A model for the stoichiometric regulation of blood coagulation

Kinetic analysis of prothrombinase assembly and substrate delivery mechanisms

Prothrombinase complex, composed of coagulation factors Xa (FXa) and Va (FVa) is a major enzyme of the blood coagulation network that produces thrombin via activation of its inactive precursor prothrombin (FII) on the surface of phospholipid membranes. However, pathways and mechanisms of prothrombinase formation and substrate delivery are still discussed. Here we designed a novel mathematical model that considered different potential pathways of FXa or FII binding (from the membrane or from solution) and analyzed the kinetics of thrombin formation in the presence of a wide range of reactants concentrations. We observed the inhibitory effect of large FVa concentrations and this effect was phospholipid concentration-dependent. We predicted that efficient FII activation occurred via formation of the ternary complex, in which FVa, FXa and FII were in the membrane-bound state. Prothrombin delivery was mostly membrane-dependent, but delivery from solution was predominant under conditions of phospholipid deficiency or FXa/FVa excess. Likewise, FXa delivery from solution was predominant in the case of FVa excess, but high FII did not switch the FXa delivery to the solution-dependent one. Additionally, the FXa delivery pathway did not depend on the phospholipid concentration, being the membrane-dependent one even in case of the phospholipid deficiency. These results suggest a flexible mechanism of prothrombinase functioning which utilizes different complex formation and even inhibitory mechanisms depending on conditions.

Mathematical modeling identifies clotting factor combinations that modify thrombin generation in normal and factor VIII-, IX-, or XI-deficient blood

Background

In healthy individuals, plasma levels of clotting proteins naturally vary within a range of 50% to 150% of their mean values. We do not know how these variations modify thrombin generation.

Objectives

To assess the impact of protein level variations on simulated thrombin generation in normal and factor (F)VIII-, FIX-, or FXI-deficient blood.

Methods

We used a mathematical model of flow-mediated coagulation to simulate thrombin generation with all possible combinations of clotting protein variations within the normal range and for various tissue factor levels. We selected, analyzed, and ranked combinations that enhanced thrombin generation compared with baseline.

Results

Protein variations most strongly affected thrombin generation at intermediate tissue factor levels. Low tissue factor levels prevented coagulation initiation, while high tissue factor levels always triggered thrombin generation. At intermediate levels, we identified protein variations that substantially modified thrombin generation. Low-normal FV shortened lag times and increased thrombin generation, whereas high-normal FV lengthened lag times and reduced thrombin generation. With severe FVIII and FIX deficiencies, low-normal tissue factor pathway inhibitor α and antithrombin amplified the effect of low-normal FV. For moderate FVIII and FIX deficiencies, high-normal tissue factor pathway inhibitor α and antithrombin enhanced the impact of high-normal FV in reducing thrombin production. In normal and FXI-deficient blood, high-normal FVIII and FIX significantly boosted thrombin generation.

Conclusion

Our mathematical model predicted how variations in clotting protein levels, within the normal range, could contribute to the variability of bleeding phenotypes observed with clotting factor deficiencies. Our study generated experimentally testable hypotheses that could aid in developing new therapies toward normal hemostasis.

Modelling the effects of 4-factor prothrombin complex concentrate for the management of factor Xa-associated bleeding

The management of factor Xa (FXa) inhibitor-associated bleeding remains a clinical challenge. Massive bleeding is often associated with complex coagulopathy and, thus, the sole reversal of FXa inhibitors might not be sufficient to restore hemostasis, requiring instead a multimodal approach. Four-factor prothrombin complex concentrate (4F-PCC) is widely recognized as a viable treatment option for FXa inhibitor-associated bleeding. Here, we applied computational models to explore the effect 4F-PCC has on the coagulation cascade and restoration of thrombin generation in a system that simulates a patient that has received a FXa inhibitor. The coagulation model is largely based on a previously developed model with modifications incorporated from various other published sources. The model was calibrated and validated using data from a phase 3 clinical trial of vitamin K antagonist reversal with 4F-PCC. Using the parameters and initial conditions determined during the calibration and validation process, the prothrombin time (PT) test simulations predicted a PT of 11.4 seconds. The model successfully simulated the effects of rivaroxaban and apixaban on total thrombin concentration and showed that 4F-PCC increased thrombin generation in the presence of rivaroxaban or apixaban.

Sulfated Polysaccharides with Anticoagulant Potential: A Review Focusing on Structure-Activity Relationship and Action Mechanism

Thromboembolism is the culprit of cardiovascular diseases, leading to the highest global mortality rate. Anticoagulation emerges as the primary approach for managing thrombotic conditions. Notably, sulfated polysaccharides exhibit favorable anticoagulant efficacy with reduced side effects. This review focuses on the structure-anticoagulant activity relationship of sulfated polysaccharides and the underlying action mechanisms. It is concluded that chlorosulfonicacid-pyridine method serves as the preferred technique to synthesize sulfated polysaccharides. The anticoagulant activity of sulfated polysaccharides is linked to the substitution site of sulfate groups, degree of substitution, molecular weight, main side chain structure, and glycosidic bond conformation. Moreover, sulfated polysaccharides exert anticoagulant activity via various pathways, including the inhibition of blood coagulation factors, activation of antithrombin III and heparin cofactor II, antiplatelet aggregation, and promotion of the fibrinolytic system.

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.

Gene Dosage of F5 c.3481C>T Stop-Codon (p.R1161Ter) Switches the Clinical Phenotype from Severe Thrombosis to Recurrent Haemorrhage: Novel Hypotheses for Readthrough Strategy

Inherited defects in the genes of blood coagulation essentially express the severity of the clinical phenotype that is directly correlated to the number of mutated alleles of the candidate leader gene (e.g., heterozygote vs. homozygote) and of possible additional coinherited traits. The F5 gene, which codes for coagulation factor V (FV), plays a two-faced role in the coagulation cascade, exhibiting both procoagulant and anticoagulant functions. Thus, defects in this gene can be predisposed to either bleeding or thrombosis. A Sanger sequence analysis detected a premature stop-codon in exon 13 of the F5 gene (c.3481C>T; p.R1161Ter) in several members of a family characterised by low circulating FV levels and contrasting clinical phenotypes. The propositus, a 29 y.o. male affected by recurrent haemorrhages, was homozygous for the F5 stop-codon and for the F5 c.1691G>A (p.R506Q; FV-Leiden) inherited from the heterozygous parents, which is suggestive of combined cis-segregation. The homozygous condition of the stop-codon completely abolished the F5 gene expression in the propositus (FV:Ag < 1%; FV:C < 1%; assessed by ELISA and PT-based one-stage clotting assay respectively), removing, in turn, any chance for FV-Leiden to act as a prothrombotic molecule. His father (57 y.o.), characterised by severe recurrent venous thromboses, underwent a complete molecular thrombophilic screening, revealing a heterozygous F2 G20210A defect, while his mother (56 y.o.), who was negative for further common coagulation defects, reported fully asymptomatic anamnesis. To dissect these conflicting phenotypes, we performed the ProC®Global (Siemens Helthineers) coagulation test aimed at assessing the global pro- and anticoagulant balance of each family member, investigating the responses to the activated protein C (APC) by means of an APC-sensitivity ratio (APC-sr). The propositus had an unexpectedly poor response to APC (APC-sr: 1.09; n.v. > 2.25), and his father and mother had an APC-sr of 1.5 and 2.0, respectively. Although ProC®Global prevalently detects the anticoagulant side of FV, the exceptionally low APC-sr of the propositus and his discordant severe-moderate haemorrhagic phenotype could suggest a residual expression of mutated FV p.506QQ through a natural readthrough or possible alternative splicing mechanisms. The coagulation pathway may be physiologically rebalanced through natural and induced strategies, and the described insights might be able to track the design of novel treatment approaches and rebalancing molecules.

