Key result
Mathematical modeling using matched asymptotic expansions provided simplified models that accurately capture the explosive growth and decay of thrombin generation.
This mathematical modeling study provides simplified, validated models of thrombin generation that capture its complex growth and decay dynamics.
Provides efficient thrombin models for in silico studies; leaves open clinical translation pending experimental validation.
We undertake a mathematical investigation of a model for the generation of thrombin, an enzyme central to haemostatic blood coagulation, as well as to thrombotic disorders, that is the end product of a complicated protein cascade with multiple feedbacks that ensures its production in the right place at the right time. In a laboratory setting, its central role is reflected in thrombin evolution over time being used as a measure of the ability of a patient's blood to clot. Here, we present a model for the generation of thrombin (based on earlier work) and analyse it using the method of matched asymptotic expansions to derive a sequence of simplified models that characterize the roles of distinct interactions over various timescales. In particular, we are able through the asymptotic analysis to provide simplified models that are an excellent substitute for the full model (capturing the explosive growth and decay of thrombin) and approximations for the key experimental measurements used to describe thrombin's characteristic evolution over time. The asymptotic results are validated against numerical simulations.
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Dunster et al. (2016) studied Thrombotic disorders. Mathematical modelling was evaluated on Thrombin evolution over time. Mathematical modeling using matched asymptotic expansions provided simplified models that accurately capture the explosive growth and decay of thrombin generation.
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