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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 14, Iss. 16 — Aug. 7, 2006
  • pp: 7172–7187
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Separately reconstructing the structural and functional parameters of a fluorescent inclusion embedded in a turbid medium

Baohong Yuan and Quing Zhu  »View Author Affiliations


Optics Express, Vol. 14, Issue 16, pp. 7172-7187 (2006)
http://dx.doi.org/10.1364/OE.14.007172


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Abstract

We report a novel imaging technique for fluorescence diffuse optical tomography (FDOT). Unlike conventional FDOT, this technique separates the imaging procedure into two steps to respectively reconstruct the structural information (such as the center position and the radius), and the functional information (such as the fluorophore concentration and/or lifetime) of a fluorescing target embedded in a turbid medium. The structural parameters of the target were estimated from the amplitude ratio and phase difference of fluorescence signals received at different detectors, because the amplitude ratio and phase difference were found independent of, or weakly related to, the functional parameters. Based on the estimated structural parameters, a dual-zone mesh technique was utilized to reconstruct the fluorophore concentration. Results of simulations and phantom experiments showed that the structural parameters could be accurately recovered, without knowing the functional information, and that the reconstruction accuracy of the functional parameter was greater than 80%.

© 2006 Optical Society of America

1. Introduction

Diffuse optical tomography (DOT) employs near infrared (NIR) diffused light to probe for functional information of biological tissues [1–7

1. T. F. Massoud and S. S. Gambhir, “Molecular imaging in living subjects: seeing fundamental biological processes in a new light,” Genes Dev. 17, 545–580 (2003). [CrossRef] [PubMed]

]. To further increase the target to background contrast, fluorescent diffusive optical tomography (FDOT) has been under intensive investigation [8–29

8. J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near–infrared fluorescence contrast-enhanced imaging,” Photochem. and Photobiol. 77, 420–430 (2003). [CrossRef]

]. Assisted by proper molecular probes, FDOT has been expanded to perform molecular imaging in small animals [17

17. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004). [CrossRef] [PubMed]

], and a new concept of fluorescent molecular tomography (FMT) has been introduced [18

18. V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002). [CrossRef] [PubMed]

, 19

19. U. Mahmood, “Near infrared optical applications in molecular imaging, earlier, more accurate assessment of disease presence, disease course, and efficacy of disease treatment,” IEEE Eng. Med. Biol. Mag. 23, 58–66 (2004). [CrossRef] [PubMed]

].

Ntziachristos et al have demonstrated [17–20

17. E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004). [CrossRef] [PubMed]

] a method of imaging tumors in mice, targeted by special fluorescing probes, using the CW system. A sub-millimeter resolution and a high reconstruction accuracy of the fluorophore concentration were obtained when a charge-couple device (CCD) camera, with a large number of pixels or measurements (up to 106), was employed [20

20. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003). [CrossRef] [PubMed]

]. However, the imaging volume of 74 cm3 was only adequate for imaging small animals [15

15. M. Gurfinkel, S Ke, X Wen, C Li, and E. M. Sevick-Muraca, “Near-infrared fluorescence optical imaging and tomography,” Dis. Markers 19,107–121 (2003, 2004).

]. In contrast, other research groups [11–13

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

] have used the frequency domain technique and increased the imaging volume to 260 cm3 and 1000 cm3, which are clinically relevant [15

15. M. Gurfinkel, S Ke, X Wen, C Li, and E. M. Sevick-Muraca, “Near-infrared fluorescence optical imaging and tomography,” Dis. Markers 19,107–121 (2003, 2004).

]. Unfortunately, the reconstruction accuracy of the fluorophore concentration is much lower than that obtained by the CW method. For example, only ∼20% of the expected value was recovered by Lee et al [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

]. Approximate 46% and 140% of the expected values were obtained by Godavarty et al [13

13. A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003). [CrossRef] [PubMed]

] for the imperfect uptake of fluorophore into the target (100:1) and for the perfect uptake (1:0), respectively. This low reconstruction accuracy may be caused by fewer measurements acquired over a larger imaging region; these were 7 × 30 (sources × detectors) measurements by Lee et al, and 27 × 128 by Godavarty et al. A commercially available time-domain fluorescence system specifically designed for small animal imaging, Explore OptixTM, has been developed by the Advanced Research Technology Inc [3

3. W. Long and M. Vernon, “Optical molecular imaging: time domain advantages with explore OptixTM,” January 2004, Advanced Research Technology Inc. http://www.art.ca/en/products/INOPaper040129.pdf.

]. From the temporal point spread function of the incident laser pulse, the structural and functional information of the inclusion can be obtained by this system. In addition, because a scanning system is adopted, the imaging region is adjustable. However, imaging a large region results in a lengthened data acquisition time. In addition, the cost of this system is significantly higher than the DC and FDPM systems.

To improve reconstruction accuracy of a fluorescence inclusion imbedded in a large imaging volume, we introduce, to the best of our knowledge, a novel technique to reconstruct the structural and functional parameters of a fluorescent target. Unlike conventional FDOT mentioned above, our new imaging technique separately reconstructs the structural parameters (such as center position and radius) and the functionally parameters (such as fluorophore concentration). The amplitude ratio and phase difference between the fluorescence signals received by different detectors are found to be independent of, or weakly depend upon, the fluorophore concentration. Therefore, the amplitude ratio and the phase difference are utilized to estimate the target’s structural information without knowing the fluorophore concentration. With the target structural information available, a dual-zone mesh technique, previously developed by our group for optical absorption and scattering imaging [30–32

30. Q. Zhu, M. Huang, N. G. Chen, K. Zarfos, B. Jagjivan, M. Kane, P. Hegde, and S. H. Kurtzman, “Ultrasound-guided optical tomographic imaging of malignant and benign breast lesions,” Neoplasia 5, 379–388 (2003). [PubMed]

], is employed to reconstruct the fluorophore concentration. By separating the imaging procedure into two steps, both the structural and functional parameters can be accurately recovered from 9 sources and 10 detectors. In addition, the total imaging volume can be expanded or localized, depending on the target volume and the design of the imaging probe.