A numerical study of the effect of thrombus breakdown on predicted thrombus formation and growth

Thrombosis is a complex biological process which involves many biochemical reactions and is influenced by blood flow. Various computational models have been developed to simulate natural thrombosis in diseases such as aortic dissection (AD), and device-induced thrombosis in blood-contacting biomedical devices. While most hemodynamics-based models consider the role of low shear stress in the initiation and growth of thrombus, they often ignore the effect of thrombus breakdown induced by elevated shear stress. In this study, a new shear stress-induced thrombus breakdown function is proposed and implemented in our previously published thrombosis model. The performance of the refined model is assessed by quantitative comparison with experimental data on thrombus formation in a backward-facing step geometry, and qualitative comparison with in vivo data obtained from an AD patient. Our results show that incorporating thrombus breakdown improves accuracy in predicted thrombus volume and captures the same pattern of thrombus evolution as measured experimentally and in vivo. In the backward-facing step geometry, thrombus breakdown impedes growth over the step and downstream, allowing a stable thrombus to be reached more quickly. Moreover, the predicted thrombus volume, height and length are in better agreement with the experimental measurements compared to the original model which does not consider thrombus breakdown. In the patient-specific AD, the refined model outperforms the original model in predicting the extent and location of thrombosis. In conclusion, the effect of thrombus breakdown is not negligible and should be included in computational models of thrombosis.

Quick model-based viscoelastic clot strength predictions from blood protein concentrations for cybermedical coagulation control

Cybermedical systems that regulate patient clotting in real time with personalized blood product delivery will improve treatment outcomes. These systems will harness popular viscoelastic assays of clot strength such as thromboelastography (TEG), which help evaluate coagulation status in numerous conditions: major surgery (e.g., heart, vascular, hip fracture, and trauma); liver cirrhosis and transplants; COVID-19; ICU stays; sepsis; obstetrics; diabetes; and coagulopathies like hemophilia. But these measurements are time-consuming, and thus impractical for urgent care and automated coagulation control. Because protein concentrations in a blood sample can be measured in about five minutes, we develop personalized, phenomenological, quick, control-oriented models that predict TEG curve outputs from input blood protein concentrations, to facilitate treatment decisions based on TEG curves. Here, we accurately predict, experimentally validate, and mechanistically justify curves and parameters for common TEG assays (Functional Fibrinogen, Citrated Native, Platelet Mapping, and Rapid TEG), and verify results with trauma patient clotting data.

Decoding thrombosis through code: a review of computational models

From the molecular level up to a blood vessel, thrombosis and hemostasis involves many interconnected biochemical and biophysical processes over a wide range of length and time scales. Computational modeling has gained eminence in offering insights into these processes beyond what can be obtained from in vitro or in vivo experiments, or clinical measurements. The multiscale and multiphysics nature of thrombosis has inspired a wide range of modeling approaches that aim to address how a thrombus forms and dismantles. Here, we review recent advances in computational modeling with a focus on platelet-based thrombosis. We attempt to summarize the diverse range of modeling efforts straddling the wide-spectrum of physical phenomena, length scales, and time scales; highlighting key advancements and insights from existing studies. Potential information gleaned from models is discussed, ranging from identification of thrombus-prone regions in patient-specific vasculature to modeling thrombus deformation and embolization in response to fluid forces. Furthermore, we highlight several limitations of current models, future directions in the field, and opportunities for clinical translation, to illustrate the state-of-the-art. There are a plethora of opportunity areas for which models can be expanded, ranging from topics of thromboinflammation to platelet production and clearance. Through successes demonstrated in existing studies described here, as well as continued advancements in computational methodologies and computer processing speeds and memory, in silico investigations in thrombosis are poised to bring about significant knowledge growth in the years to come.

Dynamic adaptive moving mesh finite-volume method for the blood flow and coagulation modeling

In this work, we develop numerical methods for the solution of blood flow and coagulation on dynamic adaptive moving meshes. We consider the blood flow as a flow of incompressible Newtonian fluid governed by the Navier-Stokes equations. The blood coagulation is introduced through the additional Darcy term, with a permeability coefficient dependent on reactions. To this end, we introduce moving mesh collocated finite-volume methods for the Navier-Stokes equations, advection-diffusion equations, and a method for the stiff cascade of reactions. A monolithic nonlinear system is solved to advance the solution in time. The finite volume method for the Navier-Stokes equations features collocated arrangement of pressure and velocity unknowns and a coupled momentum and mass flux. The method is conservative and inf-sup stable despite the saddle point nature of the system. It is verified on a series of analytical problems and applied to the blood flow problem in the deforming domain of the right ventricle, reconstructed from a time series of computed tomography scans. At last, we demonstrate the ability to model the coagulation process in deforming microfluidic capillaries.

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, [Formula: see text], and provide the governing PDEs for [Formula: see text]. This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order (p) allows balancing accuracy and computational cost providing a speedup of over N/p compared to high-fidelity models. Moreover, this cost becomes independent of the number of chemical species in the large computational meshes typical of the arterial and cardiac chamber simulations. Using a coagulation network with N = 9 and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. The thrombin concentration in these models departs from the high-fidelity solution by under 20% (p = 1) and 2% (p = 2) after 20 cardiac cycles. These multi-fidelity models could enable new coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it could be generalized to advance our understanding of other reacting systems affected by flow.

Critical evaluation of kinetic schemes for coagulation

Two well-established numerical representations of the coagulation cascade either initiated by the intrinsic system (Chatterjee et al., PLOS Computational Biology 2010) or the extrinsic system (Butenas et al., Journal of Biological Chemistry, 2004) were compared with thrombin generation assays under realistic pathological conditions. Biochemical modifications such as the omission of reactions not relevant to the case studied, the modification of reactions related to factor XI activation and auto-activation, the adaptation of initial conditions to the thrombin assay system, and the adjustment of some of the model parameters were necessary to align in vitro and in silico data. The modified models are able to reproduce thrombin generation for a range of factor XII, XI, and VIII deficiencies, with the coagulation cascade initiated either extrinsically or intrinsically. The results emphasize that when existing models are extrapolated to experimental parameters for which they have not been calibrated, careful adjustments are required.

