Abstract

We introduce a novel approach for localizing a plurality of discrete point-like fluorescent inclusions embedded in a thick turbid medium using time-domain measurements. The approach uses early photon information contained in measured time-of-flight distributions originating from fluorescence emission. Fluorescence time point-spread functions (FTPSFs) are acquired with ultrafast time-correlated single photon counting after short pulse laser excitation. Early photon arrival times are extracted from the FTPSFs obtained from several source-detector positions. Each source-detector measurement allows defining a geometrical locus where an inclusion is to be found. These loci take the form of ovals in 2D or ovoids in 3D. From these loci a map can be built, with the maxima thereof corresponding to positions of inclusions. This geometrical approach is supported by Monte Carlo simulations performed for biological tissue-like media with embedded fluorescent inclusions. To validate the approach, several experiments are conducted with a homogeneous phantom mimicking tissue optical properties. In the experiments, inclusions filled with indocyanine green are embedded in the phantom and the fluorescence response to a short pulse of excitation laser is recorded. With our approach, several inclusions can be localized with low millimeter positional error. Our results support the approach as an accurate, efficient, and fast method for localizing fluorescent inclusions embedded in highly turbid media mimicking biological tissues. Further Monte Carlo simulations on a realistic mouse model show the feasibility of the technique for small animal imaging.

© 2013 Optical Society of America

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2013

N. Valim, J. Brock, M. Leeser, and M. Niedre, “The effect of temporal impulse response on experimental reduction of photon scatter in time-resolved diffuse optical tomography,” Phys. Med. Biol. 58, 335–349 (2013).
[CrossRef]

X. Wang, B. Zhang, X. Cao, F. Liu, J. Luo, and J. Bai, “Acceleration of early photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).
[CrossRef]

2012

S. Baldwin, “Compute Canada: advancing computational research,” J. Phys. 341, 012001 (2012).
[CrossRef]

Q. Fang and D. R. Kaeli, “Accelerating mesh-based Monte Carlo method on modern CPU architectures,” Biomed. Opt. Express 3, 3223–3230 (2012).
[CrossRef]

E. Lapointe, J. Pichette, and Y. Bérubé-Lauzière, “A multi-view time-domain noncontact diffuse optical tomography scanner with dual wavelength detection for intrinsic and fluorescence small animal imaging,” Rev. Sci. Instrum. 83, 063703 (2012).
[CrossRef]

R. W. Holt, K. M. Tichauer, H. Dehghani, B. W. Pogue, and F. Leblond, “Multiple-gate time domain diffuse fluorescence tomography allows more sparse tissue sampling without compromising image quality,” Opt. Lett. 37, 2559–2561 (2012).
[CrossRef]

A. A. Bogdanov, V. Metelev, S. Zhang, and A. T. N. Kumar, “Sensing of transcription factor binding via cyanine dye pair fluorescence lifetime changes,” Mol. BioSyst. 8, 2166–2173 (2012).
[CrossRef]

C. J. Goergen, H. H. Chen, A. Bogdanov, D. E. Sosnovik, and A. T. N. Kumar, “In vivo fluorescence lifetime detection of an activatable probe in infarcted myocardium,” J. Biomed. Opt. 17, 056001 (2012).
[CrossRef]

M. B. Aldrich, R. Guilliod, C. E. Fife, E. A. Maus, L. Smith, J. C. Rasmussen, and E. M. Sevick-Muraca, “Lymphatic abnormalities in the normal contralateral arms of subjects with breast cancer-related lymphedema as assessed by near-infrared fluorescent imaging,” Biomed. Opt. Express 3, 1256–1265 (2012).
[CrossRef]

2011

2010

2009

J. Pichette, E. Lapointe, and Y. Bérubé-Lauzière, “Three-dimensional localization of discrete fluorescent inclusions from multiple tomographic projections in the time-domain,” Proc. SPIE 7174, 71741A (2009).
[CrossRef]

