A model for the formation, growth, and lysis of clots in quiescent plasma. A comparison between the effects of antithrombin III deficiency and protein C deficiency

Efficient multi-fidelity computation of blood coagulation under flow

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

Critical evaluation of kinetic schemes for coagulation

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

Efficient multi-fidelity computation of blood coagulation under flow

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

Purification and characterization of thrombin from camel plasma: interaction with camel tick salivary gland thrombin inhibitor

BACKGROUND

Thrombin is the most important enzyme in the hemostatic process by permitting rapid and localized coagulation in case of tissue damage. Camel thrombin is the natural and proper target enzyme for the previously purified camel tick salivary gland thrombin inhibitor.

RESULTS

In this study, the camel thrombin was purified homogenously in a single affinity chromatographic step on the heparin-agarose affinity column with a specific activity of 3242 NIH units/mg proteins. On SDS-PAGE, the purified camel thrombin contained two forms, 37 kDa α-thrombin and 28 kDa β-thrombin, and the camel prothrombin was visualized as 72 kDa. The camel thrombin Km value was found out as 60 µM of N-(p-Tosyl)-Gly-Pro-Arg-p-nitroanilide acetate and displayed its optimum activity at pH 8.3. The PMSF was the most potent inhibitor of camel thrombin. Camel tick salivary gland thrombin inhibitor has two binding sites on camel thrombin and inhibited it competitively with Ki value of 0.45 µM.

CONCLUSIONS

The purified camel thrombin was found to be more susceptible toward the camel tick salivary gland thrombin inhibitor than bovine thrombin.

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.

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.

Multiphysics and multiscale modeling of microthrombosis in COVID-19

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients’ fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis.

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. We employ a novel multiphysics and multiscale computational framework to investigate the underlying mechanism of the pathological formation of microthrombi and circulating cell clusters in COVID-19. We quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19, through which we identify the potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19.

Recent Advances in Computational Modeling of Biomechanics and Biorheology of Red Blood Cells in Diabetes

Diabetes mellitus, a metabolic disease characterized by chronically elevated blood glucose levels, affects about 29 million Americans and more than 422 million adults all over the world. Particularly, type 2 diabetes mellitus (T2DM) accounts for 90-95% of the cases of vascular disease and its prevalence is increasing due to the rising obesity rates in modern societies. Although multiple factors associated with diabetes, such as reduced red blood cell (RBC) deformability, enhanced RBC aggregation and adhesion to the endothelium, as well as elevated blood viscosity are thought to contribute to the hemodynamic impairment and vascular occlusion, clinical or experimental studies cannot directly quantify the contributions of these factors to the abnormal hematology in T2DM. Recently, computational modeling has been employed to dissect the impacts of the aberrant biomechanics of diabetic RBCs and their adverse effects on microcirculation. In this review, we summarize the recent advances in the developments and applications of computational models in investigating the abnormal properties of diabetic blood from the cellular level to the vascular level. We expect that this review will motivate and steer the development of new models in this area and shift the attention of the community from conventional laboratory studies to combined experimental and computational investigations, aiming to provide new inspirations for the development of advanced tools to improve our understanding of the pathogenesis and pathology of T2DM.

Mathematical and Computational Modeling of Device-Induced Thrombosis

Given the extensive and routine use of cardiovascular devices, a major limiting factor to their success is the thrombotic rate that occurs. This both poses direct risk to the patient and requires counterbalancing with anticoagulation and other treatment strategies, contributing additional risks. Developing a better understanding of the mechanisms of device-induced thrombosis to aid in device design and medical management of patients is critical to advance the ubiquitous use and durability. Thus, mathematical and computational modelling of device-induced thrombosis has received significant attention recently, but challenges remain. Additional areas that need to be explored include microscopic/macroscopic approaches, reconciling physical and numerical timescales, immune/inflammatory responses, experimental validation, and incorporating pathologies and blood conditions. Addressing these areas will provide engineers and clinicians the tools to provide safe and effective cardiovascular devices.