Efficient multi-fidelity computation of blood coagulation under flow

Clot formation is a crucial process that prevents bleeding, but can lead to severe disorders when imbalanced. This process is regulated by the coagulation cascade, a biochemical network that controls the enzyme thrombin, which converts soluble fibrinogen into the fibrin fibers that constitute clots. Coagulation cascade models are typically complex and involve dozens of partial differential equations (PDEs) representing various chemical species' transport, reaction kinetics, and diffusion. Solving these PDE systems computationally is challenging, due to their large size and multi-scale nature. We propose a multi-fidelity strategy to increase the efficiency of coagulation cascade simulations. Leveraging the slower dynamics of molecular diffusion, we transform the governing PDEs into ordinary differential equations (ODEs) representing the evolution of species concentrations versus blood residence time. We then Taylor-expand the ODE solution around the zero-diffusivity limit to obtain spatiotemporal maps of species concentrations in terms of the statistical moments of residence time, , and provide the governing PDEs for . This strategy replaces a high-fidelity system of N PDEs representing the coagulation cascade of N chemical species by N ODEs and p PDEs governing the residence time statistical moments. The multi-fidelity order( p ) allows balancing accuracy and computational cost, providing a speedup of over N/p compared to high-fidelity models. Using a simplified coagulation network and an idealized aneurysm geometry with a pulsatile flow as a benchmark, we demonstrate favorable accuracy for low-order models of p = 1 and p = 2. These models depart from the high-fidelity solution by under 16% ( p = 1) and 5% ( p = 2) after 20 cardiac cycles. The favorable accuracy and low computational cost of multi-fidelity models could enable unprecedented coagulation analyses in complex flow scenarios and extensive reaction networks. Furthermore, it can be generalized to advance our understanding of other systems biology networks affected by blood flow.

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.

A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

Despite the numerous therapeutic options to treat bleeding or thrombosis, a comprehensive quantitative mechanistic understanding of the effects of these and potential novel therapies is lacking. Recently, the quality of quantitative systems pharmacology (QSP) models of the coagulation cascade has improved, simulating the interactions between proteases, cofactors, regulators, fibrin, and therapeutic responses under different clinical scenarios. We aim to review the literature on QSP models to assess the unique capabilities and reusability of these models. We systematically searched the literature and BioModels database reviewing systems biology (SB) and QSP models. The purpose and scope of most of these models are redundant with only two SB models serving as the basis for QSP models. Primarily three QSP models have a comprehensive scope and are systematically linked between SB and more recent QSP models. The biological scope of recent QSP models has expanded to enable simulations of previously unexplainable clotting events and the drug effects for treating bleeding or thrombosis. Overall, the field of coagulation appears to suffer from unclear connections between models and irreproducible code as previously reported. The reusability of future QSP models can improve by adopting model equations from validated QSP models, clearly documenting the purpose and modifications, and sharing reproducible code. The capabilities of future QSP models can improve from more rigorous validation by capturing a broader range of responses to therapies from individual patient measurements and integrating blood flow and platelet dynamics to closely represent in vivo bleeding or thrombosis risk.

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.

Imaging and biophysical modelling of thrombogenic mechanisms in atrial fibrillation and stroke

Atrial fibrillation (AF) underlies almost one third of all ischaemic strokes, with the left atrial appendage (LAA) identified as the primary thromboembolic source. Current stroke risk stratification approaches, such as the CHA₂DS₂-VASc score, rely mostly on clinical comorbidities, rather than thrombogenic mechanisms such as blood stasis, hypercoagulability and endothelial dysfunction-known as Virchow's triad. While detection of AF-related thrombi is possible using established cardiac imaging techniques, such as transoesophageal echocardiography, there is a growing need to reliably assess AF-patient thrombogenicity prior to thrombus formation. Over the past decade, cardiac imaging and image-based biophysical modelling have emerged as powerful tools for reproducing the mechanisms of thrombogenesis. Clinical imaging modalities such as cardiac computed tomography, magnetic resonance and echocardiographic techniques can measure blood flow velocities and identify LA fibrosis (an indicator of endothelial dysfunction), but imaging remains limited in its ability to assess blood coagulation dynamics. In-silico cardiac modelling tools-such as computational fluid dynamics for blood flow, reaction-diffusion-convection equations to mimic the coagulation cascade, and surrogate flow metrics associated with endothelial damage-have grown in prevalence and advanced mechanistic understanding of thrombogenesis. However, neither technique alone can fully elucidate thrombogenicity in AF. In future, combining cardiac imaging with in-silico modelling and integrating machine learning approaches for rapid results directly from imaging data will require development under a rigorous framework of verification and clinical validation, but may pave the way towards enhanced personalised stroke risk stratification in the growing population of AF patients. This Review will focus on the significant progress in these fields.

Inhibition of platelet-surface-bound proteins during coagulation under flow I: TFPI

Blood coagulation is a self-repair process regulated by activated platelet surfaces, clotting factors, and inhibitors. Tissue factor pathway inhibitor (TFPI) is one such inhibitor, well known for its inhibitory action on the active enzyme complex comprising tissue factor (TF) and activated clotting factor VII. This complex forms when TF embedded in the blood vessel wall is exposed by injury and initiates coagulation. A different role for TFPI, independent of TF:VIIa, has recently been discovered whereby TFPI binds a partially cleaved form of clotting factor V (FV-h) and impedes thrombin generation on activated platelet surfaces. We hypothesized that this TF-independent inhibitory mechanism on platelet surfaces would be a more effective platform for TFPI than the TF-dependent one. We examined the effects of this mechanism on thrombin generation by including the relevant biochemical reactions into our previously validated mathematical model. Additionally, we included the ability of TFPI to bind directly to and inhibit platelet-bound FXa. The new model was sensitive to TFPI levels and, under some conditions, TFPI could completely shut down thrombin generation. This sensitivity was due entirely to the surface-mediated inhibitory reactions. The addition of the new TFPI reactions increased the threshold level of TF needed to elicit a strong thrombin response under flow, but the concentration of thrombin achieved, if there was a response, was unchanged. Interestingly, we found that direct binding of TFPI to platelet-bound FXa had a greater anticoagulant effect than did TFPI binding to FV-h alone, but that the greatest effects occurred if both reactions were at play. The model includes activated platelets' release of FV species, and we explored the impact of varying the FV/FV-h composition of the releasate. We found that reducing the zymogen FV fraction of this pool, and thus increasing the fraction that is FV-h, led to acceleration of thrombin generation.

Systems Biology Approach for Personalized Hemostasis Correction

The correction of blood coagulation impairments of a bleeding or thrombotic nature employs standard protocols where the type of drug, its dose and the administration regime are stated. However, for a group of patients, such an approach may be ineffective, and personalized therapy adjustment is needed. Laboratory hemostasis tests are used to control the efficacy of therapy, which is expensive and time-consuming. Computer simulations may become an inexpensive and fast alternative to real blood tests. In this work, we propose a procedure to numerically define the individual hemostasis profile of a patient and estimate the anticoagulant efficacy of low-molecular-weight heparin (LMWH) based on the computer simulation of global hemostasis assays. We enrolled a group of 12 patients receiving LMWH therapy and performed routine coagulation assays (activated partial thromboplastin time and prothrombin time) and global hemostasis assays (thrombodynamics and thrombodynamics-4d) and measured anti-Xa activity, fibrinogen, prothrombin and antithrombin levels, creatinine clearance, lipid profiles and clinical blood counts. Blood samples were acquired 3, 6 and 12 h after LMWH administration. We developed a personalized pharmacokinetic model of LMWH and coupled it with the mechanism-driven blood coagulation model, which described the spatial dynamics of fibrin and thrombin propagation. We found that LMWH clearance was significantly lower in the group with high total cholesterol levels. We generated an individual patient's hemostasis profile based on the results of routine coagulation assays. We propose a method to simulate the results of global hemostasis assays in the case of an individual response to LMWH therapy, which can potentially help with hemostasis corrections based on the output of global tests.

