Modeling thrombosis in silico: Frontiers, challenges, unresolved problems and milestones

Dissecting thrombus-directed chemotaxis and random movement in neutrophil near-thrombus motion in flow chambers

BACKGROUND

Thromboinflammation is caused by mutual activation of platelets and neutrophils. The site of thromboinflammation is determined by chemoattracting agents release by endothelium, immune cells, and platelets. Impaired neutrophil chemotaxis contributes to the pathogenesis of Shwachman-Diamond syndrome (SDS). In this hereditary disorder, neutrophils are known to have aberrant chemoattractant-induced F-actin properties. Here, we aim to determine whether neutrophil chemotaxis could be analyzed using our previously developed ex vivo assay of the neutrophils crawling among the growing thrombi.

METHODS

Adult and pediatric healthy donors, alongside with pediatric patients with SDS, were recruited for the study. Thrombus formation and granulocyte movement in hirudinated whole blood were visualized by fluorescent microscopy in fibrillar collagen-coated parallel-plate flow chambers. Alternatively, fibrinogen, fibronectin, vWF, or single tumor cells immobilized on coverslips were used. A computational model of chemokine distribution in flow chamber with a virtual neutrophil moving in it was used to analyze the observed data.

RESULTS

The movement of healthy donor neutrophils predominantly occurred in the direction and vicinity of thrombi grown on collagen or around tumor cells. For SDS patients or on coatings other than collagen, the movement was characterized by randomness and significantly reduced velocities. Increase in wall shear rates to 300-500 1/s led to an increase in the proportion of rolling neutrophils. A stochastic algorithm simulating leucocyte chemotaxis movement in the calculated chemoattractant field could reproduce the experimental trajectories of moving neutrophils for 72% of cells.

CONCLUSIONS

In samples from healthy donors, but not SDS patients, neutrophils move in the direction of large, chemoattractant-releasing platelet thrombi growing on collagen.

Antithrombotic pharmacodynamics and metabolomics study in raw and processed products of Whitmania pigra Whitman

Objective

As a traditional Chinese medicine, leech has obvious pharmacological activities in anticoagulantion and antithrombosis. Whitmania pigra Whitman (WP) is the most commonly used leech in the Chinese market. It is often used in clinical applications after high-temperature processing by talcum powder to remove the fishy taste and facilitate crushing. The anticoagulant and thrombolytic active ingredients are protein and polypeptide, which may denaturate and lose activity after high-temperature processing. The rationality of its processing has been questioned in recent years. This study aims to investigate the effect of talcum powder scalding on the antithrombotic activity of WP in vivo and to discuss its pharmacodynamic mechanism in vivo.

Methods

Raw and talcum-powdered processed WP were administered intragastrically for 14 days, and carrageenan was injected intraperitoneally to prepare a mouse model of tail vein thrombosis. The incidence rate of tail vein thrombosis and the thrombus area under pathological tissue sections were calculated to evaluate the antithrombotic effect between raw and processed WP. Non-targeted metabolomics was conducted using UPLC-Q-TOF/MS technology to analyze the changes of small molecule metabolites in the body after administration of WP.

Results

After intragastric administration, both the raw product and the processed product of WP could inhibit the thrombosis induced by carrageenan, and the processed product had a more apparent antithrombotic effect than the raw product. The administration of WP could regulate the changes of some small molecular metabolites, such as amino acids, lipids, and steroids, in Sphingolipid metabolism and Glycerophospholipid metabolism.

Conclusions

Based on the results of pharmacodynamics and metabolomics, processed WP will not reduce the antithrombotic activity of WP. This study provided a scientific basis for the rational use of leeches.

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

BACKGROUND

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

METHODS

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

RESULTS

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

CONCLUSIONS

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

Modelling of the in-stent thrombus formation by dissipative particle dynamics

BACKGROUND

Stent implantation is a highly efficacious intervention for the treatment of coronary atherosclerosis. Nevertheless, stent thrombosis and other post-operative complications persist, and the underlying mechanism of adverse event remains elusive.

METHODS

In the present study, a dissipative particle dynamics model was formulated to simulate the motion, adhesion, activation, and aggregation of platelets, with the aim of elucidating the mechanisms of in-stent thrombosis.

