OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 5, Iss. 1 — Jan. 4, 2010

Implicitly causality enforced solution of multidimensional transient photon transport equation

Chintha C Handapangoda and Malin Premaratne  »View Author Affiliations


Optics Express, Vol. 17, Issue 26, pp. 23423-23442 (2009)
http://dx.doi.org/10.1364/OE.17.023423


View Full Text Article

Enhanced HTML    Acrobat PDF (947 KB) Open Access





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A novel method for solving the multidimensional transient photon transport equation for laser pulse propagation in biological tissue is presented. A Laguerre expansion is used to represent the time dependency of the incident short pulse. Owing to the intrinsic causal nature of Laguerre functions, our technique automatically always preserve the causality constrains of the transient signal. This expansion of the radiance using a Laguerre basis transforms the transient photon transport equation to the steady state version. The resulting equations are solved using the discrete ordinates method, using a finite volume approach. Therefore, our method enables one to handle general anisotropic, inhomogeneous media using a single formulation but with an added degree of flexibility owing to the ability to invoke higher-order approximations of discrete ordinate quadrature sets. Therefore, compared with existing strategies, this method offers the advantage of representing the intensity with a high accuracy thus minimizing numerical dispersion and false propagation errors. The application of the method to one, two and three dimensional geometries is provided.

© 2009 Optical Society of America

OCIS Codes
(170.4580) Medical optics and biotechnology : Optical diagnostics for medicine
(170.6930) Medical optics and biotechnology : Tissue

ToC Category:
Medical Optics and Biotechnology

History
Original Manuscript: September 30, 2009
Revised Manuscript: October 29, 2009
Manuscript Accepted: December 4, 2009
Published: December 7, 2009

Virtual Issues
Vol. 5, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Chintha C. Handapangoda and Malin Premaratne, "Implicitly causality enforced solution of multidimensional transient photon transport equation," Opt. Express 17, 23423-23442 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-26-23423


