## Time Domain Fluorescent Diffuse Optical Tomography: analytical expressions

Optics Express, Vol. 13, Issue 7, pp. 2263-2275 (2005)

http://dx.doi.org/10.1364/OPEX.13.002263

Acrobat PDF (1166 KB)

### Abstract

Light propagation in tissue is known to be favored in the Near Infrared spectral range. Capitalizing on this fact, new classes of molecular contrast agents are engineered to fluoresce in the Near Infrared. The potential of these new agents is vast as it allows tracking non-invasively and quantitatively specific molecular events *in-vivo*. However, to monitor the bio-distribution of such compounds in thick tissue proper physical models of light propagation are necessary. To recover 3D concentrations of the compound distribution, it is necessary to perform a model based inverse problem: Diffuse Optical Tomography. In this work, we focus on Fluorescent Diffuse Optical Tomography expressed within the normalized Born approach. More precisely, we investigate the performance of Fluorescent Diffuse Optical Tomography in the case of time resolved measurements. The different moments of the time point spread function were analytically derived to construct the forward model. The derivation was performed from the zero order moment to the second order moment. This new forward model approach was validated with simulations based on relevant configurations. Enhanced performance of Fluorescent Diffuse Optical Tomography was achieved using these new analytical solutions when compared to the current formulations.

© 2005 Optical Society of America

## 1. Introduction

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

3. F. Jobsis, “Noninvasive infrared monitoring of cerebral and myocardial sufficiency and circulatory parameters,” Science **198**, 1264–1267 (1977). [CrossRef] [PubMed]

4. Y. Lin, G. Lech, S. Nioka, X. Intes, and B. Chance, “Noninvasive, low-noise, fast imaging of blood volume and deoxygenation changes in muscles using light-emitting diode continuous-wave imager,” Rev. Sci. Instrum. **73**, 3065–3074 (2002). [CrossRef]

6. B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, and T. Pham, et al., “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia **2**, 26–40 (2000). [CrossRef] [PubMed]

11. X. Intes, S. Djeziri, Z. Ichalalene, N. Mincu, Y. Wang, P. St. -Jean, F. Lesage, D. Hall, D. A. Boas, and M. Polyzos, “Time-Domain Optical Mammography Softscan^{®}: Initial Results on Detection and Characterization of Breast Tumors”, Proc. SPIE **5578**, 188–197 (2004). [CrossRef]

12. D. B. Jakubowski, A. E. Cerussi, F. Bevilacqua, N. Shah, D. Hsiang, J. Butler, and B. J. Tromberg, “Monitoring neoadjuvant chemotherapy in breast cancer using quantitative diffuse optical spectroscopy: a case study,” J Biomed Opt. **9**, 230–238 (2004). [CrossRef] [PubMed]

13. G. Strangman, D. A. Boas, and J. Sutton, “Non-invasive neuroimaging using Near-Infrared light,” Biol. Psychiatry **52**, 679–693 (2002). [CrossRef] [PubMed]

15. M. Stankovic, D. Maulik, W. Rosenfeld, P. Stubblefield, A. Kofinas, and E. Gratton, et al., “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage- a newborn piglet study,” J. Matern. Fetal Med. **9**, 142–149 (2000). [CrossRef] [PubMed]

16. J. C. Hebden, A. Gibson, T. Austin, R. M. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys Med Biol. **49**, 1117–1130 (2004). [CrossRef] [PubMed]

17. V. Quaresima, R. Lepanto, and M. Ferrari, “The use of near infrared spectroscopy in sports medicine,” J. Sports Med. Phys. Fitness **43**, 1–13 (2003). [PubMed]

18. X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. G. Yodh, and B. Chance, “In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green,” Med. Phys. **30**, 1039–1047 (2003). [CrossRef] [PubMed]

19. R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology **219**, 316–333 (2001). [PubMed]

20. J. V. Frangioni, “In vivo near-infrared fluorescence imaging,” Curr. Opin. Chem. Biol. **7**, 626–634 (2003). [CrossRef] [PubMed]

