article: Thromboembolic disease is a leading cause of morbidity and mortality worldwide. In the last several years there have been a number of studies attempting to identify mechanisms that stop thrombus growth. This paper identifies a novel mechanism related to formation of a fibrin cap. In particular, protein transport through a fibrin network, an important component of a thrombus, was studied by integrating experiments with model simulations. The network permeability and the protein diffusivity were shown to be important factors determining the transport of proteins through the fibrin network. Our previous in vivo studies in mice have shown that stabilized non-occluding thrombi are covered by a fibrin network (‘fibrin cap’). Model simulations, calibrated using experiments in microfluidic devices and accounting for the permeable structure of the fibrin cap, demonstrated that thrombin generated inside the thrombus was washed downstream through the fibrin network, thus limiting exposure of platelets on the thrombus surface to thrombin. Moreover, by restricting the approach of resting platelets in the flowing blood to the thrombus core, the fibrin cap impaired platelets from reaching regions of high thrombin concentration necessary for platelet activation and limited thrombus growth. The formation of a fibrin cap prevents small thrombi that frequently develop in the absence of major injury in the 60000 km of vessels in the body from developing into life threatening events.
  Damage or inflammation to the blood vessel wall initiates the development of intravascular clots (thrombi). Uncontrolled growth of thrombi can result in occlusion of the blood vessel, starving tissues in the flow field of nutrients and oxygen. Furthermore, clot fragments washed away from the thrombus (emboli) may lodge in the vasculature of the lungs and brain causing life threatening conditions such as pulmonary embolism and ischemic stroke. Thromboembolic disease is a major biomedical problem with 900,000 cases per year in the USA leading to 300,000 deaths [1]. We have reported [2]–[5] that following laser-induced injury to a few cells lining the vessel wall small non-occlusive thrombi initially grow rapidly by accumulating platelets. After several minutes, growth ceases and the thrombi stabilize. The cessation of growth occurs as the surface composition of the developing thrombus changes. While actively growing during the first few minutes following injury the surface is composed primarily of platelets. As the thrombus stabilizes the surface composition changes to one composed primarily of a fibrin network containing cellular and platelet clusters (Figure 1). We previously developed multi-scale models of clot formation taking into account all main components including hemodynamics, molecular signaling leading to platelet activation and coagulation biochemical reactions taking place in blood and on surfaces of platelets [4], [6]. A combination of experimental approaches, image analysis and multi-scale modeling was used for formulating a novel biological hypothesis of a fibrin cap being capable of stopping blood clot growth by interfering with the transport of thrombin to the thrombus surface. Thrombin is a potent platelet activator and is required for fibrin generation [4], [7], [8]. By interfering with thrombin transport to the thrombus surface, we hypothesize the fibrin cap can limit further growth. Because thrombin is primarily generated by coagulation reactions concentrated on the surface of activated platelets in the thrombus [9], it is important to study the movement of thrombin through the fibrin network to determine if the network limits the distribution of thrombin to affect thrombus growth. Conceivably, the fibrin network forms a diffusion and permeability barrier and prevents the transport of thrombin to the thrombus surface. This paper examines this hypothesis by studying in detail protein advection and diffusion to describe thrombin transport through fibrin networks (fibrin cap). It integrates computational and experimental analysis to show how the formation of a fibrin network limits thrombus growth. Network permeability and protein diffusion are the important factors determining the transport of proteins through the fibrin network of thrombi. We report on the experimental measurements of these factors and the development of a thrombus hemodynamics model incorporating them. We show that networks formed under physiological concentrations of fibrinogen and thrombin do not appreciably affect the diffusion of thrombin indicating the fibrin network does not provide a diffusion barrier. However, it is demonstrated that in permeable fibrin network, thrombin generated by platelets is rapidly washed downstream by advection. Only a thin band upstream and above the source of thrombin maintains an appreciable thrombin concentration, similar to the distribution expected in the absence of a fibrin network. However, the pore size in a newly formed sparse network is small enough to exclude resting platelets in flowing blood from approaching the thrombus core. The resting platelets in flowing blood contacting the thrombus therefore do not reach regions with sufficiently high thrombin concentration necessary for their activation and stable incorporation into the developing thrombus. Thus, the development of a sparse, permeable fibrin network on the thrombus surface may provide a mechanism to limit continued growth of small thrombi. The network does not provide a transport barrier for thrombin but rather a shield blocking resting platelets from approaching sites of thrombin generation. Our results identify a novel mechanism and reinforces the concept that the spatial separation of sites of factor activation and factor activity are important to understanding thrombogenesis. The suggested mechanism may prevent small thrombi, which frequently form as a result of activation or damage of a few endothelial cells, from growing into symptomatic occlusive clots.