Model reduction of coagulation cascade based on genetic algorithm

Fibrin is an important product of the coagulation cascade, and plays an eminent role in platelet stabilization. Since coagulation cascade models typically involve the reaction kinetics of dozens of proteins, which will incur burdensome computational costs when coupled to blood flow in complex geometries, researchers often ignore this process when constructing thrombosis models. However, previous studies have shown that fundamental aspects of coagulation can be reproduced with simpler models, which motivated us to obtain a reduced-order model of fibrin generation through a systematic approach. Therefore, we introduced a semi-automatic framework to perform model-reduction of cascade reactions in this study, which consisted of two processes. Specifically, the retained protein species and cascade reactions were determined based on published studies and simulation results from the full cascade model, while the optimal reaction rates for the new cascade network were determined using a genetic algorithm. The framework has been applied to a 19-species coagulation model that triggers fibrin generation in internal fields via reactive boundaries, and a 10-species reduced-order model was obtained to reproduce the kinetics of fibrinogenesis in the full cascade model at different boundary tissue factor concentrations. This reduced-order model of fibrinogenesis would be valuable for thrombosis modeling that considers both the coagulation cascade and platelet activity. Furthermore, the framework proposed herein can also be applied to the reductions of other cascade reaction models.

A System-Wide Investigation and Stratification of the Hemostatic Proteome in Premature Myocardial Infarction

Introduction

Advancing understanding of key factors that determine the magnitude of the hemostatic response may facilitate the identification of individuals at risk of generating an occlusive thrombus as a result of an atherothrombotic event such as an acute Myocardial Infarction (MI). While fibrinogen levels are a recognized risk factor for MI, the association of thrombotic risk with other coagulation proteins is inconsistent. This is likely due to the complex balance of pro- and anticoagulant factors in any individual.

Methods

We compared measured levels of pro- and anticoagulant proteins in plasma from 162 patients who suffered an MI at an early age (MI <50 y) and 186 age- and gender-matched healthy controls with no history of CAD. We then used the measurements from these individuals as inputs for an established mathematical model to investigate how small variations in hemostatic factors affect the overall amplitude of the hemostatic response and to identify differential key drivers of the hemostatic response in male and female patients and controls.

Results

Plasma from the MI patients contained significantly higher levels of Tissue Factor (P = 0.007), the components of the tenase (FIX and FVIII; P < 0.0001 for both) and the prothrombinase complexes (FX; P = 0.003), and lower levels of Tissue Factor Pathway Inhibitor (TFPI; P = 0.033) than controls. The mathematical model, which generates time-dependent predictions describing the depletion, activation, and interaction of the main procoagulant factors and inhibitors, identified different patterns of hemostatic response between MI patients and controls, and additionally, between males and females. Whereas, in males, TF, FVIII, FIX, and the inhibitor TFPI contribute to the differences seen between case and controls, and in females, FII, FVIII, and FIX had the greatest influence on the generation of thrombin. We additionally show that further donor stratification may be possible according to the predicted donor response to anticoagulant therapy.

Conclusions

We suggest that modeling could be of value in enhancing our prediction of risk of premature MI, recurrent risk, and therapeutic efficacy.

Revised model of the tissue factor pathway of thrombin generation: Role of the feedback activation of FXI

BACKGROUND

Biochemical reaction networks are self-regulated in part due to feedback activation mechanisms. The tissue factor (TF) pathway of blood coagulation is a complex reaction network controlled by multiple feedback loops that coalesce around the serine protease thrombin.

OBJECTIVES

Our goal was to evaluate the relative contribution of the feedback activation of coagulation factor XI (FXI) in TF-mediated thrombin generation using a comprehensive systems-based analysis.

MATERIALS AND METHODS

We developed a systems biology model that improves the existing Hockin-Mann (HM) model through an integrative approach of mathematical modeling and in vitro experiments. Thrombin generation measured using in vitro assays revealed that the feedback activation of FXI contributes to the propagation of thrombin generation based on the initial concentrations of TF or activated coagulation factor X (FXa). We utilized experimental data to improve the robustness of the HM model to capture thrombin generation kinetics without a role for FXI before including the feedback activation of FXI by thrombin to construct the extended (ext.) HM model.

RESULTS AND CONCLUSIONS

Using the ext.HM model, we predicted that the contribution of positive feedback of FXI activation by thrombin can be abolished by selectively eliminating the inhibitory function of tissue factor pathway inhibitor (TFPI), a serine protease inhibitor of FXa and TF-activated factor VII (FVIIa) complex. This prediction from the ext.HM model was experimentally validated using thrombin generation assays with function blocking antibodies against TFPI and plasmas depleted of FXI. Together, our results demonstrate the applications of combining experimental and modeling techniques in predicting complex biochemical reaction systems.

Personalized modulation of coagulation factors using a thrombin dynamics model to treat trauma-induced coagulopathy

Current trauma-induced coagulopathy resuscitation protocols use slow laboratory measurements, rules-of-thumb, and clinician gestalt to administer large volumes of uncharacterized, non-tailored blood products. These one-size-fits-all treatment approaches have high mortality. Here, we provide significant evidence that trauma patient survival 24 h after hospital admission occurs if and only if blood protein coagulation factor concentrations equilibrate at a normal value, either from inadvertent plasma-based modulation or from innate compensation. This result motivates quantitatively guiding trauma patient coagulation factor levels while accounting for protein interactions. Toward such treatment, we develop a Goal-oriented Coagulation Management (GCM) algorithm, a personalized and automated ordered sequence of operations to compute and specify coagulation factor concentrations that rectify clotting. This novel GCM algorithm also integrates new control-oriented advancements that we make in this work: an improvement of a prior thrombin dynamics model that captures the coagulation process to control, a use of rapidly-measurable concentrations to help predict patient state, and an accounting of patient-specific effects and limitations when adding coagulation factors to remedy coagulopathy. Validation of the GCM algorithm's guidance shows superior performance over clinical practice in attaining normal coagulation factor concentrations and normal clotting profiles simultaneously.

