56 research outputs found
Computational Algorithm for Some Problems with Variable Geometrical Structure
No full textInternational audienceThe work is devoted to the computational algorithm for a problem of plant growth. The plant is represented as a system of connected intervals corresponding to branches. We compute the concentration distributions inside the branches. The originality of the problem is that the geometry of the plant is not a priori given. It evolves in time depending on the concentrations of plant hormones found as a solution of the problem. New branches appear in the process of plant growth. The algorithm is adapted to an arbitrary plant structure and an arbitrary number of branches
Research of a possibility of resonator diagnostics of thin filamentary objects in a low part of the terahertz frequency band
No full textThe method of excitement of the open resonator by the narrow slot on a reflector formed by the waveguide with the highest modes transmitted was experimentally approved. The spectra of such resonator in the range of the frequencies of 85 GHz - 110 GHz were received. It is shown that modes with azimuthal variations of the fleld were most effectively exited. Transformations of spectra by thin dielectric cylinders were researched. A number of parameters of the open resonator, effective in schemes of resonator diagnostics of fllamentary objects with small own losses were found
Influence of Fibrinogen Deficiency on Clot Formation in Flow by Hybrid Model
No full textInternational audienceIn this work we develop the 2D model suggested in [32] in order to study the impact of fibrinogen concentration and the fibrin polymer production rate on clot growth in flow. The model is based on the method of Dissipative Particle Dynamics describing blood plasma flow and platelet suspension and on a system of partial differential equations describing blood coagulation regulatory network. We study the influence of parameters on clot development and on its final size
Research of a possibility of resonator diagnostics of thin filamentary objects in a low part of the terahertz frequency band
No full textThe method of excitement of the open resonator by the narrow slot on a reflector formed by the waveguide with the highest modes transmitted was experimentally approved. The spectra of such resonator in the range of the frequencies of 85 GHz - 110 GHz were received. It is shown that modes with azimuthal variations of the fleld were most effectively exited. Transformations of spectra by thin dielectric cylinders were researched. A number of parameters of the open resonator, effective in schemes of resonator diagnostics of fllamentary objects with small own losses were found
Schematic representation of virus infection dynamics regulation (left) and qualitative forms of the function <i>f</i>(<i>v</i>) (right).
No full textLow level infection stimulates immune response while high level infection down-regulates it. The former corresponds to the growing branch of the function f(v) while the latter to its decreasing branch.</p
Deformable cell model and its application to growth of plant meristem
No full textInternational audienceDeformable cell model is developed to study pattern formation and to simulate plant tissue growth. Each cell represents a polygon with a number of vertices connected by springs. Some cells in the tissue can grow and divide, other cells are differentiated and do not grow or divide but remain deformable. The model is used to investigate formation of self-similar structures which reproduce the same cell organization during their growth. In numerical experiments we observed that self-similar solutions can exist for a rather precise choice of plant structure and mechanical properties of cell walls. We test the model for simulation of apical meristems functioning which represent self-similar cell structures in plants. At the next stage of modelling, auxin distribution is introduced by means of diffusion and polar transport mechanisms. The existence of steady auxin distribution in a growing root is investigated. Single as well as multiple auxin maxima have been observed in model solutions
Mathematical modelling of erythropoiesis in vivo with multiple erythroblastic islands.
No full textInternational audienceErythropoiesis is a process of red blood cell production, which occurs mainly in the bone marrow. It is organized as a large number of small units called erythroblastic islands, each of them containing several dozens of cells. We show that the system of islands is unstable and that stable and constant production of erythrocytes cannot be achieved without a local control mechanism possibly provided by macrophages
Pattern Formation in Hybrid Models of Cell Population
No full textInternational audienceThe 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
Dynamics of erythroid progenitors and erythroleukemia
No full textInternational audienceThe paper is devoted to mathematical modelling of erythropoiesis, production of red blood cells in the bone marrow. We discuss intra-cellular regulatory networks which determine self-renewal and differentiation of erythroid progenitors. In the case of excessive self-renewal, immature cells can fill the bone marrow resulting in the development of leukemia. We introduce a parameter characterizing the strength of mutation. Depending on its value, leukemia will or will not develop. The simplest model of treatment of acute myeloid leukemia with chemotherapy allows us to determine the conditions of successful treatment or of its failure. We show that insufficient treatment can worsen the situation. In some cases curing may not be possible even without resistance to treatment. Modelling presented in this work is based on ordinary differential equations, reaction-diffusion systems and individual based approach
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