  Before quantifying the transport of proteins in fibrin networks, protein diameter distributions were measured using Dynamic Light Scattering (DLS) (Figure 2B). The mean hydrodynamic diameter of thrombin and Fab IgG solutes were found to be 4. 1 nm and 11. 2 nm, respectively. These are in a remarkable agreement with x-ray diffraction results, reporting the size of packing orthorhombic cells to be (4. 5 nm4. 5 nm5. 0 nm) and (8. 06 nm7. 22 nm18. 76 nm) for thrombin [11]–[13] and IgG Fab complexes [14], respectively. Permeability of the fibrin networks was quantified from Darcy' s equation using liquid flow rate and pressure gradient measurements across the fibrin networks. Our measurements showed a substantial decrease of the fibrin network permeability (Darcy' s constant) by three orders of magnitude, as the fibrinogen concentration increased from 0. 2 mg/mL to 4 mg/mL. A power law fit was used to obtain an explicit relationship between the permeability, , and the fibrin volume fraction, . This gave, with (Figure 3A). does not equal zero because it was difficult to collect consistent data for clots prepared at fibrinogen concentrations lower than 1 mg/mL. Under slight hydrostatic pressure the clot fibers deformed, broke near wall regions, and bundled together, severely disrupting the network structure. Meanwhile, clots prepared with fibrinogen concentrations higher than 1 mg/mL were stable to imposed pressure. The measured permeability was in the range from 1 to 1000. This means that the ratio of, where is the protein hydrodynamic radius, is much smaller than 1 and therefore, the effect of hydrodynamic hinderance on diffusion (Equation (2) in Text S2) can be neglected. From the relation obtained by Diamond and Anand [15], [16], (1) the fiber radius, , was found using the measured and values. The calculated fiber radii ranged from 150 nm to 500 nm (Figure 3B), which is in good agreement with the fiber thicknesses evaluated directly from confocal images and with previously reported values of hydrated fiber bundles [16], [17] of coarse gels. The average fiber radius was found to decrease from approximately 450 nm to 200 nm when fibrinogen concentration increased from 1 mg/mL to 4 mg/mL. The values of the diffusion coefficients and mobile fractions of thrombin and Fab IgG were obtained by fitting experimental data obtained by FRAP experiments (Text S1) using Levenberg-Marquardt curve-fitting [18]. The resulting diffusion coefficients are plotted as a function of fibrinogen concentration in Figure 4. For comparison, data reported by Stewart et al. 1988 [19] for BSA molecules and by Spero et al. 2010 [20] for 228 nm and 526 nm diameter PEG-coated particles are also shown. The diffusion coefficient of thrombin and Fab IgG in solution in the absence of fibrinogen were found to be 1102. 6 /s and 400. 9, respectively. By determining the corresponding molecular diameters, one can show that these are in a very good agreement with our DLS measurements. Indeed, from the Stokes-Einstein relation, it follows that. According to our FRAP measurements, the ratio of the diffusion coefficients of thrombin to that of IgG in liquid is = 2. 86. Taking 4. 1 nm, yields the hydrodynamic diameter for IgG 11. 2 nm, which is in agreement with the value given by DLS (Figure 2B). There are no noticeable changes in the diffusion coefficient of thrombin and Fab IgG up to a fibrinogen concentration of 2 mg/mL and 0. 4 mg/mL, respectively, indicating no diffusion retardation. However, the increase of fibrinogen concentration to 4 mg/mL reduced diffusivity of Fab IgG by 22% and diffusivity of thrombin by 13%, indicating that fibrin network structure impedes the molecular diffusion due to smaller gel pore size. Pore size between fibers was estimated from microscope images to vary from 10 m at 0. 4 mg/mL of fibrinogen to less than the microscope resolution of 0. 