Sensitivity analysis of a reduced model of thrombosis under flow: Roles of Factor IX, Factor XI, and γ'-Fibrin

A highly reduced extrinsic pathway coagulation model (8 ODEs) under flow considered a thin 15-micron platelet layer where transport limitations were largely negligible (except for fibrinogen) and where cofactors (FVIIa, FV, FVIII) were not rate-limiting. By including thrombin feedback activation of FXI and the antithrombin-I activities of fibrin, the model accurately simulated measured fibrin formation and thrombin fluxes. Using this reduced model, we conducted 10,000 Monte Carlo (MC) simulations for ±50% variation of 5 plasma zymogens and 2 fibrin binding sites for thrombin. A sensitivity analysis of zymogen concentrations indicated that FIX activity most influenced thrombin generation, a result expected from hemophilia A and B. Averaging all MC simulations confirmed both the mean and standard deviation of measured fibrin generation on 1 tissue factor (TF) molecule per μm2. Across all simulations, free thrombin in the layer ranged from 20 to 300 nM (mean: 50 nM). The top 2% of simulations that produced maximal fibrin were dominated by conditions with low antithrombin-I activity (decreased weak and strong sites) and high FIX concentration. In contrast, the bottom 2% of simulations that produced minimal fibrin were dominated by low FIX and FX. The percent reduction of fibrin by an ideal FXIa inhibitor (FXI = 0) ranged from 71% fibrin reduction in the top 2% of MC simulations to only 34% fibrin reduction in the bottom 2% of MC simulations. Thus, the antithrombotic potency of FXIa inhibitors may vary depending on normal ranges of zymogen concentrations. This reduced model allowed efficient multivariable sensitivity analysis.

Multi-constituent simulation of thrombus formation at LVAD inlet cannula connection: Importance of Virchow's triad

As pump thrombosis is reduced in current-generation ventricular assist devices (VAD), adverse events such as bleeding or stroke remain at unacceptable rates. Thrombosis around the VAD inlet cannula (IC) has been highlighted as a possible source of stroke events. Recent computational fluid dynamics (CFD) studies have attempted to characterize the thrombosis risk of different IC-ventricle configurations. However, purely CFD simulations relate thrombosis risk to ad hoc criteria based on flow characteristics, with little consideration of biochemical factors. This study investigates the genesis of IC thrombosis including two elements of the Virchow's triad: endothelial injury and hypercoagulability. To this end a multi-scale thrombosis simulation that includes platelet activity and coagulation reactions was performed. Our results show significant thrombin formation in stagnation regions (|u| < 0.005 m/s) close to the IC wall. In addition, high shear-mediated platelet activation was observed over the leading-edge tip of the cannula. The current study reveals the importance of biochemical factors to the genesis of thrombosis at the ventricular-cannula junction in a perioperative state. This study is a first step toward the long-term objective of including clinically relevant pharmacological kinetics such as heparin or aspirin in simulations of inflow cannula thrombosis.

Investigating the two regimes of fibrin clot lysis: an experimental and computational approach

It has been observed in vitro that complete clot lysis is generally preceded by a slow phase of lysis during which the degradation seems to be inefficient. However, this slow regime was merely noticed, but not yet quantitatively discussed. In our experiments, we observed that the lysis ubiquitously occurred in two distinct regimes, a slow and a fast lysis regime. We quantified extensively the duration of these regimes for a wide spectrum of experimental conditions and found that on average, the slow regime lasts longer than the fast one, meaning that during most of the process, the lysis is ineffective. We proposed a computational model in which the properties of the binding of the proteins change during the lysis: first, the biochemical reactions take place at the surface of the fibrin fibers, then in the bulk, resulting in the observed fast lysis regime. This simple hypothesis appeared to be sufficient to reproduce with a great accuracy the lysis profiles obtained experimentally.

Use of population PK/PD approach to model the thrombin generation assay: assessment in haemophilia A plasma samples spiked by a TFPI antibody

The thrombin generation (TG) assay is a well-established tool to capture the clotting potential of any healthy or haemophiliac subject. It measures ex vivo the kinetics of thrombin activation throughout the coagulation. Clinical studies allowed to create two databases gathering the coagulation factor levels and the thrombin generation profile of 40 healthy and 40 haemophiliac A (HA) subjects. Besides, portions of all HA samples were spiked with increasing levels of a TFPI antibody (considered as a possible therapeutic target) and corresponding TG profiles were determined. The non-linear mixed-effect (NLME) modelling aims at describing and explaining the experimentally observed important variability of the TG curves between subjects and the individual effects of spiking with a TFPI antibody. The models consist of an empirical description of the TG kinetics, accounting for an additive residual error and between-subject variability on its parameters. Factor VIII and TFPI were found to significantly explain and reduce the variability of the TG of haemophilia A samples. Besides, the model is shown to correctly reproduce the variability in the response to the ex vivo spiking with the TFPI antibody, by combining the empirical description of TG to a simple Hill equation that accounts for the binding between TFPI and different doses of its antibody. Such models can be useful for clinical practice, with the analysis and comparison of the distributions of TG profiles in healthy and haemophilia populations; and also for research, with the analysis of the effect of TFPI and its neutralization on individual TG profiles.

Patient-Specific Modelling of Blood Coagulation

Blood coagulation represents one of the most studied processes in biomedical modelling. However, clinical applications of this modelling remain limited because of the complexity of this process and because of large inter-patient variation of the concentrations of blood factors, kinetic constants and physiological conditions. Determination of some of these patients-specific parameters is experimentally possible, but it would be related to excessive time and material costs impossible in clinical practice. We propose in this work a methodological approach to patient-specific modelling of blood coagulation. It begins with conventional thrombin generation tests allowing the determination of parameters of a reduced kinetic model. Next, this model is used to study spatial distributions of blood factors and blood coagulation in flow, and to evaluate the results of medical treatment of blood coagulation disorders.

Exploring the Complex Role of Coagulation Factor VIII in Chronic Liver Disease

Chronic liver disease is one of the leading causes of death in the United States. Coagulopathy is often a sequela of chronic liver disease, however, the role and regulation of coagulation components in chronic liver injury remain poorly understood. Clinical and experimental evidence indicate that misexpression of the procoagulant factor VIII (FVIII) is associated with chronic liver disease. Nevertheless, the molecular mechanism of FVIII-induced chronic liver injury progression remains unknown. This review provides evidence supporting a pathologic role for FVIII in the development of chronic liver disease using both experimental and clinical models.

The Art and Science of Building a Computational Model to Understand Hemostasis

Computational models of various facets of hemostasis and thrombosis have increased substantially in the last decade. These models have the potential to make predictions that can uncover new mechanisms within the complex dynamics of thrombus formation. However, these predictions are only as good as the data and assumptions they are built upon, and therefore model building requires intimate coupling with experiments. The objective of this article is to guide the reader through how a computational model is built and how it can inform and be refined by experiments. This is accomplished by answering six questions facing the model builder: (1) Why make a model? (2) What kind of model should be built? (3) How is the model built? (4) Is the model a “good” model? (5) Do we believe the model? (6) Is the model useful? These questions are answered in the context of a model of thrombus formation that has been successfully applied to understanding the interplay between blood flow, platelet deposition, and coagulation and in identifying potential modifiers of thrombin generation in hemophilia A.

Computationally Driven Discovery in Coagulation

Bleeding frequency and severity within clinical categories of hemophilia A are highly variable and the origin of this variation is unknown. Solving this mystery in coagulation requires the generation and analysis of large data sets comprised of experimental outputs or patient samples, both of which are subject to limited availability. In this review, we describe how a computationally driven approach bypasses such limitations by generating large synthetic patient data sets. These data sets were created with a mechanistic mathematical model, by varying the model inputs, clotting factor, and inhibitor concentrations, within normal physiological ranges. Specific mathematical metrics were chosen from the model output, used as a surrogate measure for bleeding severity, and statistically analyzed for further exploration and hypothesis generation. We highlight results from our recent study that employed this computationally driven approach to identify FV (factor V) as a key modifier of thrombin generation in mild to moderate hemophilia A, which was confirmed with complementary experimental assays. The mathematical model was used further to propose a potential mechanism for these observations whereby thrombin generation is rescued in FVIII-deficient plasma due to reduced substrate competition between FV and FVIII for FXa (activated factor X).