This paper is organized as follows: the principle of estimating the structural parameters is introduced in 2.1, and the forward model and the inverse algorithm for reconstructing the functional parameters are presented in section 2.2. The simulation and experimental methods are detailed in section 3. The results and discussion are given in section 4, and a summary is provided in section 5.

2. Theories

2.1. Principles of estimating structural parameters of the inclusion

The new and important finding reported herein is that the ratio of fluorescence signals excited by a single source and received by two detectors depends only on the structural parameters of the inclusion; therefore, it can be used to estimate these parameters. The principle behind this finding is explained by the following theoretical analysis only when the fluorescence signals generated by the background fluorophore can be eliminated from the total fluorescence measurements (or there is perfect uptake of fluorophore into the target). When the elimination of the background signals is not feasible (or there is imperfect uptake of fluorophore into the target), the analyses based on calculations are also discussed in this section.

Assuming a spherical fluorescent target is embedded in a semi-infinite turbid medium, we define its structural parameters as center position (X, Y, and Z) and radius α. The functional parameters of the target are fluorophore concentration in the target. According to diffusion theory [10

10. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996). [CrossRef]

, 33

33. X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt. 35, 3746–3758 (1996). [CrossRef] [PubMed]

], the fluorescence fluence excited by a point source located at rS and detected by a detector located at rD can be expressed by the following equation:

ϕflrSrD=S04πDexDflΛε(1iωτ)ΩGexrSrGflrrDN(r)dr3,
(1)

where r is a spatial variable and Ω. represents the target region where fluorophore is located. S0 is the source strength and D is the diffusion coefficient. Subscripts, “ex” and “fl”, indicate that the variables are measured at the excitation and emission wavelengths, respectively. Λ, τ , and ε are the quantum yield, the lifetime, and the extinction coefficient of the fluorophore, respectively. G is Green’s function and N(r) is the fluorophore concentration.

As an example, Fig. 1(a) shows a configuration of detecting fluorescence fluences excited by a source S1 modulated at a frequency ω and detected by two detectors D1 and D2. The ratio of the fluorescence fluences detected at D2 and D1 can be obtained as:

ϕflrS1rD2ϕflrS1rD1=ΩGexrS1rGflrrD2N(r)dr3ΩGexrS1rGflrrD1N(r)dr3.
(2)

From Eq. (2) we can see that the only difference between the numerator and the denominator is the term Gfl that includes the positions of the two different detectors. Therefore, we can expect that the ratio of the fluorescence fluences is mainly dependent on Gfl , rather than Gex and N(r) . The results presented in section 4 will further validate this observation. For convenience we define two variables to describe the ratio of the fluorescence fluences: the amplitude of the ratio, R and the phase of the ratio, ΔΨ. They can be written as:

R=ϕflrS1rD2ϕflrS1rD1
(3)
ΔΨ=phase[ϕflrS1rD2ϕflrS1rD1].
(4)

Table 1. Background parameters of the medium. μα,660c and μ´ s, 660 were measured by the method used in Ref. [39]. μα,694c and μ´ s, 694 were extracted by fitting the experimental data of the homogeneous Cy5.5 solution to the theoretical data based on the measured values of μα,660c and μ´ s, 660. ε 660 and ε 694 were approximated from the maximum molar excitation coefficient of Cy5.5 in water (0.25 cm -1 μM -1) at 675 nm. Units of the absorption and scattering coefficients are cm -1

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Fig. 1. (a) Configuration of a source and two detectors for calculating R and ΔΨ in (b)-(e). (b) Calculated results of R and ΔΨ as a function of the target depth and the radius. The background concentration of fluorophore is zero. (c) Calculated R and ΔΨ as a function of the target depth with different background parameters (the target radius is 0.4 cm ). (d) Calculated R and ΔΨ as a function of the target radius with different background parameters (the target depth is 1.5 cm ). (e) Calculated R as a function of the inclusion depth at different ratios of the target concentration to background.

2.2. The forward model and the inverse algorithm for functional imaging

To demonstrate the principle of our new reconstruction scheme, we focus on the reconstruction of fluorophore concentration and lifetime is considered as a constant. To reconstruct the fluorophore concentration, a normalized Born approximation has been widely used in the literature [10

10. M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996). [CrossRef]

, 11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 14

14. 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]

]. Specifically, the Eq. (1) was discredited and normalized by a set of measurements for elimination of unknown system parameters, such as source strengths and detector gains. Several normalization schemes have been proposed [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 14

14. 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]

], and we adopted the simplest scheme for phantom experiments in which the measurement was made from a homogeneous fluorescent solution and was used to normalize the heterogeneous measurement. For clinical or animal studies, other advanced normalization [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 14

14. 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]

] schemes can be applied. Equation (5) is the normalized Born approximation technique used in this paper:

ϕflϕ0fl=j((kex2kfl2)Δv4πN0flGjrsrjGjrjrd[(GexrsrdGflrsrd)])N(rj),
(5)

where kex(fl)=(μα_ex(fl)+iω/v)/Dex(fl) is the wave vector of the diffuse photon density wave at the wavelength of the excitation (emission). μ α_ex(fl) is the absorption coefficient of the background medium at the wavelength of the excitation (emission). ω and v are the modulation frequency of the source and the speed of the light in the medium, respectively. Δv is the volume of each voxel, and N0fl is the calibrated fluorophore concentration in the homogeneous medium and is used for normalization of the heterogeneous data.