21. K. Licha, “Contrast agents for optical imaging,” Topics in Current Chemistry **222**, 1–29 (2002). [CrossRef]

23. S. Achilefu, R. Dorshow, J. Bugaj, and R. Rajagopalan, “Novel receptor-targeted fluorescent contrast agents for *in-vivo* tumor imaging,” Invest. Radiol. **35**, 479–485 (2000). [CrossRef] [PubMed]

24. Y. Chen, G. Zheng, Z. Zhang, D. Blessington, M. Zhang, and H. Li, et al., “Metabolism Enhanced Tumor Localization by Fluorescence Imaging: In Vivo Animal Studies,” Opt. Lett. **28**, 2070–2072 (2003). [CrossRef] [PubMed]

25. R. Weissleder, C. H. Tung, U. Mahmood, and A. Bogdanov, “*In vivo* imaging with protease-activated near-infrared fluorescent probes,” Nat. Biotech. **17**, 375–378 (1999). [CrossRef]

26. R. Weinberg, “How Does Cancer Arise,” Sci. Am. **275**, 62–71 (1996). [CrossRef] [PubMed]

27. X. Intes, Y. Chen, X. Li, and B. Chance, “Detection limit enhancement of fluorescent heterogeneities in turbid media by dual-interfering excitation,” Appl. Opt. **41**, 3999–4007 (2002). [CrossRef] [PubMed]

28. J. Lewis, S. Achilefu, J. R. Garbow, R. Laforest, and M. J. Welch, “Small animal imaging: current technology and perspectives for oncological imaging,” Eur. J.o Cancer **38**, 2173–88 (2002). [CrossRef]

29. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. **26**, 893–895 (2001). [CrossRef]

30. M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: Near-infrared fluorescence tomography,” Proc. Nat. Acad. Sci. Am. **99**, 9619–9624 (2002). [CrossRef]

31. A. B. Milstein, J.J. Stott, S. Oh, D. A. Boas, R. P. Millane, C. A. Bouman, and K. J. Webb, “Fluorescence optical diffusion tomography using multiple-frequency data,” J. Opt. Soc. Am. A **21**, 1035–1049 (2004). [CrossRef]

^{th}, the 1

^{st}and the 2

^{nd}moments of the fluorescent time point spread function (FTPSF). The formalism of the fluorescent normalized Born approximation [29

29. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. **26**, 893–895 (2001). [CrossRef]

## 2. Theory

### 2.1. Light propagation in tissue

**r**, t) is the photon fluence rate, D is the diffusion coefficient expressed as D=1/3µ′

_{s}with µ′

_{s}being the reduced scattering coefficient, µ

_{a}is the linear absorption coefficient, v is the speed of light in the medium and S(

**r**, t) is the source term (assumed to be a δ function in our case).

_{ex}(

**r**, t) is the concentration of excited molecules at position

**r**and time t, N

_{tot}(

**r**, t) is the concentration of total molecules of fluorophores (excited or not), τ is the radiative lifetime of the fluorescent compound (sec. or nanoseconds.), σ is the absorption cross section of the fluorophore (cm

^{2}) and Φ

^{λ1}(r, t) is the photon fluence rate (Nb photons.s

^{-1}.cm

^{-2}) at the excitation wavelength λ

_{1}. Considering that the number of excited molecule is low compared to the total molecules and taking the Fourier transform yield the expression for the concentration of excited molecules:

_{1}is the angular frequency associated with t.