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

In Silico Hemostasis Modeling and Prediction

Computational physiology, i.e., reproduction of physiological (and, by extension, pathophysiological) processes in silico, could be considered one of the major goals in computational biology. One might use computers to simulate molecular interactions, enzyme kinetics, gene expression, or whole networks of biochemical reactions, but it is (patho)physiological meaning that is usually the meaningful goal of the research even when a single enzyme is its subject. Although exponential rise in the use of computational and mathematical models in the field of hemostasis and thrombosis began in the 1980s (first for blood coagulation, then for platelet adhesion, and finally for platelet signal transduction), the majority of their successful applications are still focused on simulating the elements of the hemostatic system rather than the total (patho)physiological response in situ. Here we discuss the state of the art, the state of the progress toward the efficient "virtual thrombus formation," and what one can already get from the existing models.

Modelling the linkage between influenza infection and cardiovascular events via thrombosis

There is a heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza associated cardiac events have been linked to multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular thrombotic events, we develop a dynamic model which incorporates some key elements of the host immune response, inflammatory response, and blood coagulation. We formulate these biological systems and integrate them into a cohesive modelling framework to show how blood clotting may be connected to influenza virus infection. With blood clot formation inside an artery resulting from influenza virus infection as the primary outcome of this integrated model, we demonstrate how blood clot severity may depend on circulating prothrombin levels. We also utilize our model to leverage clinical data to inform the threshold level of the inflammatory cytokine TNFα which initiates tissue factor induction and subsequent blood clotting. Our model provides a tool to explore how individual biological components contribute to blood clotting events in the presence of influenza infection, to identify individuals at risk of clotting based on their circulating prothrombin levels, and to guide the development of future vaccines to optimally interact with the immune system.

Accelerating availability of clinically-relevant parameter estimates from thromboelastogram point-of-care device

BACKGROUND

Modeling approaches offer a novel way to detect and predict coagulopathy in trauma patients. A dynamic model, built and tested on thromboelastogram (TEG) data, was used to generate a virtual library of over 160,000 simulated RapidTEGs. The patient-specific parameters are the initial platelet count, platelet activation rate, thrombus growth rate, and lysis rate (P(0), k1, k2, and k3, respectively).

METHODS

Patient data from both STAAMP (n = 182 patients) and PAMPer (n = 111 patients) clinical trials were collected. A total of 873 RapidTEGs were analyzed. One hundred sixteen TEGs indicated maximum amplitude (MA) below normal and 466 TEGs indicated lysis percent above normal. Each patient's TEG response was compared against the virtual library of TEGs to determine library trajectories having the least sum-of-squared error versus the patient TEG up to each specified evaluation time ∈ (3, 4, 5, 7.5, 10, 15, 20 minutes). Using 10 nearest-neighbor trajectories, a logistic regression was performed to predict if the patient TEG indicated MA below normal (<50 mm), lysis percent 30 minutes after MA (LY30) greater than 3%, and/or blood transfusion need using the parameters from the dynamic model.

RESULTS

The algorithm predicts abnormal MA values using the initial 3 minutes of RapidTEG data with a median area under the curve of 0.95, and improves with more data to 0.98 by 10 minutes. Prediction of future platelet and packed red blood cell transfusion based on parameters at 4 and 5 minutes, respectively, provides equivalent predictions to the traditional TEG parameters in significantly less time. Dynamic model parameters could not predict abnormal LY30 or future fresh-frozen plasma transfusion.

CONCLUSION

This analysis could be incorporated into TEG software and workflow to quickly estimate if the MA would be below or above threshold value within the initial minutes following a TEG, along with an estimate of what blood products to have on hand.

LEVEL OF EVIDENCE

Therapeutic/Care Management: Level IV.

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.

Modeling Thrombin Generation in Plasma under Diffusion and Flow

We investigate the capacity of published numerical models of thrombin generation to reproduce experimentally observed threshold behavior under conditions in which diffusion and/or flow are important. Computational fluid dynamics simulations incorporating species diffusion, fluid flow, and biochemical reactions are compared with published data for thrombin generation in vitro in 1) quiescent plasma exposed to patches of tissue factor and 2) plasma perfused through a capillary coated with tissue factor. Clot time is correctly predicted in individual cases, and some models qualitatively replicate thrombin generation thresholds across a series of tissue factor patch sizes or wall shear rates. Numerical results suggest that there is not a genuine patch size threshold in quiescent plasma-clotting always occurs given enough time-whereas the shear rate threshold observed under flow is a genuine physical limit imposed by flow-mediated washout of active coagulation factors. Despite the encouraging qualitative results obtained with some models, no single model robustly reproduces all experiments, demonstrating that greater understanding of the underlying reaction network, and particularly of surface reactions, is required. In this direction, additional simulations provide evidence that 1) a surface-localized enzyme, speculatively identified as meizothrombin, is significantly active toward the fluorescent thrombin substrate used in the experiments or, less likely, 2) thrombin is irreversibly inhibited at a faster-than-expected rate, possibly explained by a stimulatory effect of plasma heparin on antithrombin. These results highlight the power of simulation to provide novel mechanistic insights that augment experimental studies and build our understanding of complex biophysicochemical processes. Further validation work is critical to unleashing the full potential of coagulation models as tools for drug development and personalized medicine.

Computational model of tranexamic acid on urokinase mediated fibrinolysis

Understanding the coagulation process is critical to developing treatments for trauma and coagulopathies. Clinical studies on tranexamic acid (TXA) have resulted in mixed reports on its efficacy in improving outcomes in trauma patients. The largest study, CRASH-2, reported that TXA improved outcomes in patients who received treatment prior to 3 hours after the injury, but worsened outcomes in patients who received treatment after 3 hours. No consensus has been reached about the mechanism behind the duality of these results. In this paper we use a computational model for coagulation and fibrinolysis to propose that deficiencies or depletions of key anti-fibrinolytic proteins, specifically antiplasmin, a1-antitrypsin and a2-macroglobulin, can lead to worsened outcomes through urokinase-mediated hyperfibrinolysis.

Controlled Multifactorial Coagulopathy: Effects of Dilution, Hypothermia, and Acidosis on Thrombin Generation In Vitro

BACKGROUND

Coagulopathy and hemostatic abnormalities remain a challenge in patients following trauma and major surgery. Coagulopathy in this setting has a multifactorial nature due to tissue injury, hemodilution, hypothermia, and acidosis, the severity of which may vary. In this study, we combined computational kinetic modeling and in vitro experimentation to investigate the effects of multifactorial coagulopathy on thrombin, the central enzyme in the coagulation system.

