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

A Protease from Moringa oleifera Lam. Exhibits In-vitro Blood Clot Solubilization and Fibrin Hydrolysis

Thrombosis is the formation of abnormal blood clots in the blood vessels that obstruct blood flow and lead to thrombosis. Current treatments for thrombosis are associated with serious side effects. Therefore there is a need for alternative natural therapy. A fibrinolytic protease was isolated from fresh leaves of Moringa oleifera Lam. and characterized for its potential to solubilize blood clots and hydrolyse fibrin under in-vitro conditions. The isolated protease showed a single protein band on native-PAGE. It showed optimum fibrinolytic activity at pH 8.0, 37 oC with 50 µg protein. The fibrinolytic activity of isolated protease was also confirmed by fibrin zymography. Km and Vmax of isolated protease were determined by the Lineweaver Burk plot. The isolated protease could solubilize 96.41% of blood clots by 96 h under in-vitro conditions. In-vitro fibrin hydrolysis and blood clot solubilization activities shown by an isolated protease from leaves of Moringa oleifera Lam. suggest its fibrinolytic potential to dissolve blood clots. Being a natural molecule and from a dietary plant it can be explored as an alternative natural therapy against thrombosis.

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.

Decoding thrombosis through code: a review of computational models

From the molecular level up to a blood vessel, thrombosis and hemostasis involves many interconnected biochemical and biophysical processes over a wide range of length and time scales. Computational modeling has gained eminence in offering insights into these processes beyond what can be obtained from in vitro or in vivo experiments, or clinical measurements. The multiscale and multiphysics nature of thrombosis has inspired a wide range of modeling approaches that aim to address how a thrombus forms and dismantles. Here, we review recent advances in computational modeling with a focus on platelet-based thrombosis. We attempt to summarize the diverse range of modeling efforts straddling the wide-spectrum of physical phenomena, length scales, and time scales; highlighting key advancements and insights from existing studies. Potential information gleaned from models is discussed, ranging from identification of thrombus-prone regions in patient-specific vasculature to modeling thrombus deformation and embolization in response to fluid forces. Furthermore, we highlight several limitations of current models, future directions in the field, and opportunities for clinical translation, to illustrate the state-of-the-art. There are a plethora of opportunity areas for which models can be expanded, ranging from topics of thromboinflammation to platelet production and clearance. Through successes demonstrated in existing studies described here, as well as continued advancements in computational methodologies and computer processing speeds and memory, in silico investigations in thrombosis are poised to bring about significant knowledge growth in the years to come.

Identification of thrombin inhibiting antithrombin-III like protein from Punica granatum using in silico approach and in vitro validation of thrombin inhibition activity in crude protein

Thrombosis is characterized by the formation of clots in the blood vessels. Antithrombin-III deficiency in the blood causes thrombus formation. Supplementing antithrombin-III may serve as anticoagulant therapy. In the present studies, an antithrombin like Protein from Punica granatum has been identified and characterized using in silico approach. Based on sequence homology, an ALPP was selected depending upon its highest binding affinity of -41.28 kcal/mol with thrombin. Thrombin structure complexed with ALPP was docked with TAME using AutoDock Vina. No binding was observed for TAME at Ser195 of thrombin. MD simulation (50 ns) was performed to evaluate the flexibility and stability of docked complexes. In vitro assays with crude protein showed 78% thrombin inhibition at 5 µg and calculated IC50 value was 0.188 µg. The presence of thrombin inhibitors in crude protein was also confirmed by reverse zymography. Thus, it is very likely that the protein identified from P. granatum may act as thrombin inhibitor.