2 m at 4 mg/mL of fibrinogen. These estimates did not consider pores between fibrils whose dimensions were beyond the microscope resolution limit. Our results also showed that the noticeable changes of thrombin diffusivity occurred when fibrinogen exceeded 2 mg/mL. This correlates with measurements of thrombin adsorption [21], which demonstrated the thrombin absorption increase between 2 mg/mL and 4 mg/mL of fibrinogen. Comparison of the diffusion coefficients obtained from FRAP measurements with diffusion models (Figure 4) shows that the extended Ogston' s model [22] fit the data well, whereas the Johnson model given by Equation (3) in Text S2, overestimates protein diffusion. Here, the diffusivity is plotted as a function of, where is calculated according to Equation (3). The model fitting parameters are given in Table 1. One of the factors determining thrombus growth is the spatial distribution of hemostatic activators such as thrombin which causes activation of platelets and fibrin polymerization. Based on our observations that stabilized thrombi are covered by fibrin [2] and using our in vitro fibrin permeation and protein diffusivity measurements, we built a hemodynamics model to study the effect of the fibrin network on thrombin transport. In the model (Figure 6A), the geometry of a small thrombus comprises a central non-permeable core of radius consisting of densely packed activated platelets and a permeable fibrin network covering the thrombus core. The exterior shape of a thrombus is approximated by a hemisphere of radius. The porous structure of the fibrin cap permits blood flow within the cap, and therefore the transport of proteins includes both diffusion and advection. To determine which mechanism drives protein transport in a thrombus and how it depends on permeability of the network and protein size we compared advective and diffusive fluxes within the fibrin cap. We calculated the flow field for a small thrombus with dimensions, and using solution for the stream function (Equations (13) and (14) in Text S3). We found that the variation of fibrin cap permeability from high to low values noticeably changes the flow through the cap. Highly permeable cap () hardly affects the flow outside the thrombus core (Figure 6C). As the permeability of the cap decreases down to its minimum value of 3, the cap performs almost as a non-permeable shell restricting flow within the thrombus (Figure 6B). In the vicinity of the non-permeable thrombus core, the flow velocity tends to zero according to no-slip boundary conditions, which leads to the formation of a diffusion layer near the surface of the core (Figure 7A). The thickness of this diffusion-prevailing layer can be found from the balance between advective and diffusive fluxes, , where is the thickness of the diffusion layer, is the protein concentration on the core surface, is the protein diffusivity, and is the local advection velocity. In terms of the Peclet number, , this condition means = 1, which yields the thickness of the diffusion layer profile, . Therefore, linearly depends on the protein diffusion coefficient and inversely proportional to the local advection velocity, which in turn, depends on the fibrin cap permeability (Equation (14) in Text S3). Our calculations showed that in high permeable networks the thickness of the thrombin diffusion layer was about 4% of the thrombus radius, whereas for low permeable networks ranged from 10% to 20% of. The larger Fab IgG molecules have 2x lower diffusivity resulting in a 2x thinner diffusion profile than thrombin. This points out the importance of considering effects of protein size on diffusion retardation. The presence of multiple protein molecules inside the thrombus will result in different diffusion layer profiles and therefore, different spatial distributions of proteins inside the thrombus.
