## Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates |

Biomedical Optics Express, Vol. 2, Issue 4, pp. 871-886 (2011)

http://dx.doi.org/10.1364/BOE.2.000871

Acrobat PDF (722 KB)

### Abstract

Time-resolved fluorescence optical tomography allows 3-dimensional localization of multiple fluorophores based on lifetime contrast while providing a unique data set for improved resolution. However, to employ the full fluorescence time measurements, a light propagation model that accurately simulates weakly diffused and multiple scattered photons is required. In this article, we derive a computationally efficient Monte Carlo based method to compute time-gated fluorescence Jacobians for the simultaneous imaging of two fluorophores with lifetime contrast. The Monte Carlo based formulation is validated on a synthetic murine model simulating the uptake in the kidneys of two distinct fluorophores with lifetime contrast. Experimentally, the method is validated using capillaries filled with 2.5nmol of ICG and IRDye™800CW respectively embedded in a diffuse media mimicking the average optical properties of mice. Combining multiple time gates in one inverse problem allows the simultaneous reconstruction of multiple fluorophores with increased resolution and minimal crosstalk using the proposed formulation.

© 2011 OSA

## 1. Introduction

*in vivo*fluorescence multiplexing studies are mainly conducted in pre-clinical settings with Fluorescence Reflectance Imaging (FRI) [1

1. V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. **23**(3), 313–320 (2005). [CrossRef] [PubMed]

2. E. M. Sevick-Muraca and J. C. Rasmussen, “Molecular imaging with optics: primer and case for near-infrared fluorescence techniques in personalized medicine,” J. Biomed. Opt. **13**(4), 041303 (2008). [CrossRef] [PubMed]

3. A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. **16**(1), 79–88 (2005). [CrossRef] [PubMed]

4. J. R. Mansfield, “Distinguished photons: a review of *in vivo* spectral fluorescence imaging in small animals,” Curr. Pharm. Biotechnol. **11**(6), 628–638 (2010). [CrossRef] [PubMed]

5. R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D Appl. Phys. **35**(9), R61–R76 (2002). [CrossRef]

*in vivo*.

6. L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express **16**(10), 7214–7223 (2008). [CrossRef] [PubMed]

7. V. Y. Soloviev, C. D’Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. **48**(1), 28–36 (2009). [CrossRef] [PubMed]

8. S. Lam, F. Lesage, and X. Intes, “Time domain fluorescent diffuse optical tomography: analytical expressions,” Opt. Express **13**(7), 2263–2275 (2005). [CrossRef] [PubMed]

9. A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, “Time resolved fluorescence tomography of turbid media based on lifetime contrast,” Opt. Express **14**(25), 12255–12270 (2006). [CrossRef] [PubMed]

10. A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging **27**(8), 1152–1163 (2008). [CrossRef] [PubMed]

11. M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence-lifetime measurements?” Chem. Phys. Lett. **200**(1-2), 199–204 (1992). [CrossRef]

12. F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissues,” Appl. Opt. **32**(4), 554–558 (1993). [CrossRef] [PubMed]

13. J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, “Fluorescence tomographic imaging in turbid media using early-arriving photons and Laplace transforms,” Proc. Natl. Acad. Sci. U.S.A. **94**(16), 8783–8788 (1997). [CrossRef] [PubMed]

14. M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice *in vivo*,” Proc. Natl. Acad. Sci. U.S.A. **105**(49), 19126–19131 (2008). [CrossRef] [PubMed]

17. K. Suhling, P. M. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. **4**(1), 13–22 (2005). [CrossRef] [PubMed]

18. K. Mitra and S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. **38**(1), 188–196 (1999). [CrossRef] [PubMed]

21. M. Xu, W. Cai, M. Lax, and R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **65**(6), 066609 (2002). [CrossRef] [PubMed]

22. W. Cai, M. Xu, and R. R. Alfano, “X. M, and R. Alfano, “Three-dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. **9**(2), 189–198 (2003). [CrossRef]

18. K. Mitra and S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. **38**(1), 188–196 (1999). [CrossRef] [PubMed]

20. M. Sakami, K. Mitra, and T. Vo-Dinh, “Analysis of short-pulse laser photon transport through tissues for optical tomography,” Opt. Lett. **27**(5), 336–338 (2002). [CrossRef] [PubMed]

24. L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, “True scattering coefficients of turbid matter measured by early-time gating,” Opt. Lett. **20**(8), 913–915 (1995). [CrossRef] [PubMed]

