Computational analysis of intersubject variability and thrombin generation in dilutional coagulopathy

Systems Biology Approach for Personalized Hemostasis Correction

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

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).

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

BACKGROUND

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Assessing the impact of product inhibition in a chromogenic assay

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

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

INTRODUCTION

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

AIM

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

METHODS

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

RESULTS

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

CONCLUSION

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

Impact of Tissue Factor Localization on Blood Clot Structure and Resistance under Venous Shear

The structure and growth of a blood clot depend on the localization of tissue factor (TF), which can trigger clotting during the hemostatic process or promote thrombosis when exposed to blood under pathological conditions. We sought to understand how the growth, structure, and mechanical properties of clots under flow are shaped by the simultaneously varying TF surface density and its exposure area. We used an eight-channel microfluidic device equipped with a 20- or 100-μm-long collagen surface patterned with lipidated TF of surface densities ∼0.1 and ∼2 molecules/μm². Human whole blood was perfused at venous shear, and clot growth was continually measured. Using our recently developed computational model of clot formation, we performed simulations to gain insights into the clot’s structure and its resistance to blood flow. An increase in TF exposure area resulted not only in accelerated bulk platelet, thrombin, and fibrin accumulation, but also in increased height of the platelet mass and increased clot resistance to flow. Moreover, increasing the TF surface density or exposure area enhanced platelet deposition by approximately twofold, and thrombin and fibrin generation by greater than threefold, thereby increasing both clot size and its viscous resistance. Finally, TF effects on blood flow occlusion were more pronounced for the longer thrombogenic surface than for the shorter one. Our results suggest that TF surface density and its exposure area can independently enhance both the clot’s occlusivity and its resistance to blood flow. These findings provide, to our knowledge, new insights into how TF affects thrombus growth in time and space under flow.

Computational Model for Hyperfibrinolytic Onset of Acute Traumatic Coagulopathy

The onset of acute traumatic coagulopathy in trauma patients exacerbates hemorrhaging and dramatically increases mortality. The disease is characterized by increased localized bleeding, and the mechanism for its onset is not yet known. We propose that the fibrinolytic response, specifically the release of tissue-plasminogen activator (t-PA), within vessels of different sizes leads to a variable susceptibility to local coagulopathy through hyperfibrinolysis which can explain many of the clinical observations in the early stages from severely injured coagulopathic patients. We use a partial differential equation model to examine the consequences of vessel geometry and extent of injury on fibrinolysis profiles. In addition, we simulate the efficacy of tranexamic acid treatment on coagulopathy initiated through endothelial t-PA release, and are able to reproduce the time-sensitive nature of the efficacy of this treatment as observed in clinical studies.

A reduction of prothrombin conversion by cardiac surgery with cardiopulmonary bypass shifts the haemostatic balance towards bleeding

Cardiac surgery with cardiopulmonary bypass (CPB) is associated with blood loss and post-surgery thrombotic complications. The process of thrombin generation is disturbed during surgery with CPB because of haemodilution, coagulation factor consumption and heparin administration. We aimed to investigate the changes in thrombin generation during cardiac surgery and its underlying pro- and anticoagulant processes, and to explore the clinical consequences of these changes using in silico experimentation. Plasma was obtained from 29 patients undergoing surgery with CPB before heparinisation, after heparinisation, after haemodilution, and after protamine administration. Thrombin generation was measured and prothrombin conversion and thrombin inactivation were quantified. In silico experimentation was used to investigate the reaction of patients to the administration of procoagulant factors and/or anticoagulant factors. Surgery with CPB causes significant coagulation factor consumption and a reduction of thrombin generation. The total amount of prothrombin converted and the rate of prothrombin conversion decreased during surgery. As the surgery progressed, the relative contribution of α2-macroglobulin-dependent thrombin inhibition increased, at the expense of antithrombin-dependent inhibition. In silico restoration of post-surgical prothrombin conversion to pre-surgical levels increased thrombin generation excessively, whereas co-administration of antithrombin resulted in the normalisation of post-surgical thrombin generation. Thrombin generation is reduced during surgery with cardiopulmonary bypass because of a balance shift between prothrombin conversion and thrombin inactivation. According to in silico predictions of thrombin generation, this new balance increases the risk of thrombotic complications with prothrombin complex concentrate administration, but not if antithrombin is co-administered.

