Analytical photon measurement density functions in flat and spherical layered media

VERA, DEMIÁN A.; GARCÍA, HÉCTOR A; BAEZ, GUIDO R.; WAKS SERRA, MARÍA V; CARBONE, N A; IRIARTE, DANIELA I; POMARICO, JUAN A

Munich

Conferencia; European Conference on Biomedical Optics (ECBO 2023); 2023

Optical Society of Amereica (OSA)

In last decades, the use of light in the near infrared region, specially in the so called optical window (650𝑛𝑚≤𝜆≤950𝑛𝑚) has gained attention due to its capability to noninvasively explore biological tissues at low cost usual applications of Near Infrared Spectroscopy techniques range from monitoring brain´s functional behavior or detection of injured tissue, to optical mammography. The mean penetration depth of photons, i e the depth from which information can be retrieved, depends on the optical and geometrical properties of the medium itself absorption and reduced scattering coefficients 𝜇𝑎and 𝜇𝑠′ respectively), the refractive index ( as well as the possible presence of inhomogeneities, etc together withthe particular characteristics of the measurements regime of the light source ( continuous wave, frequency modulated), distance between source and detectors optodes etc Because of this, it is of great importance to have previous knowledge about the best configuration toobtain the desired information Photon measurement density functions (PDMF)  offer a simple and intuitive tool to deal with this They are usually obtained analyticallybut, up to now, this has been possible only for homogeneous geometries for multilayered geometries, Monte Carlo ( simulations or numerical methods are needed, but these can be computationally expensive and time demanding In this work, PMDFs are obtainedanalytically for simplified, yet useful, layered geometries, such as semi infinite and spherical media a schema of these geometries is shown in Figure 1 Comparisons withMonte Carlo simulations are shown for the particular case of two layered media, which are of special interest in the field of fNIRS 3 when considering cerebral and extracerebral regions to evaluate brain hemodynamics very good agreement (error<  10%) is achieved between both methods up to three orders of magnitude below peak in the obtained profiles of the PMDFs as an additional advantage, the time taken by the theoretical calculations isseveral orders of magnitude (more than 6) lower than the corresponding Monte Carlo approach.