Abstract

We describe a novel Monte Carlo code for photon migration through 3D media with spatially varying optical properties. The code is validated against analytic solutions of the photon diffusion equation for semi-infinite homogeneous media. The code is also cross-validated for photon migration through a slab with an absorbing heterogeneity. A demonstration of the utility of the code is provided by showing time-resolved photon migration through a human head. This code, known as ‘tMCimg’, is available on the web and can serve as a resource for solving the forward problem for complex 3D structural data obtained by MRI or CT.

© Optical Society of America

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Appl. Opt. (5)

Breast Cancer Res. (1)

V. Ntziachristos and B. Chance, "Probing physiology and molecular function using optical imaging: applications to breast cancer," Breast Cancer Res. 3, 41-6 (2001).
[CrossRef] [PubMed]

Computer Methods and Programs in Biomedi (1)

L. Wang, S. L. Jacques and L. Zheng, "MCML-Monte Carlo modeling of light transport in multi-layered tissues," Computer Methods and Programs in Biomedicine 47, 131-146 (1995).
[CrossRef] [PubMed]

Inverse Problems (1)

O. Dorn, "A transport-backtransport method for optical tomography," Inverse Problems 14, 1107-1130 (1998).
[CrossRef]

J. Biomed. Opt. (1)

M. J. Holboke, B. J. Tromberg, X. Li, N. Shah, J. Fishkin, D. Kidney, J. Butler, B. Chance and A. G. Yodh, "Three-dimensional diffuse optical mammography with ultrasound localization in a human subject," J. Biomed. Opt. 5, 237-47. (2000).
[CrossRef] [PubMed]

J. Cereb. Blood Flow Metab. (1)

D. A. Benaron, S. R. Hintz, A. Villringer, D. Boas, A. Kleinschmidt, J. Frahm, C. Hirth, H. Obrig, J. C. van Houten, E. L. Kermit, W. F. Cheong and D. K. Stevenson, "Noninvasive functional imaging of human brain using light," J. Cereb. Blood Flow Metab. 20, 469-77 (2000).
[CrossRef] [PubMed]

J. Neurotrauma (1)

C. S. Robertson, S. P. Gopinath and B. Chance, "A new application for near-infrared spectroscopy: Detection of delayed intracranial hematomas after head injury," J. Neurotrauma 12, 591-600 (1995).
[CrossRef] [PubMed]

J. Opt. Soc. Am A (2)

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

T. Durduran, B. Chance, A. G. Yodh and D. A. Boas, "Does the photon diffusion coefficient depend on absorption?," J. Opt. Soc. Am A 14, 3358-3365 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

A. Kienle and M. S. Patterson, "Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from semi-infinite turbid medium," J. Opt. Soc. Am. 14, 246-254 (1997).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

J. Perinat. Med. (1)

S. R. Hintz, D. A. Benaron, A. M. Siegel, A. Zourabian, D. K. Stevenson and D. A. Boas, "Bedside functional imaging of the premature infant brain during passive motor activation," J. Perinat. Med. 29, 335-43 (2001).
[CrossRef] [PubMed]

Med. Phys. (3)

S. R. Arridge, H. Dehghani, M. Schweiger and E. Okada, "The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions," Med. Phys. 27, 252-64. (2000).
[CrossRef] [PubMed]

A. D. Klose and A. H. Hielscher, "Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer," Med. Phys. 26, 1698-707. (1999).
[CrossRef] [PubMed]

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

Neuroimage (2)

A. M. Dale, B. Fischl and M. I. Sereno, "Cortical surface-based analysis. I. Segmentation and surface reconstruction," Neuroimage 9, 179-94 (1999).
[CrossRef] [PubMed]

M. Firbank, E. Okada and D. T. Delpy, "A theoretical study of the signal contribution of regions of the adult head to near-infrared spectroscopy studies of visual evoked responses," Neuroimage 8, 69-78. (1998).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (4)

Pediatr. Res. (1)

S. R. Hintz, W. F. Cheong, J. P. van Houten, D. K. Stevenson and D. A. Benaron, "Bedside imaging of intracranial hemorrhage in the neonate using light: comparison with ultrasound, computed tomography, and magnetic resonance imaging," Pediatr. Res. 45, 54-9. (1999).
[CrossRef] [PubMed]

Phys. Med. Biol. (4)

M. Schweiger and S. R. Arridge, "Optical tomographic reconstruction in a complex head model using a priori region boundary information," Phys. Med. Biol. 44, 2703-21 (1999).
[CrossRef] [PubMed]

A. H. Hielscher, R. E. Alcouffe and R. L. Barbour, "Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues," Phys. Med. Biol. 43, 1285-302. (1998).
[CrossRef] [PubMed]

M. Firbank, S. R. Arridge, M. Schweiger and D. T. Delpy, "An investigation of light transport through scattering bodies with non-scattering regions," Phys. Med. Biol. 41, 767-83. (1996).
[CrossRef] [PubMed]