Computational Study of Thrombus Formation and Clotting Factor Effects under Venous Flow Conditions

A comprehensive understanding of thrombus formation as a physicochemical process that has evolved to protect the integrity of the human vasculature is critical to our ability to predict and control pathological states caused by a malfunctioning blood coagulation system. Despite numerous investigations, the spatial and temporal details of thrombus growth as a multicomponent process are not fully understood. Here, we used computational modeling to investigate the temporal changes in the spatial distributions of the key enzymatic (i.e., thrombin) and structural (i.e., platelets and fibrin) components within a growing thrombus. Moreover, we investigated the interplay between clot structure and its mechanical properties, such as hydraulic resistance to flow. Our model relied on the coupling of computational fluid dynamics and biochemical kinetics, and was validated using flow-chamber data from a previous experimental study. The model allowed us to identify the distinct patterns characterizing the spatial distributions of thrombin, platelets, and fibrin accumulating within a thrombus. Our modeling results suggested that under the simulated conditions, thrombin kinetics was determined predominantly by prothrombinase. Furthermore, our simulations showed that thrombus resistance imparted by fibrin was ∼30-fold higher than that imparted by platelets. Yet, thrombus-mediated bloodflow occlusion was driven primarily by the platelet deposition process, because the height of the platelet accumulation domain was approximately twice that of the fibrin accumulation domain. Fibrinogen supplementation in normal blood resulted in a nonlinear increase in thrombus resistance, and for a supplemented fibrinogen level of 48%, the thrombus resistance increased by ∼2.7-fold. Finally, our model predicted that restoring the normal levels of clotting factors II, IX, and X while simultaneously restoring fibrinogen (to 88% of its normal level) in diluted blood can restore fibrin generation to ∼78% of its normal level and hence improve clot formation under dilution.

Computational identification and analysis of signaling subnetworks with distinct functional roles in the regulation of TNF production

Inflammation is a complex process driven by the coordinated action of a vast number of pro- and anti-inflammatory molecular mediators. While experimental studies have provided an abundance of information about the properties and mechanisms of action of individual mediators, essential system-level regulatory patterns that determine the time-course of inflammation are not sufficiently understood. In particular, it is not known how the contributions from distinct signaling pathways involved in cytokine regulation combine to shape the overall inflammatory response over different time scales. We investigated the kinetics of the intra- and extracellular signaling network controlling the production of the essential pro-inflammatory cytokine, tumor necrosis factor (TNF), and its anti-inflammatory counterpart, interleukin 10 (IL-10), in a macrophage culture. To tackle the intrinsic complexity of the network, we employed a computational modeling approach using the available literature data about specific molecular interactions. Our computational model successfully captured experimentally observed short- and long-term kinetics of key inflammatory mediators. Subsequent model analysis showed that distinct subnetworks regulate IL-10 production by impacting different temporal phases of the cAMP response element-binding protein (CREB) phosphorylation. Moreover, the model revealed that functionally similar inhibitory control circuits regulate the early and late activation phases of nuclear factor κB and CREB. Finally, we identified and investigated distinct signaling subnetworks that independently control the peak height and tail height of the TNF temporal trajectories. The knowledge of such subnetwork-specific regulatory effects may facilitate therapeutic interventions aimed at precise modulation of the inflammatory response.

Mechanistic Modeling of the Effects of Acidosis on Thrombin Generation

Supplemental Digital Content is available in the text.