A Review of Quantitative Systems Pharmacology Models of the Coagulation Cascade: Opportunities for Improved Usability

Despite the numerous therapeutic options to treat bleeding or thrombosis, a comprehensive quantitative mechanistic understanding of the effects of these and potential novel therapies is lacking. Recently, the quality of quantitative systems pharmacology (QSP) models of the coagulation cascade has improved, simulating the interactions between proteases, cofactors, regulators, fibrin, and therapeutic responses under different clinical scenarios. We aim to review the literature on QSP models to assess the unique capabilities and reusability of these models. We systematically searched the literature and BioModels database reviewing systems biology (SB) and QSP models. The purpose and scope of most of these models are redundant with only two SB models serving as the basis for QSP models. Primarily three QSP models have a comprehensive scope and are systematically linked between SB and more recent QSP models. The biological scope of recent QSP models has expanded to enable simulations of previously unexplainable clotting events and the drug effects for treating bleeding or thrombosis. Overall, the field of coagulation appears to suffer from unclear connections between models and irreproducible code as previously reported. The reusability of future QSP models can improve by adopting model equations from validated QSP models, clearly documenting the purpose and modifications, and sharing reproducible code. The capabilities of future QSP models can improve from more rigorous validation by capturing a broader range of responses to therapies from individual patient measurements and integrating blood flow and platelet dynamics to closely represent in vivo bleeding or thrombosis risk.

Imaging and biophysical modelling of thrombogenic mechanisms in atrial fibrillation and stroke

Atrial fibrillation (AF) underlies almost one third of all ischaemic strokes, with the left atrial appendage (LAA) identified as the primary thromboembolic source. Current stroke risk stratification approaches, such as the CHA₂DS₂-VASc score, rely mostly on clinical comorbidities, rather than thrombogenic mechanisms such as blood stasis, hypercoagulability and endothelial dysfunction-known as Virchow's triad. While detection of AF-related thrombi is possible using established cardiac imaging techniques, such as transoesophageal echocardiography, there is a growing need to reliably assess AF-patient thrombogenicity prior to thrombus formation. Over the past decade, cardiac imaging and image-based biophysical modelling have emerged as powerful tools for reproducing the mechanisms of thrombogenesis. Clinical imaging modalities such as cardiac computed tomography, magnetic resonance and echocardiographic techniques can measure blood flow velocities and identify LA fibrosis (an indicator of endothelial dysfunction), but imaging remains limited in its ability to assess blood coagulation dynamics. In-silico cardiac modelling tools-such as computational fluid dynamics for blood flow, reaction-diffusion-convection equations to mimic the coagulation cascade, and surrogate flow metrics associated with endothelial damage-have grown in prevalence and advanced mechanistic understanding of thrombogenesis. However, neither technique alone can fully elucidate thrombogenicity in AF. In future, combining cardiac imaging with in-silico modelling and integrating machine learning approaches for rapid results directly from imaging data will require development under a rigorous framework of verification and clinical validation, but may pave the way towards enhanced personalised stroke risk stratification in the growing population of AF patients. This Review will focus on the significant progress in these fields.

Quantitative image analysis of thrombus formation in microfluidic in-vitro models

In this study, we present a method to quantitatively analyze the thrombus formation process through image analysis in an in vitro thrombus model with a circular cross section. The thrombus model used was designed based on the mechanism between the physical principle of wall shear rate (WSR) and thrombus formation. Image analysis was used to help visualize the thrombus formation process and calculate the thrombus area. Through this method, the thrombus formation and growth from the channel wall was demonstrated without the use of fluorescence. In addition, by dividing the image into sub-sections, the accuracy of the thrombus growth pattern was improved. The departing blood clots which are called embolus, were observed being separated from the thrombus.

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.

Continuum modeling of thrombus formation and growth under different shear rates

Obstruction of blood flow due to thrombosis is a major cause of ischemic stroke, myocardial infarction, and in severe cases, mortality. In particular, in blood wetting medical devices, thrombosis is a common reason for failure. The prediction of thrombosis by understanding signaling pathways using computational models, lead to identify the risk of thrombus formation in blood-contacting devices and design improvements. In this study, a mathematical model of thrombus formation and growth is presented. A biochemical model of platelet activation and aggregation is developed to predict thrombus size and shape at the site of vascular injury. Computational fluid dynamics using the finite volume method is employed to compute the velocity and pressure fields which are influenced by the growing thrombi. The passive transport of platelets, agonists, the platelet activation kinetics, their adhesion to the growing thrombi and embolization of platelets are solved by a fully coupled set of convection-diffusion-reaction equations. The thrombogenic surface representing blood-contacting material or injured blood vessel was incorporated into the model as a surface flux boundary condition to initiate thrombus formation. The blood is considered as a Newtonian fluid, while the thrombus is treated as a porous medium. The results are compared with in vitro experiments of a microfluidic chamber at an initial inlet venous shear rate of 200s^-1 using a pressure-inlet boundary condition. The thrombus development due to agonist concentrations and change in the shear rate as well as thromboembolism for this benchmark problem is successfully computed. Furthermore, to extend the current model to a physiologically relevant configuration, thrombus formation in a blood tube is simulated. Two different heterogeneous reaction rates for platelet aggregation are used to simulate thrombus growth under a constant inlet flow rate. The findings show that the thrombus shape can be substantially altered by the hemodynamic conditions, increase in the shear rate and due to the combined effects of shear induced platelet activation and the heterogeneous reaction rates. It is also concluded that the model is able to predict thrombus formation in different physiological and pathological hemodynamics.

