Relation between fluence rate and mean photons pathlengths: an interesting option for Monte Carlo based fluence calculations in biomedical optics

Traditionally, in biomedical optics, the photons mean fluence rate assessed in a sub-volume of a propagating medium is obtained with Monte Carlo (MC) simulations by calculating the deposited power by the absorbed photons in the sub-volume. We propose an alternative method based on the assessment of the mean pathlength traveled by all the injected photons inside the sub-volume. Examples of its applications are given. This method also works for nil absorption coefficient and for a non-constant spatial distribution of the absorption coefficient inside the sub-volume. The proposed approach is a re-visitation of a well-known method applied in radiation and nuclear physics. %In comparison with the previous literature, we have fully re-framed the relationship between fluence rate and pathlength within the radiative transfer theory where it can be derived in a more natural manner. The relation at the basis of the method descends from the ground definitions of quantities employed in radiative transfer. The results obtained show that a potential advantage of the proposed method is that it can improve the convergence of the MC simulations. Indeed, when calculating the fluence in a region of interest with the proposed method all the photons that cross the region are considered. While, with the traditional approach only the absorbed photons can contribute to the calculated fluence. In the latter case, this may produce a poorer MC statistic for the same number of launched photons.