Threshold of microvascular occlusion: injury size defines the thrombosis scenario

Force balance ratio is a robust predictor of arterial thrombus stability

Thrombus formation on a damaged vessel wall can lead to the formation of a stable occlusive/subocclusive clot or unstable embolizing thrombus. Both outcomes can cause significant health damage. The mechanisms that regulate maximum thrombus size, its stability, and embolization in both micro- and macrocirculation are poorly understood. To investigate the impact of flow and intrathrombus forces on the stability of homogeneous and heterogeneous platelet thrombi in a wide range of thrombus geometries, critical interplatelet forces, vessel diameters, and hydrodynamic conditions, we took advantage of the recently developed in silico models. To perform analysis of thrombus stability/embolization in arterioles, we used our previously developed particle-based 2D model with a single-platelet resolution. Its results and predictions were further extended to a 3D case and the large spatial scales of arteries using novel particle-based and continuum 3D models. We found a robust quantitative parameter, termed force balance ratio, which quantifies the balance between destabilizing hydrodynamic and stabilizing interplatelet forces. This parameter predicts whether a homogeneous thrombus (or the shell of a heterogeneous thrombus) with a particular value of critical interplatelet forces will embolize under given hydrodynamic conditions. Our simulations also predict that, for a given magnitude of critical interplatelet forces, the longer thrombi are more stable than the shorter ones. Furthermore, the aggregates formed on top of the severe stenosis are more stable than thrombi formed at moderate stenosis. Taken together, our results give new insights into the interplay between critical interplatelet forces, local hydrodynamics, and overall thrombus stability against the flow.

Clots reveal anomalous elastic behavior of fiber networks

The adaptive mechanical properties of soft and fibrous biological materials are relevant to their functionality. The emergence of the macroscopic response of these materials to external stress and intrinsic cell traction from local deformations of their structural components is not well understood. Here, we investigate the nonlinear elastic behavior of blood clots by combining microscopy, rheology, and an elastic network model that incorporates the stretching, bending, and buckling of constituent fibrin fibers. By inhibiting fibrin cross-linking in blood clots, we observe an anomalous softening regime in the macroscopic shear response as well as a reduction in platelet-induced clot contractility. Our model explains these observations from two independent macroscopic measurements in a unified manner, through a single mechanical parameter, the bending stiffness of individual fibers. Supported by experimental evidence, our mechanics-based model provides a framework for predicting and comprehending the nonlinear elastic behavior of blood clots and other active biopolymer networks in general.

Coarse-grained simulations of von Willebrand factor adsorption to collagen with consequent platelet recruitment

A multimeric glycoprotein of blood plasma-Von Willebrand factor (VWF)-mediates platelet adhesion to the fibrillar collagen of the subendothelial matrix if the blood vessel walls are damaged. The adsorption of VWF to collagen is thus essential for the initial stages of platelet hemostasis and thrombosis, as it plays a role of a molecular bridge between the injury and platelet adhesion receptors. Biomechanical complexity and sensitivity to the hydrodynamics are inherent in this system, therefore, modern computational methods supplement experimental studies of biophysical and molecular mechanisms that underlie platelet adhesion and aggregation in the blood flow. In the present paper, we propose a simulation framework for the VWF-mediated platelet adhesion to a plane wall with immobilized binding sites for VWF under the action of shear flow. VWF multimers and platelets are represented in the model by particles connected by elastic bonds and immersed in a viscous continuum fluid. This work complements the scientific field by taking into account the shape of a flattened platelet, but keeping a compromise between the detail of the description and the computational complexity of the model.

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.

Nanomechanics of Blood Clot and Thrombus Formation

Mechanical properties have been extensively studied in pure elastic or viscous materials; however, most biomaterials possess both physical properties in a viscoelastic component. How the biomechanics of a fibrin clot is related to its composition and the microenvironment where it is formed is not yet fully understood. This review gives an outline of the building mechanisms for blood clot mechanical properties and how they relate to clot function. The formation of a blood clot in health conditions or the formation of a dangerous thrombus go beyond the mere polymerization of fibrinogen into a fibrin network. The complex composition and localization of in vivo fibrin clots demonstrate the interplay between fibrin and/or fibrinogen and blood cells. Studying these protein–cell interactions and clot mechanical properties may represent new methods for the evaluation of cardiovascular diseases (the leading cause of death worldwide), creating new possibilities for clinical diagnosis, prognosis, and therapy.

