The limits of simulation of the clotting system

Influence of vortical structures on fibrin clot formation in cerebral aneurysms: A two-dimensional computational study

Thrombosis is an important contributor to cerebral aneurysm growth and progression. A number of sophisticated multiscale and multiphase in silico models have been developed with a view towards interventional planning. Many of these models are able to account for clotting outcomes, but do not provide detailed insight into the role of flow during clot development. In this study, we present idealised, two-dimensional in silico cerebral fibrin clot model based on computational fluid dynamics (CFD), biochemical modelling and variable porosity, permeability, and diffusivity. The model captures fibrin clot growth in cerebral aneurysms over a period at least 1000 s in five different geometries. The fibrin clot growth results were compared to an experiment presented in literature. The biochemistry was found to be more sensitive to mesh size compared to the haemodynamics, while larger timesteps overpredicted clot size in pulsatile flow. When variable diffusivity was used, the predicted clot size was 25.4% lesser than that with constant diffusivity. The predicted clot size in pulsatile flow was 14.6% greater than in plug flow. Different vortex modes were observed in plug and pulsatile flow; the latter presented smaller intermediate modes where the main vortex was smaller and less likely to disrupt the growing fibrin clot. Furthermore, smaller vortex modes were seen to support fibrin clot propagation across geometries. The model clearly demonstrates how the growing fibrin clot alters vortical structures within the aneurysm sac and how this changing flow, in turn, shapes the growing fibrin clot.

A bispecific antibody approach for the potential prophylactic treatment of inherited bleeding disorders

Inherited bleeding disorders such as Glanzmann thrombasthenia (GT) lack prophylactic treatment options. As a result, serious bleeding episodes are treated acutely with blood product transfusions or frequent, repeated intravenous administration of recombinant activated coagulation factor VII (rFVIIa). Here we describe HMB-001, a bispecific antibody designed to bind and accumulate endogenous FVIIa and deliver it to sites of vascular injury by targeting it to the TREM (triggering receptor expressed on myeloid cells)-like transcript-1 (TLT-1) receptor that is selectively expressed on activated platelets. In healthy nonhuman primates, HMB-001 prolonged the half-life of endogenous FVIIa, resulting in its accumulation. Mouse bleeding studies confirmed antibody-mediated potentiation of FVIIa hemostatic activity by TLT-1 targeting. In ex vivo models of GT, HMB-001 localized FVIIa on activated platelets and potentiated fibrin-dependent platelet aggregation. Taken together, these results indicate that HMB-001 has the potential to offer subcutaneous prophylactic treatment to prevent bleeds in people with GT and other inherited bleeding disorders, with a low-frequency dosing regimen.

Tracking the dynamics of thrombus formation in a blood vessel-on-chip with visible-light optical coherence tomography

Thrombus formation is a physiological response to damage in a blood vessel that relies on a complex interplay of platelets, coagulation factors, immune cells, and the vessel wall. The dynamics of thrombus formation are essential for a deeper understanding of many disease processes, like bleeding, wound healing, and thrombosis. However, monitoring thrombus formation is challenging due to the limited imaging options available to analyze flowing blood. In this work, we use a visible-light optical coherence tomography (vis-OCT) system to monitor the dynamic process of the formation of thrombi in a microfluidic blood vessel-on-chip (VoC) device. Inside the VoC, thrombi form in a channel lined with a monolayer of endothelial cells and perfused by human whole blood. We show that the correlation of the vis-OCT signal can be utilized as a marker for thrombus formation. By thresholding the correlation during thrombus formation, we track and quantify the growth of the thrombi over time. We validate our results with fluorescence microscopic imaging of fibrin and platelet markers at the end of the blood perfusion assay. In conclusion, we demonstrate that the correlation of the vis-OCT signal can be used to visualize both the spatial and temporal behavior of the thrombus formation in flowing human whole blood.

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.

VhH anti-thrombomodulin clone 1 inhibits TAFI activation and enhances fibrinolysis in human whole blood under flow

BACKGROUND

Thrombomodulin on endothelial cells can form a complex with thrombin. This complex has both anticoagulant properties, by activating protein C, and clot-protective properties, by activating thrombin-activatable fibrinolysis inhibitor (TAFI). Activated TAFI (TAFIa) inhibits plasmin-mediated fibrinolysis.