FINDINGS

The findings suggest that stent thrombosis arises from a complex interplay of multiple factors, including endothelial injury resulting from stent implantation and alterations in the hemodynamic milieu. Furthermore, the results suggest a noteworthy association between in-stent thrombosis and both the length of the endothelial injured site and the degree of stent malposition. Specifically, the incidence of stent thrombosis appears to rise in tandem with the extent of the injured site, while moderate stent malposition is more likely to result in in-stent thrombosis compared to severe or minor malposition.

INTERPRETATION

This study offers novel research avenues for investigating the plasticity mechanism of stent thrombosis, while also facilitating the clinical prediction of stent thrombosis formation and the development of more precise treatment strategies.

Nanoscaled Titanium Oxide Layer Provokes Quick Osseointegration on 3D-Printed Dental Implants: A Domino Effect Induced by Hydrophilic Surface

Three-dimensional printing is a revolutionary strategy to fabricate dental implants. Especially, 3D-printed dental implants modified with nanoscaled titanium oxide layer (H-SLM) have impressively shown quick osseointegration, but the accurate mechanism remains elusive. Herein, we unmask a domino effect that the hydrophilic surface of the H-SLM facilitates blood wetting, enhances the blood shear rate, promotes blood clotting, and changes clot features for quick osseointegration. Combining computational fluid dynamic simulation and biological verification, we find a blood shear rate during blood wetting of the hydrophilic H-SLM 1.2-fold higher than that of the raw 3D-printed implant, which activates blood clot formation. Blood clots formed on the hydrophilic H-SLM demonstrate anti-inflammatory and pro-osteogenesis effects, leading to a 1.5-fold higher bone-to-implant contact and a 1.8-fold higher mechanical anchorage at the early stage of osseointegration. This mechanism deepens current knowledge between osseointegration speed and implant surface characteristics, which is instructive in surface nanoscaled modification of multiple 3D-printed intrabony implants.

Different modeling approaches in the simulation of extrinsic coagulation factor X activation: Limitations and areas of applicability

Proteolytic reactions on the phospholipid membrane surface, so-called "membrane-dependent" reactions, play central role in the process of blood clotting. One particularly important example is FX activation by the extrinsic tenase (VIIa/TF). Here we constructed three mathematical models of FX activation by VIIa/TF: (A) a homogeneous "well-mixed" model, (B) a two-compartment "well-mixed" model, (C) a heterogeneous model with diffusion, to investigate the impact and importance of inclusion of each complexity level. All models provided good description of the reported experimental data and were equivalently applicable for <40 μM of phospholipids. Model C provided better predictions than A, B in the presence of TF-negative phospholipid microparticles. Models predicted that for high TF surface density (STF ) and FX deficiency the FX activation rate was limited by the rate of FX binding to the membrane. For low STF and excess of FX the reaction rate was limited by the tenase formation rate. The analysis of the substrate delivery pathways revealed that FX bound to VIIa/TF predominantly from solution for STF  >2.8 × 10-3  nmol/cm2 and from the membrane for lower STF . We proposed the experimental setting to distinguish between the collision-limited and non-collision-limited binding. The analysis of models in flow and non-flow conditions revealed that the model of a vesicle in flow might be substituted by model C in the absence of the substrate depletion. Together, this study was the first which provided the direct comparison of more simple and more complex models. The reaction mechanisms were studied in a wide range of conditions.

Molecular mechanisms of catch bonds and their implications for platelet hemostasis

Adhesive molecular bonds between blood cells are essential for thrombosis and hemostasis as they provide means for platelet adhesion, aggregation, and signaling in flowing blood. According to the nowadays conventional definition, a "catch" bond is a type of non-covalent bio-molecular bridge, whose dissociation lifetime counter-intuitively increases with applied tensile force. Following recent experimental findings, such receptor-ligand protein bonds are vital to the blood cells involved in the prevention of bleeding (hemostatic response) and infection (immunity). In this review, we examine the up-to-date experimental discoveries and theoretical insights about catch bonds between the blood cells, their biomechanical principles at the molecular level, and their role in platelet thrombosis and hemostasis.

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.