A dual-zone mesh method was reported to significantly improve the reconstruction accuracy [29–32

29. J. W. Bangerth and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004). [CrossRef] [PubMed]

] when the a priori target structure location is given. We have used the dual-zone mesh method in this study because the target structure is readily available from the estimation technique described in section 2.1. In the dual-zone mesh scheme, we divide the imaging region into two parts, L and B, where L is the target region and B is the background region. We then discretize the target region into a finer grid (0.1x0.1x0.5cm) and the background region into a coarser grid (1.0x1.0x0.5cm). Therefore, Eq. (5) can be further expressed as a linear matrix equation when multiple measurements are available:

[M]T×1=[WL,WB]T×N0[XL,XB]N0×1,
(6)

where M corresponds to the value on the left side of Eq. (5). WL and WB are weight matrices for the target region and the background region, respectively, and have dimensions of TxNL and TxNB, respectively. T is the total measurement. NL and NB are the total numbers of voxels in the target region and the background region, respectively. N0=NL+NB is the total number of voxels. [XL ] and [XB ] are vector representation of the distribution of fluorophore concentration in the target region and the background region, respectively. By using a dual-zone mesh, we can maintain the total number of voxels with unknown concentration on the same scale of the total measurements. As a result, the inverse problem is less underdetermined. In general, only a few iterations are needed for reconstruction to converge to a stable solution. The total least-square method and the conjugate gradient technique are used to iteratively solve Eq. (6) [30–32

30. Q. Zhu, M. Huang, N. G. Chen, K. Zarfos, B. Jagjivan, M. Kane, P. Hegde, and S. H. Kurtzman, “Ultrasound-guided optical tomographic imaging of malignant and benign breast lesions,” Neoplasia 5, 379–388 (2003). [PubMed]

]. Note that this dual-zone mesh technique [29–32

29. J. W. Bangerth and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004). [CrossRef] [PubMed]

] should not be confused with a multi-grid technique [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 40

40. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997). [CrossRef] [PubMed]

]. The multi-grid technique was used in the literature to improve calculation efficiency of the forward weight matrix, especially when a finite difference or finite element technique was used [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 40

40. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997). [CrossRef] [PubMed]

].

3. Methodology

We have designed a probe with 9 sources and 10 detectors (see Fig. 2). The total imaging volume is 324 cm3 (9 × 9 × 4 cm3). In fact, the imaging volume can be increased or decreased by adjusting the distribution of sources and detectors on the probe, as long as the signal to noise ratio is acceptable for those detectors with larger source-detector separations. For each source, a total of 45 (C102) amplitude ratios and 45 phase differences can be obtained. Thus, a total of 810 (9×45×2) measurements can be completed to determine the structural parameters (X, Y, Z, α), which is an over-determined problem. Because both amplitudes and phases are used in the imaging of the fluorophore concentration, the maximum number of measurements is 180 (9×10×2).

3.1. Simulation method

To evaluate the performance of our technique, we generated the fluorescence fluences from the analytic solution given in the Appendix and Ref [33

33. X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt. 35, 3746–3758 (1996). [CrossRef] [PubMed]

]. Five percent independent random Gaussian noise was added to both the real and imaginary parts of the data. The amplitude ratio R and phase difference ΔΨ were calculated from the simulated data and used to estimate the structural parameters. This procedure was repeated five times and the mean and the standard deviation of each estimated parameter were obtained. All the background parameters of the medium used in the calculations were listed in Table 1. These parameters correspond to the fluorescent dye Cy5.5, which will be described later. The fluorophore concentrations of the target were set as 5 μM inside, and 0.023 μM outside.

Fig. 2. The schematic of the optical probe. The total imaging region underneath the probe is 9x9x4 (X, Y, Z) cm3, which can be flexibly adjusted.

3.2. Experimental Method

In the phantom study, 0.5% Intralipid solution was used to simulate a semi-infinite medium. A hollow and transparent cube 0.8×0.8×0.8 cm3 was filled with Intralipid solution at the same concentration. A fluorescent dye of Cy5.5 (Amersham Biosciences, PA15601) was dissolved in the cube, which was submerged into the Intralipid solution. A three dimensionally adjustable micrometer was used to control the X, Y, and Z positions. The calculated concentration of Cy5.5 in the cube was 5 μM. The background concentration was controlled at 0.023 μM.

We performed three sets of measurements for estimating target structural parameters and imaging fluorescence concentration. The first set of measurements was made from the 0.5% Intralipid solution without Cy5.5 and the cube, and the measured signals should be considered as the leakage of excitation light from the two optical filters. The second set of measurements was made from the same 0.5% Intralipid solution with 0.023 μM Cy5.5 dissolved in the solution, but without submerging the cube. This set of measurements consisted of the leakage signals and the fluorescence signals generated by the background fluorophore. Subtracting the first set of signals from the second set, we obtained the background fluorescence signals that were used to normalize the measurements when the fluorescence target was submerged. The third set of measurements was made with the same conditions as the second set, but with the cube submerged in the Intralipid solution. This set of measurements consisted of leakage signals, the fluorescence signals generated from the background fluorophore, and fluorescence signals generated by the fluorophore in the cube. The leakage of the excitation light was always considered as noise and eliminated from the measurement. After subtracting the leakage signals from the third measurements, the remaining signals were used to retrieve the amplitude and phase of fluorescence signal for imaging the fluorophore concentration, and were used to calculate R s and ΔΨ s for estimating the structural parameters. The homogeneous (background) measurement is used for normalization or calibration. In this paper, we refer both the simulated data with noise added and the phantom experimental data as measured data to distinguish them from the data without adding noise and calculated by the analytical solution (A1)-(A4).