F. Leblond, H. Dehghani, D. Kepshire, and B. W. Pogue, “Early photon fluorescence tomography: spatial resolution improvements and noise stability considerations,” J. Opt. Soc. Am. A 26, 1444–1457 (2009).
[CrossRef]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
[CrossRef]

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

2008

J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
[CrossRef]

M. J. Niedre, R. 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. USA. 105, 19126–19131 (2008).
[CrossRef]

D. C. Comsa, T. J. Farrell, and M. S. Patterson, “Quantitative fluorescence imaging of point-like sources in small animals,” Phys. Med. Biol. 53, 5797–5814 (2008).
[CrossRef]

S.-H. Han and D. J. Hall, “Estimating the depth and lifetime of a fluorescent inclusion in a turbid medium using a simple time-domain optical method,” Opt. Lett. 33, 1035–1037 (2008).
[CrossRef]

V. Robichaud and Y. Bérubé-Lauzière, “A wavefront intersection algorithm for time-of-flight noncontact diffuse optical tomography of fluorescent inclusions in thick turbid media,” Proc. SPIE 6796, 67960T (2008).
[CrossRef]

J. Pichette, E. Lapointe, and Y. Bérubé-Lauzière, “Time-domain 3D localization of fluorescent inclusions in a thick scattering medium,” Proc. SPIE 7099, 709907 (2008).
[CrossRef]

2007

A. Laidevant, A. Da Silva, M. Berger, J. Boutet, J.-M. Dinten, and A. Boccara, “Analytical method for localizing a fluorescent inclusion in a turbid medium,” Appl. Opt. 46, 2131–2137 (2007).
[CrossRef]

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

Y. Bérubé-Lauzière and V. Robichaud, “Time-of-flight noncontact fluorescence diffuse optical tomography with numerical constant fraction discrimination,” Proc. SPIE 6629, 66290Y (2007).

J. Rao, A. Dragulescu-Andrasi, and H. Yao, “Fluorescence imaging in vivo: recent advances,” Curr. Opin. Biotechnol. 18, 17–25 (2007).
[CrossRef]

A. Corlu, R. Choe, T. Durduran, M. Rosen, M. Schweiger, S. Arridge, M. Schnall, and A. Yodh, “Three dimensional in vivo fluorescence diffuse optical tomography of breast cancer in humans,” Opt. Express 15, 6696–6716 (2007).
[CrossRef]

2006

V. Ntziachristos, “Fluorescence molecular imaging,” Annu. Rev. Biomed. Eng. 8, 1–33 (2006).
[CrossRef]

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

A. T. 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, 12255–12270 (2006).
[CrossRef]

Y. Bérubé-Lauzière and V. Robichaud, “Time-resolved fluorescence measurements for diffuse optical tomography using ultrafast time-correlated single photon counting,” Proc. SPIE 6372, 637206 (2006).
[CrossRef]

2005

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

A. Klose, V. Ntziachristos, and A. Hielscher, “The inverse source problem based on the radiative transfer equation in optical molecular imaging,” J. Comput. Phys. 202, 323–345 (2005).
[CrossRef]

2004

2003

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef]

2002

2001

2000

R. Rajagopalan, P. Uetrecht, J. Bugaj, S. Achilefu, and R. Dorshow, “Stabilization of the optical tracer agent indocyanine green using noncovalent interactions,” Photochem. Photobiol. 71, 347–350 (2000).
[CrossRef]

1997

J. Wu, L. Perelman, R. Dasari, and M. Feld, “Fluorescence tomographic imaging in turbid media using early arriving photons and laplace transforms,” PNAS Med. Sci. 94, 8783–8788 (1997).

1996

1995

Achilefu, S.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

R. Rajagopalan, P. Uetrecht, J. Bugaj, S. Achilefu, and R. Dorshow, “Stabilization of the optical tracer agent indocyanine green using noncovalent interactions,” Photochem. Photobiol. 71, 347–350 (2000).
[CrossRef]

Aikawa, E.

M. J. Niedre, R. 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. USA. 105, 19126–19131 (2008).
[CrossRef]

Akers, W.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

Aldrich, M. B.

Arridge, S.

Bacskai, B. J.

Bai, J.

X. Wang, B. Zhang, X. Cao, F. Liu, J. Luo, and J. Bai, “Acceleration of early photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).
[CrossRef]

B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
[CrossRef]

Baldwin, S.

S. Baldwin, “Compute Canada: advancing computational research,” J. Phys. 341, 012001 (2012).
[CrossRef]

Becker, W.

W. Becker, Advanced Time-Correlated Single Photon Counting Techniques (Springer, 2005).

W. Becker, The bh TCSPC Handbook, 5th ed. (Becker&Hickl GmbH, 2012).

Berger, M.

Bérubé-Lauzière, Y.

E. Lapointe, J. Pichette, and Y. Bérubé-Lauzière, “A multi-view time-domain noncontact diffuse optical tomography scanner with dual wavelength detection for intrinsic and fluorescence small animal imaging,” Rev. Sci. Instrum. 83, 063703 (2012).
[CrossRef]

J. Bouza Domínguez and Y. Bérubé-Lauzière, “Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations,” Biomed. Opt. Express 2, 817–837 (2011).
[CrossRef]

J. Pichette, E. Lapointe, and Y. Bérubé-Lauzière, “Three-dimensional localization of discrete fluorescent inclusions from multiple tomographic projections in the time-domain,” Proc. SPIE 7174, 71741A (2009).
[CrossRef]

J. Pichette, E. Lapointe, and Y. Bérubé-Lauzière, “Time-domain 3D localization of fluorescent inclusions in a thick scattering medium,” Proc. SPIE 7099, 709907 (2008).
[CrossRef]

V. Robichaud and Y. Bérubé-Lauzière, “A wavefront intersection algorithm for time-of-flight noncontact diffuse optical tomography of fluorescent inclusions in thick turbid media,” Proc. SPIE 6796, 67960T (2008).
[CrossRef]

Y. Bérubé-Lauzière and V. Robichaud, “Time-of-flight noncontact fluorescence diffuse optical tomography with numerical constant fraction discrimination,” Proc. SPIE 6629, 66290Y (2007).

Y. Bérubé-Lauzière and V. Robichaud, “Time-resolved fluorescence measurements for diffuse optical tomography using ultrafast time-correlated single photon counting,” Proc. SPIE 6372, 637206 (2006).
[CrossRef]

J. Bouza-Domínguez and Y. Bérubé-Lauzière, “Radiative transfer and optical imaging in biological media by low-order transport approximations: the simplified spherical polynomials (SP) approach,” in Light Scattering Reviews 8 (Springer/Praxis Publishing Ltd., 2013), Chap. 6, pp. 269–315.

Boas, D.

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

D. Boas, “Diffuse photon probes of structural and dynamical properties of turbid media: theory and biomedical applications,” Ph.D. thesis (University of Pennsylvania, 1996).

Boas, D. A.

A. T. 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, 12255–12270 (2006).
[CrossRef]

Q. Fang and D. A. Boas, “Tetrahedral mesh generation from volumetric binary and gray-scale images,” in Proceedings of the Sixth IEEE International Conference on Symposium on Biomedical Imaging: From Nano to Macro (IEEE, 2009), pp. 1142–1145.

Boccara, A.

Bogdanov, A.

C. J. Goergen, H. H. Chen, A. Bogdanov, D. E. Sosnovik, and A. T. N. Kumar, “In vivo fluorescence lifetime detection of an activatable probe in infarcted myocardium,” J. Biomed. Opt. 17, 056001 (2012).
[CrossRef]

Bogdanov, A. A.

A. A. Bogdanov, V. Metelev, S. Zhang, and A. T. N. Kumar, “Sensing of transcription factor binding via cyanine dye pair fluorescence lifetime changes,” Mol. BioSyst. 8, 2166–2173 (2012).
[CrossRef]

Boutet, J.