Published ahead of print April 2, 2015

BACKGROUND:

Acidosis, a frequent complication of trauma and complex surgery, results from tissue hypoperfusion and IV resuscitation with acidic fluids. While acidosis is known to inhibit the function of distinct enzymatic reactions, its cumulative effect on the blood coagulation system is not fully understood. Here, we use computational modeling to test the hypothesis that acidosis delays and reduces the amount of thrombin generation in human blood plasma. Moreover, we investigate the sensitivity of different thrombin generation parameters to acidosis, both at the individual and population level.

METHODS:

We used a kinetic model to simulate and analyze the generation of thrombin and thrombin–antithrombin complexes (TAT), which were the end points of this study. Large groups of temporal thrombin and TAT trajectories were simulated and used to calculate quantitative parameters, such as clotting time (CT), thrombin peak time, maximum slope of the thrombin curve, thrombin peak height, area under the thrombin trajectory (AUC), and prothrombin time. The resulting samples of parameter values at different pH levels were compared to assess the acidosis-induced effects. To investigate intersubject variability, we parameterized the computational model using the data on clotting factor composition for 472 subjects from the Leiden Thrombophilia Study. To compare acidosis-induced relative parameter changes in individual (“virtual”) subjects, we estimated the probabilities of relative change patterns by counting the pattern occurrences in our virtual subjects. Distribution overlaps for thrombin generation parameters at distinct pH levels were quantified using the Bhattacharyya coefficient.

RESULTS:

Acidosis in the range of pH 6.9 to 7.3 progressively increased CT, thrombin peak time, AUC, and prothrombin time, while decreasing maximum slope of the thrombin curve and thrombin peak height (P < 10^–5). Acidosis delayed the onset and decreased the amount of TAT generation (P < 10^–5). As a measure of intrasubject variability, maximum slope of the thrombin curve and CT displayed the largest and second-largest acidosis-induced relative changes, and AUC displayed the smallest relative changes among all thrombin generation parameters in our virtual subject group (1-sided 95% lower confidence limit on the fraction of subjects displaying the patterns, 0.99). As a measure of intersubject variability, the overlaps between the maximum slope of the thrombin curve distributions at acidotic pH levels with the maximum slope of the thrombin curve distribution at physiological pH level systematically exceeded analogous distribution overlaps for CT, thrombin peak time, and prothrombin time.

CONCLUSIONS:

Acidosis affected all quantitative parameters of thrombin and TAT generation. While maximum slope of the thrombin curve showed the highest sensitivity to acidosis at the individual-subject level, it may be outperformed by CT, thrombin peak time, and prothrombin time as an indicator of acidosis at the subject-group level.

Kinetic model facilitates analysis of fibrin generation and its modulation by clotting factors: implications for hemostasis-enhancing therapies

Current mechanistic knowledge of protein interactions driving blood coagulation has come largely from experiments with simple synthetic systems, which only partially represent the molecular composition of human blood plasma. Here, we investigate the ability of the suggested molecular mechanisms to account for fibrin generation and degradation kinetics in diverse, physiologically relevant in vitro systems. We represented the protein interaction network responsible for thrombin generation, fibrin formation, and fibrinolysis as a computational kinetic model and benchmarked it against published and newly generated data reflecting diverse experimental conditions. We then applied the model to investigate the ability of fibrinogen and a recently proposed prothrombin complex concentrate composition, PCC-AT (a combination of the clotting factors II, IX, X, and antithrombin), to restore normal thrombin and fibrin generation in diluted plasma. The kinetic model captured essential features of empirically detected effects of prothrombin, fibrinogen, and thrombin-activatable fibrinolysis inhibitor titrations on fibrin formation and degradation kinetics. Moreover, the model qualitatively predicted the impact of tissue factor and tPA/tenecteplase level variations on the fibrin output. In the majority of considered cases, PCC-AT combined with fibrinogen accurately approximated both normal thrombin and fibrin generation in diluted plasma, which could not be accomplished by fibrinogen or PCC-AT acting alone. We conclude that a common network of protein interactions can account for key kinetic features characterizing fibrin accumulation and degradation in human blood plasma under diverse experimental conditions. Combined PCC-AT/fibrinogen supplementation is a promising strategy to reverse the deleterious effects of dilution-induced coagulopathy associated with traumatic bleeding.