4. Results and Discussion

4.1. Simulation results

4.1.1. Estimation of the structural parameters

Figure 3 shows the estimated structural parameters versus their true values. In Fig. 3(a), we varied the target’s X and Y positions from -0.8 to 1.0 cm, while maintaining the depth and radius as 1.0 and 0.4 cm, respectively. The line with solid circles (blue) represents the target’s true X and Y positions, and the open circles (red) are the values of X and Y estimated by the data with noise. The corresponding values of the estimated depth Z and radius α are also given in the figure. For each target’s position, the estimated values are scattered around the true values. When the error is defined as the difference between the mean of the estimated values and the true position, the maximum error in X is 0.047 cm, and in Y is 0.065 cm. This implies that the estimation of the X and Y positions are highly accurate. Similarly, in Fig. 3(b), we varied the target depth Z and maintained X = Y =0 cm and α = 0.4 cm. The line with solid circles (blue) denotes the ideal results, and the open circles (red) represent the estimated results. The estimated values of X, Y and α and the corresponding standard deviations are also shown in the figure. Two dotted lines are used to indicate the diameter of the spherical target. It is evident that the estimated depths in Fig. 3(b) agree well with the true values. All the estimated values are within the region occupied by the target. Only when the target has a depth of 0.5 cm does the estimated value have a larger standard deviation.

Fig. 3. The structural parameters recovered from the simulation data. (a) Estimated X and Y, (b) Estimated depth Z, and (c) Estimated radius α versus their true values, respectively.

4.1.2 Reconstruction of the fluorophore concentration

A spherical target with a radius of 0.4 cm and a concentration of 5 μM was imaged and the background concentration of fluorophore was 0.023 μM. The parameters of the Cy5.5 listed in Table 1 were used in the reconstruction. The target was located at the center of the imaging region (X=Y=0.0 cm) and the target depth was 2.5 cm. The reconstructed images in X-Y plane at different depths are shown in Fig. 4(a). The reconstructed target appears only on the fifth slice, which corresponds to the imaging depth of 2.5 cm and is identical to the true target depth. Since the radius of the target is 0.4 cm, we should not expect any target mass in the fourth and the sixth layers because other slices are background regions. The percentage of the maximum reconstructed concentration with respect to its true value (5 μM) is 88.54%. The average of the reconstructed values within the full width at half maximum (FWHM) is 67.39%. For a comparison, the reconstructed images obtained from the conventional reconstruction technique (single mesh, 0.25x0.25x0.5 cm3) were shown in Fig. 4(b). The reconstructed images spread into three layers and the percentage of the maximum reconstructed value of each layer is 9.58%, 36.97%, and 12.14%, respectively, which is close to the results reported in Refs. [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 13

13. A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003). [CrossRef] [PubMed]

] but is much lower than dual-zone mesh results shown in Fig. 4(a). In order to examine the effect of the background parameters on the images, we show a set of images in Fig. 4(c) that are reconstructed based on the following parameters: μ´s_ex = 10, μα_ex = 0.02, μ´s_fl = 9, and μα_fl = 0.035 cm -1. The percentage of the maximum reconstructed concentration is 90.25%. The average of the reconstructed values within FWHM is 73.06%. In addition, we have varied the target depth and repeated the imaging processes and obtained similar results.

Fig. 4 (a) Images reconstructed from the simulated data (added with noise) using dual-zone mesh. The center of the target is located at X=Y=0.0 cm, Z=2.5 cm. The radius of the spherical target is 0.4 cm. The slices at the first row from left to right correspond to imaging depth of 0.5 cm, 1.0 cm and 1.5 cm, respectively. The slices at the second row from left to right correspond to imaging depth of 2.0 cm, 2.5 cm, and 3.0 cm, respectively. The slices at the third row correspond to imaging depth of 3.5 cm and 4.0 cm, respectively. (b) The reconstructed images with single mesh obtained from the same data. (c) The reconstructed images based on the parameters used in (a) except background parameters (see the background parameters in Sec. 4.1.2).

4.1.3. Estimation and reconstruction of two targets

In order to examine the feasibility of our new technique for reconstructing multiple targets, we positioned one spherical target at -0.4 (X), 0.0 (Y) and 1.5 (Z) cm, and the other at X=0.4 (X), 0.0 (Y) and 1.5 (Z) cm. The radius of each target is 0.4 cm. They were represented by two red dashed circles shown in Fig. 5(a). The fluorophore concentration was 5.0 μM in the left target and 4.0 μM in the right one. The forward data was generated by numerically calculating the integral in Eq. (1) with five percent random Gaussian noise added. The same methods as discussed in Sec. 2 were used to estimate the structural and fluorophore concentration distribution. The black dashed square indicated the region where the sources and the detectors were distributed. The green dashed square represented the target region L where the fine-mesh image was reconstructed. The estimation of the structural parameters was repeated five times and five estimated X-Y positions were shown by blue dots in Fig. 5(a). The estimated averages and standard derivations of the depth and radius were presented in Fig. 5(a). Since we used one target to approximate the two targets, we do expect to obtain the center positions of the two targets, but an approximate equivalent center position for two targets. All the estimated X-Y positions in Fig. 5(a) were between the centers of the two targets. This is good enough for us to localize the two targets by an appropriate target region L marked by the green dashed square. Within this region, the fluorophore concentration distribution was reconstructed and shown in Fig. 5(b). The maximum reconstructed concentrations for the two targets are 95.57% and 87.48%, respectively.

Fig. 5. Reconstruction results of two targets: (a) Reconstructed structural parameters; the red dash circles in (a) represent the positions of the two targets and the blue dots are the estimated positions. The green dashed square indicates the target region and the black dashed square shows the region where the sources and the detectors are distributed. (b) Reconstructed fluorophore concentration distribution within the region marked by the green dashed square in (a). Note the image size is 3 cm by 3 cm, which is 1/3 of the image size used in Fig. 4 for each slice.

