Surface-mediated control of blood coagulation: the role of binding site densities and platelet deposition

Coagulo-Net: Enhancing the mathematical modeling of blood coagulation using physics-informed neural networks

Blood coagulation, which involves a group of complex biochemical reactions, is a crucial step in hemostasis to stop bleeding at the injury site of a blood vessel. Coagulation abnormalities, such as hypercoagulation and hypocoagulation, could either cause thrombosis or hemorrhage, resulting in severe clinical consequences. Mathematical models of blood coagulation have been widely used to improve the understanding of the pathophysiology of coagulation disorders, guide the design and testing of new anticoagulants or other therapeutic agents, and promote precision medicine. However, estimating the parameters in these coagulation models has been challenging as not all reaction rate constants and new parameters derived from model assumptions are measurable. Although various conventional methods have been employed for parameter estimation for coagulation models, the existing approaches have several shortcomings. Inspired by the physics-informed neural networks, we propose Coagulo-Net, which synergizes the strengths of deep neural networks with the mechanistic understanding of the blood coagulation processes to enhance the mathematical models of the blood coagulation cascade. We assess the performance of the Coagulo-Net using two existing coagulation models with different extents of complexity. Our simulation results illustrate that Coagulo-Net can efficiently infer the unknown model parameters and dynamics of species based on sparse measurement data and data contaminated with noise. In addition, we show that Coagulo-Net can process a mixture of synthetic and experimental data and refine the predictions of existing mathematical models of coagulation. These results demonstrate the promise of Coagulo-Net in enhancing current coagulation models and aiding the creation of novel models for physiological and pathological research. These results showcase the potential of Coagulo-Net to advance computational modeling in the study of blood coagulation, improving both research methodologies and the development of new therapies for treating patients with coagulation disorders.

Modeling Fibrin Accumulation on Flow-Diverting Devices for Intracranial Aneurysms

The mechanisms leading to aneurysm occlusion after treatment with flow-diverting devices are not fully understood. Flow modification induces thrombus formation within the aneurysm cavity, but fibrin can simultaneously accumulate and cover the device scaffold, leading to further flow modification. However, the interplay and relative importance of these processes are not clearly understood. A computational model of fibrin accumulation and flow modification after flow diversion treatment of cerebral aneurysms has been developed under the guidance of in vitro experiments and observations. The model is based on the loose coupling of flow and transport-reaction equations that are solved separately by independent codes. Interaction or reactive terms account for thrombin production from prothrombin stimulated by thrombogenic metallic wires and inhibition by antithrombin as well as fibrin production from fibrinogen stimulated by thrombin and flow shear stress, and fibrin adhesion to device wires and already attached fibrin. The computational model was demonstrated and tested on idealized vessel and aneurysm geometries. The model was able to reproduce the salient features of fibrin accumulation after the deployment of flow-diverting devices in idealized in vitro models of cerebral aneurysms. Namely, fibrin production in regions of high shear stress, initial accumulation at the inflow zone, and progressive occlusion of the device and corresponding flow attenuation. The computational model linking flow dynamics to fibrin production, transport, and adhesion can be used to investigate and better understand the effects that lead to fibrin accumulation and the resulting aneurysm inflow reduction and intra-aneurysmal flow modulation.

Examining downstream effects of concizumab in hemophilia A with a mathematical modeling approach

BACKGROUND

Tissue factor (TF) pathway inhibitor (TFPI) is an anticoagulant protein that inhibits factor (F)Xa, the TF-FVIIa-FXa complex, and early forms of the prothrombinase complex. Concizumab is a monoclonal antibody that blocks FXa inhibition by TFPI and reduces bleeding in hemophilia.

OBJECTIVES

To examine how concizumab impacts various reactions of TFPI to restore thrombin generation in hemophilia A using mathematical models.

METHODS

A compartment model was used to estimate plasma concentrations of free concizumab and its complexes with TFPIα and TFPIβ. Concizumab was integrated into a flow-mediated mathematical model of coagulation, and a small injury was simulated under hemophilia A conditions. Simulations were then analyzed to determine how concizumab's blockade of TFPI anticoagulant activities, specifically the inhibition of FXa in plasma and on platelets, inhibition of TF:FVIIa at the subendothelium, and prior sequestration of plasma TFPIα to the endothelium via TFPIβ, altered thrombin generation.