An integrated fluid-chemical model toward modeling the thrombus formation in an idealized model of aortic dissection

Type B aortic dissection is a major aortic catastrophe that can be acutely complicated by rapid expansion, rupture, and malperfusion syndromes. The separation of the intima from aortic walls will form a second blood-filled lumen defined as "false lumen (FL)", where the thrombus is more likely to form due to the local stasis hemodynamic conditions. Complete thrombosis of FL is associated with a beneficial outcome while patency and partial thrombosis will lead to later complications. However, the thrombosis mechanism is still unclear and little is known about the impact of chemical species transported by blood flow on this process. The proteins involved in the coagulation cascade (CC) may play an important role in the process of thrombosis, especially in the activation and stabilization of platelets. Based on this hypothesis, a reduced-order fluid-chemical model was established to simulate CC in an aortic dissection phantom with two tears. A high level of fibrin is continuously observed at the top of the FL and some time-varying areas between two tears, indicating a high likelihood of thrombus formation there. This finding is consistent with the clinical observation. The time evolution of coagulation factors is greatly affected by local hemodynamics, especially in the high disturbance zone where the evolution has characteristics of periodic changes consistent with the flow field. The ability of the proposed model to reproduce the CC response provides a potential application to integrate with a model that can simulate platelet activities, forming a biochemical-based model which would help unveil the mechanisms of thrombosis in FL and the clinical decision of appropriate treatment.

Combination of polycarboxybetaine coating and factor XII inhibitor reduces clot formation while preserving normal tissue coagulation during extracorporeal life support

Blood contact with high surface area medical devices, such as dialysis and extracorporeal life support (ECLS), induces rapid surface coagulation. Systemic anticoagulation, such as heparin, is thus necessary to slow clot formation, but some patients suffer from bleeding complications. Both problems might be reduced by 1) replacing heparin anticoagulation with artificial surface inhibition of the protein adsorption that initiates coagulation and 2) selective inhibition of the intrinsic branch of the coagulation cascade. This approach was evaluated by comparing clot formation and bleeding times during short-term ECLS using zwitterionic polycarboxybetaine (PCB) surface coatings combined with either a potent, selective, bicyclic peptide inhibitor of activated Factor XII (FXII900) or standard heparin anticoagulation. Rabbits underwent venovenous ECLS with small sham oxygenators for 60 min using three means of anticoagulation (n = 4 ea): (1) PCB coating + FXII900 infusion, (2) PCB coating + heparin infusion with an activated clotting time of 220-300s, and (3) heparin infusion alone. Sham oxygenator blood clot weights in the PCB + FXII900 and PCB + heparin groups were 4% and 25% of that in the heparin group (p < 10^-6 and p < 10^-5), respectively. At the same time, the bleeding time remained normal in the PCB + FXII900 group (2.4 ± 0.2 min) but increased to 4.8 ± 0.5 and 5.1 ± 0.7 min in the PCB + heparin and heparin alone groups (p < 10^-4 and 0.01). Sham oxygenator blood flow resistance was significantly lower in the PCB + FXII900 and PCB + heparin groups than in the heparin only group (p < 10^-6 and 10^-5). These results were confirmed by gross and scanning electron microscopy (SEM) images and fibrinopeptide A (FPA) concentrations. Thus, the combined use of PCB coating and FXII900 markedly reduced sham oxygenator coagulation and tissue bleeding times versus the clinical standard of heparin anticoagulation and is a promising anticoagulation method for clinical ECLS.

Integrating blood cell mechanics, platelet adhesive dynamics and coagulation cascade for modelling thrombus formation in normal and diabetic blood

Normal haemostasis is an important physiological mechanism that prevents excessive bleeding during trauma, whereas the pathological thrombosis especially in diabetics leads to increased incidence of heart attacks and strokes as well as peripheral vascular events. In this work, we propose a new multiscale framework that integrates seamlessly four key components of blood clotting, namely transport of coagulation factors, coagulation kinetics, blood cell mechanics and platelet adhesive dynamics, to model the development of thrombi under physiological and pathological conditions. We implement this framework to simulate platelet adhesion due to the exposure of tissue factor in a three-dimensional microchannel. Our results show that our model can simulate thrombin-mediated platelet activation in the flowing blood, resulting in platelet adhesion to the injury site of the channel wall. Furthermore, we simulate platelet adhesion in diabetic blood, and our results show that both the pathological alterations in the biomechanics of blood cells and changes in the amount of coagulation factors contribute to the excessive platelet adhesion and aggregation in diabetic blood. Taken together, this new framework can be used to probe synergistic mechanisms of thrombus formation under physiological and pathological conditions, and open new directions in modelling complex biological problems that involve several multiscale processes.