OBJECTIVES

TAFIa inhibition is considered a potential antithrombotic strategy. So far, this goal has been pursued by developing compounds that directly inhibit TAFIa. In contrast, we here describe variable domain of heavy-chain-only antibody (VhH) clone 1 that inhibits TAFI activation by targeting human thrombomodulin.

METHODS

Two llamas (Lama Glama) were immunized, and phage display was used to select VhH anti-thrombomodulin (TM) clone 1. Affinity was determined with surface plasmon resonance and binding to native TM was confirmed with flow cytometry. Clone 1 was functionally assessed by competition, clot lysis, and thrombin generation assays. Last, the effect of clone 1 on tPA-mediated fibrinolysis in human whole blood was investigated in a microfluidic fibrinolysis model.

RESULTS

VhH anti-TM clone 1 bound recombinant TM with a binding affinity of 1.7 ± 0.4 nM and showed binding to native TM. Clone 1 competed with thrombin for binding to TM and attenuated TAFI activation in clot lysis assays and protein C activation in thrombin generation experiments. In a microfluidic fibrinolysis model, inhibition of TM with clone 1 fully prevented TAFI activation.

DISCUSSION

We have developed VhH anti-TM clone 1, which inhibits TAFI activation and enhances tPA-mediated fibrinolysis under flow. Different from agents that directly target TAFIa, our strategy should preserve direct TAFI activation via thrombin.

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.

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.

A novel assay for studying the involvement of blood cells in whole blood thrombin generation

BACKGROUND

Fluorogenic thrombin generation (TG) assays are commonly used to determine global coagulation phenotype in plasma. Whole blood (WB)-TG assays reach one step closer to physiology by involving the intrinsic blood cells, but erythrocytes cause variable quenching of the fluorescence signals, hampering its routine application.

OBJECTIVE

To develop a new assay for continuous WB-TG measurement.

METHODS

In the new WB-TG assay, the erythrocyte-caused distortion of signal was solved by continuously mixing the sample during the measurement. The assay was validated by evaluating the reproducibility and comparing with the paper-based WB-TG assay. Reconstituted human blood and WB from 119 healthy donors was tested to explore the influences of hematocrit and platelet count on TG.

RESULTS

This novel WB-TG assay showed good reproducibility while being less affected by contact activation compared with the previous paper-based assay. Reconstitution experiments showed that the lag time of TG was shortened by the addition of platelets but not erythrocytes. Increasing hematocrit strongly augmented the peak thrombin, even in the presence of high platelet counts. The lag time and peak of WB-TG of 119 healthy donors were positively related to erythrocyte count after adjusting for age, sex, and oral contraceptive use with multiple linear regression analyses. The reference range and interindividual variation of WB-TG were determined in the healthy cohort.

CONCLUSIONS

A novel WB-TG assay was developed, which is a straightforward tool to measure the involvement of platelets and erythrocytes in TG and may assist the research of blood cell-associated coagulation disorders.

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.

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.

COMPUTATIONAL INVESTIGATION OF THROMBIN CONCENTRATION IN CEREBRAL ANEURYSMS TREATED WITH FLOW-DIVERTING STENTS

Flow-diverting stent is an ongoing embolization device to treat cerebral aneurysms, and it diverts the flow direction to reduce the flow velocity inside the aneurysmal sacs and promote the thrombus formation. However, its effect for aneurysm embolization is controversial. A hemodynamic-biomedical coupling model was constructed to describe the generation and transport of thrombin in arteries, and the model was applied to investigate the variation of thrombin concentration, which plays a key role in thrombus formation, in two patient-specific cerebral aneurysm models when they are treated with Pipeline flow diverting stents. It is observed from computational fluid dynamics simulations that thrombin concentration in the aneurysmal sac without collateral artery increases significantly after Pipeline implantation, however, it has hardly any variation in the aneurysmal sac without collateral artery or in the giant aneurysmal sac after Pipeline implantation. Therefore, we believe that single Pipeline is very effective to embolize a small aneurysm without collateral artery, but cannot embolize a giant aneurysm or a small aneurysm with a collateral artery on its sac effectively.