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Z. Guo, and S. Kumar, "Three-dimensional discrete ordinates method in transient radiative transfer," J. Thermophys. Heat Transfer 16, 289-296 (2002). [CrossRef]
  2. K. F. Evans, "The spherical harmonics discrete ordinate method for three-dimensional atmospheric radiative transfer," J. Atmos. Sci. 55, 429-446 (1998). [CrossRef]
  3. G. L. Stephens, "Radiative transfer through arbitrarily shaped optical media. part I: A general method of solution," J. Atmos. Sci. 45, 1818-1836 (1988). [CrossRef]
  4. Z. M. Tan, and P. F. Hsu, "Transient radiative transfer in three-dimensional homogeneous and non-homogeneous participating media," J. Quantum Spectrosc. Radiat. Transfer 73, 181-194 (2002). [CrossRef]
  5. C. C. Handapangoda, M. Premaratne, D. M. Paganin, and P. R. D. S. Hendahewa, "Technique for handling wave propagation specific effects in biological tissue: Mapping of the photon transport equation to Maxwell’s equations," Opt. Express 16, 17792-17807 (2008). [CrossRef] [PubMed]
  6. K. W. Johnson, J. J. Mastrototaro, D. C. Howey, R. L. Brunelle, P. L. Burden-Brady, N. A. Bryan, C. C. Andrew, H. M. Rowe, D. J. Allen, B. W. Noffke, W. C. McMahan, R. J. Morff, D. Lipson, and R. S. Nevin, "In vivo evaluation of an electroenzymatic glucose sensor implanted in subcutaneous tissue," Biosens. Bioelectron. 7, 709-714 (1992). [CrossRef] [PubMed]
  7. D. Moatti-Sirat, F. Capron, V. Poitout, G. Reach, D. S. Bindra, Y. Zhang, G. S. Wilson, and D. R. Thevenot, "Towards continuous glucose monitoring: in vivo evaluation of a miniaturized glucose sensor implanted for several days in rat subcutaneous tissue," Diabetologia 35, 224-230 (1992). [CrossRef] [PubMed]
  8. V. Poitout, D. Moatti-Sirat, G. Reach, Y. Zhang, G. S. Wilson, F. Lemonnier, and J. C. Klein, "A glucose monitoring system for on line estimation in man of blood glucose concentration using a miniaturized glucose sensor implanted in the subcutaneous tissue and a wearable control unit," Diabetologia 36, 658-663 (1993). [CrossRef] [PubMed]
  9. C. C. Handapangoda, M. Premaratne, and D. M. Paganin, "Simulation of a device concept for noninvasive sensing of blood glucose levels," in Information and Automation for Sustainability, 2007. ICIAFS 2007. Third International Conference, (Melbourne, Australia, December 2007), pp. 31-34.
  10. C. C. Handapangoda, M. Premaratne, and D. M. Paganin, "Simulation of embedded photonic crystal structures for blood glucose measurement using Raman spectroscopy," 2008 International conference on Nanoscience and Nanotechnology, (Melbourne, Australia, February 2008).
  11. Z. Guo, and K. Kim, "Ultrafast-laser-radiation transfer in heterogeneous tissues with the discrete-ordinates method," Appl. Opt. 42, 2897-2905 (2003). [CrossRef] [PubMed]
  12. J. C. Chai, P. F. Hsu, and Y. C. Lam, "Three-dimensional transient radiative transfer modeling using the finite volume method," J. Quantum Spectrosc. Radiat. Transfer 86, 299-313 (2004). [CrossRef]
  13. A. Sawetprawichkul, P. F. Hsu, and K. Mitra, "Parallel computing of three-dimensional monte carlo simulation of transient radiative transfer in participating media," in Proceedings of the 8th AIAA/ASME Joint Thermophysics and Heat Transfer Conferece, (American Institute of Aeronautics and Astronautics, St. Louse, Missouri, 2002), pp. 1-10.
  14. J. V. P. de Oliveira, A. V. Cardona, M. T. Vilhena, and R. C. Barros, "A semi-analytical numerical method for time dependent radiative transfer prolems in slab geometry with coherent isotropic scattering," J. Quantum Spectrosc. Radiat. Transfer 73, 55-62 (2002). [CrossRef]
  15. C. C. Handapangoda, M. Premaratne, L. Yeo, and J. Friend, "Laguerre Runge-Kutta-Fehlberg method for simulating laser pulse propagation in biological tissue," IEEE J. Sel. Top. Quantum Electron. 14, 105-112 (2008). [CrossRef]
  16. M. F. Modest, "The method of discrete ordinates" in Radiative Heat Transfer, 2nd ed. (Academic Press, Boston, 2003), pp. 513-522.
  17. M. Abramomitz, and I. A. Stegun, "Orthogonal polynomials" in Handbook of mathematical functions with formulas, graphs and mathematical tables, (Dover, New York, 1965), pp. 773-784.
  18. G. A. Korn, and T. M. Korn, "Tensor analysis" in Mathematical handbook for scientists and engineers: definitions, theorems and formulas for reference and review, 2nd ed., (Dover, New York, 2000), pp. 544.
  19. C. J. Rivero-Moreno, and S. Bres, "Video spatio-temporal signatures using polynomial transforms," Lect. Notes Compt. Sci. 3736, 50-59 (2005). [CrossRef]
  20. G. A. Korn, and T. M. Korn, "Special functions" in Mathematical handbook for scientists and engineers: definitions, theorems and formulas for reference and review, 2nd ed., (Dover, New York, 2000), pp. 848-856.
  21. S. Chandrasekhar, "Quadrature formulae" in Radiative Transfer, (Dover, New York, 1960), pp. 54-60.
  22. K. D. Lathrop, "Spatial differencing of the transport equation: positive vs accuracy," J. Comput. Phys. 4, 475-498 (1968). [CrossRef]
  23. W. A. Fiveland, "Three-dimensional radiative heat-transfer solutions by the discrete-ordinates method," J. Thermophys. Heat Transfer 2, 309-316 (1988). [CrossRef]
  24. S. C. Chapra, and R. P. Canale, "Runge-Kutta methods" in Numerical Methods for Engineers, 4th ed., (McGraw-Hill, New York,2002), pp. 719-720.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited