Analytical sensitivity factors from distributions of time of flight of photons for near-infrared spectroscopy studies in multilayered turbid media.

Significance: In the last years, time-resolved near-infrared spectroscopy (TD-NIRS) has gained increasing interest as a tool for studying tissue spectroscopy with commercial devices. Although it provides much more information than its continuous wave counterpart, accurate models interpreting the measured raw data in real time are still lacking.

Aim: We introduce an analytical model that can be integrated and used in TD-NIRS data processing software and toolkits in real time. This is based on the so-called sensitivity factors (SFs) of the distributions of time of flight (DTOFs) of photons measured in optically turbid and semi-infinite multilayered media, such as the human head.

Approach: We derived analytical expressions for the SFs that link changes in the absorption coefficient of each layer to changes in the statistical moments of DTOFs acquired in a reflectance configuration. This was later validated with results from Monte Carlo (MC) simulations, which stand as the gold standard in terms of photon migration in biological tissue. Next, we designed a couple of simulated experiments depicting how the analytical SFs can be used to retrieve absorption changes in the particular case of a five-layered medium.

Results: Comparison between theory and simulations in 2-, 5-, and 10-layered media showed very good agreement (in most cases with weighted mean absolute percentage errors below 10%). Moreover, our derivations could be run in a few milliseconds (except for the extreme case of the variance SF in the 10-layered medium), which means a speedup of up to 10,000× with respect to MC simulations, with a much better spatial resolution and without their typically associated stochastic noise.

Conclusions: In summary, our method achieves performances similar to those given by MC simulations, but orders of magnitude faster, which makes it very suitable for its implementation in real-time applications.