Method of statistical imitation, its creator S. Ulam and basic principles of application for random processes modeling

: pp. 21 - 30
Lviv Polytechnic National University, Ukraine
Lviv Polytechnic National University
Lviv Polytechnic National University

The article is dedicated to famous Lviv residents, the author of the Monte Carlo method, and mathematician Marco Katsu. The method of Monte Carlo methodical algorithms for modeling statistical regularities of light passage through optically inhomogeneous media is briefly described in the article

  1. Kosobutskyy P. Statistical and Monte-Carlo Algoritms for Simulation of Random Processes in macro- and microsystems using MathCAD. Lviv: LPNU, 2014;
  2. Wang L., Jacques S. Monte-Carlo modeling of light transport in Multi-layer Tissues in Standart C. University of Texas. Anderson Cancer Center, 1992;
  3. Wang L., Jacques S.,Zheng L. MCML-Monte-Carlo modeling of light transport in multi-layer tissues. Computer Methods and Programs in Biomedicine.-Vol.47.-P.131-146 (1995).
  4. Binzoni T., Leung T.S., Gandjbakhche The use of the Heyey-Greenstein phase function in Monte Carlo simuliations in biomedical optics. Phys. Med.Biol.Vol.51.-P.N313-N322.-2006.
  5. Prahl S.A., Light transport in tissue, PhD dissertation, University of Texas at Austin, 1988.
  6. Wang L.H., Jacques S.L., Monte Carlo Modeling of Light Transport in Multi-layered Tissues in Standard C, University of Texas, M. D. Anderson Cancer Center, 1992.
  7. Wang L.H., Jacques S.L., Zheng L.-Q., MCML-Monte Carlo modeling of photon transport in multi-layered tissues, Computer Methods and Programs in Biomedicine, vol. 47, pp. 131-146, 1995.
  8. Zhu  C.,  Liu  Q.,  Review of Monte Carlo modeling of  light  transport in tissues, Journal  of Biomedical Optics 18(5), 050902, May 2013.
  9. Jacques S. L., Optical properties of biological tissues: a review, Phys. Med. Biol. 58, 2013, pp.37–61.17. Vo-Dinh T., Biomedical Photonics handbook, CRC Press, March 2003.
  10. Wang L.V., Wu H.І., Biomedical Optics: Principles and Imaging, Wiley, 2007.
  11. Boas D.A., Pitris C., Ramanujam N., Handbook of Biomedical Optics. CRC Press June 2011.
  12. Kosobutskyy P. Envelope Method in Fabry-Perot Interferometry. Lviv: LPNU, 2013.
  13. PH36010 Numerical Methods. Writing Programs in MathCAD.
  14. Salerud E.G., Biomedical Optics: Light scattering in Tissue by Monte Carlo Simulation, IMT October 2006.