Bouza Domínguez, J.

Bouza-Domínguez, J.

J. Bouza-Domínguez and Y. Bérubé-Lauzière, “Radiative transfer and optical imaging in biological media by low-order transport approximations: the simplified spherical polynomials (SP) approach,” in Light Scattering Reviews 8 (Springer/Praxis Publishing Ltd., 2013), Chap. 6, pp. 269–315.

Boverman, G.

Brock, J.

N. Valim, J. Brock, M. Leeser, and M. Niedre, “The effect of temporal impulse response on experimental reduction of photon scatter in time-resolved diffuse optical tomography,” Phys. Med. Biol. 58, 335–349 (2013).
[CrossRef]

N. Valim, J. Brock, and M. Niedre, “Experimental measurement of time-dependant photon scatter for diffuse optical tomography,” J. Biomed. Opt. 15, 065006 (2010).
[CrossRef]

Bugaj, J.

R. Rajagopalan, P. Uetrecht, J. Bugaj, S. Achilefu, and R. Dorshow, “Stabilization of the optical tracer agent indocyanine green using noncovalent interactions,” Photochem. Photobiol. 71, 347–350 (2000).
[CrossRef]

Cao, X.

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C. J. Goergen, H. H. Chen, A. Bogdanov, D. E. Sosnovik, and A. T. N. Kumar, “In vivo fluorescence lifetime detection of an activatable probe in infarcted myocardium,” J. Biomed. Opt. 17, 056001 (2012).
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X. Wang, B. Zhang, X. Cao, F. Liu, J. Luo, and J. Bai, “Acceleration of early photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).
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A. A. Bogdanov, V. Metelev, S. Zhang, and A. T. N. Kumar, “Sensing of transcription factor binding via cyanine dye pair fluorescence lifetime changes,” Mol. BioSyst. 8, 2166–2173 (2012).
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N. Valim, J. Brock, M. Leeser, and M. Niedre, “The effect of temporal impulse response on experimental reduction of photon scatter in time-resolved diffuse optical tomography,” Phys. Med. Biol. 58, 335–349 (2013).
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R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
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J. Wu, L. Perelman, R. Dasari, and M. Feld, “Fluorescence tomographic imaging in turbid media using early arriving photons and laplace transforms,” PNAS Med. Sci. 94, 8783–8788 (1997).

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E. Lapointe, J. Pichette, and Y. Bérubé-Lauzière, “A multi-view time-domain noncontact diffuse optical tomography scanner with dual wavelength detection for intrinsic and fluorescence small animal imaging,” Rev. Sci. Instrum. 83, 063703 (2012).
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[CrossRef]

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N. Valim, J. Brock, M. Leeser, and M. Niedre, “The effect of temporal impulse response on experimental reduction of photon scatter in time-resolved diffuse optical tomography,” Phys. Med. Biol. 58, 335–349 (2013).
[CrossRef]

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[CrossRef]

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J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
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B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
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Weissleder, R.

M. J. Niedre, R. 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. USA. 105, 19126–19131 (2008).
[CrossRef]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
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J. Ripoll, M. Nieto-Vesperinas, R. Weissleder, and V. Ntziachristos, “Fast analytical approximation for arbitrary geometries in diffuse optical tomography,” Opt. Lett. 27, 527–529 (2002).
[CrossRef]

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[CrossRef]

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J. K. Willmann, N. van Bruggen, L. M. Dinkelborg, and S. S. Gambhir, “Molecular imaging in drug development,” Nat. Rev. Drug Discov. 7, 591–607 (2008).
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[CrossRef]

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H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–732 (2009).
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R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
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X. Wang, B. Zhang, X. Cao, F. Liu, J. Luo, and J. Bai, “Acceleration of early photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).
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B. Zhang, X. Cao, F. Liu, X. Liu, X. Wang, and J. Bai, “Early photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation,” Appl. Opt. 50, 5397–5407 (2011).
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A. A. Bogdanov, V. Metelev, S. Zhang, and A. T. N. Kumar, “Sensing of transcription factor binding via cyanine dye pair fluorescence lifetime changes,” Mol. BioSyst. 8, 2166–2173 (2012).
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Biomed. Opt. Express

Commun. Numer. Methods Eng.

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Comput. Math. Methods Med.

X. Wang, B. Zhang, X. Cao, F. Liu, J. Luo, and J. Bai, “Acceleration of early photon fluorescence molecular tomography with graphics processing units,” Comput. Math. Methods Med. 2013, 297291 (2013).
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Curr. Opin. Biotechnol.

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J. Biomed. Opt.

R. E. Nothdurft, S. V. Patwardhan, W. Akers, Y. Ye, S. Achilefu, and J. P. Culver, “In vivo fluorescence lifetime tomography,” J. Biomed. Opt. 14, 024004 (2009).
[CrossRef]

C. J. Goergen, H. H. Chen, A. Bogdanov, D. E. Sosnovik, and A. T. N. Kumar, “In vivo fluorescence lifetime detection of an activatable probe in infarcted myocardium,” J. Biomed. Opt. 17, 056001 (2012).
[CrossRef]

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[CrossRef]

J. Comput. Phys.

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Figures (20)

Fig. 1.
Fig. 1.

Thought experiment. The laser is injected at L and a series of detectors are recording the arrival time of a fluorescence DPDW at different points D1, D2, D3, and D4 on the boundary.

Fig. 2.
Fig. 2.

Times and delays contributing to the measurement of an EPAT: time from the laser to the entry point L (T1), from the entry point to the inclusion at A (T2), from the inclusion to the exit (or detection) point D (T3), from the exit point to the detector (T4), and finally delays in the electronics and cables (T5 and T0).

Fig. 3.
Fig. 3.

(a) Experimental cylinder with embedded glass inclusions. (b) Photograph of the actual DOT scanner used.

Fig. 4.
Fig. 4.

NCFD processing applied to a measured TPSF: normalized TPSF (blue), delayed and attenuated TPSF (red), and the difference bipolar signal (magenta). The bipolar signal is analyzed to find its zero crossing, which is taken as the arrival time (EPAT). The delay and attenuation we use are, respectively, 0.244 ns (80 time bins on the TCSPC histogram) and 0.3. Note that TPSFs are first smoothed with a digital Butterworth low-pass filter of order 2 and cutoff frequency at 3 GHz prior to NCFD processing.

Fig. 5.
Fig. 5.

Coordinate system x and y for the calculation of the ovals.

Fig. 6.
Fig. 6.

Example of an ovoid in 3D space. Such an ovoid will be interpreted as a likelihood locus in the sense of a region where an inclusion is likely to be found.

Fig. 7.
Fig. 7.

(a) Cylinder’s mesh. Air shown in blue and the scattering medium in magenta. (b) Mouse mesh model. The mouse body is segmented into 21 tissue types, each having its specific optical properties, see [57,58].

Fig. 8.
Fig. 8.

Simulated fluorescence signal (red) is the result of the convolution of the field from the isotropic point source (fluorescent inclusion) within the medium at the detection point (blue), the excitation field from a collimated beam at the position of the inclusion (magenta), the fluorescence decay curve (green), and the IRF of the system (cyan); the lifetime τ of ICG was used with τ=0.56ns.

Fig. 9.
Fig. 9.

Comparison of the extracted wavefronts (orange) with circles (black) at time steps of 40 ps for the cylindrical medium. (a) Wavefronts originating from a collimated beam located at the boundary with Cartesian coordinates (24.9, 0, 0) (in mm). (b) Wavefronts originating from an isotropic point source located at the Cartesian coordinates (0, 10, 0) (in mm).

Fig. 10.
Fig. 10.

