Metodo monte carlo

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Monte Carlo Modeling of Light Propagation in Neonatal Skin
J.A. Delgado Atencio1, S.L. Jacques2 and S. Vázquez y Montiel1
2Oregon 1Instituto

Nacional de Astrofísica Óptica y Electrónica, Health & Science University-Dermatology/Biomedical Engineering, 1México 2USA

1. Introduction
The origin of the “Monte Carlo method“ historically comes from Los Alamos National Laboratory in the earlyyears after the Second World War and is related with two important events that took place in 1945: the successful test at Alamogordo and the building of the first electronic computer (the ENIAC) (Metropolis, 1987). After the review of the ENIAC results held in the spring of 1946 at Los Alamos, Stanislaw Ulam realized that statistical techniques in combination with the surprising speed and theversatility of this electronic computer could lead to a powerful tool in theoretical calculations (Metropolis, 1987). On March 11, 1947, John von Neumann in a handwritten letter included a detailed outline of a possible statistical approach (incorporating Stanislaw´s idea) to solving the problem of neutron diffusion in a spherical core of fissionable material surrounded by a shell of tamper material.At that time, Nick Metropolis suggested the name “Monte Carlo” for the re-emerging sampling technique (Metropolis, 1987). However, a previous work performed by Enrico Fermic in neutron diffusion in Rome in the early thirties, incorporated the essential principles of the Monte Carlo method when he was studying the moderation of neutrons (Metropolis, 1987). Another example of the previous use ofthis sampling technique is an ancient problem in geometric probability: “The Buffon’s needle problem” which was stated in 1733 and solved (solution published in 1777) by Geroges Louis Leclerc, Comte de Buffon (1707-1788) (Weisstein, accessed September 2010). In this problem the probability of the needle crossing a line (in a table marked with equidistant parallel lines) is proportional to theinverse of the number π provided that the length of the needle is less than the space between lines. The repetition of this experiment many times results into the assessment of π. During the post-war period the Monte Carlo (MC) method spread into many fields of knowledge such as astrophysics, solid state, optics, etc. One example in astrophysics is the study of the transfer of visible radiation throughterrestrial clouds using a MC computer program that incorporated the Henyey-Greenstein phase function to describe the scattering process of water droplet clouds (Danielson et al., 1969). Another illustration of this method appears in the book “The Monte Carlo Methods in Atmospheric Optics” (Marchuk et al., 1980) which had a first Russian edition in 1974. In the preface of this book an acceptabledefinition of the MC method is given which is reproduced here:

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Applications of Monte Carlo Methods in Biology, Medicine and Other Fields of Science

“The most universal method for solving the above mentioned problems is the Monte Carlo method, which is a numerical simulation of the radiative-transfer process. This process can be regarded as a Markov chain of photon collisions in amedium, which result in scattering or absorption. The Monte Carlo technique consists in computational simulation of that chain and in constructing statistical estimates of the desired functionals”. In 1983 the MC method was applied for the first time to determine light distribution in biological tissues (Wilson & Adam, 1983), and it was specially designed to predict the distribution of absorbed dosein homogeneous tissues irradiated either by external beam light or by mean of interstitial optical fibers. After this pioneer work, various MC approaches to deal with light propagation in turbid media has been developed and applied to specific problems in the field of biomedical optics (Hasegawa et al., 1991; Graff et al., 1993; Wang et al., 1995; Wang et al., 1997). Currently, new improvements...