S. R. Arridge, M. Cope and D. T. Delpy, "The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis," Phys. Med. Biol. 37, 1531-60 (1992).
[CrossRef] [PubMed]

Phys. Rev. E (1)

K. Furutsu and Y. Yamada, "Diffusion approximation for a dissipative random medium and the applications," Phys. Rev. E 50, 3634 (1994).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

V. Ntziachristos, A. G. Yodh, M. Schnall and B. Chance, "Concurrent MRI and diffuse optical tomography of breast after indocyanine green enhancement," Proc. Natl. Acad. Sci. U S A 97, 2767-72 (2000)
[CrossRef] [PubMed]

Radiology (1)

B. W. Pogue, S. P. Poplack, T. O. McBride, W. A. Wells, K. S. Osterman, U. L. Osterberg and K. D. Paulsen, "Quantitative hemoglobin tomography with diffuse near-infrared spectroscopy: pilot results in the breast," Radiology 218, 261-6. (2001).
[PubMed]

Science (1)

D. A. Benaron, W. F. Cheong and D. K. Stevenson, "Tissue Optics," Science 276, 2002-2003 (1997).
[CrossRef] [PubMed]

Trends Neurosci. (1)

A. Villringer and B. Chance, "Non-invasive optical spectroscopy and imaging of human brain function," Trends Neurosci. 20, 435-442 (1997).
[CrossRef] [PubMed]

Other (5)

A. Ishimaru, Wave Propagation and Scattering in Random Media (Academic Press, Inc., San Diego 1978).

S. L. Jacques and L. Wang, "Monte-Caro Modeling of Light Transport in Tissues" in Optical-Thermal Response of Laser Irradiated Tissue, A. J. Welch and M. C. J. van Gemert (Plenum, New York 1995).

J. J. Stott and D. A. Boas, tMCimg: Monte Carlo code for photon migration through general 3D Media. http://www.nmr.mgh.harvard.edu/DOT

S. L. Jacques and L. Wang, "Monte Carlo modeling of light transport in tissues" in Optical-Thermal response of laser-irradiated tissue, Welch and v. Gemert (Plenum, New York 1995).

A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York 1988).

Supplementary Material (1)

» Media 1: AVI (1000 KB)     

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Figures (7)

Figure 1.
Figure 1.

(A) A comparison of the flux of photons remitted from a semi-infinite medium as calculated by diffusion theory and Monte Carlo. (B) A comparison of the photon fluence within a semi-infinite medium. The index-matched surface is at a depth of 0 mm.

Figure 2.
Figure 2.

(A) A comparison of diffusion theory and Monte Carlo for the temporal response to a pulse of light as measured on the surface and within the medium. The black points is for the remitted flux of light 15 mm from the source. The red points indicate the fluence within the medium at a depth of 10 mm and displaced laterally 15 mm. (B) The comparison of the iso-contours for diffusion theory and Monte Carlo within the medium at 0.1, 0.5, 1.0, 1.5, and 2.0 ns after the pulse of light.

Figure 3.
Figure 3.

(A) The geometry for the Monte Carlo simulation with an absorbing inclusion. (B) The relative decrease in the detected photon flux is shown as the absorption coefficient of the inclusion is increased. A comparison of 4 methods is made. See text for details.

Figure 4.
Figure 4.

The photon fluence within a 40 mm thick homogeneous slab is shown in (A). The change in fluence due to an absorbing inclusion with μa = 0.025 mm-1 relative to

Figure 5.
Figure 5.

The photon sensitivity profile for a source-detector pair separated by 3 cm. Profiles are given for (A) a continuous-wave measurement, (B) an amplitude measurement at 200 MHz, and time-gated measurements at (C) 500 ps and (D) 2000 ps.

Figure 6.
Figure 6.

A movie of the propagation of a pulse of light through a 3D human head. The color scale is logarithmic and spans 10 orders of magnitude from a peak in the dark red to a minimum in the dark blue. The AVI movie file size is 1.0 Mega-Bytes.

Figure 7.
Figure 7.

An estimate of the SNR by running 108 photons on the 3D human head model.

Equations (7)

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

Σ surface J out ( r i ) A i + Σ volume Φ ( r i ) μ a ( r i ) V voxel = 1
Φ ( t ) = 1 N photons ( t ) Δ t i = 1 N photons ( t ) j = 1 N regions exp ( μ a , j L i , j )
Φ ( r s , r d ) = v S 4 π D [ exp ( 3 μ s ' μ a r s r d ) r s r d exp ( 3 μ s ' μ a r s , i r d ) r s , i r d ]
Φ ( r s , r d , t ) = v S ( 4 π D t ) 3 / 2 [ exp ( r s r d 2 ( 4 D t ) ) exp ( r s , i r d 2 ( 4 D t ) ) ] exp ( ν μ a t ) .
Φ = Φ o + Φ pert
Φ = Φ o exp ( Φ pert ) .
Φ pert ( r s , r d ) = 1 Φ o ( r s , r d ) Φ o ( r s , r d ) ν δ μ a ( r ) D o G ( r , r d ) d r .

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