Instabilities in fibrinolytic regulatory system. Theoretical analysis of blow-up phenomena

The network of fibrinolytic regulatory reactions is analyzed by means of a bipartite graph technique. Basic kinetic models relevant to the graphs describing the fibrinolytic regulatory system (FRS) with several degrees of resolution are derived. These models enable us to describe the phenomenon of threshold activation of fibrinolytic processes. The activation is accompanied by plasmin and urokinase blow-up generation. The areas in parametric space corresponding to threshold activation of FRS are established. It is shown that blow-up generation of plasmin may be caused by a supercritical perturbation of the values of dynamical variables (the active enzyme concentrations) as well as by the change of system parameters. An expression for the threshold activation value is suggested. Possible medical applications of the obtained results are discussed. (c) 2012 Elsevier Ltd. All rights reserved.