_{s}, the fluorescent field detected at a position

**r**

_{d}is modeled by:

^{λ2}(

**r**,

**r**

_{d}, ω) represent a propagation term of the fluorescent field from the element of volume at

**r**to the detector position

**r**

_{d}et the reemission wavelength λ

_{2}. Then, by using Eq. (4) we obtain the complete expression:

_{eff}=

*q·η.σ*is the quantum efficiency, product of q the quenching factor,

*η*the quantum yield and σ the absorption cross section of the fluorophore, Φ

^{λ1}(

**r**, t) is the photon fluence rate at the excitation wavelength λ

_{1}and at time t, and τ is the radiative lifetime of the fluorescent compound. Note that the product σ·N

_{tot}(

**r**) corresponds to the absorption coefficient of the fluorochrome and can be expressed also as ε·C

_{tot}(

**r**) where ε is the extinction coefficient of the fluorophore (cm

^{-1}. Mol

^{-1}) and C

_{tot}(

**r**) the concentration of the fluorochrome (Mol) at a position

**r**.

### 2.2. Fluorescent moment analytical expression.

29. V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. **26**, 893–895 (2001). [CrossRef]

^{λj}, at the considered wavelength λ

_{j}∈[λ

_{1}, λ

_{2}].

^{th}, 1

^{st}and 2

^{nd}moment of the TPSF [34]. The correspondence of these moments to the TPSF is illustrated in Fig. 1. The 0

^{th}moment corresponds to the integration of the counts (equivalent to the continuous mode), the 1

^{st}moment corresponds to the mean time of arrival of the photon and the 2

^{nd}moment to the variance of arrival of the photon.

35. A. Liebert, H. Wabnitz, D. Grosenick, M. Moller, R. Macdonald, and H. Rinnerberg, “Evaluation of optical properties of highly scattering media by moments of distributions of times of flight of photons,” Appl. Opt. **42**, 5785–5792 (2003). [CrossRef] [PubMed]

^{th}moment is expressed as :

_{1}=λ

_{2}=λ), i.e. typically the shift incurred under the fluorescent process will not be significant and the same propagator describes the propagation of light for both excitation and emission. Then normalizing the 1

^{st}and the 2

^{nd}moment to this first moment yields the analytical solutions: Normalized 1

^{st}moment

^{nd}moment

^{-λ2}(r

_{s},r

_{d}) corresponds to the fluorescent mean time for the particular source-detector pair considered. For simplicity, we do not present in this paper the full derivation of these analytical solutions.

^{th}source-detector pair and the j

^{th}voxel are directly derived respectively from Eqs. (9), (10) and (11). In this inverse problem, the object function is defined as the fluorophore concentration. For the cases presented herein, we implemented boundary conditions using the extrapolated boundary conditions [36

36. R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, and B. J. Tromberg, “Boundary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am A **11**, 2727–41 (1994). [CrossRef]

### 2.3. Inverse problem

37. R. Gordon, R. Bender, and G. Herman, “Algebraic reconstruction techniques (ART) for the three dimensional electron microscopy and X-Ray photography,” J. Theoret. Biol. **69**, 471–482 (1970). [CrossRef]

**b**is a vector holding the measurements for each source-detector pair,

**A**is the matrix of the forward model (weight matrix), and

**x**is the vector of unknowns (object function). ART solves this linear system by sequentially projecting a solution estimate onto the hyperplanes defined by each row of the linear system. The technique is used in an iterative scheme and the projection at the end of the k

^{th}iteration becomes the estimate for the (k+1)

^{th}iteration. This projection process can be expressed mathematically as [38]:

^{th}estimate of j

^{th}element of the object function, b

_{i}the i

^{th}measurement, aij the i-j

^{th}element of the weight matrix

**A**and ξ the relaxation parameter.

*ξ*value makes the inversion more robust but also slows down convergence. The selection of

*ξ*is most of the time, done empirically [39

39. D. Ros, C. Falcon, I. Juvells, and J. Pavia, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. **41**, 925–937 (1996). [CrossRef] [PubMed]

*ξ*=0.1 based on previous studies [40

40. X. Intes, V. Ntziachristos, J. Culver, A. G. Yodh, and B. Chance, “Projection access order in Algebraic Reconstruction Techniques for Diffuse Optical Tomography,” Phys. Med. Biol. **47**, N1–N10 (2002). [CrossRef] [PubMed]

40. X. Intes, V. Ntziachristos, J. Culver, A. G. Yodh, and B. Chance, “Projection access order in Algebraic Reconstruction Techniques for Diffuse Optical Tomography,” Phys. Med. Biol. **47**, N1–N10 (2002). [CrossRef] [PubMed]

### 2.3. Simulations

^{3}heterogeneities exhibiting a contrast of 10 in concentration. The different parameters of the simulations are provided in Table 1.