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.

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

BACKGROUND

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

METHODS

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

RESULTS

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

CONCLUSION

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

LEVEL OF EVIDENCE

Therapeutic/Care Management: Level IV.

A mathematical model to quantify the effects of platelet count, shear rate, and injury size on the initiation of blood coagulation under venous flow conditions

Platelets upregulate the generation of thrombin and reinforce the fibrin clot which increases the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the pathogenesis of venous cardiovascular diseases remains hard to quantify. An experimentally validated model of thrombin generation dynamics is formulated. The model predicts that a high platelet count increases the peak value of generated thrombin as well as the endogenous thrombin potential (ETP) as reported in experimental data. To investigate the effects of platelets density, shear rate, and wound size on the initiation of blood coagulation, we calibrate a previously developed model of venous thrombus formation and implement it in 3D using a novel cell-centered finite-volume solver. We conduct numerical simulations to reproduce in vitro experiments of blood coagulation in microfluidic capillaries. Then, we derive a reduced one-equation model of thrombin distribution from the previous model under simplifying hypotheses and we use it to determine the conditions of clotting initiation on the platelet count, the shear rate, and the plasma composition. The initiation of clotting also exhibits a threshold response to the size of the wounded region in good agreement with the reported experimental findings.

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.

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.

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.

A computational model for prediction of clot platelet content in flow-diverted intracranial aneurysms

Treatment of intracranial aneurysms with flow-diverting stents is a safe and minimally invasive technique. The goal is stable embolisation that facilitates stent endothelialisation, and elimination of the aneurysm. However, it is not fully understood why some aneurysms fail to develop a stable clot even with sufficient levels of flow reduction. Computational prediction of thrombus formation dynamics can help predict the post-operative response in such challenging cases. In this work, we propose a new model of thrombus formation and platelet dynamics inside intracranial aneurysms. Our novel contribution combines platelet activation and transport with fibrin generation, which is key to characterising stable and unstable thrombus. The model is based on two types of thrombus inside aneurysms: red thrombus (fibrin- and erythrocyte-rich) can be found in unstable clots, while white thrombus (fibrin- and platelet-rich) can be found in stable clots. The thrombus generation model is coupled to a CFD model and the flow-induced platelet index (FiPi) is defined as a quantitative measure of clot stability. Our model is validated against an in vitro phantom study of two flow-diverting stents with different sizing. We demonstrate that our model accurately predicts the lower thrombus stability in the oversized stent scenario. This opens possibilities for using computational simulations to improve endovascular treatment planning and reduce adverse events, such as delayed haemorrhage of flow-diverted aneurysms.

Coated platelets introduce significant delay in onset of peak thrombin production: Theoretical predictions

Platelets play a crucial role in the initiation, progress, termination as well as regulation of blood coagulation. Recent studies have confirmed that not all but only a small percentage of thrombin-activated platelets ("coated" platelets) exhibit procoagulant properties (namely the expression of phosphatidylserine binding sites) required for the acceleration and progress of coagulation. A mechanistic model is developed for in vitro coagulation whose key features are distinct equations for coated platelets, thrombin dose-dependence for coated platelets, and competitive binding of coagulation factors to platelet membrane. Model predictions show significant delay in the onset of peak Va production, and peak thrombin production when dose-dependence is incorporated instead of a fixed theoretical maximum percentage of coated platelets. Further, peak thrombin concentration is significantly overestimated when either fractional presence of coated platelets is ignored (by 299.4%) or when dose-dependence on thrombin is ignored (by 24.7%).