  This paper provides justification for a previously unrecognized possible mechanism limiting growth of small asymptomatic thrombi. The mechanism suggests that the fibrin network overlaying a thrombus observed in mice limits the thrombus growth by affecting the transport of proteins and by separating resting platelets in flowing blood from regions of high thrombin concentration generated by the thrombus core. Our analysis integrating experiments on protein diffusion and fluid permeation with the hemodynamic thrombus model revealed that permeability of the fibrin network and protein diffusivity are important factors affecting transport of blood proteins inside the thrombus. We found that over a physiologically relevant range of fibrinogen concentrations (0. 5 to 4 mg/mL) fibrin networks do not seem to form a strong diffusion barrier and that they minimally restrict the diffusion of thrombin. It was shown that the diffusivity of thrombin in the fibrin network can be hindered by 13%, whereas diffusivity of bigger molecules, Fab IgG, can be reduced by as much as 22%. We also found that the fibrin network permeability, , decreases by three orders of magnitude when fibrinogen concentration increases from 0. 5 to 4 mg/mL. This essentially reduces advective flow in thrombi. It should be noted that although FRAP permits measuring diffusivity of proteins in a biopolymer network environment, some limitations exist when studying diffusion in extracellular matrices. As was recently shown [26], in cases where there is cellular accumulation and degradation of the protein diffusant, if diffusion is fast enough, overall FRAP kinetics tends to reflect the time scale of uptake and degradation rather than diffusion. These effects can be important when performing FRAP of thrombin diffusing through platelet aggregates composing a thrombus core. Thrombin binding to platelets' (GP) Ib-V-IX receptors [27] makes the fluorescence recovery a complex function of both binding and diffusion and therefore, requires proper quantitative interpretation [28]. In this case, one should consider Fluorescence Correlation Spectroscopy [29] as an alternative to the FRAP method to measure molecular diffusion [26]. The experimentally obtained metrics characterizing diffusive and advective transport inside the clot were incorporated into a thrombus hemodynamical model to run predictive simulations. We showed that the size of diffusive and advective regions strongly depends on the permeability, , of the fibrin cap and the diffusion coefficient, , of the protein. We demonstrated that the presence of a permeable fibrin cap limits thrombin accumulation on the thrombus surface to its downstream zone. The thrombin concentration on the upstream thrombus surface and in the region above the core are insufficient to support activation of resting platelets in flowing blood near the thrombus. In a high permeable cap, advective flow washes thrombin produced on the surface of the platelets in the thrombus core downstream, thus limiting continued growth except at the very downstream surface of the thrombus. Meanwhile, a low permeable fibrin cap impenetrable to platelets can delay platelet exposure to thrombin and, subsequently, reduce platelet activation and aggregation. The structural composition of thrombi can vary depending on the vessel type (venous versus arterial), the nature of the vessel injury, and physiological and hemodynamic conditions. Recently, [30], [31] studied thrombus development in mouse cremaster arterioles and did not observe fibrin accumulation on the luminal thrombus surface that we see on stabilized small thrombi formed in venules. There are several differences in the injury models that might account for the reported difference in thrombus structure. Arterial thrombi form at higher shear rates and are platelet rich, while venous thrombi are fibrin rich. Additionally, the injury model reported by Stalker et al [31] involves vessel rupture and clot formation in the extravascular space while in the mesentery model thrombi formed in the absence of detectable bleeding. Thus, the extent of injury and exposure of blood to the internal layers of the vessel wall is different in the two injury models. In injuries in which we induce bleeding we observe rapid fibrin accumulation at the base of the thrombus, similar to what was observed in [31]. Recently, using thrombin-sensitive platelet binding sensor (ThS-Ab), Welsh et al. [30] identified thrombin rich regions in the developing thrombus. The sensor binds CD41 on platelets and following thrombin cleavage of the ThS moiety generates a fluorophore. According to this study, the