22. G. Zheng, Y. Chen, X. Intes, B. Chance, and J. Glickson, “Contrast-Enhanced NIR Optical Imaging for subsurface cancer detection,” J. Porphyrin and Phthalocyanines **8**, 1106–1118 (2004). [CrossRef]

### 2.3. Noise model

35. A. Liebert, H. Wabnitz, D. Grosenick, M. Moller, R. Macdonald, and H. Rinnerberg, “Evaluation of optical properties of highly scattering media by moments of distributions of times of flight of photons,” Appl. Opt. **42**, 5785–5792 (2003). [CrossRef] [PubMed]

## 3. Results

### 3.1. Sensitivy matrix

^{th}order Born approximation in continuous mode is highly sensitive to surface voxels. This is a well-known behavior that is both present in absorption and fluorescent mode. This also demonstrates the poor sensitivity of planar fluorescent techniques to deep fluorescent inclusions due to overwhelming dependence on surface interactions.

^{nd}normalized fluorescent moment provides a different kind of information compared to the 0

^{Th}normalized moment of the fluorescent TPSF (we overlooked here the 1

^{st}moment for simplicity). The incorporation of this additional information in fluorescent DOT is expected to produce more accurate reconstructions. In the next section we propose an example of 3D fluorescent reconstructions validating this hypothesis.

### 3.2. Reconstructions

^{th}normalized moment of the fluorescent TPSF and with the combined three normalized moments.

^{th}normalized moment of the fluorescent TPSF, the reconstructions exhibit strong artifacts on the boundary, artifacts that scale with the reconstructed heterogeneity. On the other hand the reconstructions based on the three moments combined (as reconstructions based on the 2

^{nd}normalized fluorescent moment solely; results not shown here) do not exhibit such strong surface artifacts. In this last case, the homogenous background fluorophore is more accurately reconstructed.

^{th}normalized moment. However, and as expected from Section 3.1, the reconstructions employing the 2

^{nd}normalized moment exhibit different performances. In the case of relatively short lifetimes, i.e., Cy 7and Cy 5.5, the reconstructions are similar and provide accurate recovery of the three heterogeneities. However, in the case of longer lifetime, i.e., Cy 3B, even though, the reconstructions are far superior when using the 3 moments simultaneously in the inverse problem, the objects are less well defined. This fact is linked to the close similarity between the spatial distributions of the 0

^{th}normalized and the 2

^{nd}normalized fluorescent moments. One should note also that the constellation of source-detector selected herein is quite sparse and such reconstructed structure is expected as seen in Ref [41

41. E. Graves, J. Culver, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A **21**, 231–241 (2004). [CrossRef]

### 3.2. Noisy reconstructions

^{nd}normalized moments are sensitive to noise, the incorporation of this information benefits the inverse problem. The objects are reconstructed with fidelity and the surface artifacts are still minimized due to the inherent spatial information of the 2

^{nd}normalized moment.