RESULTS

Concizumab improved simulated thrombin generation in hemophilia A by simultaneously altering all 3 mechanisms of the TFPI anticoagulant blockade examined. Concizumab sequestered ∼75% of plasma TFPIα through the formation of ternary TFPIα-concizumab-TFPIβ-complexes. For all TF levels, reducing the TFPIα plasma concentration had the largest impact on the lag time, followed by blocking TFPIα inhibition of TF:FVIIa:FXa and subsequently by blocking TFPIα inhibition of FXa in plasma and on the platelet surface.

CONCLUSION

The effectiveness of concizumab is mediated through the blockade of TFPI anticoagulant activities in plasma and on multiple physiological surfaces. An important and previously unrecognized function of concizumab was the sequestration of plasma TFPIα to the endothelium.

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.

A new look at TFPI inhibition of factor X activation

Blood coagulation is a vital physiological process involving a complex network of biochemical reactions, which converge to form a blood clot that repairs vascular injury. This process unfolds in three phases: initiation, amplification, and propagation, ultimately leading to thrombin formation. Coagulation begins when tissue factor (TF) is exposed on an injured vessel's wall. The first step is when activated factor VII (VIIa) in the plasma binds to TF, forming complex TF:VIIa, which activates factor X. Activated factor X (Xa) is necessary for coagulation, so the regulation of its activation is crucial. Tissue Factor Pathway Inhibitor (TFPI) is a critical regulator of the initiation phase as it inhibits the activation of factor X. While previous studies have proposed two pathways-direct and indirect binding-for TFPI's inhibitory role, the specific biochemical reactions and their rates remain ambiguous. Many existing mathematical models only assume an indirect pathway, which may be less effective under physiological flow conditions. In this study, we revisit datasets from two experiments focused on activated factor X formation in the presence of TFPI. We employ an adaptive Metropolis method for parameter estimation to reinvestigate a previously proposed biochemical scheme and corresponding rates for both inhibition pathways. Our findings show that both pathways are essential to replicate the static experimental results. Previous studies have suggested that flow itself makes a significant contribution to the inhibition of factor X activation. We added flow to this model with our estimated parameters to determine the contribution of the two inhibition pathways under these conditions. We found that direct binding of TFPI is necessary for inhibition under flow. The indirect pathway has a weaker inhibitory effect due to removal of solution phase inhibitory complexes by flow.

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.

Platelet-Rich Plasma-Embedded Porous Polycaprolactone Film with a Large Surface Area for Effective Hemostasis

BACKGROUND

Uncontrollable and widespread bleeding caused by surgery or sudden accidents can lead to death if not treated with appropriate hemostasis. To prevent excessive life-threatening bleeding, various hemostatic agents based on polymeric biomaterials with various additives for accelerated blood coagulation have been adopted in clinical fields. In particular, platelet-rich plasma (PRP), which contains many blood coagulation factors that can accelerate blood clot formation, is considered as one of the most effective hemostatic additives.

METHODS

We investigated a PRP-embedded porous film using discarded (expired) PRP and a film with a leaf-stacked structure (FLSS), as a hemostatic agent to induce rapid hemostasis. The film, which contained an LSS on one side (PCL-FLSS), was fabricated by a simple heating-cooling technique using tetraglycol and polycaprolactone (PCL) film. Activated PRP was obtained by the thawing of frozen PRP at the end of its expiration date (the platelet cell membrane is disrupted during the freezing and thawing of PRP, thus releasing various coagulation factors) and embedded in the PCL-FLSS (PRP-FLSS).

RESULTS

From in vitro and in vivo experiments using a rat hepatic bleeding model, it was recognized that PRP-FLSS is not only biocompatible but also significantly accelerates blood clotting and thus prevents rapid bleeding, probably due to a synergistic effect of the sufficient supply of various blood coagulants from activated PRP embedded in the LSS layer and the large surface area of the LSS itself.

CONCLUSION

The study suggests that PRP-FLSS, a combination of a porous polymer matrix with a unique morphology and discarded biofunctional resources, can be an advanced hemostatic agent as well as an upcycling platform to avoid the waste of biofunctional resources.

Concizumab improves clot formation in hemophilia A under flow

BACKGROUND

Inhibition of tissue factor pathway inhibitor (TFPI) is an emerging therapeutic strategy for treatment of hemophilia. Concizumab is a monoclonal antibody that binds TFPI and blocks its inhibition of factor (F)Xa thereby extending the initiation of coagulation and compensating for lack of FVIII or FIX.