Thrombosis in Cerebral Aneurysms and the Computational Modeling Thereof: A Review

Thrombosis is a condition closely related to cerebral aneurysms and controlled thrombosis is the main purpose of endovascular embolization treatment. The mechanisms governing thrombus initiation and evolution in cerebral aneurysms have not been fully elucidated and this presents challenges for interventional planning. Significant effort has been directed towards developing computational methods aimed at streamlining the interventional planning process for unruptured cerebral aneurysm treatment. Included in these methods are computational models of thrombus development following endovascular device placement. The main challenge with developing computational models for thrombosis in disease cases is that there exists a wide body of literature that addresses various aspects of the clotting process, but it may not be obvious what information is of direct consequence for what modeling purpose (e.g., for understanding the effect of endovascular therapies). The aim of this review is to present the information so it will be of benefit to the community attempting to model cerebral aneurysm thrombosis for interventional planning purposes, in a simplified yet appropriate manner. The paper begins by explaining current understanding of physiological coagulation and highlights the documented distinctions between the physiological process and cerebral aneurysm thrombosis. Clinical observations of thrombosis following endovascular device placement are then presented. This is followed by a section detailing the demands placed on computational models developed for interventional planning. Finally, existing computational models of thrombosis are presented. This last section begins with description and discussion of physiological computational clotting models, as they are of immense value in understanding how to construct a general computational model of clotting. This is then followed by a review of computational models of clotting in cerebral aneurysms, specifically. Even though some progress has been made towards computational predictions of thrombosis following device placement in cerebral aneurysms, many gaps still remain. Answering the key questions will require the combined efforts of the clinical, experimental and computational communities.

Multiscale systems biology of trauma-induced coagulopathy

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

Simultaneous measurement of thrombin generation and fibrin formation in whole blood under flow conditions

Assays based on the formation of thrombin and fibrin are frequently used, and results are considered exchangeable in research/clinical settings. However, thrombin generation and fibrin formation do not always go hand in hand and flow profoundly influences thrombus formation. We describe the technical/clinical evaluation of an assay to simultaneously measure thrombin generation and fibrin formation under conditions of flow. Introduction of a fluorometer into a 'cone and base principle'-based rheometer allowed the measurement of thrombin generation (using a thrombin-sensitive substrate) and fibrin formation (changes in viscosity), while applying a linear shear flow. Increasing shear rates inversely related with thrombin generation and fibrin formation. Increasing fibrinogen concentrations in defibrinated plasma resulted in increased thrombin generation and fibrin formation. In pre-operative samples of 70 patients undergoing cardiothoracic surgery, fibrin formation and thrombin generation parameters correlated with fibrinogen content, rotational thromboelastometry (ROTEM) and whole blood Calibrated Automated Thrombinography (CAT) parameters, respectively. Upon dividing patients into two groups based on the median clot strength, a significant difference in perioperative/total blood loss was established. In conclusion, we clinically evaluated a method capable of simultaneously measuring thrombin generation and fibrin formation in plasma/whole blood under continuous flow, rendering our method one step closer to physiology. Importantly, our test proved to be indicative for the amount of blood loss during/after cardiothoracic surgery.

Computational modelling of clot development in patient-specific cerebral aneurysm cases

ESSENTIALS: Clotting in cerebral aneurysms is a process that can either stabilize the aneurysm or lead to rupture. A patient-specific computational model capable of predicting cerebral aneurysm thrombosis is presented. The different clotting outcomes highlight the importance of personalization of treatment. Once validated, the model can be used to tailor treatment and to clarify clotting processes in aneurysms.

BACKGROUND

In cerebral aneurysms, clotting can either stabilize the aneurysm sac via aneurysm occlusion, or it can have a detrimental effect by giving rise to embolic occlusion.

OBJECTIVE

The work presented in this study details the development of an in silico model that combines all the salient, clinically relevant features of cerebral aneurysm clotting. A comprehensive computational model of clotting that accounts for biochemical complexity coupled with three-dimensional hemodynamics in image-derived patient aneurysms and in the presence of virtually implanted interventional devices is presented.

METHODS

The model is developed and presented in two stages. First, a two-dimensional computational model of clotting is presented for an idealized geometry. This enables verification of the methods with existing, physiological data before the pathological state is considered. This model is used to compare the results predicted by two different underlying biochemical cascades. The two-dimensional model is then extended to image-derived, three-dimensional aneurysmal topologies by incorporating level set methods, demonstrating the potential use of this model.

RESULTS AND CONCLUSION

As a proof of concept, comparisons are then made between treated and untreated aneurysms. The prediction of different clotting outcomes for different patients demonstrates that with further development, refinement and validation, this methodology could be used for patient-specific interventional planning.