## 4. Conclusion

^{th}, 1

^{st}and 2

^{nd}normalized moments of the fluorescent TPSF. To our knowledge, this is the first time that such higher moment expressions are derived for fluorescent diffuse optical tomography explicitly. The analytical expressions were tested with synthetic data. Simulated phantoms with a constant background of 0.1 µM of Cy 5.5, Cy 7 and Cy 3B bearing an inclusion of 1 µM of the same compound were created. The reconstructions based on a forward model using the 3 normalized moments produced superior results compared to the reconstructions based on individual moments. The higher moments of the fluorescent TPSF provide information that is less overwhelmed by the surface interactions. The gain is important when a background fluorophore concentration exists, as is generally the case in molecular imaging. Using this reconstruction technique, the background fluorophore distribution is not reconstructed as strong surface concentrations that are generally considered as plaguing artifacts in continuous wave fluorescent imaging. Especially, the incorporation of the 2

^{nd}normalized moment resulted in superior reconstructions due to higher sensitivity to deep voxels even though the 2

^{nd}moment is known to be sensitive to noise. Reconstructions based on relevant noise levels were still satisfactory. The next step will be to assess the usefulness of this forward model in simple phantoms and real case scenario.

## References and links

1. | A Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today |

2. | X. Intes and B. Chance, “Non-PET Functional Imaging Techniques Optical,” Clin. No. Am. |

3. | F. Jobsis, “Noninvasive infrared monitoring of cerebral and myocardial sufficiency and circulatory parameters,” Science |

4. | Y. Lin, G. Lech, S. Nioka, X. Intes, and B. Chance, “Noninvasive, low-noise, fast imaging of blood volume and deoxygenation changes in muscles using light-emitting diode continuous-wave imager,” Rev. Sci. Instrum. |

5. | Y. Chen, C. Mu, X. Intes, D. Blessington, and B. Chance, “Frequency domain phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,” Rev. Sci. Instrum. |

6. | B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, and T. Pham, et al., “Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia |

7. | D. Grosenick, H. Wabnitz, K. Moesta, J. Mucke, M. Moller, C. Stroszczunski, J. Stobel, B. Wassermann, P. Schlag, and H. Rinnerberg, “Concentration and oxygen saturation of haemoglobin of 50 breast tumours determined by time-domain optical mammography,” Phys Med. Biol. |

8. | H. Jiang, N. Iftimia, J. Eggert, L. Fajardo, and K. Klove, “Near-infrared optical imaging of the breast with model-based reconstruction,” Acad. Radiol. |

9. | M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, and H. Jess, et al., “Frequency-domain techniques enhance optical mammography: Initial clinical results,” Proc. Nat. Acad. Sci. Am. |

10. | S. Colak, M. van der Mark, G. Hooft, J. Hoogenraad, E. van der Linden, and F. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE J. Sel. Top. Quatum Electron. |

11. | X. Intes, S. Djeziri, Z. Ichalalene, N. Mincu, Y. Wang, P. St. -Jean, F. Lesage, D. Hall, D. A. Boas, and M. Polyzos, “Time-Domain Optical Mammography Softscan |

12. | D. B. Jakubowski, A. E. Cerussi, F. Bevilacqua, N. Shah, D. Hsiang, J. Butler, and B. J. Tromberg, “Monitoring neoadjuvant chemotherapy in breast cancer using quantitative diffuse optical spectroscopy: a case study,” J Biomed Opt. |

13. | G. Strangman, D. A. Boas, and J. Sutton, “Non-invasive neuroimaging using Near-Infrared light,” Biol. Psychiatry |

14. | Y. Chen, D. Tailor, X. Intes, and B. Chance, “Quantitative correlation between Near-Infrared spectroscopy (NIRS) and magnetic resonance imaging (MRI) on rat brain oxygenation modulation,” Phys. Med. Biol. |

15. | M. Stankovic, D. Maulik, W. Rosenfeld, P. Stubblefield, A. Kofinas, and E. Gratton, et al., “Role of frequency domain optical spectroscopy in the detection of neonatal brain hemorrhage- a newborn piglet study,” J. Matern. Fetal Med. |

16. | J. C. Hebden, A. Gibson, T. Austin, R. M. Yusof, N. Everdell, D. T. Delpy, S. R. Arridge, J. H. Meek, and J. S. Wyatt, “Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography,” Phys Med Biol. |

17. | V. Quaresima, R. Lepanto, and M. Ferrari, “The use of near infrared spectroscopy in sports medicine,” J. Sports Med. Phys. Fitness |

