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. 2016 Apr 26;110(8):1869-1885.
doi: 10.1016/j.bpj.2016.03.010.

Computational Study of Thrombus Formation and Clotting Factor Effects Under Venous Flow Conditions

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Free PMC article

Computational Study of Thrombus Formation and Clotting Factor Effects Under Venous Flow Conditions

Vijay Govindarajan et al. Biophys J. .
Free PMC article

Abstract

A comprehensive understanding of thrombus formation as a physicochemical process that has evolved to protect the integrity of the human vasculature is critical to our ability to predict and control pathological states caused by a malfunctioning blood coagulation system. Despite numerous investigations, the spatial and temporal details of thrombus growth as a multicomponent process are not fully understood. Here, we used computational modeling to investigate the temporal changes in the spatial distributions of the key enzymatic (i.e., thrombin) and structural (i.e., platelets and fibrin) components within a growing thrombus. Moreover, we investigated the interplay between clot structure and its mechanical properties, such as hydraulic resistance to flow. Our model relied on the coupling of computational fluid dynamics and biochemical kinetics, and was validated using flow-chamber data from a previous experimental study. The model allowed us to identify the distinct patterns characterizing the spatial distributions of thrombin, platelets, and fibrin accumulating within a thrombus. Our modeling results suggested that under the simulated conditions, thrombin kinetics was determined predominantly by prothrombinase. Furthermore, our simulations showed that thrombus resistance imparted by fibrin was ∼30-fold higher than that imparted by platelets. Yet, thrombus-mediated bloodflow occlusion was driven primarily by the platelet deposition process, because the height of the platelet accumulation domain was approximately twice that of the fibrin accumulation domain. Fibrinogen supplementation in normal blood resulted in a nonlinear increase in thrombus resistance, and for a supplemented fibrinogen level of 48%, the thrombus resistance increased by ∼2.7-fold. Finally, our model predicted that restoring the normal levels of clotting factors II, IX, and X while simultaneously restoring fibrinogen (to 88% of its normal level) in diluted blood can restore fibrin generation to ∼78% of its normal level and hence improve clot formation under dilution.