Hypoxia Induces a Prothrombotic State Independently of the Physical Activity

Hypoxia (oxygen deprivation) is known to be associated with deep vein thrombosis and venous thromboembolism. We attempted to get a better comprehension of its mechanism by going to high altitude, thereby including the potential contributing role of physical activity. Two groups of 15 healthy individuals were exposed to hypoxia by going to an altitude of 3900 meters, either by climbing actively (active group) or transported passively by cable car (passive group). Both groups were tested for plasma fibrinogen, von Willebrand factor and factor VIII levels, fibrinolysis, thrombin generating capacity, heart rate, oxygen saturation levels and blood pressure. As a control for the passive group, 7 healthy volunteers stayed immobile in bed for 7 days at normoxic conditions. The heart rate increased and oxygen saturation levels decreased with increasing altitude. Fibrinolysis and fibrinogen levels were not affected. Factor VIII and von Willebrand factor levels levels increased significantly in the active group, but not in the passive group. Plasma thrombin generation remained unchanged in both the active and passive group with increasing altitude and during 7 days of immobility in healthy subjects. However, by applying whole blood thrombin generation, we found an increased peak height and endogenous thrombin potential, and a decreased lagtime and time-to-peak with increasing levels of hypoxia in both groups. In conclusion, by applying whole blood thrombin generation we demonstrated that hypoxia causes a prothrombotic state. As thrombin generation in plasma did not increase, our results suggest that the cellular part of the blood is involved in the prothrombotic phenotype induced by hypoxia.

A reduced-dimensional model for near-wall transport in cardiovascular flows

Near-wall mass transport plays an important role in many cardiovascular processes, including the initiation of atherosclerosis, endothelial cell vasoregulation, and thrombogenesis. These problems are characterized by large Péclet and Schmidt numbers as well as a wide range of spatial and temporal scales, all of which impose computational difficulties. In this work, we develop an analytical relationship between the flow field and near-wall mass transport for high-Schmidt-number flows. This allows for the development of a wall-shear-stress-driven transport equation that lies on a codimension-one vessel-wall surface, significantly reducing computational cost in solving the transport problem. Separate versions of this equation are developed for the reaction-rate-limited and transport-limited cases, and numerical results in an idealized abdominal aortic aneurysm are compared to those obtained by solving the full transport equations over the entire domain. The reaction-rate-limited model matches the expected results well. The transport-limited model is accurate in the developed flow regions, but overpredicts wall flux at entry regions and reattachment points in the flow.

Mathematical Modeling of Intravascular Blood Coagulation under Wall Shear Stress

Increased shear stress such as observed at local stenosis may cause drastic changes in the permeability of the vessel wall to procoagulants and thus initiate intravascular blood coagulation. In this paper we suggest a mathematical model to investigate how shear stress-induced permeability influences the thrombogenic potential of atherosclerotic plaques. Numerical analysis of the model reveals the existence of two hydrodynamic thresholds for activation of blood coagulation in the system and unveils typical scenarios of thrombus formation. The dependence of blood coagulation development on the intensity of blood flow, as well as on geometrical parameters of atherosclerotic plaque is described. Relevant parametric diagrams are drawn. The results suggest a previously unrecognized role of relatively small plaques (resulting in less than 50% of the lumen area reduction) in atherothrombosis and have important implications for the existing stenting guidelines.

The balance of pro- and anticoagulant processes underlying thrombin generation

BACKGROUND

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

OBJECTIVES

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Global assays of hemostasis

PURPOSE OF REVIEW

There exists an imbalance between our understanding of the physiology of the blood coagulation process and the translation of this understanding into useful assays for clinical application. As technology advances, the capabilities for merging the two areas have become more attainable. Global assays have advanced our understanding of the dynamics of the blood coagulation process beyond end point assays and are at the forefront of implementation in the clinic.

RECENT FINDINGS

We will review recent advances in the main global assays with a focus on thrombin generation that have potential for clinical utility. These assays include direct (thrombogram, whole blood, purified systems) and indirect empirical measures of thrombin generation (thromboelastography) and mechanism-based computational models that use plasma composition data from individuals to generate thrombin generation profiles.

SUMMARY

Empirical thrombin generation assays (direct and indirect) and computational modeling of thrombin generation have greatly advanced our understanding of the hemostatic balance. Implementation of these types of assays and visualization approaches in the clinic will potentially provide a basis for the development of individualized patient care. Advances in both empirical and computational global assays have made the goal of predicting precrisis changes in an individual's hemostatic state one step closer.

