non-invasive determination of tissue optical properties in-vivo,” Med. Phys. |

20. | R.C. Haskell, L.O. Svaasand, T.T. Tsay, T.C. Feng, M.S. McAdams, and B.J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A |

21. | R. Aronson, “Boundary conditions for diffusion of light,” J. Opt. Soc. Am. A |

22. | 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. |

23. | V. Ntziachristos, A. Hielscher, A.G. Yodh, and B. Chance, “Performance of perturbation tomography with highly heterogeneous media under the P1 approximation,” in |

24. | V. Ntziachristos, X.H. Ma, A.G. Yodh, and B. Chance, “Multichannel photon counting instrument for spatially resolved near infrared spectroscopy,” Rev. Sci. Instr. |

**OCIS Codes**

(110.6960) Imaging systems : Tomography

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.3660) Medical optics and biotechnology : Light propagation in tissues

(170.5270) Medical optics and biotechnology : Photon density waves

(170.5280) Medical optics and biotechnology : Photon migration

(170.6960) Medical optics and biotechnology : Tomography

**ToC Category:**

Research Papers

**History**

Original Manuscript: September 8, 1999

Published: November 8, 1999

**Citation**

Vasilis Ntziachristos, Britton Chance, and Arjun Yodh, "Differential diffuse optical tomography," Opt. Express **5**, 230-242 (1999)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-5-10-230

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### References

- B. W. Pogue, "Focus issue: Biomedical diffuse optical tomography - Introduction," Opt. Express 4, 230-230 (1999). http://www.opticsexpress.org/tocv4n8.htm [CrossRef] [PubMed]
- F. Kelcz, G. Santyr, "Gadolinium-Enhanced Breast MRI," Critical Reviews in Diagnostic Imaging 36, 287-338 (1995). [PubMed]
- F. Barkhof, J. Valk, O. R.Hommes, P. Scheltens, "Meningeal Gd-DTPA enhancement in multiple-sclerosis," Am. J. Neuroradiology 13, 397-400 (1992).
- C. Tilcock, "Delivery of contrast agents for magnetic resonance imaging, computed tomography, nuclear medicine and ultrasound," Adv Drug Deliver Rev 37, 33-51 (1999). [CrossRef]
- R. P. Kedar, D. Cosgrove, V. R. McCready, J. C. Bamber, E. R. Carter, "Microbubble contrast agent for color Doppler US: Effect on breast masses," Radiology 198, 679-686 (1996). [PubMed]
- M. L. Melany, E. G. Grant, S. Farooki, et al. "Effect of US contrast agents on spectral velocities: In vitro evaluation," Radiology 211, 427-431 (1999). [PubMed]
- S. E. Thompson, V. Raptopoulos, R. L. Sheiman, M. M. J McNicholas, P. Prassopoulos, "Abdominal helical CT: Milk as a low-attenuation oral contrast agent," Radiology 211, 870-875 (1999). [PubMed]
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