Analysis of the applicability of the classical probabilistic parameters of the Monte Carlo algorithm for problems of light transport in turbid biological media with continuous absorption and discrete scattering

Simulation of light propagation by the statistical Monte Carlo (MC) method is widely used in many fields, especially in astrophysics, atmospheric optics, ocean optics, and nuclear medicine. In the optics of biological tissues, the MC method is used to simulate the luminous flux, which is formed during various medical therapeutic or diagnostic procedures inside a biological tissue and on its surface. In such calculations, the MC method is commonly considered as a reference one, which ensures an arbitrarily high accuracy with an increase in the number of 'photons'. However, it can be shown that this is not always the case. In this paper, in the methodological aspect, the idealised one-dimensional problems of the transport theory for a turbid medium with continuous absorption and scattering and a turbid medium with discrete scatterers inside a continuously absorbing medium are considered. Their exact analytical solutions are presented and compared with the results of statistical modelling by the MC method. It is found that the use of classical probabilistic parameters for a medium with continuous absorption and scattering in the MC algorithm leads to a systematic method error in determining the values of radiation fluxes for biological media with discrete scattering, up to 10% for fluxes at the boundary in some cases. The causes of the error are discussed and it is shown how to modify the probabilistic parameters of the MC algorithm to eliminate it.