18. | X. Intes, J. Ripoll, Y. Chen, S. Nioka, A. G. Yodh, and B. Chance, “In vivo continuous-wave optical breast imaging enhanced with Indocyanine Green,” Med. Phys. |

19. | R. Weissleder and U. Mahmood, “Molecular imaging,” Radiology |

20. | J. V. Frangioni, “In vivo near-infrared fluorescence imaging,” Curr. Opin. Chem. Biol. |

21. | K. Licha, “Contrast agents for optical imaging,” Topics in Current Chemistry |

22. | G. Zheng, Y. Chen, X. Intes, B. Chance, and J. Glickson, “Contrast-Enhanced NIR Optical Imaging for subsurface cancer detection,” J. Porphyrin and Phthalocyanines |

23. | S. Achilefu, R. Dorshow, J. Bugaj, and R. Rajagopalan, “Novel receptor-targeted fluorescent contrast agents for |

24. | Y. Chen, G. Zheng, Z. Zhang, D. Blessington, M. Zhang, and H. Li, et al., “Metabolism Enhanced Tumor Localization by Fluorescence Imaging: In Vivo Animal Studies,” Opt. Lett. |

25. | R. Weissleder, C. H. Tung, U. Mahmood, and A. Bogdanov, “ |

26. | R. Weinberg, “How Does Cancer Arise,” Sci. Am. |

27. | X. Intes, Y. Chen, X. Li, and B. Chance, “Detection limit enhancement of fluorescent heterogeneities in turbid media by dual-interfering excitation,” Appl. Opt. |

28. | J. Lewis, S. Achilefu, J. R. Garbow, R. Laforest, and M. J. Welch, “Small animal imaging: current technology and perspectives for oncological imaging,” Eur. J.o Cancer |

29. | V. Ntziachristos and R. Weissleder, “Experimental three-dimensional fluorescence reconstruction of diffuse media by use of a normalized Born approximation,” Opt. Lett. |

30. | M. J. Eppstein, D. J. Hawrysz, A. Godavarty, and E. M. Sevick-Muraca, “Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: Near-infrared fluorescence tomography,” Proc. Nat. Acad. Sci. Am. |

31. | A. B. Milstein, J.J. Stott, S. Oh, D. A. Boas, R. P. Millane, C. A. Bouman, and K. J. Webb, “Fluorescence optical diffusion tomography using multiple-frequency data,” J. Opt. Soc. Am. A |

32. | X. Li, “Fluorescence and diffusive wave diffraction tomographic probes in turbid media,” PhD University of Pennsylvania (1996). |

33. | M. O’Leary, “Imaging with diffuse photon density waves,” PhD University of Pennsylvania (1996). |

34. | E. Hillman, “Experimental and theoretical investigations of near infrared tomographic imaging methods and clinical applications,” PhD University College London (2002). |

35. | A. Liebert, H. Wabnitz, D. Grosenick, M. Moller, R. Macdonald, and H. Rinnerberg, “Evaluation of optical properties of highly scattering media by moments of distributions of times of flight of photons,” Appl. Opt. |

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

37. | R. Gordon, R. Bender, and G. Herman, “Algebraic reconstruction techniques (ART) for the three dimensional electron microscopy and X-Ray photography,” J. Theoret. Biol. |

38. | A. Kak and M. Slaney, “Computerized tomographic Imaging”, IEEE Press, N-Y (1987). |

39. | D. Ros, C. Falcon, I. Juvells, and J. Pavia, “The influence of a relaxation parameter on SPECT iterative reconstruction algorithms,” Phys. Med. Biol. |

40. | X. Intes, V. Ntziachristos, J. Culver, A. G. Yodh, and B. Chance, “Projection access order in Algebraic Reconstruction Techniques for Diffuse Optical Tomography,” Phys. Med. Biol. |

