Comparative Study of Diffusion and Axial Models of Radiation Passing through a Biological Scattering Layer Based on the Monte Carlo Method

Abstract

The Monte Carlo method (MCM) is used for math ematical simulation of many complicated processes [1]. Propagation of optical radiation through strongly scatter ing medium (SSM) is such a problem [2,3]. In biomedical research, SSM represents biological tissues. Near IR lasers should be used for testing such objects. The near IR range corresponds to a so called transparency window [4].The interaction of IR radiation with biological tis sues is characterized by two processes: absorption and scattering. The probability of scattering is 1 2 orders of magnitude larger than the probability of absorption. SSM is characterized by extinction coefficient and scattering indicatrix. It is difficult to monitor extinction coefficient and scattering indicatrix simultaneously. Thus, scattering coefficient is used instead of scattering indicatrix.Ultrashort laser pulses together with photon count ing are used in experiments. The propagation of pulsed radiation through SSM is described using the transient equation (TE). The TE contains optical parameters of the medium as coefficients for photon flux density. Because TE has no analytical solution, a numerical method with additional assumptions is used. Two models are most fre quently used: the diffusion [5, 6] and axial models [7].Numerical diversity of SSM optical parameters is a serious problem. This diversity is due to difference in the assumptions of different models [8]. Comparative assess ment of the models is required in controlled SSM condi tions. The MCM provides such controlled SSM condi tions.The MCM is based on the trajectory of individual photons with given optical parameters of the SSM. In the case of ultrashort laser pulses, the MCM gives temporal distribution of detected photons. Comparison of various models (MCM and other models of radiation propaga tion in SSM) allows the capacity of each model to be evaluated in terms of temporal distribution of optical parameters in individual samples. TheoryThe photon propagation trajectory through SSM is determined by scattering events. In isotropic SSM the scattering indicatrix μ s (Ω → Ω → ') determines the photon scat tering probability in direction Ω → and solid angle dΩ' near the trajectory Ω → ' during passage of distance dl:Absorption coefficient μ a , scattering coefficient μ s , and extinction coefficient μ = μ a + μ s are macroscopic optical parameters of a SSM. The anisotropy factor g is mean cosine of scattering angle: 211 0006 3398/12/4506 0211 A comparative study of the diffusion and axial models (non stationary axial model, NAM; comprehensive diffu sion model, CDM; and revised diffusion model, RDM) of radiation passing through a biological scattering layer based on the Monte Carlo method is described. NAM gives scattering coefficient close to reduced scattering coef ficient rather than to complete scattering coefficient. It is concluded that RDM is superior to CDM.