OBJECTIVES

The objective of this in vitro study was to evaluate how concizumab affects clot formation in hemophilia A under flow.

METHODS

Blood was collected from normal controls or people with hemophilia A. An anti-FVIII antibody was added to normal controls to simulate hemophilia A with inhibitory antibodies to FVIII. Whole blood and recombinant activated FVII (rFVIIa, 25 nM) or concizumab (200, 1000, and 4000 ng/mL) were perfused at 100 s-1 over a surface micropatterned with tissue factor (TF) and collagen-related peptide. Platelet and fibrin(ogen) accumulation were measured by confocal microscopy. Static thrombin generation in plasma was measured in response to rFVIIa and concizumab.

RESULTS

Concizumab (1000 and 4000 ng/mL) and rFVIIa both rescued (93%-101%) total platelet accumulation, but only partially rescued (53%-63%) fibrin(ogen) incorporation to normal control levels in simulated hemophilia A. Results using congenital hemophilia A blood confirmed effects of rFVIIa and concizumab. While these 2 agents had similar effect on clot formation under flow, concizumab enhanced thrombin generation in plasma under static conditions to a greater extent than rFVIIa.

CONCLUSION

TFPI inhibition by concizumab enhanced activation and aggregation of platelets and fibrin clot formation in hemophilia A to levels comparable with that of rFVIIa.

Simulation of the effect of hemolysis on thrombosis in blood-contacting medical devices

Heart failure, broadly characterized by the gradual decline of the ability of the heart to maintain adequate blood flow throughout the body's vascular network of veins and arteries, is one of the leading causes of death worldwide. Mechanical Circulatory Support is one of the few available alternative interventions for late-stage heart failure with reduced ejection fraction. A ventricular assist device is surgically implanted and connected to the left and or right heart ventricles to provide additional bloodflow, off-loading the work required by the heart to maintain circulation. Modern mechanical circulatory support devices generate non-physiological flow conditions that can lead to the damage and rupture of blood cells (hemolysis), and the formation of blood clots (thrombosis), which pose severe health risks to the patient. It is essential to improve prediction tools for blood damage to reduce the risk of hemolysis and thrombosis. A simulation-based approach examines the interaction between hemolysis and thrombosis. Incompressible finite-volume computational fluid dynamics simulations are executed on an open-hub axial flow ventricular assist device. A continuum model of thrombosis and the intrinsic coagulation process is extended to include the effect of hemolysis. The model accounts for the effect of activation of platelets by shear stress, paracrine signaling, adhesion, and hemoglobin and ADP released during hemolysis. The effect of hemolysis with thrombosis is modelled by accounting for the hyper-adhesivity of von-Willebrand Factor on extracellular hemoglobin, and the increased rate of platelet activation induced by ADP release. Thrombosis is assessed at varying inflow rates and rotor speeds, and cases are executed where thrombosis is affected by ADP release and Hb-induced hyper-adhesivity. It is found that there is a non-negligible effect from hemolysis on thrombosis across a range of rotor speeds, and that hyperadhesivity plays a dominant role in thrombus formation in the presence of hemolysis.

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.

Kinetics and regulation of coagulation factor X activation by intrinsic tenase on phospholipid membranes

BACKGROUND

Factor X activation by the phospholipid-bound intrinsic tenase complex is a critical membrane-dependent reaction of blood coagulation. Its regulation mechanisms are unclear, and a number of questions regarding diffusional limitation, pathways of assembly and substrate delivery remain open.

METHODS

We develop and analyze here a detailed mechanism-driven computer model of intrinsic tenase on phospholipid surfaces. Three-dimensional reaction-diffusion-advection and stochastic simulations were used where appropriate.

RESULTS

Dynamics of the system was predominantly non-stationary under physiological conditions. In order to describe experimental data, we had to assume both membrane-dependent and solution-dependent delivery of the substrate. The former pathway dominated at low cofactor concentration, while the latter became important at low phospholipid concentration. Factor VIIIa-factor X complex formation was the major pathway of the complex assembly, and the model predicted high affinity for their lipid-dependent interaction. Although the model predicted formation of the diffusion-limited layer of substrate for some conditions, the effects of this limitation on the fXa production were small. Flow accelerated fXa production in a flow reactor model by bringing in fIXa and fVIIIa rather than fX.