highest levels of thrombin arose between 40 and 160 seconds nearest the injury site where fibrin colocalized and where the thrombus was most mechanically stable. Low thrombin activity was detected away from the vessel wall in the thrombus and was below the minimum detection limit in the outer most, 10 micron thick, layer of the thrombus. Although thrombus composition is different in arterioles, these results are in agreement with our simulations for venous thrombi, showing that thrombin concentration decreases from the thrombus interior to its surface, down regulating thrombus growth. Stalker et al. [31] and Voronov et al. [32] reported the transport of different size molecules through platelet-reach thrombi. It was shown [31] that greater packing density in the core facilitated contact-dependent signaling and limited entry of plasma-borne molecules visualized with fluorophores coupled to dextran and albumin. Using Lattice Boltzmann method to simulate the flow through a reconstructed thrombus and Lagrangian Scalar Tracking with Brownian motion transport to model diffusion, transport of different factors was simulated in [32]. Modelling was performed for an input average lumen blood velocity of 0. 478 cm/s, which resulted in 0. 2 mm/s mean flow rate within the thrombus outer shell. The shell was calculated to be 100-fold more permeable than the thrombus core with core permeability of. These results support our assumption that platelet core in our thrombus model can be considered impermeable relative to the fibrin cap with permeability in the range from to. In [32] the effective diffusion coefficients of FX, ADP and Ca were calculated and the averaged tortuosity, defined as the ratio of the diffusion coefficient in pure liquid phase to that in the clot, was found to be from 2 to 2. 5. Meanwhile, our measurements provide the maximum achievable tortuosity corresponding to 4 mg/mL fibrinogen concentration to be around 1. 14 for thrombin and 1. 28 for Fab-IgG. Although these experimentally derived tortuosity values and tortuosity values calculated in [32] were obtained for different thrombus models and experimental conditions, it is likely the platelet clots hinder molecular diffusion to a greater extent than fibrin networks due to smaller platelet clot pore sizes. Our findings as well as results in [32] demonstrate that both fibrin cap and platelet-rich clots do not present a strong diffusion barrier for the relevant molecules, whereas, permeability can greatly affect protein transport in thrombi. Overall, our results complement recent studies on thrombus development and emphasize the importance of spatial distributions of sites of factor activation and factor activity in regulating thrombogenesis. Our findings suggest that timely formation of a fibrin network on the surface of a developing small thrombus could limit its further growth. The proposed mechanism can prevent small blood clots from becoming large pathological thrombi creating life threatening emboli.
summary: To restrict the loss of blood following rupture of blood vessels, the human body rapidly forms a clot consisting mainly of platelets and fibrin. However, to prevent formation of a pathological clot within vessels (thrombus) as a result of vessel damage or dysfunction, the response must be regulated, and clot formation must be limited. Our previous studies demonstrated that as a laser-induced thrombus stabilized in mice, the ratio of fibrin to platelets at the thrombus surface increased significantly. Stabilized non-occluding thrombi were observed to be covered by a fibrin network (‘fibrin cap’). In the present work the role of the fibrin network in protein transport is examined by integrating experiments in microfluidic devices with the hemodynamic thrombus model. The study reveals permeability of the fibrin network and protein diffusivity to be important factors determining the transport of blood proteins inside the thrombus. It is shown that the fibrin network does not dramatically limit the diffusion of thrombin but impairs flowing platelets in blood from reaching regions of high thrombin concentration thus, reducing the probability they are activated and stably integrated into the thrombus. This novel, counter-intuitive mechanism suggests that a fibrin network formed at early stages of thrombus initiation can prevent normally asymptomatic thrombi from developing into pathological clots.
keywords: physics
  medicine
  computer science
  computer modeling
  theoretical biology
  biology
  computational biology
  biophysics
  hematology
title: Fibrin Networks Regulate Protein Transport during Thrombus Development