Expected final online publication date for the Annual Review of Biophysics, Volume 51 is May 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Analysis of microvascular thrombus mechanobiology with a novel particle-based model

Platelet accumulation at the site of a vascular injury is regulated by soluble platelet agonists, which induce various types of platelet responses, including integrin activation and granule secretion. The interplay between local biochemical cues, mechanical interactions between platelets and macroscopic thrombus dynamics is poorly understood. Here we describe a novel computational model of microvascular clot formation for the detailed analysis of thrombus mechanics. We adopt a previously developed two-dimensional particle-based model focused on the thrombus shell formation and revise it to introduce the platelet agonists. Blood flow is simulated via a computational fluid dynamics approach. In order to model soluble platelet activators, we apply Langevin dynamics to a large number of non-dimensional virtual particles. Taking advantage of the available data on platelet dense granule secretion kinetics, we model platelet degranulation as a stochastic agonist-dependent process. The new model qualitatively reproduces the enhanced thrombus formation due to dense granule secretion, in line with in vivo findings, and provides a mechanism for the thrombin confinement at the early stages of clot formation. Our calculations also predict that the release of platelet dense granules results in the additional mechanical stabilization of the inner layers of thrombus. Distribution of the inter-platelet forces throughout the aggregate reveals multiple weak spots in the outer regions of a thrombus, which are expected to result in the mechanical disruptions at the later stages of clot formation.

Factors associated with microvascular occlusion in patients with ST elevation myocardial infarction after primary percutaneous coronary intervention

Objective

This study aimed to determine predictors of microvascular occlusion (MVO) in patients with ST elevation myocardial infarction (STEMI) after primary percutaneous coronary intervention (pPCI).

Methods

This retrospective, observational study consecutively included 113 patients with STEMI undergoing pPCI. Cardiac magnetic resonance imaging was used to determine the presence of MVO in these patients. Biomarkers in serum were routinely tested 1 day after pPCI. Multivariable logistic regression analysis was used to evaluate significant predictors of occurrence of MVO.

Results

There were 62 patients in the MVO group and 51 patients in the non-MVO group. C-reactive protein (CRP), thrombomodulin, lymphatic vessel endothelial hyaluronan receptor-1, syndecan-1, and troponin T (TnT) levels after the procedure were significantly higher in the MVO group than in the non-MVO group. CRP (hazard ratio [HR]=1.036), TnT (HR=1.316), and syndecan-1 (HR=1.986) levels were independently associated with MVO in patients with acute myocardial infarction after pPCI.

Conclusions

Levels of CRP, TnT, and syndecan-1 can be used as serum biomarkers for MVO in patients with STEMI receiving pPCI.

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.

In vitro flow-based assay: From simple toward more sophisticated models for mimicking hemostasis and thrombosis

In vitro flow-based assays are widely used to investigate the role of platelets and coagulation in hemostasis and thrombosis. Their main advantage over other assays relies on the fact that they integrate blood flow that regulates many aspects of platelet function, including adhesion, activation, and aggregation. Blood flow is also central in the regulation of coagulation through its ability to modulate the local concentrations of coagulation factors within and around thrombi. The most broadly used assay to study thrombus formation consists in perfusing whole blood over immobilized fibrillar collagen through a single channel, which helps to reproduce thrombus formation as it occurs in vivo after vascular injury, with platelets adhering, becoming activated, and forming a mural thrombus. This process can also be studied under conditions of thrombin generation, notably by recalcifying blood collected in sodium citrate. In this manuscript, we briefly discuss the advantages and limits of this broadly used "in vitro thrombus formation model." The main emphasis is on the description of the most recent developments regarding design of new flow models and new techniques, and how these may advance the landscape of in vitro studies into the formation of physiological or pathophysiological thrombi. Challenges linked to mimicking the formation of a hemostatic plug in a healthy vessel or a thrombus in diseased arteries and the complexity of reproducing the various aspects of venous thrombosis are discussed. Future directions are proposed to improve the physiological or pathophysiological relevance of current flow-based assays.

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.

Modelling the linkage between influenza infection and cardiovascular events via thrombosis

There is a heavy burden associated with influenza including all-cause hospitalization as well as severe cardiovascular and cardiorespiratory events. Influenza associated cardiac events have been linked to multiple biological pathways in a human host. To study the contribution of influenza virus infection to cardiovascular thrombotic events, we develop a dynamic model which incorporates some key elements of the host immune response, inflammatory response, and blood coagulation. We formulate these biological systems and integrate them into a cohesive modelling framework to show how blood clotting may be connected to influenza virus infection. With blood clot formation inside an artery resulting from influenza virus infection as the primary outcome of this integrated model, we demonstrate how blood clot severity may depend on circulating prothrombin levels. We also utilize our model to leverage clinical data to inform the threshold level of the inflammatory cytokine TNFα which initiates tissue factor induction and subsequent blood clotting. Our model provides a tool to explore how individual biological components contribute to blood clotting events in the presence of influenza infection, to identify individuals at risk of clotting based on their circulating prothrombin levels, and to guide the development of future vaccines to optimally interact with the immune system.