An in vitro model for Extracellular DNA Traps (ETs)-rich Human Thrombus Analogs

BACKGROUND

Extracellular DNA traps (ETs) have important implications in both thrombosis and thrombolysis. Thus, developing benchtop thrombus analogs that recapitulate clinical ETs is potentially of great value for preclinical development and testing of thrombolytic agents and thrombectomy devices. In this study, we aimed to develop ETs-rich thrombus analogs for preclinical testing.

METHODS

Red blood cell (RBC)-rich, fibrin-rich, and platelet-rich thrombus analogs were created using human whole blood, platelet-poor plasma, and platelet-rich plasma obtained from the blood bank following institutional approval. Peripheral blood mononuclear cells (9.9×106 cells/mL) isolated from human whole blood and lipopolysaccharide (1 µg/mL) were added to induce ETs. Histochemical, immunohistochemistry and immunofluorescence were used to identify thrombus components and ETs. Scanning electronic microscopy was used to investigate the ultrastructure of the thrombus analogs. The thrombus compositions, morphologic features of ETs and citrullinated histone H3 (H3Cit) expression were compared with those of thrombi retrieved from patients by thrombectomy.

RESULTS

ETs-rich thrombus analogs were more compacted th-an the ETs-poor thrombus analogs. ETs were identified in both ETs-rich thrombus analogs and patient thrombi showing morphologic features including nuclear lobulation, nuclear swelling, diffused chromatin within cytoplasm, DNA/chromatin extending intracellularly and extracellularly, and extracellular chromatin patches and bundles. In the ETs-poor thrombus analogs, ETs were not observed and H3Cit expression was absent to minimal. The compositions and H3Cit expression in the ETs-rich thrombus analogs fell in the range of patient thrombi.

CONCLUSIONS

ETs-rich thrombus analogs can be consistently created in vitro and may benefit the preclinical development and testing of new thrombolytic agents and thrombectomy devices.

Computational modeling of hypercoagulability in COVID-19

Coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), has infected more than 100 million people worldwide and claimed millions of lives. While the leading cause of mortality in COVID-19 patients is the hypoxic respiratory failure from acute respiratory distress syndrome, there is accumulating evidence that shows excessive coagulation also increases the fatalities in COVID-19. Thus, there is a pressing demand to understand the association between COVID-19-induced hypercoagulability and the extent of formation of undesired blood clots. Mathematical modeling of coagulation has been used as an important tool to identify novel reaction mechanisms and to identify targets for new drugs. Here, we employ the coagulation factor data of COVID-19 patients reported from published studies as inputs for two mathematical models of coagulation to identify how the concentrations of coagulation factors change in these patients. Our simulation results show that while the levels of many of the abnormal coagulation factors measured in COVID-19 patients promote the generation of thrombin and fibrin, two key components of blood clots, the increased level of fibrinogen and then the reduced level of antithrombin are the factors most responsible for boosting the level of fibrin and thrombin, respectively. Altogether, our study demonstrates the potential of mathematical modeling to identify coagulation factors responsible for the increased clot formation in COVID-19 patients where clinical data is scarce.

Biomechanical activation of blood platelets via adhesion to von Willebrand factor studied with mesoscopic simulations

Platelet adhesion and activation are essential initial processes of arterial and microvascular hemostasis, where high hydrodynamic forces from the bloodflow impede coagulation. The process relies on von Willebrand factor (VWF)-a linear multimeric protein of blood plasma plays a pivotal role in mechanochemical regulation of shear-induced platelet aggregation (SIPA). Adhesive interactions between VWF and glycoprotein receptors GPIb are crucial for platelet recruitment under high shear stress in fluid. Recent advances in experimental studies revealed that mechanical tension on the extracellular part of GPIb may trigger a cascade of biochemical reactions in platelets leading to activation of integrins [Formula: see text] (also known as GPIIb/IIIa) and strengthening of the adhesion. The present paper is aimed at investigation of this process by three-dimensional computer simulations of platelet adhesion to surface-grafted VWF multimers in pressure-driven flow of platelet-rich plasma. The simulations demonstrate that GPIb-mediated mechanotransduction is a feasible way of platelet activation and stabilization of platelet aggregates under high shear stress. Quantitative understanding of mechanochemical processes involved in SIPA would potentially promote the discovery of new anti-platelet medication and the development of multiscale numerical models of platelet thrombosis and hemostasis.