Computational analysis of the effects of reduced temperature on thrombin generation: the contributions of hypothermia to coagulopathy

BACKGROUND

Hypothermia, which can result from tissue hypoperfusion, body exposure, and transfusion of cold resuscitation fluids, is a major factor contributing to coagulopathy of trauma and surgery. Despite considerable efforts, the mechanisms of hypothermia-induced blood coagulation impairment have not been fully understood. We introduce a kinetic modeling approach to investigate the effects of hypothermia on thrombin generation.

METHODS

We extended a validated computational model to predict and analyze the impact of low temperatures (with or without concomitant blood dilution) on thrombin generation and its quantitative parameters. The computational model reflects the existing knowledge about the mechanistic details of thrombin generation biochemistry. We performed the analysis for an "average" subject, as well as for 472 subjects in the control group of the Leiden Thrombophilia Study.

RESULTS

We computed and analyzed thousands of kinetic curves characterizing the generation of thrombin and the formation of the thrombin-antithrombin complex (TAT). In all simulations, hypothermia in the temperature interval 31°C to 36°C progressively slowed down thrombin generation, as reflected by clotting time, thrombin peak time, and prothrombin time, which increased in all subjects (P < 10(-5)). Maximum slope of the thrombin curve was progressively decreased, and the area under the thrombin curve was increased in hypothermia (P < 10(-5)); thrombin peak height remained practically unaffected. TAT formation was noticeably delayed (P < 10(-5)), but the final TAT levels were not significantly affected. Hypothermia-induced fold changes in the affected thrombin generation parameters were larger for lower temperatures, but were practically independent of the parameter itself and of the subjects' clotting factor composition, despite substantial variability in the subject group. Hypothermia and blood dilution acted additively on the thrombin generation parameters.

CONCLUSIONS

We developed a general computational strategy that can be used to simulate the effects of changing temperature on the kinetics of biochemical systems and applied this strategy to analyze the effects of hypothermia on thrombin generation. We found that thrombin generation can be noticeably impaired in subjects with different blood plasma composition even in moderate hypothermia. Our work provides mechanistic support to the notion that thrombin generation impairment may be a key factor in coagulopathy induced by hypothermia and complicated by blood plasma dilution.

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.

The prothrombotic phenotypes in familial protein C deficiency are differentiated by computational modeling of thrombin generation

The underlying cause of thrombosis in a large protein C (PC) deficient Vermont kindred appears to be multicausal and not explained by PC deficiency alone. We evaluated the contribution of coagulation factors to thrombin generation in this population utilizing a mathematical model that incorporates a mechanistic description of the PC pathway. Thrombin generation profiles for each individual were generated with and without the contribution of the PC pathway. Parameters that describe thrombin generation: maximum level (MaxL) and rate (MaxR), their respective times (TMaxL, TMaxR), area under the curve (AUC) and clotting time (CT) were examined in individuals ± PC mutation, ± prothrombin G20210A polymorphism and ± thrombosis history (DVT or PE). This family (n = 364) is shifted towards greater thrombin generation relative to the mean physiologic control. When this family was analyzed with the PC pathway, our results showed that: carriers of the PC mutation (n = 81) had higher MaxL and MaxR and greater AUC (all p<0.001) than non-carriers (n = 283); and individuals with a DVT and/or PE history (n = 13) had higher MaxL (p = 0.005) and greater AUC (p<0.001) than individuals without a thrombosis history (n = 351). These differences were further stratified by gender, with women in all categories generating more thrombin than males. These results show that all individuals within this family with or without PC deficiency have an increased baseline procoagulant potential reflective of increased thrombin generation. In addition, variations within the plasma composition of each individual can further segregate out increased procoagulant phenotypes, with gender-associated plasma compositional differences playing a large role.