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.
We constructed a mathematical model of clotting, which is based on a current view of the molecular pathways of blood coagulation. Several hypothetical reactions are introduced to allow accurate description of the spatio-temporal dynamics of blood clotting. The resulting model describes well all spatio-temporal aspects of clotting, as well as data obtained in the homogeneous systems.
A very simple mathematical model of blood coagulation is considered, consisting of a set of three partial differential equations that treat blood as an active (excitable) medium. Many well-known phenomena (running pulses, trigger waves, and dissipative structures) can be observed in such a medium. Recent analytic and numerical results obtained by the authors using this model are presented. The following aspects of the formation of dynamic and static structures in this medium are discussed: (1) three scenarios of the formation of spatially localized standing structures (peaks) observed in the model, (2) complex dynamical modes induced by unstable trigger waves, some of the modes leading to unattenuated activity (dynamical chaos) in the entire space, and (3) a new type of excitation propagation in active media Ð stable multihumped peaks due to trigger wave bifurcation Ð predicted by the model. 6.1 Appearance of multihump pulses upon a decrease in the inhibitor diffusion coefficient; 6.2 Hypothesis of the multihump pulse origin from bifurcation of trigger waves 7. Conclusion 90 7.1 Results of the study and the general theory of active media; 7.2 Relation of the results to the current blood coagulation concepts References 93
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