Dynamics of pathologic clot formation: A mathematical model

• Mathematical model of dynamics of pathological clot formation is developed.
• The case of slow clot formation (time window: 3–6 h).
• Kinetic constants of the initiating biochemical reactions were evaluated.
• Influence of different inhibitors on clot dynamics was studied.
• Simultaneous inhibition of factors XI and XII for clot prophylaxis is proposed.

Recent studies have provided evidence of a significant role of the Hageman factor in pathologic clot formation. Since auto-activation of the Hageman factor triggers the intrinsic coagulation pathway, we study the dynamics of pathologic clot formation considering the intrinsic pathway as the predominant mechanism of this process. Our methodological approach to studying the dynamics of clot formation is based on mathematical modelling. Activation of the blood coagulation cascade, particularly its intrinsic pathway, is known to involve platelets. Therefore, equations accounting for the effects of activated platelets on the intrinsic pathway activation are included in our model. This brings about a considerable increase in the values of kinetic constants involved in the model of the principal biochemical processes resulting in clot formation.The purpose of this study is to elucidate the mechanism of pathologic clot formation. Since the time window of thrombolysis is 3–6 h, we hypothesize that in many cases the rate of pathologic clot formation is much lower than that of haemostatic clot. This assumption is used to simplify the mathematical model and to estimate kinetic constants of biochemical reactions that initiate pathologic clot formation. The insights we gained from our mathematical model may lead to new approaches to the prophylaxis of pathologic clot formation. We believe that one of the most efficient ways to prevent pathologic clot formation is simultaneous inhibition of activated factors ХII and ХI.