Model development and comparison of low hemorrhage-risk endoluminal patch thrombolytic treatment for ischemic stroke

Clot dissolution drugs delivered into the systemic circulation can dissolve intracranial blood clots in 90 min with 20-50% hemorrhage rate. Immobilizing <5% of the intravenous dosage on an endoluminal patch can reduce the dissolution time to <20 min with negligible hemorrhage risk. The thrombus dissolution behavior in endoluminal patch thrombolytic treatment is modeled and compared with experimental results from a companion study. Analyses showed that the thrombus dissolution time decreases with increasing dosage, but the dissolution time reaches a dosage-independent minimum when uPA dosage on the patch is >800 IU. Model analyses showed that dissolution time in the plateau regime is controlled by diffusion. Further results showed that dissolution time could be reduced in this regime by reducing thrombus thickness. This suggests that a stented endoluminal thrombolytic >800 IU patch that compresses the thrombus to thin the clot thickness can help reduce dissolution time. This ultra-low transition dosage (i.e., 800 IU), compared to 0.6-2.4 million IU in conventional thrombolysis suggests that hemorrhage risk in endoluminal patch thrombolytic treatment is low. The low hemorrhagic-risk endoluminal patch can be considered for use in patients who are ineligible for conventional thrombolytic treatment because of high hemorrhagic treatment risk.

Importance of Initial Concentration of Factor VIII in a Mechanistic Model of In Vitro Coagulation

This computational study generates a hypothesis for the coagulation protein whose initial concentration greatly influences the course of coagulation. Many clinical malignancies of blood coagulation arise due to abnormal initial concentrations of coagulation factors. Sensitivity analysis of mechanistic models of blood coagulation is a convenient method to assess the effect of such abnormalities. Accordingly, the study presents sensitivity analysis, with respect to initial concentrations, of a recently developed mechanistic model of blood coagulation. Both the model and parameters to which model sensitivity is being analyzed provide newer insights into blood coagulation: the model incorporates distinct equations for plasma-phase and platelet membrane-bound species, and sensitivity to initial concentrations is a new dimension in sensitivity analysis. The results show that model predictions are most uncertain with respect to changes in initial concentration of factor VIII, and this hypothesis is supported by results from other models developed independently.

A local and global sensitivity analysis of a mathematical model of coagulation and platelet deposition under flow

The hemostatic response involves blood coagulation and platelet aggregation to stop blood loss from an injured blood vessel. The complexity of these processes make it difficult to intuit the overall hemostatic response without quantitative methods. Mathematical models aim to address this challenge but are often accompanied by numerous parameters choices and thus need to be analyzed for sensitivity to such choices. Here we use local and global sensitivity analyses to study a model of coagulation and platelet deposition under flow. To relate with clinical assays, we measured the sensitivity of three specific thrombin metrics: lag time, maximum relative rate of generation, and final concentration after 20 minutes. In addition, we varied parameters of three different classes: plasma protein levels, kinetic rate constants, and platelet characteristics. In terms of an overall ranking of the model’s sensitivities, we found that the local and global methods provided similar information. Our local analysis, in agreement with previous findings, shows that varying parameters within 50-150% of baseline values, in a one-at-a-time (OAT) fashion, always leads to significant thrombin generation in 20 minutes. Our global analysis gave a different and novel result highlighting groups of parameters, still varying within the normal 50-150%, that produced little or no thrombin in 20 minutes. Variations in either plasma levels or platelet characteristics, using either OAT or simultaneous variations, always led to strong thrombin production and overall, relatively low output variance. Simultaneous variation in kinetics rate constants or in a subset of all three parameter classes led to the highest overall output variance, incorporating instances with little to no thrombin production. The global analysis revealed multiple parameter interactions in the lag time and final concentration leading to relatively high variance; high variance was also observed in the thrombin generation rate, but parameters attributed to that variance acted independently and additively.

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.

Data-driven Modeling of Hemodynamics and its Role on Thrombus Size and Shape in Aortic Dissections

