A mathematical model of tissue factor-induced blood coagulation: discrete sites of initiation and regulation under conditions of flow

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Jordan, Sumanas W.
Chaikof, Elliot L.
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A mathematical model of blood coagulation under defined flow conditions, initiated and modulated by spatially discrete regions of surface bound tissue factor (TF) and thrombomodulin (TM), respectively, is presented. The model incorporates fluid phase and surface-associated reactions of the extrinsic, intrinsic, and common pathways, as well as three inhibitory pathways. The spatially heterogeneous model is formulated by finite element method, and an effective prothrombotic zone, which quantifies the spatial propagation of thrombin generation is defined. Characteristic features of coagulation are simulated under physiologic conditions, and the behavior of the system in response to perturbations in TF and TM surface densities, TF site dimensions, and wall shear rate is explored. The major findings of these studies include: (i) The model system responds in an 'all-or-none', threshold-like manner to changes in model parameters. (ii) It was found that prothrombotic effects may extend significantly beyond the dimensions of the spatially discrete site of TF expression in both axial and radial directions. (iii) The relationship between the length of the effective prothrombotic zone and the interval distance between tandem sites of TF expression dictate the net response of the system. Additive prothrombotic effects of sub-clinical lesions as well as suppressive antithrombotic effects of intervening TM-containing regions were observed. Secondly, the computational model is applied to calculate an individualized, systems-based metric of clotting potential for 210 pre-menopausal women in the Leiden Thrombophilia Study (LETS). The simulated variable was found to be a highly predictive parameter for deep venous thrombosis risk.
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