Early stages of bone fracture healing: formation of a fibrin-collagen scaffold in the fracture hematoma

This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodeling processes will eventually result in successful bone repair. Specifically, some mathematical models are proposed to estimate the time required for (1) the formation immediately after fracture of a fibrin clot, described in terms of a phase transition in a polymerization process, and (2) the onset of EFC which is produced when fibroblasts arising from differentiation of chemotactically recruited mesenchymal stem cells remodel a previous fibrin clot by releasing a collagen matrix over it. An attempt has been made to keep models as simple as possible, so that a explicit dependence of the estimates obtained on relevant biochemical parameters involved is obtained.

Spatial aspects of blood coagulation: two decades of research on the self-sustained traveling wave of thrombin

In a number of experimental studies, it has been demonstrated that the forefront of blood coagulation can propagate in the manner of a signal relay. These data strongly support the concept that the formation of a blood clot is governed by a self-sustained traveling wave of thrombin. The present review critically appraises the experimental data obtained in recent decades concerning the self-sustained spatial propagation of thrombin. Open questions regarding the experimental detection of the self-sustained propagation of thrombin are discussed.

Personalizing flow-diverter intervention for cerebral aneurysms: from computational hemodynamics to biochemical modeling

This paper presents the computational modeling of a variety of flow-diverting stents, deployed in a number of patient-specific aneurysm geometries. We consider virtual device deployment and hemodynamics as well as thrombus formation, with the scope to assess pre-operatively the efficacy of specific devices in treating particular aneurysms. An algorithm based on a linear and torsional spring analogy is developed for the fast virtual deployment of stents and similar minimally invasive devices in patient-specific vessel geometries. The virtual deployment algorithm is used to accurately deploy a total of four stent designs in three aneurysm geometries. A variety of different flow-diverting stent designs, representing the commercially available and the entirely novel, are presented, varying in both mesh design and porosity. Transient computational hemodynamics simulations are performed on multiple patient-specific geometries to predict the reduction in aneurysm inflow after the deployment of each device. Further, a thrombosis initiation and growth model is implemented, coupled with the hemodynamic computations. Hemodynamic simulations show large variations in flow reduction between devices and across different aneurysm geometries. The industry standard of flow-diverters with 70% porosity, assumed to offer the best compromise in flexibility and flow reduction, is challenged in at least one aneurysm geometry.

A simplified mathematical model for thrombin generation

A new phenomenological mathematical model based directly on laboratory data for thrombin generation and having a patient-specific character is described. A set of the solved equations for cell-based models of blood coagulation that can reproduce the temporal evolution of thrombin generation is proposed; such equations are appropriate for use in computational fluid dynamic (CFD) simulations. The initial values for the reaction rates are either taken from already existing model or experimental data, or they can obtained from simple reasoning under certain assumptions; it is shown that coefficients can be adjusted in order to fit a range of different thrombin generation curves as derived from thrombin generation assays. The behaviour of the model for different platelet concentration seems to be in good agreement with reported experimental data. It is shown that the reduced set of equations used represents to a good approximation a low-order model of the detailed mechanism and thus it can represent a cost-effective and-case specific mathematical model of coagulation reactions up to thrombin generation.

A HYBRID-SYSTEM MODEL OF THE COAGULATION CASCADE: SIMULATION, SENSITIVITY, AND VALIDATION

The process of human blood clotting involves a complex interaction of continuous-time/continuous-state processes and discrete-event/discrete-state phenomena, where the former comprise the various chemical rate equations and the latter comprise both threshold-limited behaviors and binary states (presence/absence of a chemical). Whereas previous blood-clotting models used only continuous dynamics and perforce addressed only portions of the coagulation cascade, we capture both continuous and discrete aspects by modeling it as a hybrid dynamical system. The model was implemented as a hybrid Petri net, a graphical modeling language that extends ordinary Petri nets to cover continuous quantities and continuous-time flows. The primary focus is simulation: (1) fidelity to the clinical data in terms of clotting-factor concentrations and elapsed time; (2) reproduction of known clotting pathologies; and (3) fine-grained predictions which may be used to refine clinical understanding of blood clotting. Next we examine sensitivity to rate-constant perturbation. Finally, we propose a method for titrating between reliance on the model and on prior clinical knowledge. For simplicity, we confine these last two analyses to a critical purely-continuous subsystem of the model.