A three-dimensional multiscale model for the prediction of thrombus growth under flow with single-platelet resolution

Modeling thrombus growth in pathological flows allows evaluation of risk under patient-specific pharmacological, hematological, and hemodynamical conditions. We have developed a 3D multiscale framework for the prediction of thrombus growth under flow on a spatially resolved surface presenting collagen and tissue factor (TF). The multiscale framework is composed of four coupled modules: a Neural Network (NN) that accounts for platelet signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. A reduced model of the coagulation cascade was embedded into the framework to account for TF-driven thrombin production. The 3D model was first tested against in vitro microfluidics experiments of whole blood perfusion with various antiplatelet agents targeting COX-1, P₂Y₁, or the IP receptor. The model was able to accurately capture the evolution and morphology of the growing thrombus. Certain problems of 2D models for thrombus growth (artifactual dendritic growth) were naturally avoided with realistic trajectories of platelets in 3D flow. The generalizability of the 3D multiscale solver enabled simulations of important clinical situations, such as cylindrical blood vessels and acute flow narrowing (stenosis). Enhanced platelet-platelet bonding at pathologically high shear rates (e.g., von Willebrand factor unfolding) was required for accurately describing thrombus growth in stenotic flows. Overall, the approach allows consideration of patient-specific platelet signaling and vascular geometry for the prediction of thrombotic episodes.

The excessive formation of blood clots under flow within the circulatory system (thrombosis) is known to initiate heart attacks and strokes. Therefore, obtaining insights into the formation and progression of these clots will be useful in evaluating pharmacological options. To this end, we have developed a 3D computational model that tracks the growth of a blood clot under flow from initial platelet deposition to full vessel occlusion in the presence of soluble platelet agonists. We first validated the model against experimental predictions of blood clots formed in vitro. Due to the construction of the model in 3D, we were able to carry out simulations of clot formation under important clinical situations, namely cylindrical blood vessels and acute flow narrowings (stenoses). To our knowledge, our model is the first of its kind that can account for patient-specific platelet phenotypes to perform robust 3D simulations of thrombus growth in geometries of clinical relevance.

Numerical modelling of blood rheology and platelet activation through a stenosed left coronary artery bifurcation

Coronary bifurcations are prone to atherosclerotic plaque growth, experiencing regions of reduced wall shear stress (WSS) and increased platelet adhesion. This study compares effects across different rheological approaches on hemodynamics, combined with a shear stress exposure history model of platelets within a stenosed porcine bifurcation. Simulations used both single/multiphase blood models to determine which approach best predicts phenomena associated with atherosclerosis and atherothrombosis. A novel Lagrangian platelet tracking model was used to evaluate residence time and shear history of platelets indicating likely regions of thrombus formation. Results show a decrease in area of regions with pathologically low time-averaged WSS with the use of multiphase models, particularly in a stenotic bifurcation. Significant non-Newtonian effects were observed due to low-shear and varying hematocrit levels found on the outer walls of the bifurcation and distal to the stenosis. Platelet residence time increased 11% in the stenosed artery, with exposure times to low-shear sufficient for red blood cell aggregation (>1.5 s). increasing the risk of thrombosis. This shows stenotic artery hemodynamics are inherently non-Newtonian and multiphase, with variations in hematocrit (0.163-0.617) and elevated vorticity distal to stenosis (+15%) impairing the function of the endothelium via reduced time-averaged WSS regions, rheological properties and platelet activation/adhesion.

