Journal of Biomedicine and Biotechnology
Volume 2008 (2008), Article ID 784354, 5 pages
doi:10.1155/2008/784354
Research Article
An Approximate Numerical Technique for
Characterizing Optical Pulse Propagation in Inhomogeneous Biological Tissue
Advanced Computing and Simulation Laboratory (AXL), Department of Electrical and Computer Systems Engineering, Monash University, Clayton, VIC 3800, Australia
Received 8 September 2007; Accepted 19 December 2007
Academic Editor: Daniel Howard
Copyright © 2008 Chintha C. Handapangoda and Malin Premaratne. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Linked References
- S. B. Colak, M. B. van der Mark, G. W. 'T Hooft, J. H. Hoogenraad, E. S. van der Linden, and F. A. Kuijpers, “Clinical optical tomography and NIR spectroscopy for breast cancer detection,” IEEE Journal on Selected Topics in Quantum Electronics, vol. 5, no. 4, pp. 1143–1158, 1999. View at Publisher · View at Google Scholar
- B. D. Cameron, H. W. Gorde, B. Satheesan, and G. L. Cote, “The use of polarized laser light through the eye for noninvasive glucose monitoring,” Diabetes Technology & Therapeutics, vol. 1, no. 2, pp. 135–143, 1999. View at Publisher · View at Google Scholar
- F. Liu, K. M. Yoo, and R. R. Alfano, “Ultrafast laser-pulse transmission and imaging through biological tissues,” Applied Optics, vol. 32, no. 4, pp. 554–558, 1993.
- G. Yao and L. V. Wang, “Theoretical and experimental studies of ultrasound-modulated optical tomography in biological tissue,” Applied Optics, vol. 39, no. 4, pp. 659–664, 2000. View at Publisher · View at Google Scholar
- A. D. Klose, U. Netz, J. Beuthan, and A. H. Hielscher, “Optical tomography using the time-dependent equation of radiative transfer—part 1: forward model,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 72, no. 5, pp. 691–713, 2002. View at Publisher · View at Google Scholar
- M. Premaratne, E. Premaratne, and A. J. Lowery, “The photon transport equation for turbid biological media with spatially varying isotropic refractive index,” Optics Express, vol. 13, no. 2, pp. 389–399, 2005. View at Publisher · View at Google Scholar
- K. Stamnes, S. Tsay, W. Wiscombe, and K. Jayaweera, “Numerically stable algorithm for discrete-ordinate-method for radiative transfer in multiple scattering and emitting layered media,” Applied Optics, vol. 27, no. 12, pp. 2502–2509, 1988.
- A. D. Kim and M. Moscoso, “Chebyshev spectral methods for radiative transfer,” SIAM Journal on Scientific Computing, vol. 23, no. 6, pp. 2074–2094, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
- J. V. P. de Oliveira, A. V. Cardona, and M. T. M. B. de Vilhena, “Solution of the one-dimensional time-dependent discrete ordinates problem in a slab by
the spectral and methods,” Annals of Nuclear Energy, vol. 29, no. 1, pp. 13–20, 2002. View at Publisher · View at Google Scholar
- M. Sakami, K. Mitra, and P.-F. Hsu, “Analysis of light pulse transport through two-dimensional scattering and absorbing media,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 73, no. 2–5, pp. 169–179, 2002. View at Publisher · View at Google Scholar
- T. Khan and H. Jiang, “A new diffusion approximation to the radiative transfer equation for scattering media
with spatially varying refractive indices,” Journal of Optics A: Pure and Applied Optics, vol. 5, no. 2, pp. 137–141, 2003. View at Publisher · View at Google Scholar
- H. Dehghani, B. Brooksby, K. Vishwanath, B. W. Pogue, and K. D. Paulsen, “The effects of internal refractive index variation in near-infrared optical tomography:
a finite element modelling approach,” Physics in Medicine and Biology, vol. 48, no. 16, pp. 2713–2727, 2003. View at Publisher · View at Google Scholar
- G. Bal, “Radiative transfer equations with varying refractive index: a mathematical perspective,” Journal of the Optical Society of America A, vol. 23, no. 7, pp. 1639–1644, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
- M. L. Shendeleva and J. A. Molly, “Scaling property of the diffusion equation for light in a turbid medium with varying refractive index,” Journal of the Optical Society of America A, vol. 24, no. 9, pp. 2902–2910, 2007. View at Publisher · View at Google Scholar
- L. Martí-López, J. Bouza-Domínguez, R. A. Martínez-Celorio, and J. C. Hebden, “An investigation of the ability of modified radiative transfer equations to accommodate laws of geometrical optics,” Optics Communications, vol. 266, no. 1, pp. 44–49, 2006. View at Publisher · View at Google Scholar
- A. Sharma, D. V. Kumar, and A. K. Ghatak, “Tracing rays through graded-index media: a new method,” Applied Optics, vol. 21, no. 6, pp. 984–987, 1982.
- B. Richerzhagen, “Finite element ray tracing: a new method for ray tracing in gradient-index media,” Applied Optics, vol. 35, no. 31, pp. 6186–6189, 1996.
- H. A. Ferwerda, “Radiative transfer equation for scattering media with a spatially varying refractive index,” Journal of Optics A: Pure and Applied Optics, vol. 1, no. 3, pp. L1–L2, 1999. View at Publisher · View at Google Scholar
- C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, “Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 14, no. 1, 2008. View at Publisher · View at Google Scholar
- M. Born and E. Wolf, Principles of Optics, Cambridge University Press, Cambridge, UK, 7th edition, 1999.
- M. Premaratne, “Numerical simulation of nonuniformly time-sampled pulse propagation in nonlinear fiber,” Journal of Lightwave Technology, vol. 23, no. 8, pp. 2434–2442, 2005. View at Publisher · View at Google Scholar
- A. D. Greenwood and J.-M. Jin, “A field picture of wave propagation in inhomogeneous dielectric lenses,” IEEE Antennas and Propagation Magazine, vol. 41, no. 5, pp. 9–18, 1999. View at Publisher · View at Google Scholar
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, “Integration of functions,” in Numerical Recipes in C++, pp. 152–157, Cambridge University Press, Cambridge, UK, 2003.
- M. Abramomitz and I. A. Stegun, “Orthogonal polynomials,” in Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, pp. 773–784, Dover, New York, NY, USA, 1965.
- S. C. Chapra and R. P. Canale, “Runge-Kutta methods,” in Numerical Methods for Engineers, pp. 719–720, McGraw-Hill, New York, NY, USA, 4th edition, 2002.
- M. P. Mengüç and R. Viskanta, “Radiative transfer in three-dimensional rectangular enclosures containing inhomogeneous,
anisotropically scattering media,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 33, no. 6, pp. 533–549, 1985. View at Publisher · View at Google Scholar
- G. E. Thomas and K. Stamnes, Radiative Transfer in the Atmosphere and Ocean, Cambridge University Press, Cambridge, UK, 1999.