Currently there is a growing demand for production made from nanomaterials. For example, argentum nanoparticles have found their application in agriculture, light industry and medicine. But the problem of estimation of the extent of their danger for human health is still a subject of scientific discussion.

A 4th year student of MEPhI Department № 85 E.S. Kormazeva (supervisor – the Head of the Laboratory of technology-related risks of the Federal Medical Biophysical Center A.I. Burnazian, FMBA of Russia V.Yu. Soloviev) has worked out a mathematical model of biokinetics of spherical argentum nanoparticles of different sizes. “It is possible not only to estimate the contents of nanoparticles in vital organs of animals, but also make a prognosis of their distribution in human organisms with its help”, - commented Ekaterina Kormazeva.

The model of nanoparticles’ biokinetics considers 3 possible ways of nanoparticles’ getting into the organism (peroral, inhalation and intravenous) and two modes of injection (one-time and chronic). The mathematical model is described by the system of equations made on the basis of physiologically based pharmacokinetic modeling.

Fig.1. System of equations where M(i) stands for nanoparticles in i-th organ , Ktb(i), Kbt(i) – biokinetic constants of i-th organ, K1ex, K2ex, K3ex – constants modelling nanoparticles’ drainage from the organism, F(D,t) – functions, modelling nanoparticles’ injection.

Fig.2. Biokinetics model scheme

Experimental values of the distribution of argentum nanoparticles in the organs of male rats of the Wistar-line for one-time intragastric injection have been taken as baseline data. Constants for each of the organs have been found by the method of successive approximation.

As constants in Physiologically based pharmacokinetic modeling are dependent on physiological parametres of the organism, re-calculation of constants from laboratory animals to humans has been made.

Fig.3. Distribution of spherical argentum nanoparticles with diameter of 35 nm in one-time peroral injection into the organism of a) a rat; b) a human being

The algorithm of constants’ calculation can be applied to the nanoparticles of other shape, size and form. The results of the constants will allow model other conditions of the experiment.