Microstructure aware modeling of biochemical transport in arterial blood clots

Flow-mediated transport of biochemical species is central to thrombotic phenomena. Comprehensive three-dimensional modeling of flow-mediated transport around realistic macroscale thrombi poses challenges owing to their arbitrary heterogeneous microstructure. Here, we develop a microstructure aware model for species transport within and around a macroscale thrombus by devising a custom preconditioned fictitious domain formulation for thrombus-hemodynamics interactions, and coupling it with a fictitious domain advection-diffusion formulation for transport. Microstructural heterogeneities are accounted through a hybrid discrete particle-continuum approach for the thrombus interior. We present systematic numerical investigations on unsteady arterial flow within and around a three-dimensional macroscale thrombus; demonstrate the formation of coherent flow structures around the thrombus which organize advective transport; illustrate the role of the permeation processes at the thrombus boundary and subsequent intra-thrombus transport; and characterize species transport from bulk flow to the thrombus boundary and vice versa.

Particle hydrodynamic simulation of thrombus formation using velocity decay factor

BACKGROUND AND OBJECTIVE

Thrombus simulation plays an important role in many specialist areas in the field of medicine such as surgical education and training, clinical diagnosis and prediction, treatment planning, etc. Although a considerable number of methods have been developed to simulate various kinds of fluid flows, it remains a non-trivial task to effectively simulate thrombus because of its unique physiological properties in contrast to other types of fluids. To tackle this issue, this study introduces a novel method to model the formation mechanism of thrombus and its interaction with blood flow.

METHODS

The proposed method for thrombus formation simulation mainly consists of three steps. First, we formulate the formation of thrombus as a particle-based model and obtain the fibrin concentration of the particles with a discretized form of the convection-diffusion-reaction equation; then, we calculate the velocity decay factor using the obtained fibrin concentration. Finally, the formation of thrombus can be simulated by applying the velocity decay factor on particles.

RESULTS

We carried out extensive experiments under different settings to verify the efficacy of the proposed method. The experimental results demonstrate that our method can yield more realistic simulation of thrombus and is superior to peer method in terms of computational efficiency, maintaining the stability of the dynamic particle motion, and preventing particle penetration at the boundary.

CONCLUSION

The proposed method can simulate the formation mechanism of thrombus and the interaction between blood flow and thrombus both efficiently and effectively.

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.

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.

Injury Length and Arteriole Constriction Shape Clot Growth and Blood-Flow Acceleration in a Mouse Model of Thrombosis

OBJECTIVE

Quantitative relationships between the extent of injury and thrombus formation in vivo are not well understood. Moreover, it has not been investigated how increased injury severity translates to blood-flow modulation. Here, we investigated interconnections between injury length, clot growth, and blood flow in a mouse model of laser-induced thrombosis. Approach and Results: Using intravital microscopy, we analyzed 59 clotting events collected from the cremaster arteriole of 14 adult mice. We regarded injury length as a measure of injury severity. The injury caused transient constriction upstream and downstream of the injury site resulting in a 50% reduction in arteriole diameter. The amount of platelet accumulation and fibrin formation did not depend on arteriole diameter or deformation but displayed an exponentially increasing dependence on injury length. The height of the platelet clot depended linearly on injury length and the arteriole diameter. Upstream arteriolar constriction correlated with delayed upstream velocity increase, which, in turn, determined downstream velocity. Before clot formation, flow velocity positively correlated with the arteriole diameter. After the onset of thrombus growth, flow velocity at the injury site negatively correlated with the arteriole diameter and with the size of the above-clot lumen.

CONCLUSIONS

Injury severity increased platelet accumulation and fibrin formation in a persistently steep fashion and, together with arteriole diameter, defined clot height. Arterial constriction and clot formation were characterized by a dynamic change in the blood flow, associated with increased flow velocity.

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.