CONCLUSIONS

This analysis suggests a concept of intrinsic tenase that is non-stationary, employs several pathways of substrate delivery depending on the conditions, and is not particularly limited by diffusion of the substrate.

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.

clotFoam: An Open-Source Framework to Simulate Blood Clot Formation Under Arterial Flow

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.

clotFoam: An open-source framework to simulate blood clot formation under arterial flow

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.

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.

A model of fluid-structure and biochemical interactions for applications to subclinical leaflet thrombosis

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis because they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction.

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.

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.

Inhibition of platelet-surface-bound proteins during coagulation under flow II: Antithrombin and heparin

Blood coagulation is a self-repair process regulated by activated platelet surfaces, clotting factors, and inhibitors. Antithrombin (AT) is one such inhibitor that impedes coagulation by targeting and inactivating several key coagulation enzymes. The effect of AT is greatly enhanced in the presence of heparin, a common anticoagulant drug. When heparin binds to AT, it either bridges with the target enzyme or induces allosteric changes in AT leading to more favorable binding with the target enzyme. AT inhibition of fluid-phase enzymes caused little suppression of thrombin generation in our previous mathematical models of blood coagulation under flow. This is because in that model, flow itself was a greater inhibitor of the fluid-phase enzymes than AT. From clinical observations, it is clear that AT and heparin should have strong inhibitory effects on thrombin generation, and thus we hypothesized that AT could be inhibiting enzymes bound to activated platelet surfaces that are not subject to being washed away by flow. We extended our mathematical model to include the relevant reactions of AT inhibition at the activated platelet surfaces as well as those for unfractionated heparin and a low molecular weight heparin. Our results show that AT alone is only an effective inhibitor at low tissue factor densities, but in the presence of heparin, it can greatly alter, and in some cases shut down, thrombin generation. Additionally, we studied each target enzyme separately and found that inactivation of no single enzyme could substantially suppress thrombin generation.

von Willebrand factor unfolding mediates platelet deposition in a model of high-shear thrombosis

Thrombosis under high-shear conditions is mediated by the mechanosensitive blood glycoprotein von Willebrand factor (vWF). vWF unfolds in response to strong flow gradients and facilitates rapid recruitment of platelets in flowing blood. While the thrombogenic effect of vWF is well recognized, its conformational response in complex flows has largely been omitted from numerical models of thrombosis. We recently presented a continuum model for the unfolding of vWF, where we represented vWF transport and its flow-induced conformational change using convection-diffusion-reaction equations. Here, we incorporate the vWF component into our multi-constituent model of thrombosis, where the local concentration of stretched vWF amplifies the deposition rate of free-flowing platelets and reduces the shear cleaning of deposited platelets. We validate the model using three benchmarks: in vitro model of atherothrombosis, a stagnation point flow, and the PFA-100, a clinical blood test commonly used for screening for von Willebrand disease (vWD). The simulations reproduced the key aspects of vWF-mediated thrombosis observed in these experiments, such as the thrombus location, thrombus growth dynamics, and the effect of blocking platelet-vWF interactions. The PFA-100 simulations closely matched the reported occlusion times for normal blood and several hemostatic deficiencies, namely, thrombocytopenia, vWD type 1, and vWD type 3. Overall, this multi-constituent model of thrombosis enables macro-scale 3D simulations of thrombus formation in complex geometries over a wide range of shear rates and accounts for qualitative and quantitative hemostatic deficiencies in patient blood.

Fibrin Sealants: Challenges and Solutions

Intraoperative bleeding and postoperative bleeding are major surgical complications. Tissue sealants, hemostats, and adhesives provide the armamentarium for establishing hemostatic balance, including the tissue sealant fibrin. Fibrin sealants combine advantages including instantaneous effect, biocompatibility, and biodegradability. However, several challenges remain. This review summarizes current fibrin product generations and highlights new trends and potential strategies for future improvement.

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.

DEVELOPMENT OF FIBRIN BRANCH STRUCTURE BEFORE AND AFTER GELATION

In [Fogelson and Keener, Phys. Rev. E, 81 (2010), 051922], we introduced a kinetic model of fibrin polymerization during blood clotting that captured salient experimental observations about how the gel branching structure depends on the conditions under which the polymerization occurs. Our analysis there used a moment-based approach that is valid only before the finite time blow-up that indicates formation of a gel. Here, we extend our analyses of the model to include both pre-gel and post-gel dynamics using the PDE-based framework we introduced in [Fogelson and Keener, SIAM J. Appl. Math., 75 (2015), pp. 1346-1368]. We also extend the model to include spatial heterogeneity and spatial transport processes. Studies of the behavior of the model reveal different spatial-temporal dynamics as the time scales of the key processes of branch formation, monomer introduction, and diffusion are varied.