Aortic dissection is a pathology that manifests due to microstructural defects in the aortic wall. Blood enters the damaged wall through an intimal tear, thereby creating a so-called false lumen and exposing the blood to thrombogenic intramural constituents such as collagen. The natural history of this acute vascular injury thus depends, in part, on thrombus formation, maturation, and possible healing within the false lumen. A key question is: Why do some false lumens thrombose completely while others thrombose partially or little at all? An ability to predict the location and extent of thrombus in subjects with dissection could contribute significantly to clinical decision-making, including interventional design. We develop, for the first time, a data-driven particle-continuum model for thrombus formation in a murine model of aortic dissection. In the proposed model, we simulate a final-value problem in lieu of the original initial-value problem with significantly fewer particles that may grow in size upon activation, thus representing the local concentration of blood-borne species. Numerical results confirm that geometry and local hemodynamics play significant roles in the acute progression of thrombus. Despite geometrical differences between murine and human dissections, mouse models can provide considerable insight and have gained popularity owing to their reproducibility. Our results for three classes of geometrically different false lumens show that thrombus forms and extends to a greater extent in regions with lower bulk shear rates. Dense thrombi are less likely to form in high-shear zones and in the presence of strong vortices. The present data-driven study suggests that the proposed model is robust and can be employed to assess thrombus formation in human aortic dissections.

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

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

Reaction-diffusion waves of blood coagulation

One of the main characteristics of blood coagulation is the speed of clot growth. In the current work we consider a mathematical model of the coagulation cascade and study existence, stability and speed of propagation of the reaction-diffusion waves of blood coagulation. We also develop a simplified one-equation model that reflects the main features of the thrombin wave propagation. For this equation we estimate the wave speed analytically. The resulting formulas provide a good approximation for the speed of wave propagation in a more complex model as well as for the experimental data.

Multi-Constituent Simulation of Thrombus Deposition

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

A General Shear-Dependent Model for Thrombus Formation

Modeling the transport, activation, and adhesion of platelets is crucial in predicting thrombus formation and growth following a thrombotic event in normal or pathological conditions. We propose a shear-dependent platelet adhesive model based on the Morse potential that is calibrated by existing invivo and invitro experimental data and can be used over a wide range of flow shear rates (100<γ˙<28,000s-1). We introduce an Eulerian-Lagrangian model where hemodynamics is solved on a fixed Eulerian grid, while platelets are tracked using a Lagrangian framework. A force coupling method is introduced for bidirectional coupling of platelet motion with blood flow. Further, we couple the calibrated platelet aggregation model with a tissue-factor/contact pathway coagulation cascade, representing the relevant biology of thrombin generation and the subsequent fibrin deposition. The range of shear rates covered by the proposed model encompass venous and arterial thrombosis, ranging from low-shear-rate conditions in abdominal aortic aneurysms and thoracic aortic dissections to thrombosis in stenotic arteries following plaque rupture, where local shear rates are extremely high.

Hemostasis (thrombus formation) is the normal physiological response that prevents significant blood loss after vascular injury. The resulting clots can form under different flow conditions in the veins as well as the arteries. The excessive and undesirable formation of clots (i.e., thrombosis) in our circulatory system may lead to significant morbidity and mortality. Some of these pathologies are deep vein thrombosis and pulmonary embolism and atherothrombosis (thrombosis triggered by plaque rupture) in coronary arteries, to name a few. The process of clot formation and growth at a site on a blood vessel wall involves a number of simultaneous processes including: multiple chemical reactions in the coagulation cascade, species transport and platelet adhesion all of which are strongly influenced by the hydrodynamic forces. Numerical models for blood clotting normally focus on one of the processes under a specific flow condition. Here, we propose a general numerical model that encompass a wide range of hemodynamic conditions in the veins and arteries, with individual platelets and their adhesive dynamics included explicitly in the models. Further, we include the biochemistry of coagulation cascade, which is essential to modeling thrombus formation, and couple that to our platelet aggregation model. The simulation results—tested against three different experiments—demonstrate that the proposed model is effective in capturing the invivo and invitro experimental observations.

In vitro examination of the pressure effect on clot dissolution with thrombolytic patch

Bio-kinetic thrombus dissolution model has been developed to describe the thrombus dissolution behavior during endoluminal thrombolytic patch treatment to recanalize blocked vessel in ischemic strokes. The initial model ignored the effect of pulsatile pressure in the lumen. However, pulsatile pressure in the lumen may affect molecule diffusion and bio-chemical reaction rate and accelerate clot dissolution. The effect of pressure on the dissolution rate was examined in this study. The dissolution behaviors of 100-400 μm thick blood clot specimens subject to diastolic, systolic, and pulsatile pressure were characterized using Raman spectroscopy. The results showed that dissolution time was reduced by less than 2 mins and is negligible in comparison with total treatment time. The effect of pressure may be ignored and the developed bio-kinetic model may be used in surgical applications of endoluminal thrombolytic patch to estimate treatment time in ischemic stroke.