METHODS

We measured thrombin generation in platelet-poor plasma from 10 healthy volunteers using the calibrated automated thrombogram assay (CAT). We considered 3 temperature levels (31°C, 34°C, and 37°C), 3 pH levels (6.9, 7.1, and 7.4), and 3 degrees of dilution with normal saline (no dilution, 3-fold dilution, and 5-fold dilution). We measured thrombin-generation time courses for all possible combinations of these conditions. For each combination, we analyzed 2 scenarios: without and with (15 nM) supplementation of thrombomodulin, a key natural regulator of thrombin generation. For each measured thrombin time course, we recorded 5 quantitative parameters and analyzed them using multivariable regression. Moreover, for multiple combinations of coagulopathic conditions, we performed routine coagulation tests: prothrombin time (PT) and activated partial thromboplastin time (aPTT). We compared the experimental results with simulations using a newly developed version of our computational kinetic model of blood coagulation.

RESULTS

Regression analysis allowed us to identify trends in our data (P < 10). In both model simulations and experiments, dilution progressively reduced the peak of thrombin generation. However, we did not experimentally detect the model-predicted delay in the onset of thrombin generation. In accord with the model predictions, hypothermia delayed the onset of thrombin generation; it also increased the thrombin peak time (up to 1.30-fold). Moreover, as predicted by the kinetic model, the experiments showed that hypothermia increased the area under the thrombin curve (up to 1.97-fold); it also increased the height of the thrombin peak (up to 1.48-fold). Progressive acidosis reduced the velocity index by up to 24%; acidosis-induced changes in other thrombin generation parameters were much smaller or none. Acidosis increased PT by 14% but did not influence aPTT. In contrast, dilution markedly prolonged both PT and aPTT. In our experiments, thrombomodulin affected thrombin-generation parameters mainly in undiluted plasma.

CONCLUSIONS

Dilution with normal saline reduced the amount of generated thrombin, whereas hypothermia increased it and delayed the time of thrombin accumulation. In contrast, acidosis in vitro had little effect on thrombin generation.

Continuous Detection of Increasing Concentrations of Thrombin Employing a Label-Free Photonic Crystal Aptasensor

Thrombin generation is a complex and finely regulated pathway that provokes dynamical changes of thrombin concentration in blood when a vascular injury occurs. In order to characterize the initiation phase of such process, when thrombin concentration is in the nM range, a label-free optical aptasensor is proposed here. This aptasensor combines a 1D photonic crystal structure consisting of a silicon corrugated waveguide with thrombin binding aptamers on its surface as bioreceptors. As a result, this aptasensor has been demonstrated to specifically detect thrombin concentrations ranging from 270 pM to 27 nM with an estimated detection limit of 33.5 pM and a response time of ~2 min. Furthermore, it has also been demonstrated that this aptasensor is able to continuously respond to consecutive increasing concentrations of thrombin and to detect binding events as they occur. All these features make this aptasensor a good candidate to continuously study how thrombin concentration progressively increases during the initiation phase of the coagulation cascade.

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.

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.

Automated reduction of blood coagulation models

Mathematical modeling of thrombosis typically involves modeling the coagulation cascade. Models of coagulation generally involve the reaction kinetics for dozens of proteins. The resulting system of equations is difficult to parameterize, and its numerical solution is challenging when coupled to blood flow or other physics important to clotting. Prior research suggests that essential aspects of coagulation may be reproduced by simpler models. This evidence motivates a systematic approach to model reduction. We herein introduce an automated framework to generate reduced-order models of blood coagulation. The framework consists of nested optimizations, where an outer optimization selects the optimal species for the reduced-order model and an inner optimization selects the optimal reaction rates for the new coagulation network. The framework was tested on an established 34-species coagulation model to rigorously consider what level of model fidelity is necessary to capture essential coagulation dynamics. The results indicate that a nine-species reduced-order model is sufficient to reproduce the thrombin dynamics of the benchmark 34-species model for a range of tissue factor concentrations, including those not included in the optimization process. Further model reduction begins to compromise the ability to capture the thrombin generation process. The framework proposed herein enables automated development of reduced-order models of coagulation that maintain essential dynamics used to model thrombosis.

Assessing the impact of product inhibition in a chromogenic assay

Chromogenic substrates (CS) are synthetic substrates used to monitor the activity of a target enzyme. It has been reported that some CSs display competitive product inhibition with their target enzyme. Thus, in assays where enzyme activity is continuously monitored over long periods of time, the product inhibition may significantly interfere with the reactions being monitored. Despite this knowledge, it is rare for CSs to be directly incorporated into mathematical models that simulate these assays. This devalues the predictive power of the models. In this study, we examined the interactions between a single enzyme, coagulation factor Xa, and its chromogenic substrate. We developed, and experimentally validated, a mathematical model of a chromogenic assay for factor Xa that explicitly included product inhibition from the CS. We employed Bayesian inference, in the form of Markov-Chain Monte Carlo, to estimate the strength of the product inhibition and other sources of uncertainty such as pipetting error and kinetic rate constants. Our model, together with carefully calibrated biochemistry experiments, allowed for full characterization of the strength and impact of product inhibition in the assay. The effect of CS product inhibition in more complex reaction mixtures was further explored using mathematical models.

Mathematical model of thrombin generation and bleeding phenotype in Amish carriers of Factor IX:C deficiency vs. controls

INTRODUCTION

Factor IX:C (FIX:C) levels vary in hemophilia B carriers even in pedigrees with a unifying genetic defect. Analyzing the balance between pro-and anticoagulants might increase our understanding of carriers' bleeding potential.

AIM

In this research study, we evaluated bleeding scores (BS) and a novel mathematical model of thrombin generation (TG) in Amish FIX:C deficient carriers and controls.

METHODS

Blood samples and BS were obtained from post-menarchal females, including 59 carriers and 57 controls from the same extended pedigree. Factors II, V, VII, VIII, IX, X, antithrombin, tissue factor pathway inhibitor and protein C were assayed to generate mathematical models of TG in response to 5pM tissue factor (TF) and for TF + thrombomodulin. BS was based on a modification of the MCMDM-1VWD scoring system.

RESULTS

Carriers had a lower mean FIX:C (68% vs. 119%), von Willebrand factor antigen (108 vs.133) and Tissue activatable fibrinolysis inhibitor (103 vs. 111) compared to controls; both groups had a similar mean BS. Carriers demonstrated significantly lower TG parameters on both mathematical models compared to controls. Carriers with FIX:C ≤ 50% had lower TG curves than those >50% but similar BS.

CONCLUSION

Thrombin generation showed significant differences between carriers and controls, between low (≤50%) and high (>50%) FIX:C carriers, and specifically in the TF + thrombomodulin model, between high FIX:C carriers and controls, although the BS were not different.