41. | E. Graves, J. Culver, J. Ripoll, R. Weissleder, and V. Ntziachristos, “Singular-value analysis and optimization of experimental parameters in fluorescence molecular tomography,” J. Opt. Soc. Am. A |

**OCIS Codes**

(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

(170.6920) Medical optics and biotechnology : Time-resolved imaging

(260.2510) Physical optics : Fluorescence

**ToC Category:**

Research Papers

**History**

Original Manuscript: January 24, 2005

Revised Manuscript: February 25, 2005

Published: April 4, 2005

**Citation**

S. Lam, F. Lesage, and X. Intes, "Time Domain Fluorescent Diffuse Optical Tomography: analytical expressions," Opt. Express **13**, 2263-2275 (2005)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-7-2263

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### References

- A Yodh and B. Chance, �??Spectroscopy and imaging with diffusing light,�?? Phys. Today 48, 34-40 (1995). [CrossRef]
- X. Intes and B. Chance, �??Non-PET Functional Imaging Techniques Optical,�?? Clin. No. Am. 43, 221-234 (2005).
- F. Jobsis, �??Noninvasive infrared monitoring of cerebral and myocardial sufficiency and circulatory parameters,�?? Science 198, 1264-1267 (1977). [CrossRef] [PubMed]
- Y. Lin, G. Lech, S. Nioka, X. Intes and B. Chance, �??Noninvasive, low-noise, fast imaging of blood volume and deoxygenation changes in muscles using light-emitting diode continuous-wave imager,�?? Rev. Sci. Instrum. 73, 3065-3074 (2002). [CrossRef]
- Y. Chen, C. Mu, X. Intes, D. Blessington and B. Chance, �??Frequency domain phase cancellation instrument for fast and accurate localization of fluorescent heterogeneity,�?? Rev. Sci. Instrum. 74, 3466-3473 (2003). [CrossRef]
- B. Tromberg, N. Shah, R. Lanning, A. Cerussi, J. Espinoza, T. Pham, et al., �??Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy,�?? Neoplasia 2, 26-40 (2000). [CrossRef] [PubMed]
- D. Grosenick, H. Wabnitz, K. Moesta, J. Mucke, M. Moller, C. Stroszczunski, J. Stobel, B. Wassermann, P. Schlag and H. Rinnerberg, �??Concentration and oxygen saturation of haemoglobin of 50 breast tumours determined by time-domain optical mammography,�?? Phys Med. Biol. 49, 1165-1181 (2004). [CrossRef] [PubMed]
- H. Jiang, N. Iftimia, J. Eggert, L. Fajardo and K. Klove, �??Near-infrared optical imaging of the breast with model-based reconstruction,�?? Acad. Radiol. 9, 186-194 (2002). [CrossRef] [PubMed]
- M. Franceschini, K. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, et al., �??Frequency-domain techniques enhance optical mammography: Initial clinical results,�?? Proc. Nat. Acad. Sci. Am. 94, 6468-6473 (1997). [CrossRef]
- S. Colak, M. van der Mark, G. Hooft, J. Hoogenraad, E. van der Linden, F. Kuijpers, �??Clinical optical tomography and NIR spectroscopy for breast cancer detection,�?? IEEE J. Sel. Top. Quatum Electron. 5, 1143-1158 (1999). [CrossRef]
- X. Intes, S. Djeziri, Z. Ichalalene, N. Mincu, Y. Wang, P. St.-Jean, F. Lesage, D. Hall, D. A. Boas, M. Polyzos, �??Time-Domain Optical Mammography Softscan®: Initial Results on Detection and Characterization of Breast Tumors�??, Proc. SPIE 5578, 188-197 (2004). [CrossRef]
- D. B. Jakubowski, A. E. Cerussi, F. Bevilacqua, N. Shah, D. Hsiang, J. Butler, B. J. Tromberg, �??Monitoring neoadjuvant chemotherapy in breast cancer using quantitative diffuse optical spectroscopy: a case study,�?? J. Biomed Opt. 9, 230-238 (2004). [CrossRef] [PubMed]
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