Recent advances in computational modeling of fibrin clot formation: A review

The field of thrombosis and hemostasis is crucial for understanding and developing new therapies for pathologies such as deep vein thrombosis, diabetes related strokes, pulmonary embolisms, and hemorrhaging related diseases. In the last two decades, an exponential growth in studies related to fibrin clot formation using computational tools has been observed. Despite this growth, the complete mechanism behind thrombus formation and hemostasis has been long and rife with obstacles; however, significant progress has been made in the present century. The computational models and methods used in this context are diversified into different spatiotemporal scales, yet there is no single model which can predict both physiological and mechanical properties of fibrin clots. In this review, we list the major strategies employed by researchers in modeling fibrin clot formation using recent and existing computational techniques. This review organizes the computational strategies into continuum level, system level, discrete particle (DPD), and multi-scale methods. We also discuss strengths and weaknesses of various methods and future directions in which computational modeling of fibrin clots can advance.

A density-dependent FEM-FCT algorithm with application to modeling platelet aggregation

Upon injury to a blood vessel, flowing platelets will aggregate at the injury site, forming a plug to prevent blood loss. Through a complex system of biochemical reactions, a stabilizing mesh forms around the platelet aggregate forming a blood clot that further seals the injury. Computational models of clot formation have been developed to a study intravascular thrombosis, where a vessel injury does not cause blood leakage outside the blood vessel but blocks blood flow. To model scenarios in which blood leaks from a main vessel out into the extravascular space, new computational tools need to be developed to handle the complex geometries that represent the injury. We have previously modeled intravascular clot formation under flow using a continuum approach wherein the transport of platelet densities into some spatial location is limited by the platelet fraction that already reside in that location, i.e., the densities satisfy a maximum packing constraint through the use of a hindered transport coefficient. To extend this notion to extravascular injury geometries, we have modified a finite element method flux-corrected transport (FEM-FCT) scheme by prelimiting antidiffusive nodal fluxes. We show that our modified scheme, under a variety of test problems, including mesh refinement, structured vs unstructured meshes, and for a range of reaction rates, produces numerical results that satisfy a maximum platelet-density packing constraint.

Microfluidic and computational study of structural properties and resistance to flow of blood clots under arterial shear

The ability of a blood clot to modulate blood flow is determined by the clot’s resistance, which depends on its structural features. For a flow with arterial shear, we investigated the characteristic patterns relating to clot shape, size, and composition on the one hand, and its viscous resistance, intraclot axial flow velocity, and shear distributions on the other. We used microfluidic technology to measure the kinetics of platelet, thrombin, and fibrin accumulation at a thrombogenic surface coated with collagen and tissue factor (TF), the key clot-formation trigger. We subsequently utilized the obtained data to perform additional calibration and validation of a detailed computational fluid dynamics model of spatial clot growth under flow. We then ran model simulations to gain insights into the resistance of clots formed under our experimental conditions. We found that increased thrombogenic surface length and TF surface density enhanced the bulk thrombin and fibrin generation in a nonadditive, synergistic way. The height of the platelet deposition domain—and, therefore, clot occlusivity—was rather robust to thrombogenic surface length and TF density variations, but consistently increased with time. Clot viscous resistance was non-uniform and tended to be higher in the fibrin-rich, inner “core” region of the clot. Interestingly, despite intraclot structure and viscous resistance variations, intraclot flow velocity variations were minor compared to the abrupt decrease in flow velocity around the platelet deposition region. Our results shed new light on the connection between the structure of clots under arterial shear and spatiotemporal variations in their resistance to flow.

In vivo measurement of blood clot mechanics from computational fluid dynamics based on intravital microscopy images

Ischemia which leads to heart attacks and strokes is one of the major causes of death in the world. Whether an occlusion occurs or not depends on the ability of a growing thrombus to resist flow forces exerted on its structure. This manuscript provides the first known in vivo measurement of how much stress a clot can withstand, before yielding to the surrounding blood flow. Namely, Lattice-Boltzmann Method flow simulations are performed based on 3D clot geometries, which are estimated from intravital microscopy images of laser-induced injuries in cremaster microvasculature of live mice. In addition to reporting the blood clot yield stresses, we also show that the thrombus "core" does not experience significant deformation, while its "shell" does. This indicates that the shell is more prone to embolization. Therefore, drugs should be designed to target the shell selectively, while leaving the core intact to minimize excessive bleeding. Finally, we laid down a foundation for a nondimensionalization procedure which unraveled a relationship between clot mechanics and biology. Hence, the proposed framework could ultimately lead to a unified theory of thrombogenesis, capable of explaining all clotting events. Thus, the findings presented herein will be beneficial to the understanding and treatment of heart attacks, strokes and hemophilia.