15. M. Niedre and V. Ntziachristos, “Comparison of fluorescence tomographic imaging in mice with early-arriving and quasi-continuous-wave photons,” Opt. Lett. **35**(3), 369–371 (2010). [CrossRef] [PubMed]

19. I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. **36**(25), 6529–6538 (1997). [CrossRef] [PubMed]

21. M. Xu, W. Cai, M. Lax, and R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. **65**(6), 066609 (2002). [CrossRef] [PubMed]

22. W. Cai, M. Xu, and R. R. Alfano, “X. M, and R. Alfano, “Three-dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. **9**(2), 189–198 (2003). [CrossRef]

25. A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express **16**(17), 13188–13202 (2008). [CrossRef] [PubMed]

10. A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging **27**(8), 1152–1163 (2008). [CrossRef] [PubMed]

## 2. Methodology

### 2.1. Time-resolved Monte Carlo forward model

*W*′ is given by:

^{−t/τ}over time, where

*τ*is the lifetime of the fluorophore. We can then write the fluorescence intensity measured at

*r*and time

_{d}*t*for an impulsive excitation at

*r*and

_{s}*t*

_{0}= 0 as:

*in silico*studies herein, the synthetic fluorescence measurements were based on this approach.

### 2.2. Calculation of the time-resolved Jacobians

*η*(

*r*), Eq. (4) is written as:

*W*is the lifetime based weight function defined as:

*W*′ can be calculated knowing

*A*(

*r*,

_{s}*r*,

*t*) and

*E*(

*r*,

*r*,

_{d}*t*) explicitly. This time convolution is extremely computationally intensive, and simulations with numerous photons at each position

*r*in the region of interest are required to obtain statistically reliable calculation of

*E*(

*r*,

*r*,

_{d}*t*). Thus this algorithm is computationally inefficient especially in FMT applications where a large number of voxels are considered. However, a more manageable formulation can be derived by considering an assumption commonly employed in FMT, namely that the scattering coefficients are identical at

*λ*and

_{x}*λ*. In the NIR spectral range, the scattering coefficient is expected to vary less than 20% over the Stokes shift gap of organic fluorophores [30

_{m}30. J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. **37**(16), 3586–3593 (1998). [CrossRef] [PubMed]

25. A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express **16**(17), 13188–13202 (2008). [CrossRef] [PubMed]

*i*photon in an excitation simulation that propagates from a discrete source point

^{th}*r*and then detected at the detector position

_{s}*r*at time

_{d}*t*. Following the White Monte Carlo (WMC) [31

31. E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. **13**(4), 041304 (2008). [CrossRef] [PubMed]

*r*at time

*t*

_{s,r}, the weight of the

*i*excitation photon

^{th}*w*at

^{x}_{i}*r*has decreased to:

*w*

_{i,0}is the initial weight of this photon,

*r*(

_{j}*j*= 1, ...,

*p*) are the sub-regions that the photon consequently passes through from

_{i}*r*to

_{s}_{r}, and

*l*(

_{i}*r*) is the path length that the photon passes at

_{j}*r*. Note that the total number of

_{j}*p*is photon dependent and the sub-regions for different photons are not necessarily the same. At

_{i}*r*, the absorbed photon weight is given by:

*η*(

*r*) is then converted to the initial weight of the fluorescence photon. We can calculate the final weight of the fluorescence photon detected at

*r*as:

_{d}*t*

_{r,d}is the time that the photon passes from

*r*to

*r*and

_{d}*r*(

_{j}*j*=

*p*+ 1, ...,

_{i}*q*) is the photon path from

_{i}*r*to

*r*. Note that sum of

_{d}*t*

_{s,r}and

*t*

_{r,d}is the total time

*t*that the excitation photon travels from

*r*till is detected, and that the sub-regions

_{s}*r*(

_{j}*j*= 1, ...,

*q*) denote the total photon path. By summing up

_{i}*n*detected emission photons for

*r*and

_{s}*r*, we can obtain

_{d}*U*′

*defined in Eq. (2). Comparing Eq. (9) to Eq. (2), we have:*

_{F}*r*and detector

_{s}*r*at time

_{d}*t*can be easily calculated using the photon paths and the absorption coefficients. This formulation should be employed in the case that the absorption coefficient at the excitation significantly differs from that at the emission wavelength, which might be the case for wavelengths below 700nm. However, the absorption optical spectra of bio-tissues is relatively flat in tissue in the NIR window [32]. Thus for simplicity, and following standard assumption in FMT, we assume that the absorption coefficients at the excitation and emission wavelengths are identical, that is,

*μ*=

^{x}_{a}*μ*. We therefore obtain:

^{m}_{a}*w*(

^{x}_{i}*r*,

_{s}*r*,

_{d}*t*) is the final weight of the

*i*excitation photon from

^{th}*r*and detected by

_{s}*r*at

_{d}*t*, defined as:

*μ*(

^{x}_{af}*r*)

*l*(

_{i}*r*) is small, which is the case in the voxelized geometry, from Taylor expansion, we can further simplify Eq. (12) to:

33. J. Chen and X. Intes, “Time-gated perturbation Monte Carlo for whole body functional imaging in small animals,” Opt. Express **17**(22), 19566–19579 (2009). [CrossRef] [PubMed]

*W*(

_{k}*k*= 1, ...,

*N*, where

_{F}*N*is the number of species) for different lifetimes

_{F}*τ*(

_{k}*k*= 1, ...,

*N*) according to Eq. (6). This allows for a fast and efficient computational implementation to simultaneously reconstruct multiple fluorophores based on one forward simulation. Note that for simplicity, all the above equations use

_{F}*r*and

_{s}*r*as discrete points, but they can be extended to any illumination or detection strategies applied to complex boundaries by collecting the photons generated or detected inside the areas. In this study, we employed an original broad field illumination strategy which is a new technique that we are currently developing [34

_{d}34. J. Chen, V. Venugopal, F. Lesage, and X. Intes, “Time-resolved diffuse optical tomography with patterned-light illumination and detection,” Opt. Lett. **35**(13), 2121–2123 (2010). [CrossRef] [PubMed]

### 2.3. Inverse problem

35. A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging **24**(10), 1377–1386 (2005). [CrossRef] [PubMed]

*α*incorporates unknown constants associated with wavelength-dependent gains and attenuations that can be measured once for every imaging system,

*M*(

^{m}*r*,

_{s}*r*,

_{d}*t*) is the total signal from all fluorophores with different lifetimes at the emission wavelength measured at the boundary position

*r*and

_{d}*t*excited from the source at

*r*,

_{s}*M*(

^{x}*r*,

_{s}*r*) and

_{d}*U*(

^{x}*r*,

_{s}*r*) are the measured and simulated, respectively, total excitation flux measured by a photo-detector at

_{d}*r*. This normalization efficiently mitigates the dependence of the detected fluorescent signal on the optical properties of the examined tissue [35

_{d}35. A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging **24**(10), 1377–1386 (2005). [CrossRef] [PubMed]

36. C. Vinegoni, D. Razansky, J.-L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. **34**(3), 319–321 (2009). [CrossRef] [PubMed]

*N*is the total number of measurements, that is, the product of the number of S-D pairs and the number of time gates) where it can be used as part of an inverse problem. Similarly, the

_{m}*k*effective quantum yield for the entire imaging volume can be written as

^{th}*N*is the total number of voxels in the region of interest. Overall, the forward problem can be expressed in a matrix form:

_{V}*W*

^{Ω}

_{s,k}is the weight function for the

*s*(

^{th}*s*= 1, ...,

*N*) measurement and the

_{m}*k*fluorophore species over the volume Ω, and

^{th}*β*=

_{s}*α*/

_{s}*U*is the normalization factor for the

^{x}_{s}*s*measurement and the corresponding weight function. The above equation has a general form

^{th}*A*=

_{x}*b*, then

*λ*(

*r*) is a spatially variant regularization parameter to compensate for the spatial dependence of the contrast and resolution in the reconstruction [37

37. B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. **38**(13), 2950–2961 (1999). [CrossRef] [PubMed]

### 2.4. Reconstruction algorithm

*λ*and

_{x}*λ*are assumed to be identical, can be used for computational efficiency. The lifetime-based weight matrices are then calculated by Eq. (6) in [C]. Knowing the experimental measurements, a conjugate gradient method is applied in [D] to minimize the objective function defined in Eq. (17) and obtain the fluorescence yield distribution. The fluorescence measurements in this study are either from an actual experiment or an emission Monte Carlo simulation at

_{m}*λ*based on the absorption probability calculated in [A].