Continuum modeling of thrombus formation and growth under different shear rates

Obstruction of blood flow due to thrombosis is a major cause of ischemic stroke, myocardial infarction, and in severe cases, mortality. In particular, in blood wetting medical devices, thrombosis is a common reason for failure. The prediction of thrombosis by understanding signaling pathways using computational models, lead to identify the risk of thrombus formation in blood-contacting devices and design improvements. In this study, a mathematical model of thrombus formation and growth is presented. A biochemical model of platelet activation and aggregation is developed to predict thrombus size and shape at the site of vascular injury. Computational fluid dynamics using the finite volume method is employed to compute the velocity and pressure fields which are influenced by the growing thrombi. The passive transport of platelets, agonists, the platelet activation kinetics, their adhesion to the growing thrombi and embolization of platelets are solved by a fully coupled set of convection-diffusion-reaction equations. The thrombogenic surface representing blood-contacting material or injured blood vessel was incorporated into the model as a surface flux boundary condition to initiate thrombus formation. The blood is considered as a Newtonian fluid, while the thrombus is treated as a porous medium. The results are compared with in vitro experiments of a microfluidic chamber at an initial inlet venous shear rate of 200s^-1 using a pressure-inlet boundary condition. The thrombus development due to agonist concentrations and change in the shear rate as well as thromboembolism for this benchmark problem is successfully computed. Furthermore, to extend the current model to a physiologically relevant configuration, thrombus formation in a blood tube is simulated. Two different heterogeneous reaction rates for platelet aggregation are used to simulate thrombus growth under a constant inlet flow rate. The findings show that the thrombus shape can be substantially altered by the hemodynamic conditions, increase in the shear rate and due to the combined effects of shear induced platelet activation and the heterogeneous reaction rates. It is also concluded that the model is able to predict thrombus formation in different physiological and pathological hemodynamics.

A three-dimensional multiscale model for the prediction of thrombus growth under flow with single-platelet resolution

Modeling thrombus growth in pathological flows allows evaluation of risk under patient-specific pharmacological, hematological, and hemodynamical conditions. We have developed a 3D multiscale framework for the prediction of thrombus growth under flow on a spatially resolved surface presenting collagen and tissue factor (TF). The multiscale framework is composed of four coupled modules: a Neural Network (NN) that accounts for platelet signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. A reduced model of the coagulation cascade was embedded into the framework to account for TF-driven thrombin production. The 3D model was first tested against in vitro microfluidics experiments of whole blood perfusion with various antiplatelet agents targeting COX-1, P₂Y₁, or the IP receptor. The model was able to accurately capture the evolution and morphology of the growing thrombus. Certain problems of 2D models for thrombus growth (artifactual dendritic growth) were naturally avoided with realistic trajectories of platelets in 3D flow. The generalizability of the 3D multiscale solver enabled simulations of important clinical situations, such as cylindrical blood vessels and acute flow narrowing (stenosis). Enhanced platelet-platelet bonding at pathologically high shear rates (e.g., von Willebrand factor unfolding) was required for accurately describing thrombus growth in stenotic flows. Overall, the approach allows consideration of patient-specific platelet signaling and vascular geometry for the prediction of thrombotic episodes.

The excessive formation of blood clots under flow within the circulatory system (thrombosis) is known to initiate heart attacks and strokes. Therefore, obtaining insights into the formation and progression of these clots will be useful in evaluating pharmacological options. To this end, we have developed a 3D computational model that tracks the growth of a blood clot under flow from initial platelet deposition to full vessel occlusion in the presence of soluble platelet agonists. We first validated the model against experimental predictions of blood clots formed in vitro. Due to the construction of the model in 3D, we were able to carry out simulations of clot formation under important clinical situations, namely cylindrical blood vessels and acute flow narrowings (stenoses). To our knowledge, our model is the first of its kind that can account for patient-specific platelet phenotypes to perform robust 3D simulations of thrombus growth in geometries of clinical relevance.