Aptamers Regulating the Hemostasis System

The hemostasis system is a complex structure that includes the fibrinolysis system, and Yes this is correct coagulation and anticoagulation parts. Due to the multicomponent nature, it becomes relevant to study the key changes in the functioning of signaling pathways, and develop new diagnostic methods and modern drugs with high selectivity. One of the ways to solve this problem is the development of molecular recognition elements capable of blocking one of the hemostasis systems and/or activating another. Aptamers can serve as ligands for targeting specific clinical needs, promising anticoagulants with minor side effects and significant biological activity. Aptamers with several clotting factors and platelet proteins are used for the treatment of thrombosis. This review is focused on the aptamers used for the correction of the hemostasis system, and their structural and functional features. G-rich nucleic acid aptamers, mostly versatile G-quadruplexes, recognize different components of the hemostasis system and are capable of correcting the functioning.

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.

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

Introduction

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

Methods

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

Results

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

Conclusions

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

Uncertainty quantification of a thrombosis model considering the clotting assay PFA-100®

Mathematical models of thrombosis are currently used to study clinical scenarios of pathological thrombus formation. As these models become more complex to predict thrombus formation dynamics high computational cost must be alleviated and inherent uncertainties must be assessed. Evaluating model uncertainties allows to increase the confidence in model predictions and identify avenues of improvement for both thrombosis modeling and anti-platelet therapies. In this work, an uncertainty quantification analysis of a multi-constituent thrombosis model is performed considering a common assay for platelet function (PFA-100®). The analysis is facilitated thanks to time-evolving polynomial chaos expansions used as a parametric surrogate for the full thrombosis model considering two quantities of interest; namely, thrombus volume and occlusion percentage. The surrogate is thoroughly validated and provides a straightforward access to a global sensitivity analysis via computation of Sobol' coefficients. Six out of 15 parameters linked to thrombus consitution, vWF activity, and platelet adhesion dynamics were found to be most influential in the simulation variability considering only individual effects; while parameter interactions are highlighted when considering the total Sobol' indices. The influential parameters are related to thrombus constitution, vWF activity, and platelet to platelet adhesion dynamics. The surrogate model allowed to predict realistic PFA-100® closure times of 300,000 virtual cases that followed the trends observed in clinical data. The current methodology could be used including common anti-platelet therapies to identify scenarios that preserve the hematological balance.

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.

Modeling Thrombus Shell: Linking Adhesion Receptor Properties and Macroscopic Dynamics

Damage to arterial vessel walls leads to the formation of platelet aggregate, which acts as a physical obstacle for bleeding. An arterial thrombus is heterogeneous; it has a dense inner part (core) and an unstable outer part (shell). The thrombus shell is very dynamic, being composed of loosely connected discoid platelets. The mechanisms underlying the observed mobility of the shell and its (patho)physiological implications are unclear. To investigate arterial thrombus mechanics, we developed a novel, to our knowledge, two-dimensional particle-based computational model of microvessel thrombosis. The model considers two types of interplatelet interactions: primary reversible (glycoprotein Ib (GPIb)-mediated) and stronger integrin-mediated interaction, which intensifies with platelet activation. At high shear rates, the former interaction leads to adhesion, and the latter is primarily responsible for stable platelet aggregation. Using a stochastic model of GPIb-mediated interaction, we initially reproduced experimental curves that characterize individual platelet interactions with a von Willebrand factor-coated surface. The addition of the second stabilizing interaction results in thrombus formation. The comparison of thrombus dynamics with experimental data allowed us to estimate the magnitude of critical interplatelet forces in the thrombus shell and the characteristic time of platelet activation. The model predicts moderate dependence of maximal thrombus height on the injury size in the absence of thrombin activity. We demonstrate that the developed stochastic model reproduces the observed highly dynamic behavior of the thrombus shell. The presence of primary stochastic interaction between platelets leads to the properties of thrombus consistent with in vivo findings; it does not grow upstream of the injury site and covers the whole injury from the first seconds of the formation. А simplified model, in which GPIb-mediated interaction is deterministic, does not reproduce these features. Thus, the stochasticity of platelet interactions is critical for thrombus plasticity, suggesting that interaction via a small number of bonds drives the dynamics of arterial thrombus shell.

