Application limits of the scaling relations for Monte Carlo simulations in diffuse optics. Part 2: results

The limits of applicability of scaling relations to generate new simulations of photon migration in scattering media by re-scaling an existing Monte Carlo simulation are investigated both for the continuous wave and the time domain case. We analyzed the convergence properties in various scenarios by numerical methods, trying to derive practical guidelines for the judicious use of this approach, as well as a deeper understanding of the physics behind such relations. In the case of scaling of the absorption coefficient, the convergence is always rigorous both for the forward and inverse problems, relying on the derivatives with respect to the absorption coefficient. Also, the regenerated simulation inherits the very same noise of the original Monte Carlo simulation. In the case of scaling of the scattering coefficient, the situation is more critical. For forward problems, even for just a 10% uniform increase in scattering, appreciable deviations are observed whenever a high number of scattering interactions is involved. We tested a practical criterion based on the number of scattering events in the original simulation to judge the convergence of the scaling factors. For inverse problems, the scaling relations provide accurate regenerated simulations apart from the noise level that is increased with respect to the initial simulation, although anyway lower than the noise level obtained by implementing the direct calculation. The results of this study are important whenever an increase of Monte Carlo code throughput is mandatory, e.g., for fast data analysis of diffuse data, or in machine-learning scenarios, when generating huge datasets is needed.