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Modern approaches to the application of mathematical modeling methods in biomedical research

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This paper presents a brief overview of the main approaches to mathematical modeling of the interaction of optical radiation with biological tissues. In the case of light propagation in tissue, the Monte Carlo method is an approximation of the solution of the radiation transfer equation. This is done by sampling the set of all possible trajectories of light quanta (photon packets) as they pass through the tissue. Such a stochastic model makes it possible to simulate the propagation of light in a turbid (scattering) medium. The main types of interaction between photons and tissue are considered: scattering, absorption, and reflection/refraction at the boundary of the medium. The algorithm of the method is based on the statistical approximation of the estimated parameters instead of using non-linear functional transformations. Efficient methods for modeling the problem of Raman spectroscopy in turbid media are shown, taking into account the parameters of the detector and the sample size. Two fundamental approaches to the numerical simulation of Raman scattering are considered. Based on data from open literary sources, a variant of modeling Raman scattering in normal multilayer human skin in the near infrared wavelength range is shown. The Raman spectra of ex vivo normal skin tissue sections are presented to quantify various intrinsic micro spectral properties of different skin layers. The reconstructed Raman spectrum of the skin is compared with clinically measured skin spectra in vivo. The overall good agreement between the simulated process and experimental data is shown. The possibility of using the sequential Monte Carlo method for data processing in correlation wide-field optical coherence tomography for the study of biological objects is shown.

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