Figures

Figure 1
Figure 1
Schematic of the biochemical network represented in our model of blood coagulation. Coagulation reactions begin when blood leaking from a breached vessel comes into contact with the tissue factor (TF) expressed extravascularly. Colored arrows show the type of reaction, as indicated in the legend. Reactions shown inside the gray sphere are the platelet-surface reactions, and reactions outside the gray sphere are the reactions taking place in the blood plasma. The biochemical blood coagulation network comprises zymogens, proteolytic enzymes, and their cofactors. Among the key proteins (in an inactive form) are the factors V, VII, VIII, IX, X, and II (prothrombin). Their active counterparts are designated with the suffix “a.” Reactions begin when TF is exposed to the flowing blood and binds with factor VIIa to form the TF:VIIa complex (extrinsic tenase). This is followed by the activation of factors IX and X to IXa and Xa, respectively, by TF:VIIa. Factor Xa in plasma activates plasma prothrombin to form trace amounts of factor IIa (thrombin). Platelet-bound factor Xa activates factors V and VIII to form factors Va and VIIIa, respectively. Factor IXa binds with factor VIIIa on the activated platelet surface to form the complex IXa:VIIIa (intrinsic tenase). Factor Xa binds with factor Va on the surfaces of activated platelets to form the complex Xa:Va (prothrombinase). Extrinsic and intrinsic tenases activate factor X to Xa, with intrinsic tenase acting as the main activator. Prothrombinase activates platelet-bound prothrombin to thrombin, which in turn performs several functions essential for efficient blood coagulation. Thrombin activates factors V and VIII, both on the surface of activated platelets and in plasma. This promotes the formation of intrinsic tenase and prothrombinase, acting as a positive feedback loop increasing thrombin generation. Importantly, thrombin converts fibrinogen to fibrin, which stabilizes the thrombus. The natural anticoagulation mechanisms (i.e., the TF pathway inhibitor and antithrombin III) negatively regulate thrombin generation and activity. The inhibitory protein antithrombin III (ATIII) inactivates several enzymes in the coagulation system, namely, factors IIa, Xa, and IXa, whereas the TF pathway inhibitor (TFPI) inhibits the TF:VIIa complex. To see this figure in color, go online.
Figure 2
Figure 2
Two-dimensional (2D) geometric representation of the flow chamber. (A) Photograph of the overall setup of the flow chamber (image reproduced with permission from Colace et al. (31)). Thrombus formation is initiated when blood flows over a thrombogenic surface in the chamber’s channels. Under the pressure-relief mode, one of the channels is coated with a thrombogenic surface. When a thrombus begins to occlude the channel, blood flow is increased in the thrombus-free channel to maintain a constant outflow (withdrawn from a syringe at the outlet) (31). (B) Three-dimensional geometry of the flow-chamber section that consists of two separate inlets and a single outlet. The dimensions of the channels are as indicated in the figure. (C) The geometry of the flow chamber was constructed to provide a 2D representation (as in (31)). This 2D geometry was constructed so that it maintained a channel height of 60 μm. The channel without a thrombogenic surface is stacked above the channel with one. This reconstructed geometry allowed us to perform simulations in the pressure-relief mode in a 2D setting. Also indicated are the flow boundary conditions used in our simulations. The notation U = 0, V = 0 reflects the no-slip and no-penetration conditions imposed on the walls, where U and V denote the x and y velocity components, respectively. To see this figure in color, go online.
Figure 3
Figure 3
The computational model captures the dynamics of thrombus growth. (A) Model-predicted and experimentally measured platelet accumulation. The solid line (no symbols) shows the normalized model-predicted values of the integral of the concentrations of bound platelets calculated over the entire flow domain. The solid line with square markers shows normalized platelet fluorescence intensity, which represents platelet accumulation observed in the flow-chamber experiment (31). Data points, represented by the markers, were connected with solid lines to enhance the visual representation of the displayed trends. To facilitate data comparisons, the model-generated and experimental data were independently normalized to their corresponding maximal values. (B) Spatial distribution of the deposited platelets at 430 s. The bottom panel shows an enlargement of the model-predicted platelet deposition domain. The experimentally measured platelet accumulation (data extracted from Fig. 7 B in (31)) is indicated by the black line superimposed over the color image. The vertical white dashed lines indicate the beginning and end of the thrombogenic surface. (C) Spatial distribution of the deposited fibrin at 430 s. The experimentally measured fibrin accumulation (data extracted from Fig. 7 C in (31)) is indicated by the black line superimposed over the color image. The vertical white dashed lines indicate the beginning and end of the thrombogenic surface. To see this figure in color, go online.
Figure 4
Figure 4
Fibrin deposition is determined by thrombin generation. (A) Time-dependent maximal values of the model-predicted spatial distribution of thrombin concentration. (B) Fibrin deposition predicted by the model is compared with data from flow-chamber experiments. The solid line (no symbols) shows the normalized integral of the model-predicted fibrin concentration calculated over the entire flow domain. The lines with markers represent the normalized fibrin levels (determined using fluorescence-intensity measurements) reported in different flow-chamber experiments. Data points, represented by the symbols, were connected with solid lines to enhance the visual representation of the displayed trends. To facilitate data comparisons, the model-generated and experimental data were independently normalized to their corresponding maximal values. (C) Time-dependent maximal values of the model-predicted spatial distribution of the intrinsic tenase concentration. (D) Time-dependent maximal values of the model-predicted spatial distribution of the prothrombinase concentration.
Figure 5
Figure 5
Spatial distribution of bound platelets deposited at the thrombogenic surface. (AE) The colors represent the fraction of bound platelets at distinct times in the simulation. This fraction was calculated as the concentration of bound platelets divided by the maximal possible number of platelets in a unit volume (see Supporting Material for details). Only the flow-chamber channel with the thrombogenic surface is shown. To see this figure in color, go online.
Figure 6
Figure 6
Spatial distribution of generated thrombin (left) and deposited fibrin (right) in the simulation. (AE) The colors represent the concentrations of thrombin and fibrin at distinct times in the simulation. Only the flow-chamber channel with the thrombogenic surface is shown. To see this figure in color, go online.
Figure 7
Figure 7
Platelet and fibrin deposition occludes the flow through the bottom channel of the flow chamber. (AE) The colors represent the hydraulic resistance (left) and axial flow velocity (right) in the flow chamber at distinct times in the simulation. To see this figure in color, go online.
Figure 8
Figure 8
The model predicted an increase in hydraulic resistance upon fibrinogen supplementation. (A) Fibrin generation for various fibrinogen supplementation levels (16%, 32%, and 48% beyond the normal level of 5.4 μM). (B) Maximal hydraulic resistance imparted by the generated fibrin in the flow chamber at 430 s. The initial data point (at 0% supplemented fibrinogen level) represents the maximal resistance imparted at the default fibrinogen level. (C) Spatial distribution of hydraulic resistance imparted by normal fibrinogen level and by 48% fibrinogen supplementation at 430 s. (D) Flow axial velocity plotted against the vertical distance from the thrombogenic surface at the region of maximal hydraulic resistance (indicated by the white line in C) within the clot at 430 s. Each axial velocity curve corresponds to one of the considered fibrinogen levels. To see this figure in color, go online.
Figure 9
Figure 9
Effects of blood dilution, fibrinogen supplementation, and PCC supplementation on thrombus development. (A) Thrombin generation for various fibrinogen supplementation levels (16%, 32%, and 48% of 5.4 μM beyond the diluted level of 2.16 μM and PCC supplementation). Note that the thrombin level did not change during fibrinogen supplementation hence the overlap between the curves for diluted blood and those for fibrinogen supplementation. (B) Fibrin generation for various fibrinogen supplementation levels and 48%+PCC fibrin supplementation. (C) Maximal hydraulic resistance imparted by generated fibrin for different fibrinogen supplementation levels and for 48%+PCC fibrin supplementation at 430 s. (D) Flow axial velocity plotted against the vertical distance from the thrombogenic surface at the region of maximal hydraulic resistance within the clot at 430 s. Each axial velocity curve corresponds to one of the considered fibrinogen supplementation levels. To see this figure in color, go online.

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