_{m}## 3. In silico study

### 3.1. Simulation setup

*in silico*in a model replicating small animal fluorescence imaging. The Monte Carlo simulations were performed on a mouse geometry with the kidneys and the skin shape extracted from a whole-body atlas [38

38. B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. **52**(3), 577–587 (2007). [CrossRef] [PubMed]

^{3}. The optical properties were set to

*μ*= 0.3cm

^{x}_{ab}^{−1},

*μ*′

*= 25cm*

^{x}_{s}^{−1},

*μ*= 0.36cm

^{m}_{a}^{−1},

*μ*′

*= 20cm*

^{m}_{s}^{−1}over the entire body, to simulate the different optical properties of mouse tissues at different wavelengths in the NIR window [32]. The kidneys were considered to be labeled with two distinct fluorophores with lifetime of 0.5ns (black) and 1ns (red), respectively. The

*μ*for both kidneys were set to 0.1 times of the background absorption coefficient

_{af}*μ*, and the quantum yield was set to 1. 36 bar-shaped patterns were used as the source with each pattern illuminating half of the imaged surface along the x and y axes independently (Fig. 2(b)). A grid of 64 point detectors in transmission geometry were arranged covering a 31mm×27mm×18mm volume spanning the abdomen. The sources and detectors are projected to the surface along the

^{x}_{ab}*z*axis. The initial positions of the photons were randomly spanned (that is, uniformly distributed) over the illuminated area to accommodate the broad field illumination. The detectors had a 2mm separation along the

*y*axis and a 2.2mm separation along the

*x*axis with a radius of 1mm.

### 3.2. Gate information content for fluorophore multiplexing

*η*

_{1}is defined as

*Q*

_{1}= max[

*η*

_{1}(Ω

_{1})]/

*H*

_{1}(Ω

_{1}), where Ω

_{1}denotes the known location of the inclusions with lifetime

*τ*

_{1}= 0.5ns and

*H*

_{1}denotes the expected value of

*η*

_{1}. The crosstalk is defined as

*X*

_{1}= max[

*η*

_{2}(Ω

_{1})]/max[

*η*

_{1}(Ω

_{1})] to quantify the separability of the two inclusions with lifetime contrast. The quantification and yield crosstalk for the 1ns component was similarly evaluated. Note that

*Q*and

*X*are overestimated using the definitions based on only maximum value in the region of interest. The spatial resolution is measured as the full width at half maximum (FWHM) of the point spread functions (PSF). PSFs are created by simulating a perturbation at a single point. The simulated perturbation,

*x*, is a vector of zeros except for one target pixel at the center of the reconstructed volume with a value of one. We then generated simulated measurements

_{sim}*y*=

_{sim}*Ax*and reconstructed the image. The cube root of the volume of voxels within half the peak reconstructed value is defined as FWHM. Plots of the quantification, crosstalk and FWHM of PSFs are shown in Fig. 4. Note that for all these reconstructions, the inverse problem size was identical and that the same iteration number (150) was used in the CG algorithm. This ensured consistency between the different reconstructions.

_{sim}*t*= 2.8ns) results in the most accurate quantification and the least crosstalk for the compound with the longer lifetime, implying the necessity of the late gates for effective separation of the objects with lifetime contrast. It is impossible to achieve the best quantification and minimum crosstalk using only the early gates because of the comparable contribution of the two fluorophores at the early time points (Fig. 3). As expected, the steadily increasing FWHM of PSFs with time indicates that the early gates provide improved resolution when compared to the late gates [7

7. V. Y. Soloviev, C. D’Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. **48**(1), 28–36 (2009). [CrossRef] [PubMed]

15. M. Niedre and V. Ntziachristos, “Comparison of fluorescence tomographic imaging in mice with early-arriving and quasi-continuous-wave photons,” Opt. Lett. **35**(3), 369–371 (2010). [CrossRef] [PubMed]

*gate (*

_{th}*t*= 0.2ns) does not follow the trend due to the poor statistics of the weight matrix at the early gates, where the number of detected photons is insufficient to generate reliable statistics. It results in increased artifacts in the reconstructions when using very early gates. From the above analysis, we conclude that multiple fluorophores with lifetime contrast cannot be efficiently separated with minimal crosstalk if a single gate of the TPSF is used.

### 3.3. Lifetime multiplexing tomography based on multiple gates

## 4. Experiment

### 4.1. Diffuse optical tomography system

16. V. Venugopal, J. Chen, F. Lesage, and X. Intes, “Full-field time-resolved fluorescence tomography of small animals,” Opt. Lett. **35**(19), 3189–3191 (2010). [CrossRef] [PubMed]

40. V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using wide-field excitation,” Biomed. Opt. Express **1**(1), 143–156 (2010). [CrossRef] [PubMed]

41. C. D’Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D Appl. Phys. **36**(14), 1675–1681 (2003). [CrossRef]

### 4.2. Phantom setup

*τ*

_{1}= 0.45ns) and IRDye 800CW (

*τ*

_{2}= 0.8ns) dissolved in 180

*µ*L ethanol, respectively. The effective quantum yields of the two tubes was externally calibrated and tube I was found to have 1.5 times the yield of tube II. The tank was filled with a mixture of Intralipid-20% (Sigma-Aldrich) and a water-soluble NIR Dye (Epolight 2717, Epolin) diluted in water to simulate the average optical properties (

*μ*= 0.16cm

_{a}^{−1}and

*μ*′

*= 17cm*

_{s}^{−1}) of murine models.

