Monte Carlo models for light transport in a scattering medium have been and are used in many different disciplines. The following gives an impression of the different areas of application of Monte Carlo models for light transport, with an emphasis on the application in medicine, and discusses some of the differences in implementation,.
Monte Carlo modelling has been widely used in Oceanography to simulate scattering by sea organisms and small particles (Hessel and LaGrone, 1970; Lemer and
Summers, 1982) and in the areas of remote sensing and LIDAR (Meier, 1978). Other areas include astronomy, to model multiple scattering by dust and other particles constituting interstellar matter (Witt, 1977), and in photography for the determination of the optical properties of photographic emulsions (Bowker, 1962; DePalma and Gasper, 1972).
Presently numerous applications exist in medicine. The model of Meier et al (Meier, 1978) was used by Groenhuis et al (Groenhuis, 1983) to look at the radial distribution of light reflected off turbid materials, with the aim of determining the optical parameters of human dental enamel. To look at light flux distributions in tissue for the application of photodynamic therapy, Wilson and Adam used a MC model where they made the assumption of isotropic scattering (Wilson and Adam, 1983). Maarek and Jarry developed a MC simulation to model transmission and reflection in a ’slab’ of blood (Maarek and Jarry, 1984). They further developed their model to study the propagation of an ultra short pulse through a heterogeneous biological specimen to simulate time resolved imaging (Maarek, 1986).
A method which is strongly related to the Monte Carlo technique or which could perhaps even be classified as Monte Carlo is the random walk model. Here the more realistic physical interactions in a Monte Carlo method are replaced by a random walk on an evenly spaced discrete cubic lattice where ’scattering’ is always over a multiple of 90°. This technique has been used by Bonner, Nossal and Weiss to look at the mean path length and light distributions for detected photons emerging from a biological medium (Bonner, 1987; Nossal, 1988; Weiss, 1989).
Recently, MC models have been used to study the use of time resolved techniques. Patterson et al looked at the time resolved transmittance and reflectance of
tissue to determine tissue optical properties (Patterson, 1989). Jacques has used MC models to predict the presence of single or two-photon reactions when using ultra short pulses within biological tissues (Jacques, 1989). Delpy et al used a time resolved MC simulation to determine the effective optical path length for light in highly scattering tissues (Delpy, 1988).
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Chapter 7
Monte Carlo model, implementation
1 Introduction
In this chapter a detailed explanation will be given of the particular features and implementation details of the Monte Carlo model that was developed for the purposes of i) the determination of the tissue optical parameters from measurements, ii) to aid in the interpretation and quantification of tissue spectroscopic data and iii) to examine the possibility of optical imaging through tissue. The features that were desired for these purposes are set out below. In the section on the implementation, some of the assumptions inherent in the model are explained, followed by details on how they were implemented, together with some of the computational ’tricks’ used to speed up the operation of the computer program for the model.
Before putting one’s faith in the numbers produced by any model, it has to be thoroughly checked and tested. The random number generators used were therefore subjected to statistical tests for randomness, and the coordinate transformations and the specular reflection and refraction corrections were compared with exact calculations. The resulting model as a whole has been validated against data obtained hrom numerical solutions of the Transport Equation. The results of these validations are included in this chapter. In Chapter 10 some of the results obtained with the Monte Carlo model, and
a comparison with experimentally measured data and analitically obtained data are presented. This includes the spatial broadening of light transmitted through or reflected from a slab, the imaging of an artery in a finger, and results for the determination of the effective path length.