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.

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.

Computational Model for Hyperfibrinolytic Onset of Acute Traumatic Coagulopathy

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

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.

Molecular dynamics simulations indicate that deoxyhemoglobin, oxyhemoglobin, carboxyhemoglobin, and glycated hemoglobin under compression and shear exhibit an anisotropic mechanical behavior

We developed a new mechanical model for determining the compression and shear mechanical behavior of four different hemoglobin structures. Previous studies on hemoglobin structures have focused primarily on overall mechanical behavior; however, this study investigates the mechanical behavior of hemoglobin, a major constituent of red blood cells, using steered molecular dynamics (SMD) simulations to obtain anisotropic mechanical behavior under compression and shear loading conditions. Four different configurations of hemoglobin molecules were considered: deoxyhemoglobin (deoxyHb), oxyhemoglobin (HbO₂), carboxyhemoglobin (HbCO), and glycated hemoglobin (HbA_1C). The SMD simulations were performed on the hemoglobin variants to estimate their unidirectional stiffness and shear stiffness. Although hemoglobin is structurally denoted as a globular protein due to its spherical shape and secondary structure, our simulation results show a significant variation in the mechanical strength in different directions (anisotropy) and also a strength variation among the four different hemoglobin configurations studied. The glycated hemoglobin molecule possesses an overall higher compressive mechanical stiffness and shear stiffness when compared to deoxyhemoglobin, oxyhemoglobin, and carboxyhemoglobin molecules. Further results from the models indicate that the hemoglobin structures studied possess a soft outer shell and a stiff core based on stiffness.

Prediction of Thrombus Growth: Effect of Stenosis and Reynolds Number

Shear stresses play a major role in platelet-substrate interactions and thrombus formation and growth in blood flow, where under both pathological and physiological conditions platelet adhesion and accumulation occur. In this study, a shear-dependent continuum model for platelet activation, adhesion and aggregation is presented. The model was first verified under three different shear conditions and at two heparin levels. Three-dimensional simulations were then carried out to evaluate the performance of the model for severely damaged (stripped) aortas with mild and severe stenosis degrees in laminar flow regime. For these cases, linear shear-dependent functions were developed for platelet-surface and platelet-platelet adhesion rates. It was confirmed that the platelet adhesion rate is not only a function of Reynolds number (or wall shear rate) but also the stenosis severity of the vessel. General correlations for adhesion rates of platelets as functions of stenosis and Reynolds number were obtained based on these cases. Finally using the new platelet adhesion rates, the model was applied to different experimental systems and shown to agree well with measured platelet deposition.

Numerical Simulation of Thrombotic Occlusion in Tortuous Arterioles

Tortuous microvessels alter blood flow and stimulate thrombosis but the physical mechanisms are poorly understood. Both tortuous microvessels and abnormally large platelets are seen in diabetic patients. Thus, the objective of this study was to determine the physical effects of arteriole tortuosity and platelet size on the microscale processes of thrombotic occlusion in microvessels. A new lattice-Boltzmann method-based discrete element model was developed to simulate the fluid flow field with fluid-platelet coupling, platelet interactions, thrombus formation, and thrombotic occlusion in tortuous arterioles. Our results show that vessel tortuosity creates high shear stress zones that activate platelets and stimulate thrombus formation. The growth rate depends on the level of tortuosity and the pressure and flow boundary conditions. Once thrombi began to form, platelet collisions with thrombi and subsequent activations were more important than tortuosity level. Thrombus growth narrowed the channel and reduced the flow rate. Larger platelet size leads to quicker decrease of flow rate due to larger thrombi that occluded the arteriole. This study elucidated the important roles that tortuosity and platelet size play in thrombus formation and occlusion in arterioles.