### 4.3. Experimental reconstruction

*τ*

_{1}= 0.45ns (ICG) and the longer lifetime at

*τ*

_{2}= 0.8ns (IRdye™) using Eq. (6). In

*in vivo*applications, the lifetime of the dye within a control animal should be separately estimated due to the possible fluctuation of the fluorophore lifetime under different micro environments.

*in silico*results. The two objects are separated with crosstalk

*X*

_{1}= 28.51% and

*X*

_{2}= 26.24%. The ratio of the mean reconstructed yields within the 50% isovolume of tube I and II was found to be 1.52. The average dimension of the reconstructed tubes was 34.5% larger along the

*x*axis and 85% larger along the

*z*axis (depth). This difference in resolution is due to the transmittance arrangement of the S-D pairs, which smears the resolution along the

*z*axis. Hence, the diameter of the reconstructed isosurface is approximately 2 times bigger than the actual diameter due to the loss in the depth dimension, which can be attributed to the high scattering, and to the position of the two objects in the middle of the phantom, where the weight matrix has the least sensitivity. The CW reconstruction using one wavelength presented in Fig. 7(b), shows poor resolution (103% increase in depth) and no separation (100% crosstalk).

## 5. Discussion

*in silico*and experimental studies. The formulation is computationally efficient and offers three distinct advantages. First, once the excitation simulation is computed, it can be used to rapidly calculate the weight functions for multiple fluorophores with different lifetimes. Thus this method becomes attractive for lifetime multiplexed studies. Second, this scheme can be extended to multi-spectral imaging where the absorption coefficients can be modified in Eq. (14) to accommodate the changes in extinction coefficients at different wavelengths without the need of simulating another set of absorption coefficients. Third, using Eq. (11) the difference between

*μ*and

^{x}_{a}*μ*can be taken into account, noticing that there are no significant increase of computational burden using Eqs. (11) and (14) thanks to the WMC method [31

^{m}_{a}31. E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. **13**(4), 041304 (2008). [CrossRef] [PubMed]

*in silico*study and an improvement less than 5% was achieved using the corrected

*μ*, implying the proposed approach is robust for reconstructions in the NIR window. On the other hand, the scattering coefficient cannot be rescaled like the absorption coefficient due to the transmittance geometry employed in this work [31

^{m}_{a}31. E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. **13**(4), 041304 (2008). [CrossRef] [PubMed]

*μ*varies more slowly (seldom more than 20%) over the spectral range in the NIR window [30

_{s}30. J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. **37**(16), 3586–3593 (1998). [CrossRef] [PubMed]

*μ*will result in less than 15% error in diffuse optical tomography [42

_{s}42. X. Cheng and D. Boas, “Systematic diffuse optical image errors resulting from uncertainty in the background optical properties,” Opt. Express **4**(8), 299–307 (1999). [CrossRef] [PubMed]

15. M. Niedre and V. Ntziachristos, “Comparison of fluorescence tomographic imaging in mice with early-arriving and quasi-continuous-wave photons,” Opt. Lett. **35**(3), 369–371 (2010). [CrossRef] [PubMed]

*in vivo*.

## 6. Conclusion

*in silico*and experimental studies demonstrate that this new formulation can simultaneously reconstruct two fluorophores with improved resolution and reduced crosstalk when multiple gates are employed, whereas the two fluorophores cannot be resolved if only early gates are employed.

## Acknowledgment

## References and links

1. | V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. |

2. | E. M. Sevick-Muraca and J. C. Rasmussen, “Molecular imaging with optics: primer and case for near-infrared fluorescence techniques in personalized medicine,” J. Biomed. Opt. |

3. | A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. |

4. | J. R. Mansfield, “Distinguished photons: a review of |

5. | R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D Appl. Phys. |

6. | L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express |

7. | V. Y. Soloviev, C. D’Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. |

8. | S. Lam, F. Lesage, and X. Intes, “Time domain fluorescent diffuse optical tomography: analytical expressions,” Opt. Express |

9. | A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, “Time resolved fluorescence tomography of turbid media based on lifetime contrast,” Opt. Express |

10. | A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging |

11. | M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence-lifetime measurements?” Chem. Phys. Lett. |

12. | F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissues,” Appl. Opt. |

13. | J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, “Fluorescence tomographic imaging in turbid media using early-arriving photons and Laplace transforms,” Proc. Natl. Acad. Sci. U.S.A. |

14. | M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice |

15. | M. Niedre and V. Ntziachristos, “Comparison of fluorescence tomographic imaging in mice with early-arriving and quasi-continuous-wave photons,” Opt. Lett. |

16. | V. Venugopal, J. Chen, F. Lesage, and X. Intes, “Full-field time-resolved fluorescence tomography of small animals,” Opt. Lett. |

17. | K. Suhling, P. M. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. |

18. | K. Mitra and S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. |

19. | I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. |

20. | M. Sakami, K. Mitra, and T. Vo-Dinh, “Analysis of short-pulse laser photon transport through tissues for optical tomography,” Opt. Lett. |

21. | M. Xu, W. Cai, M. Lax, and R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. |

22. | W. Cai, M. Xu, and R. R. Alfano, “X. M, and R. Alfano, “Three-dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. |

23. | J. C. Rasmussen, T. Pan, A. Joshi, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Comparison of radiative transport, Monte Carlo, and diffusion forward models for small animal optical tomography,” in“2007 IEEE ISBI,” (2007), pp. 824–827. |

24. | L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, “True scattering coefficients of turbid matter measured by early-time gating,” Opt. Lett. |

25. | A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express |

26. | J. Swartling, A. Pifferi, A. M. K. Enejder, and S. Andersson-Engels, “Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues,” J. Opt. Soc. Am. A |

27. | D. A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express |

28. | X. Zhang, C. Badea, M. Jacob, and G. A. Johnson, “Development of a noncontact 3-d fluorescence tomography system for small animal |

29. | A. J. Welch, C. M. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. |

30. | J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. |

31. | E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. |

32. | A. Roggan, K. Dorschel, O. Minet, D. Wolff, and G. Muller, “The optical properties of biological tissue in the near infrared wavelength range : review and measurements,” in |

33. | J. Chen and X. Intes, “Time-gated perturbation Monte Carlo for whole body functional imaging in small animals,” Opt. Express |

34. | J. Chen, V. Venugopal, F. Lesage, and X. Intes, “Time-resolved diffuse optical tomography with patterned-light illumination and detection,” Opt. Lett. |

35. | A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging |

36. | C. Vinegoni, D. Razansky, J.-L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. |

37. | B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. |

38. | B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. |

39. | “Computational Center for Nanotechnology Innovations (CCNI),” http://www.rpi.edu/research/ccni/. |

40. | V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using wide-field excitation,” Biomed. Opt. Express |

41. | C. D’Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D Appl. Phys. |

42. | X. Cheng and D. Boas, “Systematic diffuse optical image errors resulting from uncertainty in the background optical properties,” Opt. Express |

**OCIS Codes**

(110.6960) Imaging systems : Tomography

(170.3010) Medical optics and biotechnology : Image reconstruction techniques

(170.3650) Medical optics and biotechnology : Lifetime-based sensing

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

(110.1758) Imaging systems : Computational imaging

**ToC Category:**

Image Reconstruction and Inverse Problems

**History**

Original Manuscript: January 4, 2011

Revised Manuscript: February 25, 2011

Manuscript Accepted: February 26, 2011

Published: March 14, 2011

**Citation**

Jin Chen, Vivek Venugopal, and Xavier Intes, "Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates," Biomed. Opt. Express **2**, 871-886 (2011)

http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-2-4-871

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### References

- V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23(3), 313–320 (2005). [CrossRef] [PubMed]
- E. M. Sevick-Muraca and J. C. Rasmussen, “Molecular imaging with optics: primer and case for near-infrared fluorescence techniques in personalized medicine,” J. Biomed. Opt. 13(4), 041303 (2008). [CrossRef] [PubMed]
- A. H. Hielscher, “Optical tomographic imaging of small animals,” Curr. Opin. Biotechnol. 16(1), 79–88 (2005). [CrossRef] [PubMed]
- J. R. Mansfield, “Distinguished photons: a review of in vivo spectral fluorescence imaging in small animals,” Curr. Pharm. Biotechnol. 11(6), 628–638 (2010). [CrossRef] [PubMed]
- R. Cubeddu, D. Comelli, C. D’Andrea, P. Taroni, and G. Valentini, “Time-resolved fluorescence imaging in biology and medicine,” J. Phys. D Appl. Phys. 35(9), R61–R76 (2002). [CrossRef]
- L. Zhang, F. Gao, H. He, and H. Zhao, “Three-dimensional scheme for time-domain fluorescence molecular tomography based on Laplace transforms with noise-robust factors,” Opt. Express 16(10), 7214–7223 (2008). [CrossRef] [PubMed]
- V. Y. Soloviev, C. D’Andrea, G. Valentini, R. Cubeddu, and S. R. Arridge, “Combined reconstruction of fluorescent and optical parameters using time-resolved data,” Appl. Opt. 48(1), 28–36 (2009). [CrossRef] [PubMed]
- S. Lam, F. Lesage, and X. Intes, “Time domain fluorescent diffuse optical tomography: analytical expressions,” Opt. Express 13(7), 2263–2275 (2005). [CrossRef] [PubMed]
- A. T. N. Kumar, S. B. Raymond, G. Boverman, D. A. Boas, and B. J. Bacskai, “Time resolved fluorescence tomography of turbid media based on lifetime contrast,” Opt. Express 14(25), 12255–12270 (2006). [CrossRef] [PubMed]
- A. T. N. Kumar, S. B. Raymond, A. K. Dunn, B. J. Bacskai, and D. A. Boas, “A time domain fluorescence tomography system for small animal imaging,” IEEE Trans. Med. Imaging 27(8), 1152–1163 (2008). [CrossRef] [PubMed]
- M. Köllner and J. Wolfrum, “How many photons are necessary for fluorescence-lifetime measurements?” Chem. Phys. Lett. 200(1-2), 199–204 (1992). [CrossRef]
- F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissues,” Appl. Opt. 32(4), 554–558 (1993). [CrossRef] [PubMed]
- J. Wu, L. Perelman, R. R. Dasari, and M. S. Feld, “Fluorescence tomographic imaging in turbid media using early-arriving photons and Laplace transforms,” Proc. Natl. Acad. Sci. U.S.A. 94(16), 8783–8788 (1997). [CrossRef] [PubMed]
- M. J. Niedre, R. H. de Kleine, E. Aikawa, D. G. Kirsch, R. Weissleder, and V. Ntziachristos, “Early photon tomography allows fluorescence detection of lung carcinomas and disease progression in mice in vivo,” Proc. Natl. Acad. Sci. U.S.A. 105(49), 19126–19131 (2008). [CrossRef] [PubMed]
- M. Niedre and V. Ntziachristos, “Comparison of fluorescence tomographic imaging in mice with early-arriving and quasi-continuous-wave photons,” Opt. Lett. 35(3), 369–371 (2010). [CrossRef] [PubMed]
- V. Venugopal, J. Chen, F. Lesage, and X. Intes, “Full-field time-resolved fluorescence tomography of small animals,” Opt. Lett. 35(19), 3189–3191 (2010). [CrossRef] [PubMed]
- K. Suhling, P. M. French, and D. Phillips, “Time-resolved fluorescence microscopy,” Photochem. Photobiol. Sci. 4(1), 13–22 (2005). [CrossRef] [PubMed]
- K. Mitra and S. Kumar, “Development and comparison of models for light-pulse transport through scattering-absorbing media,” Appl. Opt. 38(1), 188–196 (1999). [CrossRef] [PubMed]
- I. V. Yaroslavsky, A. N. Yaroslavsky, V. V. Tuchin, and H.-J. Schwarzmaier, “Effect of the scattering delay on time-dependent photon migration in turbid media,” Appl. Opt. 36(25), 6529–6538 (1997). [CrossRef] [PubMed]
- M. Sakami, K. Mitra, and T. Vo-Dinh, “Analysis of short-pulse laser photon transport through tissues for optical tomography,” Opt. Lett. 27(5), 336–338 (2002). [CrossRef] [PubMed]
- M. Xu, W. Cai, M. Lax, and R. R. Alfano, “Photon migration in turbid media using a cumulant approximation to radiative transfer,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(6), 066609 (2002). [CrossRef] [PubMed]
