Mathematical modeling of blood coagulation cascade: kinetics of intrinsic and extrinsic pathways in normal and deficient conditions

Mathematical models of coagulation-are we there yet?

BACKGROUND

Mathematical models of coagulation have been developed to mirror thrombin generation in plasma, with the aim of investigating how variation in coagulation factor levels regulates hemostasis. However, current models vary in the reactions they capture and the reaction rates used, and their validation is restricted by a lack of large coherent datasets, resulting in questioning of their utility.

OBJECTIVES

To address this debate, we systematically assessed current models against a large dataset, using plasma coagulation factor levels from 348 individuals with normal hemostasis to identify the causes of these variations.

METHODS

We compared model predictions with measured thrombin generation, quantifying and comparing the ability of each model to predict thrombin generation, the contributions of the individual reactions, and their dependence on reaction rates.

RESULTS

We found that no current model predicted the hemostatic response across the whole cohort and all produced thrombin generation curves that did not resemble those obtained experimentally. Our analysis has identified the key reactions that lead to differential model predictions, where experimental uncertainty leads to variability in predictions, and we determined reactions that have a high influence on measured thrombin generation, such as the contribution of factor XI.

CONCLUSION

This systematic assessment of models of coagulation, using large dataset inputs, points to ways in which these models can be improved. A model that accurately reflects the effects of the multiple subtle variations in an individual's hemostatic profile could be used for assessing antithrombotics or as a tool for precision medicine.

An adjoint-based method for the computation of gradients in coagulation schemes

An adjoint-based methodology is proposed to compute the gradient of the outcomes of mathematical models for the coagulation cascade. The method is first exposed and validated by considering a simple, analytically tractable case involving only 3 species. Its potential is further illustrated by considering a detailed model for the extrinsic pathway involving 34 chemical species interacting through 45 chemical reactions and for which the gradient of Endogeneous Thrombin Potential, clotting time, maximum rate and peak value of thrombin with respect to the initial concentrations and reactions rates are computed. It is shown that the method produces gradients estimates that are fully consistent with the finite differences approximation used so far in the literature, but at a much lower computational cost.

Computational modeling of hypercoagulability in COVID-19

Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has infected more than 100 million people worldwide and claimed millions of lives. While the leading cause of mortality in COVID-19 patients is the hypoxic respiratory failure from acute respiratory distress syndrome, there is accumulating evidence that shows excessive coagulation also increases the fatalities in COVID-19. Thus, there is a pressing demand to understand the association between COVID-19-induced hypercoagulability and the extent of formation of undesired blood clots. Mathematical modeling of coagulation has been used as an important tool to identify novel reaction mechanisms and to identify targets for new drugs. Here, we employ the coagulation factor data of COVID-19 patients reported from published studies as inputs for two mathematical models of coagulation to identify how the concentrations of coagulation factors change in these patients. Our simulation results show that while the levels of many of the abnormal coagulation factors measured in COVID-19 patients promote the generation of thrombin and fibrin, two key components of blood clots, the increased level of fibrinogen and then the reduced level of antithrombin are the factors most responsible for boosting the level of fibrin and thrombin, respectively. Altogether, our study demonstrates the potential of mathematical modeling to identify coagulation factors responsible for the increased clot formation in COVID-19 patients where clinical data is scarce.

Immobilized thrombin on X-ray radiopaque polyvinyl alcohol/chitosan embolic microspheres for precise localization and topical blood coagulation

