A hybrid model of red blood cell production, where cells are considered as discreteobjects while intra-cellular proteins and extra-cellular biochemical substances aredescribed with continuous models, is proposed. Spatial organization and regulation of redblood cell production (erythropoiesis) are investigated. Normal erythropoiesis issimulated in two dimensions, and the influence on the output of the model of someparameters involved in cell fate (differentiation, self-renewal, and death by apoptosis)is studied.

This paper proposes a quantitative model of the reaction-diffusion type to examine thedistribution of interferon-α (IFNα) in a lymph node(LN). The numerical treatment of the model is based on using an original unstructured meshgeneration software Ani3D and nonlinear finite volume method for diffusion equations. Thestudy results in suggestion that due to the variations in hydraulic conductivity ofvarious zones of the secondary lymphoid organs the spatial stationary distribution ofIFNα is essentially heterogeneous across the organs. Highly protecteddomains such as sinuses, conduits, co-exist with the regions in which where the stationaryconcentration of IFNα is lower by about 100-fold. This is the first studywhere the spatial distribution of soluble immune factors in secondary lymphoid organs ismodelled for a realistic three-dimensional geometry.

A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour growth rate depends on the tissue oxygen level in a threshold manner.

The paper is devoted to the method of computer simulation of protein interactions takingpart in photosynthetic electron transport reactions. Using this method we have studiedkinetic characteristics of protein-protein complex formation for four pairs of proteinsinvolved in photosynthesis at a variety of ionic strength values. Computer simulationsdescribe non-monotonic dependences of complex formation rates on the ionic strength as theresult of long-range electrostatic interactions. Calculations confirm that the decrease inthe association second order rate constant at low values of the ionic strength is causedby the protein pairs spending more time in “wrong” orientations which do not satisfy thedocking conditions and so do not form the final complex capable of the electrontransfer.

Blood clotting system (BCS) modelling is an important issue with a plenty of applications in medicine and biophysics. The BCS main function is to form a localized clot at the site of injury preventing blood loss. Mutual influence of fibrin clot consisting mainly of fibrin polymer gel and blood flow is an important factor for BCS to function properly. The process of fibrin polymer mesh formation has not adequately been described by current mathematical models. That is why it is not possible to define the borders of growing clot and model its interaction with a blood flow. This paper main goal is to propose physically well-founded mathematical model of fibrin polymerization and gelation. The proposed model defines the total length of fibrin polymer fibers in the unit volume, determines a position of the border between gel and liquid and allows to evaluate the permeability of growing gel. Without significant structural changes the proposed model could be modified to include the blood shear rate influence on the fibrin polymerization and gelation.

This paper is devoted to solving of dynamic problems in biomechanics that requiredetailed study of fast processes. Numerical method of characteristics is used to model thetemporal development of the processes with high accuracy.

There are two mathematical models of elastic walls of healthy and atherosclerotic bloodvessels developed and studied. The models are included in a numerical model of globalblood circulation via recovery of the vessel wall state equation. The joint model allowsus to study the impact of arteries atherosclerotic disease of a set of arteries onregional haemodynamics.