Mathematical model of binding of albumin-bilirubin complex to the surface of carbon pyropolymer.

We proposed a mathematical model and estimated the parameters of adsorption of albumin-bilirubin complex to the surface of carbon pyropolymer. Design data corresponded to the results of experimental studies. Our findings indicate that modeling of this process should take into account fractal properties of the surface of carbon pyropolymer.

The effect of convective flows on blood coagulation processes.

Two mathematical models of clot growth in the fluid flows have been considered. The first one is the model of embolus growth in a wall-adjacent flow. The effect of hydrodynamic flows on proceeding chemical reactions and the backward effect of the growing clot on the flow are taken into account. The growing thrombus is assumed to be porous and having low permeability, that is in good agreement with experimental data. The exact solutions determining the distribution of a fluid velocity close to the embolus have been used. Numerical analysis of these solutions have demonstrated that hydrodynamic flows can essentially affect the processes of blood coagulation, and consequently on the clot structure. Their presence might lead to the destruction of chemical fronts having a cylindrical symmetry and formation of the so-called chemical spots. The second model describes the initial stage of thrombus growing in the hemorrhage into a natural internal space. It permits accounting for vessel geometry and provides studying the effects of geometric parameters on fluid flows and coagulation processes. The process of thrombus growth is shown to depend on the ratio of typical values of blood velocity in the vessel and rate of chemical reactions.

[New spatial-temporal dynamics in a reaction-electrodiffusion system]. / Novye prostranstvenno-vremennye rezhimy v sisteme reaktsiia-élektrodiffuziia.

The properties of a system reaction-electrodiffusion were studied using two-component model of interaction and diffusion of charged particles near membrane in solutions of low ionic strength to which traditional assumptions about local electroneutrality of medium are not applicable. It is shown that the effect of self-consistent electric field leads to bistability, the appearance of localized structures with contrast charge distribution and regimes aperiodical in time and in space.

[Analysis of seasonal fluctuations in the Lotka-Volterra model]. / Uchet sezonnosti v modeli Lotki-Vol'terra.

A modification of the Lotka-Volterra model was proposed. The modification takes into account the factor of seasonal fluctuations in a "predator-prey" model. In this modification, interactions between species in summer are described by the Lotka-Volterra equations; in winter, individuals of both species extinct. This generalization makes the classic model unrough, which substantially extends the field of its application. The results of numerical simulation illustrate the statement formulated above.

[The effect of electric field on the spatial-time patterns in the reaction-diffusion system]. / Vliianie élektricheskogo polia na prostranstvenno-vremennye struktury v sisteme "reaktsiia-diffusiia".

A model of electrodiffusion processes in the vicinity of cell membrane was developed. The model takes into account chemical reactions, Coulomb interactions between charged particles and the effect of external electric field. It was concluded that the applied electric field can change the characteristics of space-time patterns in the system. Dissipative structures slowly move and this is accompanied by a change in the number of structure elements. The characteristic equation includes odd powers of the wavenumber, which can lead to the appearance of soliton-like structures. The dissipative structures can appear not only due to the Turing diffusion instability but due to the disperse instability under electric field the applied.