| Description |
Fibrin fibers are an essential component of blood clots. They provide structural support and prevent embolism. Formation of fibrin fibers is initiated by the enzyme thrombin, which is a product of the coagulation cascade. It converts fibrinogen into fibrin monomers. Fibrin monomers polymerize to form half-staggered protofibrils that laterally aggregate to form fibrin fibers. Fibrin fibers form a mesh or gel-like structure over an injury zone and in and around platelet aggregates. It is known that the structure of fibers are dependent on the conditions in which they are formed. We present a two-dimensional mathematical model of fibrin polymerization in flow with feedback on the fluid. We include a spatial-temporal source of fibrin monomers from a simplified coagulation scheme. In the model, fibrin polymerizes by forming linear bonds between any two oligomers and by forming branch points between any three oligomers. Because we want to track oligomer concentrations composed of any number of monomers and branch points, we have a doubly infinite set of PDEs which include diffusion and advection of oligomers. Using a generating function and a change of variable, we find a closed system of equations to study fibrin gelation and postgelation dynamics. The model tracks both branch point and fibrin mass densities of the gel which are used to calculate a distribution of fiber diameters and pore sizes. The permeability of the gel, which is calculated from the volume fraction of fibrin and the fiber diameters, is used to hinder the fluid velocity through a Brinkman term. We vary model parameters, such as the thrombin production rate and the rate of branch point formation, to find what effect this has on clot structure. We also present two model modifications. We alter the model to include thrombin production on three different distributions of platelet aggregates. We also modify the model to include hindered transport on all proteins. The diffusivity and advection of oligomers and coagulation proteins are dependent on the amount of gel at each spatial locations. An additional velocity term is included that moves proteins from areas of high volume fraction of gel to areas of low gel volume fraction of gel. |