Models for thrombin generation and risk of disease

Computational models can offer an integrated view of blood clotting dynamics and may ultimately be instructive regarding an individual's risk of bleeding or clotting. Appropriately, developed and validated models could allow clinicians to simulate the outcomes of therapeutics and estimate risk of disease. Computational models that describe the dynamics of thrombin generation have been developed and have been used in combination with empirical studies to understand thrombin dynamics on a mechanistic basis. The translation of an individual's specific coagulation factor composition data using these models into an integrated assessment of hemostatic status may provide a route for advancing the long-term goal of individualized medicine. This review details the integrated approaches to understanding: (i) What is normal thrombin generation in individuals? (ii) What is the effect of normal range plasma composition variation on thrombin generation in pathologic states? (iii) Can disease progression or anticoagulation be followed by understanding the boundaries of normal thrombin generation defined by plasma composition? (iv) What are the controversies and limitations of current computational approaches? Progress in these areas can bring us closer to developing models that can be used to aid in identifying hemostatic risk.

Antiplatelet agents can promote two-peaked thrombin generation in platelet rich plasma: mechanism and possible applications

BACKGROUND

Thrombin generation assay is a convenient and widely used method for analysis of the blood coagulation system status. Thrombin generation curve (TGC) is usually bell-shaped with a single peak, but there are exceptions. In particular, TGC in platelet-rich plasma (PRP) can sometimes have two peaks.

OBJECTIVE

We sought to understand the mechanism underlying the occurrence of two peaks in the PRP thrombin generation curve.

METHODS

Tissue factor-induced thrombin generation in PRP and platelet-poor plasma (PPP) was monitored using continuous measurement of the hydrolysis rate of the thrombin-specific fluorogenic substrate Z-Gly-Gly-Arg-AMC. Expression of phosphatidylserine (PS) and CD62P on the surface of activated platelets was measured by flow cytometry using corresponding fluorescently labeled markers.

RESULTS

The addition of the P(2)Y(12) receptor antagonist MeS-AMP (160 µM), 83 nM prostaglandin E(1) (PGE(1)), or 1.6% DMSO to PRP caused the appearance of two peaks in the TGC. The PS exposure after thrombin activation on washed platelets in a suspension supplemented with DMSO, PGE(1) or MeS-AMP was delayed, which could indicate mechanism of the second peak formation. Supplementation of PRP with 1.6% DMSO plus 830 nM PGE(1) mediated the disappearance of the second peak and decreased the amplitude of the first peak. Increasing the platelet concentration in the PRP promoted the consolidation of the two peaks into one.

CONCLUSIONS

Procoagulant tenase and prothrombinase complexes in PRP assemble on phospholipid surfaces containing PS of two types--plasma lipoproteins and the surface of activated platelets. Thrombin generation in the PRP can be two-peaked. The second peak appears in the presence of platelet antagonists as a result of delayed PS expression on platelets, which leads to delayed assembly of the membrane-dependent procoagulant complexes and a second wave of thrombin generation.

Data management in thrombin generation

To obtain a thrombin generation (TG) curve from the conversion of added fluorogenic substrate, thrombin concentrations are to be derived from the observed velocity of increase of fluorescence (dF/dt). The relation between velocity and thrombin concentration varies during the experiment because substrate is consumed and because fluorescence is not linear with the concentration of product. Here we review the techniques that we developed to:

Whole-blood thrombin generation monitored with a calibrated automated thrombogram-based assay

BACKGROUND

The calibrated automated thrombogram (CAT) assay in plasma is a versatile tool to investigate patients with hypo- or hypercoagulable phenotypes. The objective was to make this method applicable for whole blood measurements.

METHODS

Thin-layer technology and the use of a rhodamine 110-based thrombin substrate appear to be essential for a reliable thrombin generation (TG) assay in whole blood. Using this knowledge we developed a whole blood CAT-based assay.

