Mathematical models of fibrin polymerization: past, present, and future

Blood clotting is a complex biochemical and biophysical process that leads to the formation of a stabilizing fibrin mesh. Fibrin polymerization is a necessary, multi-stage component of this process and occurs on multiple temporal and spatial scales. These complexities make it difficult to predict how polymerization is affected by perturbations or under varying conditions. Mathematical modeling has been a fruitful approach in generating and testing novel hypotheses about this process. In this review, we focus on the historical context leading to current mathematical models of fibrin polymerization and discuss the contributions of biochemical interactions between thrombin, fibrin(ogen), and factor XIII. We highlight mathematical models that encompass multiple spatial and temporal scales (coarse-grain models, kinetic models, and models incorporating flow and transport effects). We also discuss the unique sets of challenges and benefits of each of these models, and finally, we suggest directions for future focus.