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Three dimensional Monte Carlo code for photon migration through complex heterogeneous media including the adult human head

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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.

©2002 Optical Society of America

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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)

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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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