4.2. Experimental results

4.2.1. Recovery of the structural parameters

We simultaneously changed the target positions X and Y, and controlled the target at a depth of approximately 1.98 cm (measured from the micrometer). Figure 6(a) provides the estimated X and Y values versus their expected values. The blue circles indicate the measured center positions of the cube in the X-Y plane and the error bars along X and Y denotes the length and width of the cube. The red squares show the estimated positions of the cube; the estimated depth and radius are also shown and the numbers in parentheses are the corresponding standard deviations. It can be seen that the estimated X and Y are considerably close to their expected values. The estimated depth Z and radius α are also close to the expected values of 1.98 cm and 0.4 cm, respectively. In view of the fact that light propagation in the highly scattering medium is governed by diffusion theory, we do not attempt here to obtain an exact shape of the cube. Therefore, the expected “radius” of the cube is considered as half the thickness of the cube. In Fig. 6(b), we controlled X=0.24 cm and Y=-0.33 cm, and varied the depth Z. The dashed line with solid circles represents the ideal results and the red squares show the estimated depths. Two dotted lines are used to indicate the thickness of the target. The target occupies the region within the two dotted lines. It can be seen that all estimated values are within the occupied regions of the cube. Relatively large errors are evident when the target is located at a greater depth; this is reasonable, because a deep target generates weaker signals than a shallow one. Note that in order to avoid the effect of the background concentration on the amplitude ratio and phase difference, only those measurements with the distances longer than 1.5 cm were used. In addition, to preserve high signal to noise ratio of the data, only those measurements with distances shorter than 3.0 cm were use in the estimation of the structural parameters.

Fig. 6. The structural parameters recovered from the experimental data. (a) the estimated X and Y, and (b) the estimated depth Z versus their expected values, respectively.

4.2.2. Reconstruction of the fluorophore concentration

An example of the reconstructed images from the experimental data is shown in Fig. 7. The center of the target is located at X= 0.24 cm, Y= -0.33 cm, and Z=2.65 cm and the target is a 0.4x0.4x0.4 cm3 cube. The imaging depth of each slice is the same as used in Fig. 4. From Fig. 7(a) (dual-zone mesh), we can see that the reconstructed images appear in both fifth and sixth slices, which correspond to the imaging depth of 2.5 cm and 3.0 cm. This result agrees with the target location which has occupied two layers. Other slices are the background regions. The percentage of the maximum reconstructed concentration with respect to its true value (5 μM) is 93.37% and 94.85% in the fifth and the sixth slices, respectively. The corresponding average of the reconstructed concentrations within the FWHM is 68.57% and 70.21%, respectively. The reconstruction results using a single mesh from the same data are shown in Fig. 7(b). The reconstructed images occupied the third, fourth and fifth layers and the percentage of the maximum reconstructed value relative the true value is 15.53%, 48.45% and 18.92%, respectively. These values are close to the results reported in Refs. [11

11. J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

, 13

13. A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003). [CrossRef] [PubMed]

] but are much lower than the values obtained from the dual-zone mesh shown in Fig. 7(a). In addition, we have moved the target to different depths of 1.6 cm and 1.98 cm, respectively, and repeated the imaging processes. Similar results were obtained.

Fig. 7 (a) Images reconstructed from the experimental data with dual-zone mesh. The center of the target is located at X= 0.24 cm, Y= -0.33 cm, and Z=2.65 cm. The target is a 0.4x0.4x0.4 cm3 cube. The imaging depth used for each slice is the same as Fig. 4. The reconstructed images occur at both the fifth and sixth slices, which corresponds to imaging depths of 2.5 cm and 3.0 cm, respectively. (b) The reconstructed images with single mesh from the same data.

5. Summary

Since the analytical solution of a spherical target is used to estimate the structural parameters, this may give certain errors when the target has an irregular shape. Also, we have assumed the concentrations both inside and outside the target were constant in the estimation of the structural parameters. This may results in certain errors in the estimation of the center position of the target. These limitations can be overcome if we use multiple targets in our forward model, which will be discussed in a future publication.

To compare with other’s work (9, 11, 13), we adopted three typical concentration contrasts (1:0, 200:1, and 100:1) that were often used in the literature (see Ref. [13

13. A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003). [CrossRef] [PubMed]

] for a detailed review). In general, the reconstruction accuracy of the structural and functional parameters is affected by the contrast [36

36. X. Li, B. Chance, and A. G. Yodh, “Fluorescent Heterogeneities in turbid media: Limits for detection, characterization and comparison with aAbsorption,” Appl. Opt. 37, 6833–6844 (1998). [CrossRef]

]. For cases of lower contrast, we suggest to use the source-detector pairs with larger separation to avoid the strong background fluorescence signal. With the single detector system used in acquiring the reported experimental data, we could not perform in vivo studies. Currently, we are upgrading the single channel system to multiple detection channels and will perform in vivo studies to further validate this technique.

Appendix

When a spherical fluorescing target with a radius α is embedded into a highly scattering medium with an infinite geometry, the fluorescence fluence detected at rd and excited by a point source at rs with a modulation frequency ω can expressed as [33

33. X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt. 35, 3746–3758 (1996). [CrossRef] [PubMed]

]

ϕflrsrd=ϕoutflrsrd+ϕinflrsrrd
(A1)
ϕoutflrsrd=S0DexDflΛσNbg(1iωτ)14π1(kex2kfl2)×[(GexrsrdGflrsrd)]
(A2)
ϕinsidersrrd=S0ΛσNin1iωτα2kin_ex2kin_fl2
×lm{[kin_fljl(kin_exα)jl(kin_flα)kin_exjl(kin_exα)jl(kin_flα)]
×RlexRlflhl(1)(kout_flrdr)hl(1)(kout_exrsr)Ylm(Ωd,r)Ylm*(Ωs,r)}
(A3)
Gex(fl)rsrd=exp(ikex(fl)rsrd)rsrd
(A4)

Subscripts, “in” and “out”, denote the inside and outside of the spherical inclusion, respectively. Subscripts, “ex” and “fl“, indicate that the variables are measured at the excitation and emission wavelengths, respectively. k is the wave vector. Nbg and Nin are the concentrations of fluorophore in the background and the inclusion, respectively. Rlex , Rlfl , jl , l , hl(1), h´l(1), Ylm , and Y*lm are special functions (see a detailed description about equations (A1-A4) in Ref. [33

33. X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt. 35, 3746–3758 (1996). [CrossRef] [PubMed]

]). Other parameters are same as in Eq. 1. Based on Eqs. (A1–A4) and an extrapolated boundary condition with a semi-infinite geometry [34

34. R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, and B. J. Tromberg, “Bondary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 10, 2727–2741 (1994). [CrossRef]

, 35

35. J. C. J. Passchens and G. W. ’t Hooft, “Influence of boundaries on the imaging of objects in turbid media,” J. Opt. Soc. Am. A 15, 1797–1812 (1998). [CrossRef]

], the amplitude and phase of the fluorescence photon density wave at any position can be obtained and therefore the amplitude ratio R and phase difference ΔΨ at any two positions can be calculated.

