A numerical analysis of factor X activation in the presence of tissue factor--factor VIIa complex in a flow reactor

Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

Membrane-mimetic films containing thrombomodulin and heparin inhibit tissue factor-induced thrombin generation in a flow model

Membrane-mimetic thin films containing thrombomodulin (TM) and/or heparin were produced and their capacity to inhibit thrombin generation evaluated in a continuous flow system. Tissue factor (TF) along with TM and heparin were immobilized in spatially restricted zones as components of a membrane-mimetic film. Specifically, TF was positioned as an upstream trigger for thrombin generation and TM and/or heparin positioned over the remaining downstream portion of test films. Peak and steady-state levels of thrombin were decreased by antithrombin III (ATIII), as well as by surface bound heparin and TM. Although physiologic concentrations of ATIII have the capacity to significantly inhibit thrombin activity, surface bound TM and heparin nearly abolished steady-state thrombin responses. In particular, surface bound TM appears to be superior to heparin in reducing local thrombin concentrations. These studies are the first to demonstrate the additive effect of surface bound heparin and TM as a combined interactive strategy to limit TF-induced thrombin formation.

A Model Incorporating Some of the Mechanical and Biochemical Factors Underlying Clot Formation and Dissolution in Flowing Blood

Multiple interacting mechanisms control the formation and dissolution of clots to maintain blood in a state of delicate balance. In addition to a myriad of biochemical reactions, rheological factors also play a crucial role in modulating the response of blood to external stimuli. To date, a comprehensive model for clot formation and dissolution, that takes into account the biochemical, medical and rheological factors, has not been put into place, the existing models emphasizing either one or the other of the factors. In this paper, after discussing the various biochemical, physiologic and rheological factors at some length, we develop a model for clot formation and dissolution that incorporates many of the relevant crucial factors that have a bearing on the problem. The model, though just a first step towards understanding a complex phenomenon, goes further than previous models in integrating the biochemical, physiologic and rheological factors that come into play.

Surface-dependent coagulation enzymes. Flow kinetics of factor Xa generation on live cell membranes

The initial surface reactions of the extrinsic coagulation pathway on live cell membranes were examined under flow conditions. Generation of activated coagulation factor X (fXa) was measured on spherical monolayers of epithelial cells with a total surface area of 41-47 cm(2) expressing tissue factor (TF) at >25 fmol/cm(2). Concentrations of reactants and product were monitored as a function of time with radiolabeled proteins and a chromogenic substrate at resolutions of 2-8 s. At physiological concentrations of fVIIa and fX, the reaction rate was 3.05 +/- 0.75 fmol fXa/s/cm(2), independent of flux, and 10 times slower than that expected for collision-limited reactions. Rates were also independent of surface fVIIa concentrations within the range 0.6-25 fmol/cm(2). The transit time of fX activated on the reaction chamber was prolonged relative to transit times of nonreacting tracers or preformed fXa. Membrane reactions were modeled using a set of nonlinear kinetic equations and a lagged normal density curve to track the expected surface concentration of reactants for various hypothetical reaction mechanisms. The experimental results were theoretically predicted only when the models used a slow intermediate reaction step, consistent with surface diffusion. These results provide evidence that the transfer of substrate within the membrane is rate-limiting in the kinetic mechanisms leading to initiation of blood coagulation by the TF pathway.