Reduced model to predict thrombin and fibrin during thrombosis on collagen/tissue factor under venous flow: Roles of γ'-fibrin and factor XIa

During thrombosis, thrombin generates fibrin, however fibrin reversibly binds thrombin with low affinity E-domain sites (K_D = 2.8 μM) and high affinity γ’-fibrin sites (K_D = 0.1 μM). For blood clotting on collagen/tissue factor (1 TF-molecule/μm²) at 200 s^-1 wall shear rate, high μM-levels of intraclot thrombin suggest robust prothrombin penetration into clots. Setting intraclot zymogen concentrations to plasma levels (and neglecting cofactor rate limitations) allowed the linearization of 7 Michaelis-Menton reactions between 6 species to simulate intraclot generation of: Factors FXa (via TF/VIIa or FIXa), FIXa (via TF/FVIIa or FXIa), thrombin, fibrin, and FXIa. This reduced model [7 rates, 2 K_D’s, enzyme half-lives~1 min] predicted the measured clot elution rate of thrombin-antithrombin (TAT) and fragment F1.2 in the presence and absence of the fibrin inhibitor Gly-Pro-Arg-Pro. To predict intraclot fibrin reaching 30 mg/mL by 15 min, the model required fibrinogen penetration into the clot to be strongly diffusion-limited (actual rate/ideal rate = 0.05). The model required free thrombin in the clot (~100 nM) to have an elution half-life of ~2 sec, consistent with measured albumin elution, with most thrombin (>99%) being fibrin-bound. Thrombin-feedback activation of FXIa became prominent and reached 5 pM FXIa at >500 sec in the simulation, consistent with anti-FXIa experiments. In predicting intrathrombus thrombin and fibrin during 15-min microfluidic experiments, the model revealed “cascade amplification” from 30 pM levels of intrinsic tenase to 15 nM prothrombinase to 15 μM thrombin to 90 μM fibrin. Especially useful for multiscale simulation, this reduced model predicts thrombin and fibrin co-regulation during thrombosis under flow.

During blood clotting events, a complex series of reaction are involved. Simulation gives insights to the concentration of different enzymes which are at too low of concentration to be detected. However, the models are often large and difficult to solve for clotting under flow conditions. With a thin film approximation, we were able to simplify clotting under flow with parameters from literature, with only 3 adjusted in order to fit the experimental data. This model gave insights into the dynamics of the species involved, and the roles of γ’-fibrin and thrombin feedback activation. This reduced model may be useful in further multiscale simulations.

Utilizing Plasma Composition Data to Help Determine Procoagulant Dynamics in Patients with Thermal Injury: A Computational Assessment

INTRODUCTION

The development of methods that generate individualized assessments of the procoagulant potential of burn patients could improve their treatment. Beyond its role as an essential intermediate in the formation of thrombin, factor (F)Xa has systemic effects as an agonist to inflammatory processes. In this study, we use a computational model to study the FXa dynamics underlying tissue factor-initiated thrombin generation in a small cohort of burn patients.

MATERIALS AND METHODS

Plasma samples were collected upon admission (Hour 0) from nine subjects (five non-survivors) with major burn injuries and then at 48 hours. Coagulation factor concentrations (II, V, VII, VIII, IX, X, TFPI, antithrombin (AT), protein C (PC)) were measured and used in a computational model to generate time course profiles for thrombin (IIa), FXa, extrinsic tenase, intrinsic tenase and prothrombinase complexes upon a 5 pM tissue factor stimulus in the presence of 1 nM thrombomodulin. Parameters were extracted from the thrombin and FXa profiles (including max rate (MaxRIIa and MaxRFXa) and peak level (MaxLIIa and MaxLFXa)). Procoagulant potential was also evaluated by determining the concentration of the complexes at select times. Parameter values were compared between survivors and non-survivors in the burn cohort and between the burn cohort and a simulation based on the mean physiological (100%) concentration for all factor levels.

RESULTS

Burn patients differed at Hour 0 (p < 0.05) from 100% mean physiological levels for all coagulation factor levels except FV and FVII. The concentration of FX, FII, TFPI, AT and PC was lower; FIX and FVIII were increased. The composition differences resulted in all nine burn patients at Hour 0 displaying a procoagulant phenotype relative to 100% mean physiological simulation (MaxLIIa (306 ± 90 nM vs. 52 nM), MaxRIIa (2.9 ± 1.1 nM/s vs. 0.3 nM/s), respectively p < 0.001); MaxRFXa and MaxLFXa were also an order of magnitude greater than 100% mean physiological simulation (p < 0.001). When grouped by survival status and compared at the time of admission, non-survivors had lower PC levels (56 ± 18% vs. 82 ± 9%, p < 0.05), and faster MaxRFXa (29 ± 6 pM/s vs. 18 ± 6 pM/s, p < 0.05) than those that survived; similar trends were observed for all other procoagulant parameters. At 48 hours when comparing non-survivors to survivors, TFPI levels were higher (108 ± 18% vs. 59 ± 18%, p < 0.05), and MaxRIIa (1.5 ± 1.4 nM/s vs. 3.6 ± 0.7 nM/s, p < 0.05) and MaxRFXa (13 ± 12 pM/s vs. 35 ± 4 pM/s, p < 0.05) were lower; similar trends were observed with all other procoagulant parameters. Overall, between admission and 48 hours, procoagulant potential, as represented by MaxR and MaxL parameters for thrombin and FXa, in non-survivors decreased while in survivors they increased (p < 0.05). In patients that survived, there was a positive correlation between FX levels and MaxLFXa (r = 0.96) and reversed in mortality (r= -0.91).

CONCLUSIONS

Thrombin and FXa generation are increased in burn patients at admission compared to mean physiological simulations. Over the first 48 hours, burn survivors became more procoagulant while non-survivors became less procoagulant. Differences between survivors and non-survivors appear to be present in the underlying dynamics that contribute to FXa dynamics. Understanding how the individual specific balance of procoagulant and anticoagulant proteins contributes to thrombin and FXa generation could ultimately guide therapy and potentially reduce burn injury-related morbidity and mortality.

Protein Z-dependent protease inhibitor (ZPI) is a physiologically significant inhibitor of prothrombinase function

Current thought holds that factor Xa (FXa) bound in the prothrombinase complex is resistant to regulation by protein protease inhibitors during prothrombin activation. Here we provide evidence that, contrary to this view, the FXa-specific serpin inhibitor, protein Z-dependent protease inhibitor (ZPI), complexed with its cofactor, protein Z (PZ), functions as a physiologically significant inhibitor of prothrombinase-bound FXa during prothrombin activation. Kinetics studies showed that the rapid rate of inhibition of FXa by the ZPI-PZ complex on procoagulant membrane vesicles (k_{a (app)} ∼10⁷ m^-1 s^-1) was decreased ∼10-fold when FXa was bound to FVa in prothrombinase and a further ∼3-4-fold when plasma levels of S195A prothrombin were present (k_{a (app)} 2 × 10⁵ m^-1 s^-1). Nevertheless, the ZPI-PZ complex produced a major inhibition of thrombin generation during prothrombinase-catalyzed activation of prothrombin under physiologically relevant conditions. The importance of ZPI-PZ complex anticoagulant regulation of FXa both before and after incorporation into prothrombinase was supported by thrombin generation assays in plasma. These showed enhanced thrombin generation when the inhibitor was neutralized with a PZ-specific antibody and decreased thrombin generation when exogenous ZPI-PZ complex was added whether prothrombin was activated directly by FXa or through extrinsic or intrinsic pathway activators. Moreover, the PZ antibody enhanced thrombin generation both in the absence and presence of activated protein C (APC) anticoagulant activity. Taken together, these results suggest an important anticoagulant role for the ZPI-PZ complex in regulating both free FXa generated in the initiation phase of coagulation as well as prothrombinase-bound FXa in the propagation phase that complement prothrombinase regulation by APC.