Trans-catheter arterial embolization (TAE) plays an important role in treating various diseases. The available embolic agents lack X-ray visibility and do not prevent the reflux phenomenon, thus hindering their application for TAE therapy. Herein, we aim to develop a multifunctional embolic agent that combines the X-ray radiopacity with local procoagulant activity. The barium sulfate nanoparticles (BaSO₄ NPs) were synthesized and loaded into the polyvinyl alcohol/chitosan (PVA/CS) to prepare the radiopaque BaSO₄/PVA/CS microspheres (MS). Thereafter, thrombin was immobilized onto the BaSO₄/PVA/CS MS to obtain the thrombin@BaSO₄/PVA/CS MS. The prepared BaSO₄/PVA/CS MS were highly spherical with diameters ranging from 100 to 300 μm. In vitro CT imaging showed increased X-ray visibility of BaSO₄/PVA/CS MS with the increased content of BaSO₄ NPs in the PVA/CS MS. The biocompatibility assessments demonstrated that the MS were non-cytotoxic and possessed permissible hemolysis rate. The biofunctionalized thrombin@BaSO₄/PVA/CS MS showed improved hemostatic capacity and facilitated hemostasis in vitro. Additionally, in vivo study performed on a rabbit ear embolization model confirmed the excellent X-ray radiopaque stability of the BaSO₄/PVA/CS MS. Moreover, both the BaSO₄/PVA/CS and thrombin@BaSO₄/PVA/CS MS achieved superior embolization effects with progressive ischemic necrosis on the ear tissue and induced prominent ultrastructural changes in the endothelial cells. The findings of this study suggest that the developed MS could act as a radiopaque and hemostatic embolic agent to improve the embolization efficiency.

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Excellent in vitro and in vivo visibility of BaSO₄/PVA/CS MS.

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Excellent cytocompatibility and hemocompatibility of BaSO₄/PVA/CS MS.

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Enhanced hemostatic capacity and hemostasis of thrombin@BaSO₄/PVA/CS MS.

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Potential application of thrombin@BaSO₄/PVA/CS MS for in vivo embolization.

Exploring the efficiency of thrombin inhibitors with a quantitative model of the coagulation cascade

A detailed mathematical description of the coagulation cascade is a challenging task due to a huge set of protein-protein interactions. Simplified models do not permit quantitative description of anticoagulants. The detailed mathematical model presented here was constructed with 98 reactions between 70 species. The model was verified using experimental data on thrombin generation. Four thrombin inhibitors, which have different inhibitory mechanisms, were incorporated into the model. All four thrombin inhibitors delayed prothrombin conversion into thrombin, but did not preclude it. At high inhibitor concentration, thrombin-mediated positive feedback loops were strongly inhibited and the proportion of prothrombin, converted with factor Xa only, was considerably increased. The most potent inhibitor of prothrombin conversion was aptamer NU172, which also binds prothrombin and inhibits its conversion.

Recent advances in computational modeling of fibrin clot formation: A review

The field of thrombosis and hemostasis is crucial for understanding and developing new therapies for pathologies such as deep vein thrombosis, diabetes related strokes, pulmonary embolisms, and hemorrhaging related diseases. In the last two decades, an exponential growth in studies related to fibrin clot formation using computational tools has been observed. Despite this growth, the complete mechanism behind thrombus formation and hemostasis has been long and rife with obstacles; however, significant progress has been made in the present century. The computational models and methods used in this context are diversified into different spatiotemporal scales, yet there is no single model which can predict both physiological and mechanical properties of fibrin clots. In this review, we list the major strategies employed by researchers in modeling fibrin clot formation using recent and existing computational techniques. This review organizes the computational strategies into continuum level, system level, discrete particle (DPD), and multi-scale methods. We also discuss strengths and weaknesses of various methods and future directions in which computational modeling of fibrin clots can advance.

Distinct features of bivalent direct thrombin inhibitors, hirudin and bivalirudin, revealed by clot waveform analysis and enzyme kinetics in coagulation assays

AIMS

Bivalent direct thrombin inhibitors (DTIs), hirudin and bivalirudin, bind to the active site and exosite 1 of thrombin irreversibly and reversibly, respectively. The present study aims to assess in vitro effects of hirudin and bivalirudin through clot waveform analysis (CWA) and enzyme kinetics in coagulation assays.