Blood Clot Phenotyping by Rheometry: Platelets and Fibrinogen Chemistry Affect Stress-Softening and -Stiffening at Large Oscillation Amplitude

(1) Background: Together with treatment protocols, viscoelastic tests are widely used for patient care. Measuring at broader ranges of deformation than currently done will add information on a clot’s mechanical phenotype because fibrin networks follow different stretching regimes, and blood flow compels clots into a dynamic non-linear response. (2) Methods: To characterize the influence of platelets on the network level, a stress amplitude sweep test (LAOStress) was applied to clots from native plasma with five platelet concentrations. Five species were used to validate the protocol (human, cow, pig, rat, horse). By Lissajous plots the oscillation cycle for each stress level was analyzed. (3) Results: Cyclic stress loading generates a characteristic strain response that scales with the platelet quantity at low stress, and that is independent from the platelet count at high shear stress. This general behavior is valid in the animal models except cow. Here, the specific fibrinogen chemistry induces a stiffer network and a variant high stress response. (4) Conclusions: The protocol provides several thresholds to connect the softening and stiffening behavior of clots with the applied shear stress. This points to the reversible part of deformation, and thus opens a new route to describe a blood clot’s phenotype.

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.

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.

Thrombus growth modelling and stenosis prediction in the cerebral microvasculature

Cerebral microvascular occlusions cause restriction of blood supply to the brain, thus potentially severely impacting cognitive abilities. Thus, accurate prediction of thrombus growth in realistic geometries is important. Thrombi growth in an existing 13-generation cerebral microvasculature network is simulated here to study the haemodynamic effects of single and multiple blockages on the occlusion of the network. Compared to a single vessel, in a network, the occlusion probability is found to be different. It is the downstream/smaller arterioles (i.e. the 3rd, 4th, 5th, 6th generation arterioles in this study) that tend to reach occlusion first in a network and thus are the critical vessels. Simulations of simultaneous growth of two independent thrombi in the network (referred to here as the two-block case) show a close coupling between the locations of the various blocks in the network, each influencing the other's growth. The presence of the lead block (LB) slows the growth of the trailing block (TB). In some cases, it stops the TB's growth thereby preventing it from occluding the vessel. Findings in this work thus indicate that, to prevent ischaemia, blocks in the smaller arterioles need to be identified and treated first, and that this is more critical if the number of simultaneous blocks is higher.

Modeling the effect of blood vessel bifurcation ratio on occlusive thrombus formation

Vascular geometry is a major determinant of the hemodynamics that promote or prevent unnecessary vessel occlusion from thrombus formation. Bifurcations in the vascular geometry are repeating structures that introduce flow separation between parent and daughter vessels. We modelled the blood flow and shear rate in a bifurcation during thrombus formation and show that blood vessel bifurcation ratios determine the maximum shear rate on the surface of a growing thrombus. We built an analytical model that may aid in predicting microvascular bifurcation ratios that are prone to occlusive thrombus formation. We also observed that bifurcation ratios that adhere to Murray's law of bifurcations may be protected from occlusive thrombus formation. These results may be useful in the rational design of diagnostic microfluidic devices and microfluidic blood oxygenators.

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

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

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.

Model predictions of deformation, embolization and permeability of partially obstructive blood clots under variable shear flow

Thromboembolism, one of the leading causes of morbidity and mortality worldwide, is characterized by formation of obstructive intravascular clots (thrombi) and their mechanical breakage (embolization). A novel two-dimensional multi-phase computational model is introduced that describes active interactions between the main components of the clot, including platelets and fibrin, to study the impact of various physiologically relevant blood shear flow conditions on deformation and embolization of a partially obstructive clot with variable permeability. Simulations provide new insights into mechanisms underlying clot stability and embolization that cannot be studied experimentally at this time. In particular, model simulations, calibrated using experimental intravital imaging of an established arteriolar clot, show that flow-induced changes in size, shape and internal structure of the clot are largely determined by two shear-dependent mechanisms: reversible attachment of platelets to the exterior of the clot and removal of large clot pieces. Model simulations predict that blood clots with higher permeability are more prone to embolization with enhanced disintegration under increasing shear rate. In contrast, less permeable clots are more resistant to rupture due to shear rate-dependent clot stiffening originating from enhanced platelet adhesion and aggregation. These results can be used in future to predict risk of thromboembolism based on the data about composition, permeability and deformability of a clot under specific local haemodynamic conditions.