Patient-Specific Modelling of Blood Coagulation

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

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

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

Development of margination of platelet-sized particles in red blood cell suspensions flowing through Y-shaped bifurcating microchannels

BACKGROUND

In the blood flow through microvessels, platelets exhibit enhanced concentrations in the layer free of red blood cells (cell-free layer) adjacent to the vessel wall. The motion of platelets in the cell-free layer plays an essential role in their interaction with the vessel wall, and hence it affects their functions of hemostasis and thrombosis.

OBJECTIVE

We aimed to estimate the diffusivity of platelet-sized particles in the transverse direction (the direction of vorticity) across the channel width in the cell-free layer by in vitro experiments for the microchannel flow of red blood cell (RBC) suspensions containing platelet-sized particles.

METHODS

Fluorescence microscope observations were performed to measure the transverse distribution of spherical particles immersed in RBC suspensions flowing through a Y-shaped bifurcating microchannel. We examined the development of the particle concentration profiles along the flow direction in the daughter channels, starting from asymmetric distributions with low concentrations on the inner side of the bifurcation at the inlet of the daughter channels.

RESULTS

In daughter channels of 40 μm width, reconstruction of particle margination revealed that a symmetric concentration profile was attained in ∼30 mm from the bifurcation, independent of flow rate.

CONCLUSIONS

We presented experimental evidence of particle margination developing in a bifurcating flow channel where the diffusivity of 2.9-μm diameter particles was estimated to be ∼40 μm2/s at a shear rate of 1000 s-1 and hematocrit of 0.2.

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).

Prothrombotic effects of high uric acid in mice via activation of MEF2C-dependent NF-κB pathway by upregulating let-7c

Serum uric acid is reportedly associated with thrombosis development. However, still unclear is the mechanism of high uric acid in thrombosis with the involvement of let-7c. In an aim to fill this void, we conducted this study by treating mice and human umbilical vein endothelial cells with high uric acid. Analysis indicated that let-7c was upregulated in hyperuricemia patients as well as in mice and human umbilical vein endothelial cells treated with high uric acid. Furthermore, high uric acid inhibited myocyte enhancer factor-2C, but activated nuclear factor-kappa B pathway in human umbilical vein endothelial cells. Then the targeting relationship between let-7c and myocyte enhancer factor-2C was verified. On the one hand, high uric acid shortened activated partial thromboplastin time and prothrombin time of mice and declined tissue plasminogen activator level. Additionally, the treatment prolonged thrombin time and elevated the levels of thrombosis related molecules or proteins such as Fibrinogen and D-dimer. Nevertheless, these alternations could be reversed by inhibition of let-7c and nuclear factor-kappa B pathway or overexpressing myocyte enhancer factor-2C. To sum up, our results uncovered the pro-thrombotic effect of high uric acid in mice by activating myocyte enhancer factor-2C-dependent nuclear factor-kappa B pathway via let-7c upregulation.

In Silico Hemostasis Modeling and Prediction

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

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

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

Modeling Thrombin Generation in Plasma under Diffusion and Flow

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

Redistribution of TPA Fluxes in the Presence of PAI-1 Regulates Spatial Thrombolysis

The fibrin clot is gelatinous matter formed upon injury to stop blood loss and is later destroyed by fibrinolysis, an enzymatic cascade with feedback. Pharmacological fibrinolysis stimulation is also used to destroy pathological, life-threatening clots and thrombi (thrombolysis). The regulation of the nonlinear spatially nonuniform fibrinolytic process in thrombolysis is not currently well understood. We developed a reaction-diffusion-advection model of thrombolysis by tissue plasminogen activator (TPA) in an occluded vessel with a pressure gradient. Sensitivity-analysis-based model reduction was used to reveal the critical processes controlling different steps of thrombolysis. The propagation of thrombolysis in the system without flow was predominantly controlled by TPA diffusion, whereas transport of other active components was rendered nonessential either by their high fibrin-binding parameters and short lifetimes or their initial uniform distribution. The concentration of the main TPA inhibitor plasminogen activator inhibitor 1 (PAI-1) controlled both the extent of lysis propagation and the shape of fibrin spatial distribution during lysis. Interestingly, PAI-1 remained important even when its concentration was an order of magnitude below that of TPA because of its role at the edge of the diffusing TPA front. The system was robust to reaction rate constant perturbations. Using these data, a reduced model of thrombolysis was proposed. In the presence of flow, convection of TPA was the critical controlling process; although the role of PAI-1 concentration was much less in the presence of flow, its influence became greater in the presence of collateral bypassing vessels, which sufficiently reduced TPA flux through the thrombus. Flow bypass through the collateral vessel caused a decrease in TPA flux in the clotted vessel, which increased the PAI-1/TPA ratio, thus making PAI-1-induced inhibition relevant for the regulation of spatial lysis up to its arrest.

