Mathematical models of thrombin generation

Thrombin generation is a key step in the formation of a blood clot. It is the only enzyme able to cleave the protein fibrinogen into fibrin, which is vital to both the structure and stability of a clot. The formation of thrombin is the result of many positive and negative feedback loops, controlled by a series of proteins called coagulation factors, whose concentrations vary both between individuals and over time. It is the combined effects of all coagulation factors that regulate both the rate and amount of thrombin that is generated. Many models have been developed to predict the rate of thrombin generation and how it varies under differing conditions. An accurate and reliable model could prove to be a vital tool in drug development, such as for antithrombotics, and could aid in improving our understanding of both haemophilia and cardiovascular disease. However, while these models are validated qualitatively against variation in a few coagulation factors, they have rarely been validated quantitatively under variation in all factors, matching the variation seen in patient data. This sets up the key questions of this work; can any of these models accurately predict thrombin generation across variation in all coagulation factors, and if not, what changes need to be made to achieve this? In this work, we assess the accuracy of eight existing models against coagulation data from a large cohort of donors (n=348), showing none of these models are able to reliably reproduce thrombin generation. We then conduct multiple stages of exploratory analysis, identifying which reactions, reaction rates and coagulation factors control each of the model's predictions. Most notably, we observe a large amount of uncertainty in the reaction rates used to construct these models. We construct a new model of thrombin generation that quantifies the uncertainty in its reaction rates and addresses other issues seen in the current models. We use this new model to show that the uncertainty in these reaction rates results in high levels of uncertainty in model outputs and that the use of parameter inference methods significantly reduces this uncertainty. We conduct a simulation study, identifying improvements in the parameter inference methods we use and test assumptions made during model development. Finally, we outline future improvements and key next steps in the development of these models, most prominently, how to analyse and address model discrepancy and improve model specification