Acknowledgments

We acknowledge the funding support of DOD Breast Cancer Program (W81XWH-04-1-0415) and National Institute of Health (R01EB002136).

References and links

1.

T. F. Massoud and S. S. Gambhir, “Molecular imaging in living subjects: seeing fundamental biological processes in a new light,” Genes Dev. 17, 545–580 (2003). [CrossRef] [PubMed]

2.

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

3.

W. Long and M. Vernon, “Optical molecular imaging: time domain advantages with explore OptixTM,” January 2004, Advanced Research Technology Inc. http://www.art.ca/en/products/INOPaper040129.pdf.

4.

J. Skoch, A. Dunn, B. T. Hyman, and B. J. Bacskai, “Development of an optical approach for noninvasive imaging of Alzheimer’s disease pathology,” J. Biomed. Opt. 10, 011007–1–7 (2005). [CrossRef]

5.

A. Yodh and B. Chance, “Spectroscopy and imaging with diffusing light,” Phys. Today 3, 34–40 (1995). [CrossRef]

6.

N. Tromberg, R. Shah, A. Lanning, J. Cerussi, T. Espinoza, L. Pham, L. Svaasand, and J. Butler, “Noninvasive in vivo characterization of breast tumors using photon migration spectroscopy,” Neoplasia 2, 26–40 (2000). [CrossRef] [PubMed]

7.

B. Murphy, Fundamentals of light microscopy and electronic imaging (Wiley-Liss, 2001).

8.

J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near–infrared fluorescence contrast-enhanced imaging,” Photochem. and Photobiol. 77, 420–430 (2003). [CrossRef]

9.

A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, “Fluorescence optical diffusion tomography,” Appl. Opt. 42, 3081–3094 (2003). [CrossRef] [PubMed]

10.

M. A. O’Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, “Fluorescence lifetime imaging in turbid media,” Opt. Lett. 21, 158–160 (1996). [CrossRef]

11.

J. Lee and E. M. Sevick-Muraca, “Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths,” J. Opt. Soc. Am. A 19, 759–771 (2002). [CrossRef]

12.

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. Natl. Acad. Sci. USA 99, 9619–9624 (2002). [CrossRef] [PubMed]

13.

A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, “Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera,” Phys. Med. Biol. 48, 1701–1720 (2003). [CrossRef] [PubMed]

14.

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]

15.

M. Gurfinkel, S Ke, X Wen, C Li, and E. M. Sevick-Muraca, “Near-infrared fluorescence optical imaging and tomography,” Dis. Markers 19,107–121 (2003, 2004).

16.

M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, “Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques,” J. Photochem. and Photobiol. 66, 55–64 (1997). [CrossRef]

17.

E. Graves, R. Weissleder, and V. Ntziachristos, “Fluorescence molecular imaging of small animal tumor models,” Curr. Mol. Med. 4, 419–430 (2004). [CrossRef] [PubMed]

18.

V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, “Fluorescence molecular tomography resolves protease activity in vivo,” Nat. Med. 8, 757–760 (2002). [CrossRef] [PubMed]

19.

U. Mahmood, “Near infrared optical applications in molecular imaging, earlier, more accurate assessment of disease presence, disease course, and efficacy of disease treatment,” IEEE Eng. Med. Biol. Mag. 23, 58–66 (2004). [CrossRef] [PubMed]

20.

E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, “A submillimeter resolution fluorescence molecular imaging system for small animal imaging,” Med. Phys. 30, 901–911 (2003). [CrossRef] [PubMed]

21.

V. Ntziachristos and R. Weissleder, “Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media,” Med. Phys. 29, 803–809 (2002). [CrossRef] [PubMed]

22.

V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, J. L. Josephson, and R. Weissleder, “Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate,” Proc. Natl. Acad. Sci. USA 101, 12294–12299 (2004). [CrossRef] [PubMed]

23.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Experimental fluorescence tomography of tissues with noncontact measurements,” IEEE Trans. Med. Imaging 23, 492–500 (2004). [CrossRef] [PubMed]

24.

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Noncontact optical tomography of turbid media,” Opt. Lett. 28, 1701–1703 (2003). [CrossRef] [PubMed]

25.

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]

26.

D. J. Hawrysz, M. J. Eppstein, J. Lee, and E. M. Sevick-Muraca, “Error consideration in contrast-enhanced three-dimensional optical tomography,” Opt. Lett. 26, 704–706 (2001). [CrossRef]

27.

S. Lam, F. Lesage, and X. Intes, “Tim domain fluorescent diffuse optical tomography: analytical expressions,” Opt. Express 13, 2263–2275 (2005). [CrossRef] [PubMed]

28.

S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, “Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice,” Opt. Express 13, 2564–2577 (2005). [CrossRef] [PubMed]

29.

J. W. Bangerth and E. M. Sevick-Muraca, “Adaptive finite element based tomography for fluorescence optical imaging in tissue,” Opt. Express 12, 5402–5417 (2004). [CrossRef] [PubMed]

30.