A computational model based on fibrin accumulation for the prediction of stasis thrombosis following flow-diverting treatment in cerebral aneurysms

Flow diverters, the specially designed low porosity stents, have been used to redirect blood flow from entering aneurysm, which induces flow stasis in aneurysm and promote thrombosis for repairing aneurysm. However, it is not clear how thrombus develops following flow-diversion treatment. Our objective was to develop a computation model for the prediction of stasis-induced thrombosis following flow-diversion treatment in cerebral aneurysms. We proposed a hypothesis to initiate coagulation following flow-diversion treatment. An experimental model was used by ligating rat's right common carotid artery (RCCA) to create flow-stasis environment. Thrombus formed in RCCA as a result of flow stasis. The fibrin distributions in different sections along the axial length of RCCA were measured. The fibrin distribution predicted by our computational model displayed a trend of increase from the proximal neck to the distal tip, consistent with the experimental results on rats. The model was applied on a saccular aneurysm treated with flow diverter to investigate thrombus development following flow diversion. Thrombus was predicted to form inside the sac, and the aneurysm was occluded with only a small remnant neck remained. Our model can serve as a tool to evaluate flow-diversion treatment outcome and optimize the design of flow diverters.

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.

[ACTIVATION OF PROTEIN C IN THE IN VITRO THROMBOLYSIS]

Physiological conditions of formation and subsequent lysis of thrombus were reconstituted in vitro in our research. Thrombus formation was initiated either by addition of exogenous thrombin or by contact of blood with anionic surface, which stimulates spontaneous coagulation of blood. Tissue plasminogen activator and/or protein C were previously added in the blood sample. The time of the beginning and total degradation of formed thrombi as well as the level of PC in lysates was controlled then. Only an addition of protein C alone or in combination with tissue plasminogen activator led to the most effective lysis of thrombi: their residual weight was 18% and 5% comparing to control. Addition of exogenous tissue plasminogen activator alone or in combination with protein C caused a 83% and 74% decrease of PC level in lysates of spontaneously formed thrombi, and 72% and 56% decrease for thrombi formed by thrombin, respectively. Without an addition of tissue plasminogen activator protein C level in lysates of thrombi formed by thrombin was 54% down on spontaneously formed thrombi. Thus, changes of PC concentration in isolated volume of clot seem to be controlled by thrombin at the stage of thrombus formation and by fibrinolytic system at the stage of fibrinolysis. Concentration of PC in lysates from clots formed by exogenous thrombin was decreasing over the next 10 hours of thrombolysis, which can also be the evidence of the interaction between the fibrinolytic and PC activation systems. A hypothesis is. formulated about an existence of endothelium-independent mechanism of PC activation in blood plasma with blood cells participation, which effectiveness increases in the process of thrombolysis.

Numerical validation of a synthetic cell-based model of blood coagulation

In Fasano et al. (2012) a new reduced mathematical model for blood coagulation was proposed, incorporating biochemical and mechanical actions of blood flow and including platelets activity. The model was characterized by a considerable simplification of the differential system associated to the biochemical network and it incorporated the role of blood slip at the vessel wall as an extra source of activated platelets. The purpose of this work is to check the validity of the reduced mathematical model, using as a benchmark the model presented in Anand et al. (2008), and to investigate the importance of the blood slip velocity in the blood coagulation process.

Transport dissipative particle dynamics model for mesoscopic advection-diffusion-reaction problems

