UC Merced

Blood coagulation is a complex system comprised of numerous biochemical reactions. Due to this complexity, mathematical modeling has been used to increase the overall understanding of the system as a whole, determine previously unknown mechanisms, and to predict system responses. These models, however, may involve uncertainty in both parameter values and kinetic schemes that describe the reactions; this dissertation examines two such ideas. First, we examine the interactions between a specific coagulation factor, FXa, and an experimental tool designed to measure its action, a chromogenic substrate. Second, we examine a more complex mathematical model in regards to its parametric uncertainty. Chapter 1 gives a background on the mathematical tools used in this dissertation and necessary for uncertainty quantification (UQ) and an overview of the two aforementioned systems. In Chapter 2 we demonstrate how an application of UQ identifies a new model for product inhibition between FXa and its chromogenic substrate, which is validated experimentally. In Chapter 3 we conduct an extensive local and global sensitivity analysis for a mathematical model of flow-mediated blood coagulation. We determined that for many cases a local analysis is sufficient to understand the uncertainty in the model’s output, but that for certain cases there are classes of parameters that exhibit strong synergistic behavior, and so a global method that is capable of resolving interaction effects is necessary. These results motivated the work in Chapter 4 where we used global sensitivity analysis on a mathematical model to identify a novel mechanism for recovering a normal clotting response in hemophilia A; the potential mechanism was further supported by experimental validation. Chapter 5 summarizes the conclusions from the preceding chapters and presents ongoing work relating to the two projects.