Q. Zhu, M. Huang, N. G. Chen, K. Zarfos, B. Jagjivan, M. Kane, P. Hegde, and S. H. Kurtzman, “Ultrasound-guided optical tomographic imaging of malignant and benign breast lesions,” Neoplasia 5, 379–388 (2003). [PubMed]

31.

Q. Zhu, N. G. Chen, and S. Kurtzman, “Imaging tumor angiogenesis using combined near infrared diffusive light and ultrasound,” Opt. Lett. 28, 337–339 (2003). [CrossRef] [PubMed]

32.

N. G. Chen, P. Guo, S. Yan, D. Piao, and Q. Zhu, “Simultaneous near infrared diffusive light and ultrasound imaging,” Appl. Opt. 40, 6367–6280 (2001). [CrossRef]

33.

X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, “Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications,” Appl. Opt. 35, 3746–3758 (1996). [CrossRef] [PubMed]

34.

R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, and B. J. Tromberg, “Bondary conditions for the diffusion equation in radiative transfer,” J. Opt. Soc. Am. A 10, 2727–2741 (1994). [CrossRef]

35.

J. C. J. Passchens and G. W. ’t Hooft, “Influence of boundaries on the imaging of objects in turbid media,” J. Opt. Soc. Am. A 15, 1797–1812 (1998). [CrossRef]

36.

X. Li, B. Chance, and A. G. Yodh, “Fluorescent Heterogeneities in turbid media: Limits for detection, characterization and comparison with aAbsorption,” Appl. Opt. 37, 6833–6844 (1998). [CrossRef]

37.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 10.

38.

N. G. Chen, M. M. Huang, H. Xia, D. Piao, and Q. Zhu, “Portable near-infrared diffusive light imager for breast cancer detection,” J. Biomed. Opt. 9, 504–510 (2004). [CrossRef] [PubMed]

39.

B. Yuan and Q. Zhu, “Emission and absorption properties of indocyanine green in Intralipid solution,” J. Biomed. Opt. 9, 497–503 (2004). [CrossRef] [PubMed]

40.

D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, “Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media,” Appl. Opt. 36, 2260–2272 (1997). [CrossRef] [PubMed]

OCIS Codes
(170.5270) Medical optics and biotechnology : Photon density waves
(170.5280) Medical optics and biotechnology : Photon migration
(260.2510) Physical optics : Fluorescence

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: April 6, 2006
Revised Manuscript: May 26, 2006
Manuscript Accepted: May 30, 2006
Published: August 7, 2006

Virtual Issues
Vol. 1, Iss. 9 Virtual Journal for Biomedical Optics

Citation
Baohong Yuan and Quing Zhu, "Separately reconstructing the structural and functional parameters of a fluorescent inclusion embedded in a turbid medium," Opt. Express 14, 7172-7187 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-16-7172