We present a transport dissipative particle dynamics (tDPD) model for simulating mesoscopic problems involving advection-diffusion-reaction (ADR) processes, along with a methodology for implementation of the correct Dirichlet and Neumann boundary conditions in tDPD simulations. tDPD is an extension of the classic dissipative particle dynamics (DPD) framework with extra variables for describing the evolution of concentration fields. The transport of concentration is modeled by a Fickian flux and a random flux between tDPD particles, and the advection is implicitly considered by the movements of these Lagrangian particles. An analytical formula is proposed to relate the tDPD parameters to the effective diffusion coefficient. To validate the present tDPD model and the boundary conditions, we perform three tDPD simulations of one-dimensional diffusion with different boundary conditions, and the results show excellent agreement with the theoretical solutions. We also performed two-dimensional simulations of ADR systems and the tDPD simulations agree well with the results obtained by the spectral element method. Finally, we present an application of the tDPD model to the dynamic process of blood coagulation involving 25 reacting species in order to demonstrate the potential of tDPD in simulating biological dynamics at the mesoscale. We find that the tDPD solution of this comprehensive 25-species coagulation model is only twice as computationally expensive as the conventional DPD simulation of the hydrodynamics only, which is a significant advantage over available continuum solvers.

Modelling of platelet-fibrin clot formation in flow with a DPD-PDE method

The paper is devoted to mathematical modelling of clot growth in blood flow. Great complexity of the hemostatic system dictates the need of usage of the mathematical models to understand its functioning in the normal and especially in pathological situations. In this work we investigate the interaction of blood flow, platelet aggregation and plasma coagulation. We develop a hybrid DPD-PDE model where dissipative particle dynamics (DPD) is used to model plasma flow and platelets, while the regulatory network of plasma coagulation is described by a system of partial differential equations. Modelling results confirm the potency of the scenario of clot growth where at the first stage of clot formation platelets form an aggregate due to weak inter-platelet connections and then due to their activation. This enables the formation of the fibrin net in the centre of the platelet aggregate where the flow velocity is significantly reduced. The fibrin net reinforces the clot and allows its further growth. When the clot becomes sufficiently large, it stops growing due to the narrowed vessel and the increase of flow shear rate at the surface of the clot. Its outer part is detached by the flow revealing the inner part covered by fibrin. This fibrin cap does not allow new platelets to attach at the high shear rate, and the clot stops growing. Dependence of the final clot size on wall shear rate and on other parameters is studied.

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.

Modeling thrombin generation: plasma composition based approach

Thrombin has multiple functions in blood coagulation and its regulation is central to maintaining the balance between hemorrhage and thrombosis. Empirical and computational methods that capture thrombin generation can provide advancements to current clinical screening of the hemostatic balance at the level of the individual. In any individual, procoagulant and anticoagulant factor levels together act to generate a unique coagulation phenotype (net balance) that is reflective of the sum of its developmental, environmental, genetic, nutritional and pharmacological influences. Defining such thrombin phenotypes may provide a means to track disease progression pre-crisis. In this review we briefly describe thrombin function, methods for assessing thrombin dynamics as a phenotypic marker, computationally derived thrombin phenotypes versus determined clinical phenotypes, the boundaries of normal range thrombin generation using plasma composition based approaches and the feasibility of these approaches for predicting risk.

A numerical study of blood flow using mixture theory

In this paper, we consider the two dimensional flow of blood in a rectangular microfluidic channel. We use Mixture Theory to treat this problem as a two-component system: One component is the red blood cells (RBCs) modeled as a generalized Reiner-Rivlin type fluid, which considers the effects of volume fraction (hematocrit) and influence of shear rate upon viscosity. The other component, plasma, is assumed to behave as a linear viscous fluid. A CFD solver based on OpenFOAM® was developed and employed to simulate a specific problem, namely blood flow in a two dimensional micro-channel, is studied. Finally to better understand this two-component flow system and the effects of the different parameters, the equations are made dimensionless and a parametric study is performed.

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.

A review of macroscopic thrombus modeling methods

Hemodynamics applied to mechanobiology offers powerful means to predict thrombosis, and to understand the kinetics of thrombus formation on areas of vascular damage in blood flowing through the human circulatory system. Specifically, the advances in computational processing and the progress in modeling complex biological processes with spatio-temporal multi-scale methods have the potential to shift the way in which cardiovascular diseases are diagnosed and treated. This article systematically surveys the state of the art of macroscopic computational fluid dynamics (CFD) Computational fluid dynamics techniques for modeling thrombus formation, highlighting their strengths and weaknesses. In particular, a comprehensive and systematic revision of the hemodynamics models and methods is given, and the strengths and weaknesses of those employed for studying thrombus formation are highlighted.

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.