METHODS

The pooled normal plasma and its dilutions were spiked with hirudin or bivalirudin. The activated partial thromboplastin time (APTT) assay and the Clauss fibrinogen assay were performed using the CS-5100 (Sysmex). The APTT-CWA data were automatically gained by the CS-5100 programme.

RESULTS

In APTT-CWA, the maximum coagulation velocity, acceleration and deceleration were decreased dependently on the drug concentrations, demonstrating evidence for the blockade of thrombin-positive feedback by hirudin or bivalirudin. The Hill plot analysis was applied to the dose-dependent curves in bivalirudin. The Hill coefficients were greater than 1, showing positive anticoagulant cooperativity. Regarding the dose-dependent curves in hirudin, all the parameters dropped to almost zero without making an asymptotic line. In the Clauss fibrinogen assay, the Lineweaver-Burk plots demonstrated that both drugs exhibit mixed inhibition mimicking uncompetitive binding. The Dixon plots in bivalirudin were linear and supported the inhibition type described above. The Dixon plots in hirudin were non-linear and inappropriate to use for determination of the inhibition type. In addition, the inverse function of the clotting time appeared to drop to zero without making an asymptotic line, suggesting complete loss of thrombin activity by irreversible binding.

CONCLUSIONS

The results provide insights into anticoagulation with bivalent DTIs.

Assessment of in vitro effects of direct thrombin inhibitors and activated factor X inhibitors through clot waveform analysis

Aims

Clot waveform analysis (CWA) has been reported to extend the interpretation of clotting time measurement. The parameters obtained from successive derivatives of the clotting reaction curves reflect the rates of activation of individual coagulation factors, theoretically dissecting the cascade pathway. This study aims to assess the in vitro effects of direct thrombin inhibitors (DTIs) and activated factor X (FXa) inhibitors.

Methods

CWA was applied to the activated partial thromboplastin time (APTT) assay of plasma samples spiked with each drug. For CWA of APTT measurement curves (APTT-CWA), the positive mode of clotting reaction curves was defined as the direction towards fibrin generation.

Results

All the maximum positive values in the successive derivatives were decreased dependently on the concentrations of each drug. Moreover, the negative values in the second and third derivatives appeared putatively due to consumption of thrombin and factor FXa, respectively, to form complexes with plasma serine protease inhibitors. The decrease of the maximum negative values observed dependently on the concentrations of each drug appeared to be consistent with the decreased generation of thrombin and factor FXa. The analysis of Hill coefficients of each drug in the dose–response of changes in the APTT-CWA parameters revealed a difference in anticoagulant cooperativity between DTIs versus FXa inhibitors.

Conclusions

The APTT-CWA demonstrated evidence for the blockade of thrombin-positive feedback by DTIs and FXa inhibitors and that for the differences in anticoagulant cooperativity between them. The results demonstrate the usability of CWA for assessment of anticoagulation and provide insights into direct anticoagulants.

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.

Introducing the pro-coagulant contact system in the numerical assessment of device-related thrombosis

Thrombosis is a major concern in blood-coated medical devices. Contact activation, which is the initial part of the coagulation cascade in device-related thrombosis, is not considered in current thrombus formation models. In the present study, pro-coagulant reactions including the contact activation system are coupled with a fluid solver in order to evaluate the potential of the contact system to initiate thrombin production. The biochemical/fluid model is applied to a backward-facing step configuration, a flow configuration that frequently appears in medical devices. In contrast to the in vivo thrombosis models in which a specific thrombotic zone (injury region) is set a priori by the user to initiate the coagulation reaction, a reactive surface boundary condition is applied to the whole device wall. Simulation results show large thrombin concentration in regions related to recirculation zones without the need of an a priori knowledge of the thrombus location. The numerical results align well with the regions prone to thrombosis observed in experimental results reported in the literature. This approach could complement thrombus formation models that take into account platelet activity and thrombus growth to optimize a wide range of medical devices.

