Abstract

Optical Coherence Tomography (OCT) is a new technique mainly used in biomedical imaging. We present here a Particle-Fixed Monte Carlo (PFMC) simulation for OCT signal. In the PFMC model, the scattering particles of the sample are assumed to be temporarily fixed and randomly distributed in the simulation of the backscattered light. An efficient partitioning scheme is proposed to speed up this simulation process. The new model explains the exponential decay signal at the interfaces of different media layers observed in OCT experimental measurements.

© 2005 Optical Society of America

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References

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Acta Optica Sinica

Y. Chen, P. Xue, T. Yuan, W. Chen, and D. Chen, �??Simulation of light scattering in optical coherence tomography,�?? Acta Optica Sinica 19, 486�??490 (1999).

Appl. Opt.

Communications of the ACM

J. L. Bentley, �??Multidimensional binary search trees used for associative searching,�?? Communications of the ACM 18, 509�??517 (1975).
[CrossRef]

Computer Methods and Programs in Biomedi

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]

J. Opt. Soc. Am. A

Opt. Lett.

Phys. Med. Biol.

D. J. Smithies, T. Lindmo, Z. Chen, J. S. Nelson, and T. E. Milner, �??Signal attenuation and localization in optical coherence tomography studied by Monte Carlo simulation,�?? Phys. Med. Biol. 43, 3025�??3044 (1998).
[CrossRef] [PubMed]

G. Yao, and L. V. Wang, �??Monte Carlo simulation of an optical coherence tomography signal in homogeneous turbid media,�?? Phys. Med. Biol. 44, 2307�??2320 (1999).
[CrossRef] [PubMed]

P. E. Andersen, L. Thrane, H. T. Yura, A. Tycho, T. M. Jørgensen, and M. H. Frosz, �??Advanced modelling of optical coherence tomography systems,�?? Phys. Med. Biol. 49, 1307�??1327 (2004).
[CrossRef] [PubMed]

Proc. SPIE

B. C. Karamata, P. Lambelet, M. Leutenegger, M. Laubscher, S. Bourquin, and T. Lasser, �??A semi-analytical model accounting for multiple scattering in optical coherence tomography,�?? in Coherence Domain Optical Methods and Optical Coherence Tomography in Biomedicine IX , V. V. Tuchin, J. A. Izatt and J. G. Fujimoto, eds. , Proc. SPIE 5690, 386�??396 (2005).

Science

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, �??Optical coherence tomography,�?? Science 254, 1178�??1181 (1991).
[CrossRef] [PubMed]

Trans. Biomed. Eng.

M. J. C. V. Gemert, S. L. Jacques, H. J. C. M. Sterenborg, and W. M. Star, �??Skin optics,�?? IEEE Trans. Biomed. Eng. 36, 1146�??1154 (1989).
[CrossRef] [PubMed]

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Figures (10)

Fig. 1.
Fig. 1.

The conventional simulation of the path-length-resolved reflectance of a semi-infinite medium: refractive index 1.37, absorption coefficient 0.08mm -1, scattering coefficient 10.0mm -1 and anisotropy factor 0.7. The curve is almost continuous.

Fig. 2.
Fig. 2.

The OCT signal obtained by the conventional models and by experiment. (a) The conventional simulation of the OCT signal: coherence length 17µm and center wavelength 850nm. The signal only occurs at the surface; (b) The OCT signal of Intralipid 10% obtained by experiment. An exponential tail penetrating into the media is observed. There is a obvious discrepancy between the conventional model and experiment.

Fig. 3.
Fig. 3.

Schematic of OCT experimental setup: SLD, super-luminescent diode; DC, dispersion compensator; PC, personal computer. The reference mirror is moving at a constant speed to produce interference modulation, which is demodulated by the electronics and digitized via A/D converter to the computer for processing and OCT imaging display.

Fig. 4.
Fig. 4.

The particle distribution pattern in the PFMC model. The location of particles is randomly sampled and fixed throughout the simulation process. Every particle has an interaction sphere around it, shown as a dotted circle. The upside red dot denotes the incident photon.

Fig. 5.
Fig. 5.

The flow chart of PFMC model

Fig. 6.
Fig. 6.

The light transport process and detection geometry of the PFMC model. The shaded area represents the simulating tissue. Dots in tissue represent the scattering particles and dashed circle around it marks the interaction region. The escaping photons within the restriction: ϕ<ϕ 0, l<l 0 are collected and thus contribute to the calculation of path-length-resolved reflectance according to the experiment setup in Fig. 3. Two example trajectories of photons, which are supposed to be collected, are also shown. The typical values are ϕ 0=15° and l 0=10µm.

Fig. 7.
Fig. 7.

Path-length-resolved reflectance simulated by the PFMC model and by conventional model. (a) The simulation of a semi-infinite medium: n=1.1,d=5mm,ρ=4.4×106/mm 3,µst =0.98,g=0.7, r=0.001mm by the PFMC model. The simulating mean free path is 0.069mm, corresponding to µt =14.5mm -1. The upper-right inset is the detail curve with path-length between 0.2 and 0.5mm; (b) The simulation of a semi-infinite medium: n=1.1,d=5mm,µst =0.98,g=0.7,µt =14.5mm -1 by conventional model.

Fig. 8.
Fig. 8.

The convolution and demodulation OCT signal of Fig.(a). (a) The convolution signal between path-length-resolved reflectance and the self-coherence function. It contains an envelope modulated by a carrier frequency; (b) The OCT signal obtained by quadrature demodulation of the convolution signal.

Fig. 9.
Fig. 9.

Comparison of simulation and experiment results. The red dashed curve is the OCT signal of Intralipid-10% and The blue solid curve shows the PFMC simulation OCT signal. The maximum of both curved are normalized to 1 for easy comparison.

Fig. 10.
Fig. 10.

Path-length-resolved reflectance simulated by the PFMC model and by conventional model. (a) The simulation of a three layer medium with different refractive indices: n 1=n 3=1.1,n 2=1.4,d 1=d 2=0.1mm,d 3=1.5mm,ρ=5.0×106/mm 3,µst =0.98,g=0.7, r=0.001mm by PFMC; (b) The simulation of the same medium by conventional model (corresponding µt =15.0mm -1). Both of the simulation results are not continuous at the interfaces, but only the result by PFMC shows discontinuities between interfaces.

Equations (10)

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

I d ( τ ) = [ E s ( t ) + E r ( t + τ ) ] [ E s ( t ) + E r ( t + τ ) ] *
= [ E s ( t , L s ) d L s + E r ( t + τ ) ] [ E s ( t , L s ) d L s + E r ( t + τ ) ] *
I d ( L r ) = I s + I r + 2 ( I r I s ) 1 2 [ R ( L s ) ] 1 2 g ( L r L s ) d L s
I ( L r ) [ R ( L s ) ] 1 2 g ( L r L s ) d L s
= [ R ( L r ) ] 1 2 g ( L r )
G ( k ) exp [ ( k k 0 ) 2 ( L c 4 ) 2 ]
p ( d ) = 1 μ t exp ( μ t d )
Δ W = μ a μ t W
p ( cos θ ) = 1 g 2 2 ( 1 + g 2 2 g cos θ ) 3 2
r ( α i ) = 1 2 [ sin 2 ( α i α t ) sin 2 ( α i + α t ) + tan 2 ( α i α t ) tan 2 ( α i + α t ) ]

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