A Hybrid-System Model of the Coagulation Cascade

The process of human blood clotting involves a complex interaction of continuous-time/continuous-state processes and discrete-event/discrete-state phenomena, where the former comprise the various chemical rate equations and the latter comprise both thresholdlimited behaviors and binary states (presence/absence of a chemical). Whereas previous blood-clotting models used only continuous dynamics and perforce addressed only portions of the coagulation cascade, we capture both continuous and discrete aspects by modeling it as a hybrid dynamical system. The model was implemented as a hybrid Petri net, a graphical modeling language that extends ordinary Petri nets to cover continuous quantities and continuous-time flows. The primary focus is simulation; specifically, we are interested in (1) fidelity of simulation to the actual clotting process in terms of clotting factor concentrations and elapsed time; (2) simulating known clotting pathologies; and (3) providing fine-grained predictions which may be used to refine clinical understanding of blood clotting. Finally, we examine the sensitivity of a critical purely-continuous subsystem to rate-constant perturbation.