The potential roles of Von Willebrand factor and neutrophil extracellular traps in the natural history of hypertrophic and hypertensive cardiomyopathy

Inflammation is often applied broadly to human disease. Despite its general familiarity, inflammation is highly complex. There are numerous injurious, immune and infectious determinants, functional elements and signaling pathways, ranging from genetic to epigenetic, environmental, racial, molecular and cellular that participate in disease onset and progression, phenotypic heterogeneity, and treatment selection and response. In addition, inflammation can be tissue and organ specific, adding a layer of complexity to achieving a detailed and translatable understanding of its role in health and disease. The following review takes a close look at inflammation in the context of two common heart diseases, hypertrophic cardiomyopathy and hypertensive cardiomyopathy.

Clustering of Thrombin Generation Test Data Using a Reduced Mathematical Model of Blood Coagulation

Correct interpretation of the data from integral laboratory tests, including Thrombin Generation Test (TGT), requires biochemistry-based mathematical models of blood coagulation. The purpose of this study is to describe the experimental TGT data from healthy donors and hemophilia A (HA) and B (HB) patients. We derive a simplified ODE model and apply it to analyze the TGT data from healthy donors and HA/HB patients with in vitro added tissue factor pathway inhibitor (TFPI) antibody. This model allows the characterization of hemophilia patients in the space of three most important model parameters. The proposed approach may provide a new quantitative tool for the analysis of experimental TGT. Also, it gives a reduced model of coagulation verified against clinical data to be used in future theoretical large-scale modeling of thrombosis in flow.

Effects of hydrophobicity, tethering and size on flow-induced activation of von Willebrand factor multimers

Von Willebrand factor (VWF) is a multimeric protein of blood plasma that mediates platelet adhesion to injury under strong hemodynamic flows in arterias and microvasvulature. We present a 3D coarse-grained computer model of VWF multimers in flowing viscous fluid that explicitely grasps the dynamics, the conformational changes and the hydrodynamics-induced activation of adhesivity of these protein concatamers to GPIb receptor of blood platelets. The model is based on the fluctuating Lattice Boltzmann method for modelling the hydrodynamics in the simulation box and the Lagrangian particle dynamics coupled to the fluid by a viscous drag force. The model has been validated by the comparison with the experimental data found in literature. We studied the effect of hydrophobic interactions on the conformational dynamics of VWF multimers. The simulations suggest that the contour length is an important parameter that controls the functionality of VWF multimers in blood. We also demonstrate that tethering to the surface of a vessel wall promoted the flow-induced activation of VWF, while those multimers that remain untethered and move freely in the blood plasma require a stronger shearing to get activated.

Review of quantitative systems pharmacological modeling in thrombosis

Hemostasis and thrombosis are often thought as two sides of the same clotting mechanism whereas hemostasis is a natural protective mechanism to prevent bleeding and thrombosis is a blood clot abnormally formulated inside a blood vessel, blocking the normal blood flow. The evidence to date suggests that at least arterial thrombosis results from the same critical pathways of hemostasis. Analysis of these complex processes and pathways using quantitative systems pharmacological model-based approach can facilitate the delineation of the causal pathways that lead to the emergence of thrombosis. In this paper, we provide an overview of the main molecular and physiological mechanisms associated with hemostasis and thrombosis, and review the models and quantitative system pharmacological modeling approaches that are relevant in characterizing the interplay among the multiple factors and pathways of thrombosis. An emphasis is given to computational models for drug development. Future trends are discussed.