All achievements

Development of viral infection in the tissues such as lymph nodes or spleen is studied depending on virus multiplication in the host cells, their transport and on the immune response. The properties of the cells of the immune system and the initial viral load determine the spatiotemporal regimes of infection dynamics. It is shown that infection can be completely eliminated or it can persist at some level together with a certain chronic immune response in a spatially uniform or oscillatory mode. Finally, the immune cells can be completely exhausted leading to a high viral load persistence in the tissue. Our study shows that both the motility of immune cells and the virus infection propagation represented by the diffusion rate coefficients are relevant control parameters determining the fate of virus-host interaction. 
Reaction-diffusion equation with delay arising in modeling the immune response is investigated. We prove the existence of traveling waves in the bistable case using the Leray– Schauder method. Differently from the previous works, we do not assume here quasi-monotonicity of the delayed reaction term.

Following a stroke, cortical networks in the penumbra area become fragmented and partly deactivated. We develop a model to study the propagation of waves of electric potential in the cortical tissue with integrodifferential equations arising in neural field models. The wave speed is characterized by the tissue excitability and connectivity determined through parameters of the model. Post-stroke tissue damage in the penumbra area creates a hypoconnectivity and decreases the speed of wave propagation. It is proposed that external stimulation could restore the wave speed in the penumbra area under certain conditions of the parameters. Model guided cortical stimulation could be used to improve the functioning of cortical networks.

Formation of blood clot in response to the vessel damage is triggered by the complex network of biochemical reactions of the coagulation cascade. The process of clot growth can be modeled as a traveling wave solution of the bistable reaction–diffusion system. The critical value of the initial condition which leads to convergence of the solution to the traveling wave corresponds to the pulse solution of the corresponding stationary problem. In the current study we prove the existence of the pulse solution for the stationary problem in the model of the main reactions of the blood coagulation cascade using the Leray–Schauder method.
The mechanics of platelet initial adhesion due to interactions between GPIb receptor with von Willebrand factor (vWf) multimers is essential for thrombus growth and the regulation of this process. Multimeric structure of vWf is known to make adhesion sensitive to the hydrodynamic conditions, providing intensive platelet aggregation in bulk fluid for high shear rates. But it is still unclear how it affects the dynamics of platelet motion near vessel walls and efficiency of their adhesion to surfaces. Our goal is to resolve the principal issues in the mechanics of platelet initial attachment via GPIb-vWf bonds in near-wall flow conditions: when the platelet tends to roll or slide and how this dynamics depends on the size, conformation and adhesive properties of the vWf multimers. We employ a 3D computer model based on a combination of the Lattice Boltzmann method with mesoscopic particle dynamics for explicit simulation of vWf-mediated blood platelet adhesion in shear flow. Our results reveal the link between the mechanics of platelet initial adhesion and the physico-chemical properties of vWf multimers. This has implications in further theoretical investigation of thrombus growth dynamics, as well as the interpretation of in vitro experimental data.

Complex multiscale models of the cardiovascular system (CVS) are widely used for the numerical investigation of various CVS pathologies. In particular, the models can be applied to examine the effects of pathological changes in the electromechanical properties of cardiac muscle (myocardium) or diseases of the heart valves on the heart performance. The models of that type combine descriptions of the electromechanics of a cardiac cell, myocardium tissue, heart geometry and vascular bed. The last one is usually specified by simple closed-loop lumped parameter models, which treat the CVS as a set of elastic or viscoelastic reservoirs. In our study we have developed a new model of myocardium mechanics. This model was applied to an axisymetric approximation of the left ventricle of the heart; along with a new lumped parameter model of the CVS, it was used for the simulation of the heart performance at different conditions. The effects of some arrhythmias and the stenosis and insufficiency of the aortic and mitral valves on the haemodynamic variables were simulated. Our study is focused on the development of a 3D model of the heart including a complete electromechanical model of the myocardium within the CVS. Such model could be used for the investigation of effects of local heart tissue electromechanical disorders on the heart performance in medical practice. With further development, the model of the CVS could be used for a decision making in surgery.