Comparison of the extracted wavefronts (orange) with circles (black) at time steps of 20 ps for the mouse model. (a) Wavefronts originating from a collimated beam located at the boundary with Cartesian coordinates (4.5, 57.5, 7.5) (in mm). (b) Wavefronts originating from an isotropic point source located at the Cartesian coordinates (18, 65, 10) (in mm).

Fig. 11.
Fig. 11.

(a),(c) Show clouds whose density maps are displayed in (b) and (d), respectively. (a), (b) were obtained from a simulation using 72 ovals, whereas (c), (d) were obtained from a simulation using 2556 ovals. The simulated fluorescent inclusions are shown in red and their localizations in blue. See text for details.

Fig. 12.
Fig. 12.

Ovoids (blue) drawn constructed from different EPATs are intersecting at the position of an inclusion (magenta). (a) 3D view. (b) Top view.

Fig. 13.
Fig. 13.

(a) Measured EPATs sinograms used for calibration, each color representing a different projection. Computed sinograms from the model with optimized values are shown in dotted red. (b) Reconstructed point density map where the peak gives the position of the inclusion, validating the extracted calibration parameters. Localization is displayed in blue and exact position in red (both are superimposed).

Fig. 14.
Fig. 14.

(a) EPATs sinograms for a single slice, each color representing a different projection. (b) 2D localization with three inclusions in the medium. Localizations are displayed in blue and exact positions in red.

Fig. 15.
Fig. 15.

3D localization with two inclusions in the medium: localizations in blue and exact positions in red. (a) 3D view. (b) Top view.

Fig. 16.
Fig. 16.

3D localization with four inclusions in the medium: localizations in blue and exact positions in red. (a) 3D view. (b) Top view.

Fig. 17.
Fig. 17.

Measurements in the presence of background fluorescence. (a) Corresponds to the inclusion plus background. ICG background concentrations are 0mol/l (blue), 8.0×1010mol/l (green), 1.6×109mol/l (red), 2.4×109mol/l (cyan), and 3.2×109mol/l (magenta). (b) Shows the background alone, with the blue solid curve showing the signal from the inclusion alone as a reference.

Fig. 18.
Fig. 18.

3D localization with four inclusions in the medium with background fluorescence: localizations in blue and exact positions in red. (a) 3D view. (b) Top view.

Fig. 19.
Fig. 19.

Nine TPSFs measured directly in front of the inclusion (225°). In (a): the amplitude is decreasing from one experiment to the next (blue to orange) due to photobleaching. In (b): once normalized, the shape of the TPSFs remain the same, leading to identical EPATs.

Fig. 20.
Fig. 20.

2D localization with three inclusions in the medium. Localizations are displayed with blue rings and exact positions with red rings. The colorbar shows the value of α (see text) that was used for displaying each height on this graph.

Tables (4)

Tables Icon

Table 1. Localization Results for the 2D Experiment with Three Inclusions

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Table 2. 3D Localization Results with Two Inclusions

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Table 3. 3D Localization Results with Four Inclusions

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Table 4. Localization of Four Inclusions with Background Fluorescence; Background ICG Concentration of 3.2×109mol/l (Worst Case in Fig. 17)

Equations (4)

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

tin=T2+T3=|LA¯|vex+|AD¯|vfl,
tin=|LA¯|vex+|AD¯|vflwith|LA¯|=(x+xf)2+y2and|AD¯|=(xxf)2+y2.
y=±1vfl2vex2(2vex4xxfvex4x2vfl4xf2vex4xf22vfl4xxfvfl4x2+vfl2vex4tin2+vfl4vex2tin2+2vfl2vex2x2+2vfl2vex2xf22vfl2vex2tinvfl2vex2tin24xxfvfl2+4xxfvex2)12.
ε=ϕ,θ[|r⃗L(ϕ)r⃗A|vex+|r⃗Ar⃗D(ϕ,θ)|vfltm(ϕ,θ)]2,

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