Long ligands reinforce biological adhesion under shear flow

In this work, computer modeling has been used to show that longer ligands allow biological cells (e.g., blood platelets) to withstand stronger flows after their adhesion to solid walls. A mechanistic model of polymer-mediated ligand-receptor adhesion between a microparticle (cell) and a flat wall has been developed. The theoretical threshold between adherent and non-adherent regimes has been derived analytically and confirmed by simulations. These results lead to a deeper understanding of numerous biophysical processes, e.g., arterial thrombosis, and to the design of new biomimetic colloid-polymer systems.

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

Hemostasis is a complex physiological mechanism that functions to maintain vascular integrity under any conditions. Its primary components are blood platelets and a coagulation network that interact to form the hemostatic plug, a combination of cell aggregate and gelatinous fibrin clot that stops bleeding upon vascular injury. Disorders of hemostasis result in bleeding or thrombosis, and are the major immediate cause of mortality and morbidity in the world. Regulation of hemostasis and thrombosis is immensely complex, as it depends on blood cell adhesion and mechanics, hydrodynamics and mass transport of various species, huge signal transduction networks in platelets, as well as spatiotemporal regulation of the blood coagulation network. Mathematical and computational modeling has been increasingly used to gain insight into this complexity over the last 30 years, but the limitations of the existing models remain profound. Here we review state-of-the-art-methods for computational modeling of thrombosis with the specific focus on the analysis of unresolved challenges. They include: a) fundamental issues related to physics of platelet aggregates and fibrin gels; b) computational challenges and limitations for solution of the models that combine cell adhesion, hydrodynamics and chemistry; c) biological mysteries and unknown parameters of processes; d) biophysical complexities of the spatiotemporal networks' regulation. Both relatively classical approaches and innovative computational techniques for their solution are considered; the subjects discussed with relation to thrombosis modeling include coarse-graining, continuum versus particle-based modeling, multiscale models, hybrid models, parameter estimation and others. Fundamental understanding gained from theoretical models are highlighted and a description of future prospects in the field and the nearest possible aims are given.

Modeling of the effects of IL-17 and TNF-α on endothelial cells and thrombus growth

Rheumatoid and psoriatic arthritis are chronic inflammatory diseases, with massive increase of cardiovascular events (CVE), and contribution of the cytokines TNF-α and IL-17. Chronic inflammation inside the joint membrane or synovium results from the activation of fibroblasts/synoviocytes, and leads to the release of cytokines from monocytes (Tumor Necrosis Factor or TNF) and from T lymphocytes (Interleukin-17 or IL-17). At the systemic level, the very same cytokines affect endothelial cells and vessel wall. We have previously shown [1,2] that IL-17 and TNF-α, specifically when combined, increase procoagulation, decrease anticoagulation and increase platelet aggregation, leading to thrombosis. These results are the basis for the models of interactions between IL-17 and TNF, and genes expressed by activated endothelial cells. This work is devoted to mathematical modeling and numerical simulations of blood coagulation and clot growth under the influence of IL-17 and TNF-α. We show that they can provoke thrombosis, leading to the complete or partial occlusion of blood vessels. The regimes of blood coagulation and conditions of occlusion are investigated in numerical simulations and in approximate analytical models. The results of mathematical modeling allow us to predict thrombosis development for an individual patient.

Continuous Modeling of Arterial Platelet Thrombus Formation Using a Spatial Adsorption Equation

In this study, we considered a continuous model of platelet thrombus growth in an arteriole. A special model describing the adhesion of platelets in terms of their concentration was derived. The applications of the derived model are not restricted to only describing arterial platelet thrombus formation; the model can also be applied to other similar adhesion processes. The model reproduces an auto-wave solution in the one-dimensional case; in the two-dimensional case, in which the surrounding flow is taken into account, the typical torch-like thrombus is reproduced. The thrombus shape and the growth velocity are determined by the model parameters. We demonstrate that the model captures the main properties of the thrombus growth behavior and provides us a better understanding of which mechanisms are important in the mechanical nature of the arterial thrombus growth.