Adaptive release of heparin from anticoagulant hydrogels triggered by different blood coagulation factors

Feedback-controlled anticoagulant hydrogels were formed by crosslinking the anticoagulant heparin with star-shaped poly(ethylene glycol) using peptide linkers, which are selectively cleaved by different activated blood coagulation factors acting as proteolytic enzymes. Various cleavable peptide units, differing either in their thrombin turnover rates or in their responsiveness to factors activated earlier in the course of blood coagulation, were used for the formation of the biohybrid materials. Release triggered by the early coagulation factors Xa (FXa) or FXIIa/kallikrein was shown to enhance the efficiency of the released anticoagulant. Furthermore, FXa-cleavable gels enabled a faster release of heparin, which was attributed to the lower affinity of the factor for heparin. Combining early and fast responses, FXa-cleavable gels were shown to provide anticoagulant protection of biomaterial surfaces at low levels of released heparin in human whole-blood incubation experiments. The results demonstrate the potential for employing biomolecular circuits in the design of functional biomaterials to tailor the adaptive delivery of bioactive molecules.

Multi-Constituent Simulation of Thrombus Deposition

In this paper, we present a spatio-temporal mathematical model for simulating the formation and growth of a thrombus. Blood is treated as a multi-constituent mixture comprised of a linear fluid phase and a thrombus (solid) phase. The transport and reactions of 10 chemical and biological species are incorporated using a system of coupled convection-reaction-diffusion (CRD) equations to represent three processes in thrombus formation: initiation, propagation and stabilization. Computational fluid dynamic (CFD) simulations using the libraries of OpenFOAM were performed for two illustrative benchmark problems: in vivo thrombus growth in an injured blood vessel and in vitro thrombus deposition in micro-channels (1.5 mm × 1.6 mm × 0.1 mm) with small crevices (125 μm × 75 μm and 125 μm × 137 μm). For both problems, the simulated thrombus deposition agreed very well with experimental observations, both spatially and temporally. Based on the success with these two benchmark problems, which have very different flow conditions and biological environments, we believe that the current model will provide useful insight into the genesis of thrombosis in blood-wetted devices, and provide a tool for the design of less thrombogenic devices.

The balance of pro- and anticoagulant processes underlying thrombin generation

BACKGROUND

The generation of thrombin in time is the combined effect of the processes of prothrombin conversion and thrombin inactivation. Measurement of prothrombin consumption used to provide valuable information on hemostatic disorders, but is no longer used, due to its elaborate nature.

OBJECTIVES

Because thrombin generation (TG) curves are easily obtained with modern techniques, we developed a method to extract the prothrombin conversion curve from the TG curve, using a computational model for thrombin inactivation.

METHODS

Thrombin inactivation was modelled computationally by a reaction scheme with antithrombin, α(2) Macroglobulin and fibrinogen, taking into account the presence of the thrombin substrate ZGGR-AMC used to obtain the experimental data. The model was validated by comparison with data obtained from plasma as well as from a reaction mixture containing the same reactants as plasma.

RESULTS

The computational model fitted experimental data within the limits of experimental error. Thrombin inactivation curves were predicted within 2 SD in 96% of healthy subjects. Prothrombin conversion was calculated in 24 healthy subjects and validated by comparison with the experimental consumption of prothrombin during TG. The endogenous thrombin potential (ETP) mainly depends on the total amount of prothrombin converted and the thrombin decay capacity, and the peak height is determined by the maximum prothrombin conversion rate and the thrombin decay capacity.

CONCLUSIONS

Thrombin inactivation can be accurately predicted by the proposed computational model and prothrombin conversion can be extracted from a TG curve using this computational prediction. This additional computational analysis of TG facilitates the analysis of the process of disturbed TG.

