Hybrid System Modeling of Human Blood Clotting

The process of human blood clotting involves a com- plex interaction of continuous-time/continuous-state processes and discrete-event/discrete-state phenomena, where the former comprise the various chemical rate equations (which can be written as differential equations) and the latter comprise both threshold-limited behaviors and qualitative facets of the coagu- lation cascade. We model this process as a hybrid dynamical system, consisting of both discrete and continuous dynamics. Previous blood clotting models used only continuous dynamics and perforce addressed only portions of the coagulation cascade. 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 deficiencies, sur- feits, and other perturbations of initial values of blood proteins, and their consequences for clotting factor concentrations and for clotting time, especially in the context of known clotting pathologies; and (3) providing fine-grained predictions which may be used to refine clinical understanding of blood clotting.