- W. Cai, M. Xu, and R. R. Alfano, “X. M, and R. Alfano, “Three-dimensional radiative transfer tomography for turbid media,” IEEE J. Sel. Top. Quantum Electron. 9(2), 189–198 (2003). [CrossRef]
- J. C. Rasmussen, T. Pan, A. Joshi, T. Wareing, J. McGhee, and E. M. Sevick-Muraca, “Comparison of radiative transport, Monte Carlo, and diffusion forward models for small animal optical tomography,” in“2007 IEEE ISBI,” (2007), pp. 824–827.
- L. Wang, X. Liang, P. Galland, P. P. Ho, and R. R. Alfano, “True scattering coefficients of turbid matter measured by early-time gating,” Opt. Lett. 20(8), 913–915 (1995). [CrossRef] [PubMed]
- A. Liebert, H. Wabnitz, N. Zołek, and R. Macdonald, “Monte Carlo algorithm for efficient simulation of time-resolved fluorescence in layered turbid media,” Opt. Express 16(17), 13188–13202 (2008). [CrossRef] [PubMed]
- J. Swartling, A. Pifferi, A. M. K. Enejder, and S. Andersson-Engels, “Accelerated Monte Carlo models to simulate fluorescence spectra from layered tissues,” J. Opt. Soc. Am. A 20(4), 714–727 (2003). [CrossRef] [PubMed]
- D. A. Boas, J. P. Culver, J. J. Stott, and A. K. Dunn, “Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head,” Opt. Express 10(3), 159–170 (2002). [PubMed]
- X. Zhang, C. Badea, M. Jacob, and G. A. Johnson, “Development of a noncontact 3-d fluorescence tomography system for small animal in vivo imaging,” SPIE 7171, 71910D (2009).
- A. J. Welch, C. M. Gardner, R. Richards-Kortum, E. Chan, G. Criswell, J. Pfefer, and S. Warren, “Propagation of fluorescent light,” Lasers Surg. Med. 21(2), 166–178 (1997). [CrossRef] [PubMed]
- J. R. Mourant, J. P. Freyer, A. H. Hielscher, A. A. Eick, D. Shen, and T. M. Johnson, “Mechanisms of light scattering from biological cells relevant to noninvasive optical-tissue diagnostics,” Appl. Opt. 37(16), 3586–3593 (1998). [CrossRef] [PubMed]
- E. Alerstam, S. Andersson-Engels, and T. Svensson, “White Monte Carlo for time-resolved photon migration,” J. Biomed. Opt. 13(4), 041304 (2008). [CrossRef] [PubMed]
- A. Roggan, K. Dorschel, O. Minet, D. Wolff, and G. Muller, “The optical properties of biological tissue in the near infrared wavelength range : review and measurements,” in Laser-induced Interstitial Thermotherapy (SPIE, Bellingham WA, Etats-Unis, 1995), pp. 10–44.
- J. Chen and X. Intes, “Time-gated perturbation Monte Carlo for whole body functional imaging in small animals,” Opt. Express 17(22), 19566–19579 (2009). [CrossRef] [PubMed]
- J. Chen, V. Venugopal, F. Lesage, and X. Intes, “Time-resolved diffuse optical tomography with patterned-light illumination and detection,” Opt. Lett. 35(13), 2121–2123 (2010). [CrossRef] [PubMed]
- A. Soubret, J. Ripoll, and V. Ntziachristos, “Accuracy of fluorescent tomography in the presence of heterogeneities: study of the normalized Born ratio,” IEEE Trans. Med. Imaging 24(10), 1377–1386 (2005). [CrossRef] [PubMed]
- C. Vinegoni, D. Razansky, J.-L. Figueiredo, M. Nahrendorf, V. Ntziachristos, and R. Weissleder, “Normalized Born ratio for fluorescence optical projection tomography,” Opt. Lett. 34(3), 319–321 (2009). [CrossRef] [PubMed]
- B. W. Pogue, T. O. McBride, J. Prewitt, U. L. Osterberg, and K. D. Paulsen, “Spatially variant regularization improves diffuse optical tomography,” Appl. Opt. 38(13), 2950–2961 (1999). [CrossRef] [PubMed]
- B. Dogdas, D. Stout, A. F. Chatziioannou, and R. M. Leahy, “Digimouse: a 3D whole body mouse atlas from CT and cryosection data,” Phys. Med. Biol. 52(3), 577–587 (2007). [CrossRef] [PubMed]
- “Computational Center for Nanotechnology Innovations (CCNI),” http://www.rpi.edu/research/ccni/ .
- V. Venugopal, J. Chen, and X. Intes, “Development of an optical imaging platform for functional imaging of small animals using wide-field excitation,” Biomed. Opt. Express 1(1), 143–156 (2010). [CrossRef] [PubMed]
- C. D’Andrea, D. Comelli, A. Pifferi, A. Torricelli, G. Valentini, and R. Cubeddu, “Time-resolved optical imaging through turbid media using a fast data acquisition system based on a gated CCD camera,” J. Phys. D Appl. Phys. 36(14), 1675–1681 (2003). [CrossRef]
- X. Cheng and D. Boas, “Systematic diffuse optical image errors resulting from uncertainty in the background optical properties,” Opt. Express 4(8), 299–307 (1999). [CrossRef] [PubMed]

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