Control of Blood Coagulation by Hemocompatible Material Surfaces-A Review

Hemocompatibility of biomaterials in contact with the blood of patients is a prerequisite for the short- and long-term applications of medical devices such as cardiovascular stents, artificial heart valves, ventricular assist devices, catheters, blood linings and extracorporeal devices such as artificial kidneys (hemodialysis), extracorporeal membrane oxygenation (ECMO) and cardiopulmonary bypass. Although lower blood compatibility of materials and devices can be handled with systemic anticoagulation, its side effects, such as an increased bleeding risk, make materials that have a better hemocompatibility highly desirable, particularly in long-term applications. This review provides a short overview on the basic mechanisms of blood coagulation including plasmatic coagulation and blood platelets, as well as the activation of the complement system. Furthermore, a survey on concepts for tailoring the blood response of biomaterials to improve the hemocompatibility of medical devices is given which covers different approaches that either inhibit interaction of material surfaces with blood components completely or control the response of the coagulation system, blood platelets and leukocytes.

Thrombosis and Hemodynamics: external and intrathrombus gradients

Distinct from dilute, isotropic, and homogeneous reaction systems typically used in laboratory kinetic assays, blood is concentrated, two-phase, flowing, and highly anisotropic when clotting on a surface. This review focuses on spatial gradients that are generated and can dictate thrombus structure and function. Novel experimental and computational tools have recently emerged to explore reaction-transport coupling during clotting. Multiscale simulations help bridge tissue length scales (the coronary arteries) to millimeter scales of a growing clot to the microscopic scale of single-cell signaling and adhesion. Microfluidic devices help create and control pathological velocity profiles, albeit at a low Reynolds number. Since rate processes and force loading are often coupled, this review highlights prevailing convective-diffusive transport physics that modulate cellular and molecular processes during thrombus formation.

Computational modeling of blood component transport related to coronary artery thrombosis in Kawasaki disease

Coronary artery thrombosis is the major risk associated with Kawasaki disease (KD). Long-term management of KD patients with persistent aneurysms requires a thrombotic risk assessment and clinical decisions regarding the administration of anticoagulation therapy. Computational fluid dynamics has demonstrated that abnormal KD coronary artery hemodynamics can be associated with thrombosis. However, the underlying mechanisms of clot formation are not yet fully understood. Here we present a new model incorporating data from patient-specific simulated velocity fields to track platelet activation and accumulation. We use a system of Reaction-Advection-Diffusion equations solved with a stabilized finite element method to describe the evolution of non-activated platelets and activated platelet concentrations [AP], local concentrations of adenosine diphosphate (ADP) and poly-phosphate (PolyP). The activation of platelets is modeled as a function of shear-rate exposure and local concentration of agonists. We compared the distribution of activated platelets in a healthy coronary case and six cases with coronary artery aneurysms caused by KD, including three with confirmed thrombosis. Results show spatial correlation between regions of higher concentration of activated platelets and the reported location of the clot, suggesting predictive capabilities of this model towards identifying regions at high risk for thrombosis. Also, the concentration levels of ADP and PolyP in cases with confirmed thrombosis are higher than the reported critical values associated with platelet aggregation (ADP) and activation of the intrinsic coagulation pathway (PolyP). These findings suggest the potential initiation of a coagulation pathway even in the absence of an extrinsic factor. Finally, computational simulations show that in regions of flow stagnation, biochemical activation, as a result of local agonist concentration, is dominant. Identifying the leading factors to a pro-coagulant environment in each case—mechanical or biochemical—could help define improved strategies for thrombosis prevention tailored for each patient.

Computational studies aiming to model thrombosis often rely on an arterial wall injury. Collagen and other extracellular matrix components are exposed to the bloodstream, which facilitates platelet adhesion to the wall and subsequent clot formation. However, these models are not adequate to explain thrombosis in other settings where even in the absence of a focal lesion, clots may still form under certain flow conditions. Coronary artery aneurysm thrombosis following KD is an example of the need to understand the mechanisms of thrombus initiation in the absence of an extrinsic factor. This study provides a new framework to investigate thrombus initiation in KD from a patient-specific perspective, which integrates fluid mechanics and biochemistry and which could help quantify the pro-coagulant environment induced by the aneurysm and become a predictive tool. The work presented here has broad relevance to other clinical situations where flow stagnation and transport are driving factors in thrombus formation.