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References

  1. T. F. Massoud and S. S. Gambhir, "Molecular imaging in living subjects: seeing fundamental biological processes in a new light," Genes Dev. 17, 545-580 (2003). [CrossRef] [PubMed]
  2. R. Weissleder and U. Mahmood, "Molecular Imaging," Radiology 219,316-333 (2001). [PubMed]
  3. W. Long and M. Vernon, "Optical molecular imaging: time domain advantages with explore OptixTM," January 2004, Advanced Research Technology Inc. http://www.art.ca/en/products/INOPaper040129.pdf.
  4. J. Skoch, A. Dunn, B. T. Hyman, and B. J. Bacskai, "Development of an optical approach for noninvasive imaging of Alzheimer’s disease pathology," J. Biomed. Opt. 10, 011007-1-7 (2005). [CrossRef]
  5. A. Yodh and B. Chance, "Spectroscopy and imaging with diffusing light," Phys. Today 3, 34-40 (1995). [CrossRef]
  6. N. Tromberg, R. Shah, A. Lanning, J. Cerussi, T. Espinoza, L. Pham, L. Svaasand, and J. Butler, "Non-invasive in vivo characterization of breast tumors using photon migration spectroscopy," Neoplasia 2, 26-40 (2000). [CrossRef] [PubMed]
  7. B. Murphy, Fundamentals of light microscopy and electronic imaging (Wiley-Liss, 2001).
  8. J. P. Houston, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, "Sensitivity and depth penetration of continuous wave versus frequency-domain photon migration near-infrared fluorescence contrast-enhanced imaging," Photochem. and Photobiol. 77, 420-430 (2003). [CrossRef]
  9. A. B. Milstein, S. Oh, K. J. Webb, C. A. Bouman, Q. Zhang, D. A. Boas, and R. P. Millane, "Fluorescence optical diffusion tomography," Appl. Opt. 42, 3081-3094 (2003). [CrossRef] [PubMed]
  10. M. A. O'Leary, D. A. Boas, X. D. Li, B. Chance, and A. G. Yodh, "Fluorescence lifetime imaging in turbid media," Opt. Lett. 21, 158-160 (1996). [CrossRef]
  11. J. Lee and E. M. Sevick-Muraca, "Three-dimensional fluorescence enhanced optical tomography using referenced frequency domain photon migration measurements at emission and excitation wavelengths," J. Opt. Soc. Am. A 19, 759-771 (2002). [CrossRef]
  12. 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. Natl. Acad. Sci. USA 99, 9619-9624 (2002). [CrossRef] [PubMed]
  13. A. Godavarty, M. J. Eppstein, C. Zhang, S. Theru, A. B. Thompson, M. Gurfinkel, and E. M. Sevick-Muraca, "Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera," Phys. Med. Biol. 48, 1701-1720 (2003). [CrossRef] [PubMed]
  14. 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]
  15. M. Gurfinkel, S Ke, X Wen, C Li, and E. M. Sevick-Muraca, "Near-infrared fluorescence optical imaging and tomography," Dis. Markers 19, 107-121 (2003, 2004).
  16. M. Sevick-Muraca, G. Lopez, J. S. Reynolds, T. L. Troy, and C. L. Hutchinson, "Fluorescence and absorption contrast mechanisms for biomedical optical imaging using frequency-domain techniques," J. Photochem. and Photobiol. 66, 55-64 (1997). [CrossRef]
  17. E. Graves, R. Weissleder, and V. Ntziachristos, "Fluorescence molecular imaging of small animal tumor models," Curr. Mol. Med. 4, 419-430 (2004). [CrossRef] [PubMed]
  18. V. Ntziachristos, C. Tung, C. Bremer, and R. Weissleder, "Fluorescence molecular tomography resolves protease activity in vivo," Nat. Med. 8, 757-760 (2002). [CrossRef] [PubMed]
  19. U. Mahmood, "Near infrared optical applications in molecular imaging, earlier, more accurate assessment of disease presence, disease course, and efficacy of disease treatment," IEEE Eng. Med. Biol. Mag. 23, 58-66 (2004). [CrossRef] [PubMed]
  20. E. Graves, J. Ripoll, R. Weissleder, and V. Ntziachristos, "A submillimeter resolution fluorescence molecular imaging system for small animal imaging," Med. Phys. 30, 901-911 (2003). [CrossRef] [PubMed]
  21. V. Ntziachristos and R. Weissleder, "Charge-coupled-device based scanner for tomography of fluorescent near-infrared probes in turbid media," Med. Phys. 29, 803-809 (2002). [CrossRef] [PubMed]
  22. V. Ntziachristos, E. A. Schellenberger, J. Ripoll, D. Yessayan, E. Graves, A. Bogdanov, J. L. Josephson, and R. Weissleder, "Visualization of antitumor treatment by means of fluorescence molecular tomography with an annexin V-Cy5.5 conjugate," Proc. Natl. Acad. Sci. USA 101, 12294-12299 (2004). [CrossRef] [PubMed]
  23. R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Experimental fluorescence tomography of tissues with noncontact measurements," IEEE Trans. Med. Imaging 23,492-500 (2004). [CrossRef] [PubMed]
  24. R. B. Schulz, J. Ripoll, and V. Ntziachristos, "Noncontact optical tomography of turbid media," Opt. Lett. 28,1701-1703 (2003). [CrossRef] [PubMed]
  25. 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]
  26. D. J. Hawrysz, M. J. Eppstein, J. Lee, and E. M. Sevick-Muraca, "Error consideration in contrast-enhanced three-dimensional optical tomography," Opt. Lett. 26, 704-706 (2001). [CrossRef]
  27. S. Lam, F. Lesage, and X. Intes, "Tim domain fluorescent diffuse optical tomography: analytical expressions," Opt. Express 13, 2263-2275 (2005). [CrossRef] [PubMed]
  28. S. V. Patwardhan, S. R. Bloch, S. Achilefu, and J. P. Culver, "Time-dependent whole-body fluorescence tomography of probe bio-distributions in mice," Opt. Express 13, 2564-2577 (2005). [CrossRef] [PubMed]
  29. J. W. Bangerth and E. M. Sevick-Muraca, "Adaptive finite element based tomography for fluorescence optical imaging in tissue," Opt. Express 12,5402-5417 (2004). [CrossRef] [PubMed]
  30. Q. Zhu, M. Huang, N. G. Chen, K. Zarfos, B. Jagjivan, M. Kane, P. Hegde, and S. H. Kurtzman, "Ultrasound-guided optical tomographic imaging of malignant and benign breast lesions," Neoplasia 5, 379-388 (2003). [PubMed]
  31. Q. Zhu, N. G. Chen, and S. Kurtzman, "Imaging tumor angiogenesis using combined near infrared diffusive light and ultrasound," Opt. Lett. 28, 337-339 (2003). [CrossRef] [PubMed]
  32. N. G. Chen, P. Guo, S. Yan, D. Piao, and Q. Zhu, "Simultaneous near infrared diffusive light and ultrasound imaging," Appl. Opt. 40, 6367-6380 (2001). [CrossRef]
  33. X. D. Li, M. A. O’Leary, D. A. Boas, B. Chance, and A. G. Yodh, "Fluorescent diffuse photon density waves in homogeneous and heterogeneous turbid media: analytic solutions and applications," Appl. Opt. 35, 3746-3758 (1996). [CrossRef] [PubMed]
  34. R. C. Haskell, L. O. Svaasand, T. Tsay, T. Feng, M. S. McAdams, and B. J. Tromberg, "Bondary conditions for the diffusion equation in radiative transfer," J. Opt. Soc. Am. A 10, 2727-2741 (1994). [CrossRef]
  35. J. C. J. Passchens and G. W. ‘t Hooft, "Influence of boundaries on the imaging of objects in turbid media," J. Opt. Soc. Am. A 15, 1797-1812 (1998). [CrossRef]
  36. X. Li, B. Chance, and A. G. Yodh, "Fluorescent Heterogeneities in turbid media: Limits for detection, characterization and comparison with aAbsorption," Appl. Opt. 37,6833-6844 (1998). [CrossRef]
  37. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C (Cambridge U. Press, New York, 1992), Chap. 10.
  38. N. G. Chen, M. M. Huang, H. Xia, D. Piao, and Q. Zhu, ‘‘Portable near-infrared diffusive light imager for breast cancer detection,’’J. Biomed. Opt. 9, 504-510 (2004). [CrossRef] [PubMed]
  39. B. Yuan and Q. Zhu, "Emission and absorption properties of indocyanine green in Intralipid solution," J. Biomed. Opt. 9, 497-503 (2004). [CrossRef] [PubMed]
  40. D. Y. Paithankar, A. U. Chen, B. W. Pogue, M. S. Patterson, and E. M. Sevick-Muraca, "Imaging of fluorescent yield and lifetime from multiply scattered light reemitted from random media," Appl. Opt. 36, 2260-2272 (1997). [CrossRef] [PubMed]

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