RESULTS

We demonstrated that the whole blood CAT-based assay is a sensitive and rapid screening test to assess function of the hemostatic system under more nearly physiological conditions than the TG assay in plasma. Under conditions of low tissue factor concentration (0.5 pmol/L) and 50% diluted blood, the intraassay CV of the thrombogram parameters, endogenous thrombin potential and thrombin peak height, were 6.7% and 6.5%, respectively. The respective interassay CVs were 12% and 11%. The mean interindividual variation (SD) of 40 healthy volunteers was 633 (146) nmol · min/L for the endogenous thrombin potential and 128 (23) nmol/L for the thrombin peak. Surprisingly, erythrocytes contributed more than platelets to the procoagulant blood cell membranes necessary for optimal TG. Statistically significant (P < 0.001) and potentially clinically significant correlations were observed between circulating factor-VIII concentrations in blood of hemophilia A patients and endogenous thrombin potential (r = 0.62) and thrombin peak height (r = 0.58).

CONCLUSIONS

We have developed a reliable method to measure TG in whole blood. The assay can be performed with a drop of blood and may provide a useful measurement of TG under more physiological conditions than plasma.

Modeling of human factor Va inactivation by activated protein C

BACKGROUND

Because understanding of the inventory, connectivity and dynamics of the components characterizing the process of coagulation is relatively mature, it has become an attractive target for physiochemical modeling. Such models can potentially improve the design of therapeutics. The prothrombinase complex (composed of the protease factor (F)Xa and its cofactor FVa) plays a central role in this network as the main producer of thrombin, which catalyses both the activation of platelets and the conversion of fibrinogen to fibrin, the main substances of a clot. A key negative feedback loop that prevents clot propagation beyond the site of injury is the thrombin-dependent generation of activated protein C (APC), an enzyme that inactivates FVa, thus neutralizing the prothrombinase complex. APC inactivation of FVa is complex, involving the production of partially active intermediates and "protection" of FVa from APC by both FXa and prothrombin. An empirically validated mathematical model of this process would be useful in advancing the predictive capacity of comprehensive models of coagulation.

RESULTS

A model of human APC inactivation of prothrombinase was constructed in a stepwise fashion by analyzing time courses of FVa inactivation in empirical reaction systems with increasing number of interacting components and generating corresponding model constructs of each reaction system. Reaction mechanisms, rate constants and equilibrium constants informing these model constructs were initially derived from various research groups reporting on APC inactivation of FVa in isolation, or in the presence of FXa or prothrombin. Model predictions were assessed against empirical data measuring the appearance and disappearance of multiple FVa degradation intermediates as well as prothrombinase activity changes, with plasma proteins derived from multiple preparations. Our work integrates previously published findings and through the cooperative analysis of in vitro experiments and mathematical constructs we are able to produce a final validated model that includes 24 chemical reactions and interactions with 14 unique rate constants which describe the flux in concentrations of 24 species.

CONCLUSION

This study highlights the complexity of the inactivation process and provides a module of equations describing the Protein C pathway that can be integrated into existing comprehensive mathematical models describing tissue factor initiated coagulation.

Fluorogenic peptide-based substrates for monitoring thrombin activity

The synthesis of a series of peptides containing C-terminal 7-amino-4-methylcoumarin (AMC) for use in the thrombin generation test (TGT) is described. The lead structure in this project was H-Gly-Gly-Arg-AMC, of which the water solubility and kinetic parameters (K(M) and k(cat)) are greatly improved over those of the substrate in current use in the TGT: Cbz-Gly-Gly-Arg-AMC. A series of N-terminally substituted Gly-Gly-Arg-AMC derivatives were synthesized, as well as implementation of structural changes at either the P(2) or P(3) position of the peptide backbone. Furthermore, two substrates were synthesized that have structural similarities to the chromogenic thrombin substrate SQ68 or that contain a 1,2,3-triazole moiety in the peptide chain, mimicking an amide bond. To determine the applicability of newly synthesized fluorogenic substrates for monitoring continuous thrombin generation, the K(M) and k(cat) values of the conversion of these fluorogenic substrates by thrombin (FIIa) and factor Xa (FXa) were quantified. An initial selection was made on basis of these data, and suitable substrates were further evaluated as substrates in the thrombin generation assay. Assessment of the acquired data showed that several substrates, including the SQ68 derivative Et-malonate-Gly-Arg-AMC and N-functionalized Gly-Gly-Arg-AMC derivatives, are suitable candidates for replacement of the substrate currently in use.

Use of models in identification and prediction of physiology in critically ill surgical patients

BACKGROUND

With higher-throughput data acquisition and processing, increasing computational power, and advancing computer and mathematical techniques, modelling of clinical and biological data is advancing rapidly. Although exciting, the goal of recreating or surpassing in silico the clinical insight of the experienced clinician remains difficult. Advances toward this goal and a brief overview of various modelling and statistical techniques constitute the purpose of this review.

