CC BY
2Monte Carlo-based semi-analytical approximation for diffuse reflectance spectroscopy
V. Perekatova1*, M. Kirillin1, A. Khilov1, E. Sergeeva1, D. Kurakina1, I. Turchin1
1-A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, 46 Ul'yanov Street,
Nizhny Novgorod, 603950, Russia
A number of applied studies require quantitative characterization of concentrations of biological chromophores within studied tissue. Diffuse reflectance spectroscopy (DRS) is recognized as a go-to technique for non-invasive reconstruction of concentrations of various tissue chromophores [1] from absorption and scattering spectra of a tissue reconstructed from measured diffuse reflectance spectrum.
The diversity of absorption and scattering spectra of various chromophores presented in tissues makes the reconstruction problem multiparametric and causes the necessity of the most accurate possible solution of direct problem of light transport in tissue.
The simplest approach to the reconstruction of optical properties from diffuse reflectance spectrum uses the solution of Radiative Transfer Equation (RTE) for an infinite medium and diffusion approximation [2]. A more precise analytical model reported by Farrell et al [3] is also based on diffusion approximation of RTE and accounts for semi-infinite refraction-mismatched boundary. However, this model is not applicable at for source-detector distances (SDD) less than a few transport lengths of the tissue. A refined model of diffuse reflectance recently proposed by Sergeeva et al [4] is also based on diffusion approximation of RTE, however, it accounts for the detection fiber diagram.
An alternative way to obtain analytical expressions for diffuse reflectance is to approximate in silico or experimental data with analytical functions. Monte Carlo look-up table for a single SDD value of 0.25 mm and variations of absorption from 0.1 to 5 mm-1 and scattering from 0 to 5 mm-1 was reported in [5], while in look-up [6] tables were created from diffuse reflectance spectra obtained on calibrated phantoms for SDD values of 0.75, 2.00, 3.00, and 4.00 mm with interpolation for reduced scattering values between 0.4 and 1.2 mm-1 and absorption values between 0 and 0.8 mm-1.
We report on a novel semi-analytical fit (SAF) of Monte Carlo simulated diffuse reflectance spectra for SDDs in the range of 0.3 - 9.9 mm and wide range of reduced scattering and absorption coefficients values that covers the physiological range for human skin and most of soft tissues. The comparison of presented model and analytical models based on diffuse approximations reveals the areas of the models' applicability. In this study we also demonstrate a comparison of the accuracy of reconstructing chromophore concentrations from DR spectra simulated for generic tissue using different analytical models and SAF.
The developments of MC platform, semi-analytical fit, comparison of different analytical models with semi-analytical fit are supported by the Center of Excellence "Center of Photonics" funded by The Ministry of Science and Higher Education of the Russian Federation, Contract No. 075-15-2022-316. The reconstruction accuracy analysis of chromophores concentrations is supported by the Russian Science Foundation (project No. 24-75-10068).
[1] R. Nachabe, B.H. Hendriks, M. van der Voort, A.E. Desjardins, H.J. Sterenborg, Estimation of biological chromophores using diffuse optical spectroscopy: benefit of extending the UV-VIS wavelength range to include 1000 to 1600 nm, Biomedical optics express 1, 1432-1442 (2010).
[2] M.S. Patterson, B. Chance, B.C. Wilson, Time resolved reflectance and transmittance for the noninvasive measurement of tissue optical properties, Applied optics 28, 2331-2336 (1989).
[3] T. J. Farrell, M.S. Patterson, B. Wilson, A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo, Medical physics 19, 879-888 (1992).
[4] E. Sergeeva, D. Kurakina, I. Turchin, M. Kirillin, A refined analytical model for reconstruction problems in diffuse reflectance spectroscopy, Journal of Innovative Optical Health Sciences, 2342002 (2024).
[5] R. Hennessy, S.L. Lim, M.K. Markey, J.W. Tunnell, Monte Carlo lookup table-based inverse model for extracting optical properties from tissue-simulating phantoms using diffuse reflectance spectroscopy, Journal of biomedical optics 18, 037003-037003 (2013).
[6] G. Greening, A. Mundo, N. Rajaram, T.J. Muldoon, Sampling depth of a diffuse reflectance spectroscopy probe for in-vivo physiological quantification of murine subcutaneous tumor allografts, Journal of biomedical optics 23, 085006-085006 (2018).
