[A numerical study of the stability of some autowave solutions in a mathematical model of blood coagulation]

The stability of some types of solutions of a system of equations in a mathematical model of blood coagulation has been considered. The numerical methods of solving the perturbation problems and the apparatus of adjoint equations were used. The conclusion was made that spiral waves are stable in the system under consideration, and traveling pulses at parameters corresponding to the chaotic regime in the punctual problem are unstable.

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.

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.

[Analysis of seasonal fluctuations in the Lotka-Volterra model]

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.

[New spatial-temporal dynamics in a reaction-electrodiffusion system]

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.

Dynamics of spatially nonuniform patterning in the model of blood coagulation

We propose a reaction-diffusion model that describes in detail the cascade of molecular events during blood coagulation. In a reduced form, this model contains three equations in three variables, two of which are self-accelerated. One of these variables, an activator, behaves in a threshold manner. An inhibitor is also produced autocatalytically, but there is no inhibitor threshold, because it is generated only in the presence of the activator. All model variables are set to have equal diffusion coefficients. The model has a stable stationary trivial state, which is spatially uniform and an excitation threshold. A pulse of excitation runs from the point where the excitation threshold has been exceeded. The regime of its propagation depends on the model parameters. In a one-dimensional problem, the pulse either stops running at a certain distance from the excitation point, or it reaches the boundaries as an autowave. However, there is a parameter range where the pulse does not disappear after stopping and exists stationarily. The resulting steady-state profiles of the model variables are symmetrical relative to the center of the structure formed. (c) 2001 American Institute of Physics.

[The effect of electric field on the spatial-time patterns in the reaction-diffusion system]

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.

[Reconstructive surgery in post-traumatic lesions of the thyreohyoid membrane]

A new method of surgical intervention to treat problems in the dividing function of the larynx is described. The de novo produced anastomosis between the hyoid bone and the larynx is supported by a muscular-fascial graft formed from the superior laryngeal muscles. This operation has been successfully performed in three patients with severe lesions of the thyrohyoid membrane.