N. Bessonov

The role of spatial organization of cells in erythropoiesis

Erythropoiesis, the process of red blood cell production, occurs mainly in the bone marrow. The functional unit of mammalian erythropoiesis, the erythroblastic island, consists of a central macrophage surrounded by adherent erythroid progenitor cells (CFU-E/Pro-EBs) and their differentiating progeny, the erythroblasts. Central macrophages display on their surface or secrete various growth or inhibitory factors that influence the fate of the surrounding erythroid cells. CFU-E/Pro-EBs have three possible fates: (a) expansion of their numbers without differentiation, (b) differentiation into reticulocytes that are released into the blood, (c) death by apoptosis. CFU-E/Pro-EB fate is under the control of a complex molecular network, that is highly dependent upon environmental conditions in the erythroblastic island. In order to assess the functional role of space coupled with the complex network behavior in erythroblastic islands, we developed hybrid discrete-continuous models of erythropoiesis. A model was developed in which cells are considered as individual physical objects, intracellular regulatory networks are modeled with ordinary differential equations and extracellular concentrations by partial differential equations. We used the model to investigate the impact of an important difference between humans and mice in which mature late-stage erythroblasts produce the most Fas-ligand in humans, whereas early-stage erythroblasts produce the most Fas-ligand in mice. Although the global behaviors of the erythroblastic islands in both species were similar, differences were found, including a relatively slower response time to acute anemia in humans. Also, our modeling approach was very consistent with in vitro culture data, where the central macrophage in reconstituted erythroblastic islands has a strong impact on the dynamics of red blood cell production. The specific spatial organization of erythroblastic islands is key to the normal, stable functioning of mammalian erythropoiesis, both in vitro and in vivo. Our model of a simplified molecular network controlling cell decision provides a realistic functional unit of mammalian erythropoiesis that integrates multiple microenvironmental influences within the erythroblastic island with those of circulating regulators of erythropoiesis, such as EPO and glucocorticosteroids, that are produced at remote sites.

Design and Testing of Coils for Pulsed Electromagnetic Forming

Coil design influences the distribution of electromagnetic forces applied to both the blank and the coil. The required energy of the process is usually defined by deformation of the blank. However, the discharge also results in a significant amount of heat being generated and accumulating in the coil. Therefore, EMF process design involves working with three different problems: 1) propagation of an electromagnetic field through the coil-blank system and generation of pulsed electromagnetic pressure in specified areas, 2) high-rate deformation of the blank, and 3) heat accumulation and transfer through the coil with the cooling system. In the current work, propagation of an electromagnetic field in the coil, blank, die and surrounding air was defined using a consistent set of quasi stationary Maxwell equations applying a corresponding set of parameters for each media. Furthermore, a deformation of the blank driven by electromagnetic forces distributed through the volume of the blank was modeled using a solid mechanics equation of motion and the elastic plastic flow theory. During the discharge of capacitors the process was considered to be adiabatic due to the short duration of the pulse, so a heat transfer during the discharge time was neglected. The distribution of electric current density integrated during the discharge process defines the increase of temperature at every element of the coil. The distribution of temperature was calculated as a function of time using the energy conservation law.

Modelling of thrombus growth and growth stop in flow by the method of dissipative particle dynamics

Abstract Platelet aggregation at the site of the vascular injury leads to the formation of a hemostatic plug covering the injury site, or a thrombus in the pathological case. The mechanisms that control clot growth or lead to growth arrest are not yet completely understood. In order to study these mechanisms theoretically, we use the Dissipative Particle Dynamics method, which allows us to model individual platelets in the flow and in the clot. The model takes into account different stages of the platelet adhesion process. First, a platelet is captured reversibly by the aggregate, then it is activated and adheres firmly, becoming a part of its core.We suggest that the core of the clot is composed of platelets unable to attach new platelets from the flow due to their activation by thrombin and/or wrapping by the fibrin mesh. The simulations are in a good agreement with the experimental results [9]. Modelling shows that stopping the growth of a hemostatic plug (and thrombus) may result from its exterior part being removed by the flow and exposed its non-adhesive core to the flow.