METHODS

A review of the literature and experience with models and physiological state representation and prediction after injury was undertaken.

RESULTS

A brief overview of models and the thinking behind their use for surgeons new to the field is presented, including an introduction to visualization and modelling work in surgical care, discussion of state identification and prediction, discussion of causal inference statistical approaches, and a brief introduction to new vital signs and waveform analysis.

CONCLUSION

Modelling in surgical critical care can provide a useful adjunct to traditional reductionist biological and clinical analysis. Ultimately the goal is to model computationally the clinical acumen of the experienced clinician.

The paradoxical stimulation by a reversible thrombin inhibitor of thrombin generation in plasma measured with thrombinography is caused by alpha-macroglobulin-thrombin

BACKGROUND

Thrombin generation (TG) in plasma can be monitored continuously with a fluorogenic thrombin substrate using calibrated automated thrombinography (CAT). In the presence of low concentrations of a reversible direct thrombin inhibitor (DTI), CAT shows an unexpected effect: the endogenous thrombin potential (ETP) increases at low concentrations of the inhibitor to subsequently decrease concentration dependently at higher concentrations (> approximately 100 nm).

OBJECTIVES

To find an explanation for this phenomenon, we measured the concentrations of free thrombin and alpha(2)-macroglobulin-thrombin complex (alpha(2)MT) with a sub-sampling technique in the presence of AR-H067637, a selective DTI.

RESULTS

At all concentrations of the DTI there was a gradual dose-dependent decrease in the concentration of free, not-inhibited thrombin but a transient increase in free alpha(2)MT due to competition of thrombin and alpha(2)MT for the inhibitor. Because the CAT technique uses an algorithm to subtract alpha(2)MT activity from the total amidolytic activity, this transient increase in alpha(2)MT activity is not subtracted and erroneously attributed to thrombin itself.

CONCLUSIONS

This study explains the spurious increase in ETP observed at low DTI concentrations. The results obtained in plasma were corroborated by observations in a thrombin generating system reconstituted with purified factors. In practise, the effect of DTIs on TG can be reliably evaluated from the area under the curve till time-to-peak.

The impact of uncertainty in a blood coagulation model

Deterministic mathematical models of biochemical processes operate as if the empirically derived rate constants governing the dynamics are known with certainty. Our objective in this study was to explore the sensitivity of a deterministic model of blood coagulation to variations in the values of its 44 rate constants. This was accomplished for each rate constant at a given time by defining a normalized ensemble standard deviation (w(k(i))(f)(t)) that accounted for the sensitivity of the predicted concentration of each protein species to variation in that rate constant (from 10 to 1000% of the accepted value). A mean coefficient of variation derived from (w(k(i))(f)(t)) values for all protein species was defined to quantify the overall variation introduced into the model's predictive capacity at that time by the assumed uncertainty in that rate constant. A time-average value of the coefficient of variation over the 20-min simulation for each rate constant was then used to rank rate constants. The model's predictive capacity is particularly sensitive (50% of the aggregate variation) to uncertainty in five rate constants involved in the regulation of the formation and function of the factor VIIa-tissue factor complex. Therefore, our analysis has identified specific rate constants to which the predictive capability of this model is most sensitive and thus where improvements in measurement accuracy will yield the greatest increase in predictive capability.

Acoustic determination of early stages of intravascular blood coagulation

The blood coagulation system (BCS) is a complex biological system playing a principal role in the maintenance of haemostasis. Insufficient activity of the BCS may lead to bleeding and blood loss (e.g. in the case of haemophilia). On the other hand, excessive activity may cause intravascular blood coagulation, thromboses and embolization. Most of the methods currently used for BCS monitoring suffer from the major disadvantage of being invasive. The purpose of the present work is to demonstrate the feasibility of using ultrasonic methods for non-invasive registration of the early stages of blood coagulation processes in intensive flows. With this purpose, a special experimental set-up was designed, facilitating the simultaneous detection of optical and acoustic signals during the clotting process. It was shown that (i) as microemboli appear in the flow during the early stage of blood coagulation, the intensity of the Doppler signal increases twofold, and (ii) microemboli formation in the early stages of blood clotting always reveals itself through an acoustic contrast. Both of these effects are well defined, so we hope that they may be used for non-invasive BCS monitoring in clinical practice.