Spatiotemporal dynamics of fibrin formation and spreading of active thrombin entering non-recalcified plasma by diffusion

Comparative Analysis of Thrombin Calibration Algorithms and Correction for Thrombin-α2macroglobulin Activity

Background: The thrombin generation (TG) test is useful for characterizing global hemostasis potential, but fluorescence substrate artifacts, such as thrombin-α2macroglobulin (T-α2MG) signal, inner filter effect (IFE), substrate consumption, and calibration algorithms have been suggested as sources of intra- and inter-laboratory variance, which may limit its clinical utility. Methods: Effects of internal vs. external normalization, IFE and T-α2MG on TG curves in normal plasma supplemented with coagulation factors, thrombomodulin, and tissue factor were studied using the Calibrated Automated Thrombinography (CAT; Diagnostica Stago, Parsippany, NJ, USA) and in-house software. Results: The various calibration methods demonstrated no significant difference in producing TG curves, nor increased the robustness of the TG assay. Several TG parameters, including thrombin peak height (TPH), produced from internal linear calibration did not differ significantly from uncalibrated TG parameters. Further, TPH values from internal linear and nonlinear calibration with or without T-α2MG correction correlated well with TPH from external calibration. Higher coefficients of variation (CVs) for TPH values were observed in both platelet-free and platelet-rich plasma with added thrombomodulin. Conclusions: Our work suggests minimal differences between distinct computational approaches toward calibrating and correcting fluorescence signals into TG levels, with most samples returning similar or equivalent TPH results.

A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions

Platelets upregulate the generation of thrombin and reinforce the fibrin clot which increases the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the pathogenesis of venous cardiovascular diseases remains hard to quantify. An experimentally validated model of thrombin generation dynamics is formulated. The model predicts that a high platelet count increases the peak value of generated thrombin as well as the endogenous thrombin potential (ETP) as reported in experimental data. To investigate the effects of platelets density, shear rate, and wound size on the initiation of blood coagulation, we calibrate a previously developed model of venous thrombus formation and implement it in 3D using a novel cell-centered finite-volume solver. We conduct numerical simulations to reproduce in vitro experiments of blood coagulation in microfluidic capillaries. Then, we derive a reduced one-equation model of thrombin distribution from the previous model under simplifying hypotheses and we use it to determine the conditions of clotting initiation on the platelet count, the shear rate, and the plasma composition. The initiation of clotting also exhibits a threshold response to the size of the wounded region in good agreement with the reported experimental findings.

Clustering of Thrombin Generation Test Data Using a Reduced Mathematical Model of Blood Coagulation

Correct interpretation of the data from integral laboratory tests, including Thrombin Generation Test (TGT), requires biochemistry-based mathematical models of blood coagulation. The purpose of this study is to describe the experimental TGT data from healthy donors and hemophilia A (HA) and B (HB) patients. We derive a simplified ODE model and apply it to analyze the TGT data from healthy donors and HA/HB patients with in vitro added tissue factor pathway inhibitor (TFPI) antibody. This model allows the characterization of hemophilia patients in the space of three most important model parameters. The proposed approach may provide a new quantitative tool for the analysis of experimental TGT. Also, it gives a reduced model of coagulation verified against clinical data to be used in future theoretical large-scale modeling of thrombosis in flow.

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.

Conditions of microvessel occlusion for blood coagulation in flow

Vessel occlusion is a perturbation of blood flow inside a blood vessel because of the fibrin clot formation. As a result, blood circulation in the vessel can be slowed down or even stopped. This can provoke the risk of cardiovascular events. In order to explore this phenomenon, we used a previously developed mathematical model of blood clotting to describe the concentrations of blood factors with a reaction-diffusion system of equations. The Navier-Stokes equations were used to model blood flow, and we treated the clot as a porous medium. We identify the conditions of partial or complete occlusion in a small vessel depending on various physical and physiological parameters. In particular, we were interested in the conditions on blood flow and diameter of the wounded area. The existence of a critical flow velocity separating the regimes of partial and complete occlusion was demonstrated through the mathematical investigation of a simplified model of thrombin wave propagation in Poiseuille flow. We observed different regimes of vessel occlusion depending on the model parameters both for the numerical simulations and in the theoretical study. Then, we compared the rate of clot growth in flow obtained in the simulations with experimental data. Both of them showed the existence of different regimes of clot growth depending on the velocity of blood flow.