Multi-omics approaches for revealing the complexity of cardiovascular disease

The development and progression of cardiovascular disease (CVD) can mainly be attributed to the narrowing of blood vessels caused by atherosclerosis and thrombosis, which induces organ damage that will result in end-organ dysfunction characterized by events such as myocardial infarction or stroke. It is also essential to consider other contributory factors to CVD, including cardiac remodelling caused by cardiomyopathies and co-morbidities with other diseases such as chronic kidney disease. Besides, there is a growing amount of evidence linking the gut microbiota to CVD through several metabolic pathways. Hence, it is of utmost importance to decipher the underlying molecular mechanisms associated with these disease states to elucidate the development and progression of CVD. A wide array of systems biology approaches incorporating multi-omics data have emerged as an invaluable tool in establishing alterations in specific cell types and identifying modifications in signalling events that promote disease development. Here, we review recent studies that apply multi-omics approaches to further understand the underlying causes of CVD and provide possible treatment strategies by identifying novel drug targets and biomarkers. We also discuss very recent advances in gut microbiota research with an emphasis on how diet and microbial composition can impact the development of CVD. Finally, we present various biological network analyses and other independent studies that have been employed for providing mechanistic explanation and developing treatment strategies for end-stage CVD, namely myocardial infarction and stroke.

In-silico trial of intracranial flow diverters replicates and expands insights from conventional clinical trials

The cost of clinical trials is ever-increasing. In-silico trials rely on virtual populations and interventions simulated using patient-specific models and may offer a solution to lower these costs. We present the flow diverter performance assessment (FD-PASS) in-silico trial, which models the treatment of intracranial aneurysms in 164 virtual patients with 82 distinct anatomies with a flow-diverting stent, using computational fluid dynamics to quantify post-treatment flow reduction. The predicted FD-PASS flow-diversion success rates replicate the values previously reported in three clinical trials. The in-silico approach allows broader investigation of factors associated with insufficient flow reduction than feasible in a conventional trial. Our findings demonstrate that in-silico trials of endovascular medical devices can: (i) replicate findings of conventional clinical trials, and (ii) perform virtual experiments and sub-group analyses that are difficult or impossible in conventional trials to discover new insights on treatment failure, e.g. in the presence of side-branches or hypertension.

In-silico trials rely on virtual populations and interventions simulated using patient-specific models and may offer a solution to lower costs. Here, the authors present the flow diverter performance assessment in-silico trial, which models the treatment of intracranial aneurysms with a flow-diverting stent.

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.

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.

A MATHEMATICAL MODEL OF PLATELET AGGREGATION IN AN EXTRAVASCULAR INJURY UNDER FLOW

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODEs) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical adenosine diphosphate hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool of primary and secondary hemostasis.

Combination targeting of 'platelets + fibrin' enhances clot anchorage efficiency of nanoparticles for vascular drug delivery

Occlusive thrombosis is a central pathological event in heart attack, stroke, thromboembolism, etc. Therefore, pharmacological thrombolysis or anticoagulation is used for treating these diseases. However, systemic administration of such drugs causes hemorrhagic side-effects. Therefore, there is significant clinical interest in strategies for enhanced drug delivery to clots while minimizing systemic effects. One such strategy is by using drug-carrying nanoparticles surface-decorated with clot-binding ligands. Efforts in this area have focused on binding to singular targets in clots, e.g. platelets, fibrin, collagen, vWF or endothelium. Targeting vWF, collagen or endothelium maybe sub-optimal since in vivo these entities will be rapidly covered by platelets and leukocytes, and thus inaccessible for sufficient nanoparticle binding. In contrast, activated platelets and fibrin are majorly accessible for particle-binding, but their relative distribution in clots is highly heterogeneous. We hypothesized that combination-targeting of 'platelets + fibrin' will render higher clot-binding efficacy of nanoparticles, compared to targeting platelets or fibrin singularly. To test this, we utilized liposomes as model nanoparticles, decorated their surface with platelet-binding peptides (PBP) or fibrin-binding peptides (FBP) or combination (PBP + FBP) at controlled compositions, and evaluated their binding to human blood clots in vitro and in a mouse thrombosis model in vivo. In parallel, we developed a computational model of nanoparticle binding to single versus combination entities in clots. Our studies indicate that combination targeting of 'platelets + fibrin' enhances the clot-anchorage efficacy of nanoparticles while utilizing lower ligand densities, compared to targeting platelets or fibrin only. These findings provide important insights for vascular nanomedicine design.