Agent based modeling of blood coagulation system: implementation using a GPU based high speed framework

The coagulation and fibrinolytic systems are complex, inter-connected biological systems with major physiological roles. The complex, nonlinear multi-point relationships between the molecular and cellular constituents of two systems render a comprehensive and simultaneous study of the system at the microscopic and macroscopic level a significant challenge. We have created an Agent Based Modeling and Simulation (ABMS) approach for simulating these complex interactions. As the scale of agents increase, the time complexity and cost of the resulting simulations presents a significant challenge. As such, in this paper, we also present a high-speed framework for the coagulation simulation utilizing the computing power of graphics processing units (GPU). For comparison, we also implemented the simulations in NetLogo, Repast, and a direct C version. As our experiments demonstrate, the computational speed of the GPU implementation of the million-level scale of agents is over 10 times faster versus the C version, over 100 times faster versus the Repast version and over 300 times faster versus the NetLogo simulation.

Effect of hemodilution on coagulation and recombinant factor VIIa efficacy in human blood in vitro

BACKGROUND

This study evaluates the effect of hemodilution by various common resuscitation fluids, and the efficacy of activated recombinant factor VII (rFVIIa) on coagulation parameters in human blood in vitro.

METHODS

Samples from normal healthy volunteers (n = 9) were hemodiluted from 0% to 90% with normal saline, or 0%, 40%, 60%, and 80% with 5% albumin, Hespan, Hextend, normal saline, or lactated Ringer's, and incubated at 37°C ± 1°C for 30 minutes with and without rFVIIa (1.26 μg/mL).

RESULTS

There was a strong correlation between the dilution of hemoglobin (Hb), platelets, or fibrinogen and coagulation parameters. Hemodilution 0% to 90% changed coagulation parameters (prothrombin time [PT], activated partial thromboplastin time [aPTT], and thromboelastography) in an exponential fashion; the greatest changes occurred after hemodilution lowered Hb <6 mg/dL, platelet count < 100,000/mm(3), and fibrinogen concentration <200 mg/dL. PT and aPTT were significantly prolonged after 60% and 80% dilution for all fluids. Hemodilution of 60% and 80% significantly decreased clot strength (maximum amplitude) and the kinetics of clot development (α angle) and increased the clot formation time (K). Hemodilution with Hextend and Hespan decreased maximum amplitude and α angle >5% albumin, lactated Ringer's, or normal saline. rFVIIa significantly improved PT at 60% and 80% dilutions, and aPTT at 80% dilution. There was a significant effect of dilution, but not fluid type, on the efficacy of rFVIIa to change PT and aPTT, and the onset of clotting (R).

CONCLUSIONS

We have strong in vitro evidence that Hb <6 mg/dL, platelet count <100,000/mm(3), and fibrinogen concentration <200 mg/dL can be used as indexes of hemodilution-induced coagulopathy. This study also shows that Hextend and Hespan tend to decrease the clotting ability >5% albumin or the crystalloids. rFVIIa significantly decreased PT at all dilutions and aPTT at the highest dilution. The effectiveness of rFVIIa on PT and aPTT was significantly affected by the degree of dilution, but not by the type of fluid.

In vitro analysis of polyurethane foam as a topical hemostatic agent

Topical hemostatic agents can be used to treat problematic bleedings in patients who undergo surgery. Widely used are the collagen- and gelatin-based hemostats. This study aimed to develop a fully synthetic, biodegradable hemostatic agent to avoid exposure to animal antigens. In this in vitro study the suitability of different newly developed polyurethane-based foams as a hemostatic agent has been evaluated and compared to commonly used agents. An experimental in vitro test model was used in which human blood flowed through the test material. Different modified polyurethane foams were compared to collagen and gelatin. The best coagulation was achieved with collagen. The results of the polyurethane foam improved significantly by increasing the amount of polyethylene glycol. Therefore, the increase of the PEG concentration seems a promising approach. Additional in vivo studies will have to be implemented to assess the application of polyurethane foam as a topical hemostatic agent.