Reaction-diffusion waves of blood coagulation

One of the main characteristics of blood coagulation is the speed of clot growth. In the current work we consider a mathematical model of the coagulation cascade and study existence, stability and speed of propagation of the reaction-diffusion waves of blood coagulation. We also develop a simplified one-equation model that reflects the main features of the thrombin wave propagation. For this equation we estimate the wave speed analytically. The resulting formulas provide a good approximation for the speed of wave propagation in a more complex model as well as for the experimental data.

Modelling of platelet-fibrin clot formation in flow with a DPD-PDE method

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD-PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.

Modular chemical mechanism predicts spatiotemporal dynamics of initiation in the complex network of hemostasis

This article demonstrates that a simple chemical model system, built by using a modular approach, may be used to predict the spatiotemporal dynamics of initiation of blood clotting in the complex network of hemostasis. Microfluidics was used to create in vitro environments that expose both the complex network and the model system to surfaces patterned with patches presenting clotting stimuli. Both systems displayed a threshold response, with clotting initiating only on isolated patches larger than a threshold size. The magnitude of the threshold patch size for both systems was described by the Damköhler number, measuring competition of reaction and diffusion. Reaction produces activators at the patch, and diffusion removes activators from the patch. The chemical model made additional predictions that were validated experimentally with human blood plasma. These experiments show that blood can be exposed to significant amounts of clot-inducing stimuli, such as tissue factor, without initiating clotting. Overall, these results demonstrate that such chemical model systems, implemented with microfluidics, may be used to predict spatiotemporal dynamics of complex biochemical networks.

Matrix protein microarrays for spatially and compositionally controlled microspot thrombosis under laminar flow

Microarraying allows the spatial and compositional control of surfaces, typically for the purpose of binding reactions. Collagen and/or von Willebrand Factor (vWF) in 5% glycerol was contact printed onto glass slides to create defined microspots (176-microm diameter) of adsorbed protein without sample dehydration. The arrays were mounted on flow chambers allowing video microscopy during perfusion (wall shear rate of 100-500 s(-1)) of recalcified corn trypsin inhibitor-treated whole blood or platelet rich plasma and subsequent array scanning via anti-GPIbalpha and anti-fibrin(ogen) immunofluorescence. To mimic the subendothelial matrix, vWF was microarrayed over sonicated type I collagen microspots. For whole blood perfusion (500 s(-1), 10 min) over collagen, vWF, and collagen/vWF microspots, the amount of platelet deposition on the collagen/vWF spots was approximately 2 times greater in comparison to the collagen spots and approximately 18 times greater in comparison to the vWF spots. The amount of fibrin(ogen) deposition on the collagen/vWF spots was approximately 2 times greater in comparison to the collagen spots and approximately 4 times greater in comparison to the vWF spots. This protocol allowed for highly uniform (CV = 18%) and precisely located thrombus formation at a density of >or=400 spots/cm(2). Microarrays are ideal for the combinatorial assembly of adhesive and procoagulant proteins to study thrombosis as well as to study axial and lateral transport effects between discrete microspots of distinct composition.

Hemophilia A and B are associated with abnormal spatial dynamics of clot growth

To gain greater insight into the nature of the bleeding tendency in hemophilia, we compared the spatial dynamics of clotting in platelet-free plasma from healthy donors and from patients with severe hemophilia A or B (factor VIII:C or IX:C<1%). Clotting was initiated via the intrinsic or extrinsic pathway in a thin layer of nonstirred plasma by bringing it in contact with the glass or fibroblast monolayer surface. The results suggest that clot growth is a process consisting of two distinct phases, initiation and elongation. The clotting events on the activator surface and the preceding period free of visible signs of clotting are the initiation phase. In experiments with and without stirring alike, this phase is prolonged in hemophilic plasma activated by the intrinsic, but not the extrinsic pathway. Strikingly, both hemophilia A and B are associated with a significant deterioration in the elongation phase (clot thickening), irrespective of the activation pathway. The rate of clot growth in hemophilic plasma is significantly lower than normal and declines quickly. The resulting clots are thin, which may account for the bleeding disorder.