MATHEMATICAL SIMULATIONS

      Linear models of light propagation in turbid biological media and tissues.
      The key element of development of methods and devices for noninvasive medical spectrophotometry (NMS) is the theoretical simulation of a distribution of incident and second low-intensity light in randomly non-homogeneous (turbid) biological tissues and liquids. In the modern mathematical physics such modeling is most often carried out within the limits of the so-called photometric (energetic) Radiative Transport Theory (RTT) or of its different approaches - approximation by Eddington, Shuster-Schwarzschild, Milne, diffusion approach, Pn-method, a method of moments etc. The main problem is a calculation of a distribution of a radiation field inside and on a surface of biological media for various boundary conditions and optic-physical characteristics of the medium for the purpose of competent development of data processing algorithms which have to work with the use of a principle of the inverse optical tasks solution. 
Scientific achievements of our laboratory in this issue consist of a number of obtained new exact and analytical closed-form theoretical solutions of a number of important and interesting problems in RTT, which was not resolved before. It should be specially noted, that just analytical, exact and closed-form solutions, not approximate numerical methods are needed in NMS, because the instruments must work in real time and must solve the inverse problem in time, not more than 100 milliseconds, and with an accuracy of at least 95% (the error of the count should not be more than 5% ).

     Mathematical simulation of the processes in the blood microcirculation system
     A considerable quantity of various diseases is interfaced to disorders in a blood microcirculation system very much. Microcirculation infringements in tissues and organs come to light not only for the overwhelming majority of cardiovascular diseases, but also for tumoral processes, diabetes, stomach ulcers, a chronic obstructive bronchitis, etc. Therefore a considerable quantity of medical treatments is usually directed on normalization of microhaemodynamics and improvement of tissues' metabolism. Molecules of nitrogen oxide (NO) are known factor of endothelium vasodilatation of vessels. In one of our research in 2011 we have used exogenous NO at therapy of patients with diseases of head & neck organs. A study of dynamics of blood microcirculation by a method Laser Doppler Flowmetry was in parallel conducted and the theoretical estimation of diffusion of NO through a skin and a mucous membrane of a cavity of a nose has been executed.