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).

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.

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.

Heterogeneity of Integrin αIIbβ3 Function in Pediatric Immune Thrombocytopenia Revealed by Continuous Flow Cytometry Analysis

Immune thrombocytopenia (ITP) is an autoimmune condition primarily induced by the loss of immune tolerance to the platelet glycoproteins. Here we develop a novel flow cytometry approach to analyze integrin α_IIbβ₃ functioning in ITP in comparison with Glanzmann thrombasthenia (GT) (negative control) and healthy pediatric donors (positive control). Continuous flow cytometry of Fura-Red-loaded platelets from whole hirudinated blood was used for the characterization of platelet responses to conventional activators. Calcium levels and fibrinogen binding were normalized to ionomycin-induced responses. Ex vivo thrombus formation on collagen was observed in parallel-plate flow chambers. Platelets from all ITP patients had significantly higher cytosolic calcium concentration in the quiescent state compared to healthy donors (15 ± 5 nM vs. 8 ± 5 nM), but calcium increases in response to all activators were normal. Clustering analysis revealed two subpopulations of ITP patients: the subgroup with high fibrinogen binding (HFB), and the subgroup with low fibrinogen binding (LFB) (8% ± 5% for LFB vs. 16% ± 3% for healthy donors in response to ADP). GT platelets had calcium mobilization (81 ± 23 nM), fibrinogen binding (5.1% ± 0.3%) and thrombus growth comparable to the LFB subgroup. Computational modeling suggested phospholipase C-dependent platelet pre-activation for the HFB subgroup and lower levels of functional integrin molecules for the LFB group.

A mathematical model of coagulation under flow identifies factor V as a modifier of thrombin generation in hemophilia A

BACKGROUND

The variability in bleeding patterns among individuals with hemophilia A, who have similar factor VIII (FVIII) levels, is significant and the origins are unknown.

OBJECTIVE

To use a previously validated mathematical model of flow-mediated coagulation as a screening tool to identify parameters that are most likely to enhance thrombin generation in the context of FVIII deficiency.

METHODS

We performed a global sensitivity analysis (GSA) on our mathematical model to identify potential modifiers of thrombin generation. Candidates from the GSA were confirmed by calibrated automated thrombography (CAT) and flow assays on collagen-tissue factor (TF) surfaces at a shear rate of 100 per second.

RESULTS

Simulations identified low-normal factor V (FV) (50%) as the strongest modifier, with additional thrombin enhancement when combined with high-normal prothrombin (150%). Low-normal FV levels or partial FV inhibition (60% activity) augmented thrombin generation in FVIII-inhibited or FVIII-deficient plasma in CAT. Partial FV inhibition (60%) boosted fibrin deposition in flow assays performed with whole blood from individuals with mild and moderate FVIII deficiencies. These effects were amplified by high-normal prothrombin levels in both experimental models.

CONCLUSIONS

These results show that low-normal FV levels can enhance thrombin generation in hemophilia A. Further explorations with the mathematical model suggest a potential mechanism: lowering FV reduces competition between FV and FVIII for factor Xa (FXa) on activated platelet surfaces (APS), which enhances FVIII activation and rescues thrombin generation in FVIII-deficient blood.

Simulation of thrombosis in a stenotic microchannel: The effects of vWF-enhanced shear activation of platelets

This study was undertaken to develop a numerical/computational simulation of von Willebrand Factor (vWF) - mediated platelet shear activation and deposition in an idealized stenosis. Blood is treated as a multi-constituent mixture comprised of a linear fluid component and a porous solid component (thrombus). Chemical and biological species involved in coagulation are modeled using a system of coupled convection-reaction-diffusion (CRD) equations. This study considers the cumulative effect of shear stress (history) on platelet activation. The vWF activity is modeled as an enhancement function for the shear stress accumulation and is related to the experimentally-observed unfolding rate of vWF. A series of simulations were performed in an idealized stenosis in which the predicted platelets deposition agreed well with previous experimental observations spatially and temporally, including the reduction of platelet deposition with decreasing expansion angle. Further simulation indicated a direct relationship between vWF-mediated platelet deposition and degree of stenosis. Based on the success with these benchmark simulations, it is hoped that the model presented here may provide additional insight into vWF-mediated thrombosis and prove useful for the development of more hemo-compatible blood-wetted devices in the future.

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.

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.