Model of mucociliary clearance in cystic fibrosis lungs

Mucus clearance is a primary innate defense mechanism in the human airways. Cystic fibrosis (CF) is a genetic disease caused by mutations in the gene encoding the cystic fibrosis transmembrane conductance regulator (CFTR) protein. CF is characterized by dehydration of airway surface liquid and impaired mucociliary clearance. As a result, microorganisms are not efficiently removed from the airways, and patients experience chronic pulmonary infections and inflammation. We propose a new physiologically based mathematical model of muco-ciliary transport consisting of the two major components of the mucociliary clearance system: (i) periciliary liquid layer (PCL) and (ii) mucus layer. We study mucus clearance under normal conditions and in CF patients. Restoring impaired clearance of airway secretions in one of the major goals of therapy in patients with CF. We consider the action of the aerosolized and inhaled medication dornase alfa, which reduces the viscosity of cystic fibrosis mucus, by selectively cleaving the long DNA strands it contains. The results of the model simulations stress the potential relevance of the location of the drug deposition in the central or peripheral airways. Mucus clearance was increased in case the drug was primarily deposited peripherally, i.e. in the small airways.

Numerical Simulation of Pulsed Electromagnetic Stamping Processes

In earlier published papers simulation of electromagnetic forming (EMF) was often conducted assuming that pulsed electromagnetic load can be replaced by the pulse of mechanical force calculating its parameters similar to R-L-C electric circuit. However, in many practical cases, parameters of this circuit are variable during the process because of the displacement of the blank and from one operation to another due to the accumulation of heat in the coil. The distribution of electromagnetic forces is also non-uniform and may affect the quality of the part being stamped. In our opinion, the accuracy of the simulation of EMF can be significantly improved if the formulation of the problem includes Maxwell equations of the electromagnetic field propagation, equations of dynamic elastic-plastic deformation, and heat transfer equations all coupled together. In addition, this approach may provide knowledge of electromagnetic coil deformation, which was investigated earlier with significant simplifications. The complexity of the problem is defined by mutual dependence of all three physical processes (electromagnetic field propagation, dynamic elastic-plastic deformation, and heat transfer) and variable boundary conditions. The propagation of the electromagnetic field is defined by quasi-stationary Maxwell equations transformed in Lagrangian form. The dynamics of elastic-plastic deformation is modeled using the solid mechanics equation of motion, the modified theory of elastic plastic flow, and the Von Mises yield criterion. The energy conservation law is employed for the simulation of heat transfer, which is important to define the appropriate stamping rate without overheating the coil. The developed methodology is illustrated by 2D examples of cone formation from sheet using a flat coil and the conical die and 2D plane strain sheet formation by direct propagation of the electric current through the metal bar, serving as a coil, and through the deformed sheet.

Continuous Modeling of Arterial Platelet Thrombus Formation Using a Spatial Adsorption Equation

In this study, we considered a continuous model of platelet thrombus growth in an arteriole. A special model describing the adhesion of platelets in terms of their concentration was derived. The applications of the derived model are not restricted to only describing arterial platelet thrombus formation; the model can also be applied to other similar adhesion processes. The model reproduces an auto-wave solution in the one-dimensional case; in the two-dimensional case, in which the surrounding flow is taken into account, the typical torch-like thrombus is reproduced. The thrombus shape and the growth velocity are determined by the model parameters. We demonstrate that the model captures the main properties of the thrombus growth behavior and provides us a better understanding of which mechanisms are important in the mechanical nature of the arterial thrombus growth.

Pattern Formation in Hybrid Models of Cell Populations

The paper is devoted to hybrid discrete-continuous models of cell populations dynamics. Cells are considered as individual objects which can divide, die by apoptosis, differentiate and move under external forces. Intra-cellular regulatory networks are described by ordinary differential equations while extracellular species by partial differential equations. We illustrate the application of this approach to some model examples and to the problem of tumor growth. Hybrid models of cell populations present an interesting nonlinear dynamics which is not observed for the conventional continuous models.

Analysis of Blank-Die Contact Interaction in Pulsed Forming Processes

During recent decade, significant efforts were dedicated to increasing the amount of Aluminum Alloys in automotive parts in order to reduce the net weight of cars. Processes of pulsed forming are known to expand the capabilities of traditional stamping operations. Propagation of pulsed electromagnetic field can be defined by quasi-stationary Maxwell equations, solved numerically using a non-orthogonal Lagrangian mesh. Suggested formulation included modelling of contact interaction of the blank with deformable die. Mild contact model based on introduction of acting-in-vicinity forces repelling the surfaces to be in contact was employed. It was tested by analyzing the elastic impact of bars and then was applied to the corner filling operation. This operation was analysed as a single pulse and as a multi pulse forming process. It indicated that some compromise between the blank formability enhancement and level of contact stresses on the die surface can be found. In addition, some examples of tubular parts pulsed press fitting using tube expansion with pulsed pressure were analyzed. Specific attention was paid to the analysis of factors playing important role in residual contact pressure between the exterior and interior tubes in pulsed press fitting operation.