Multiscale prediction of patient-specific platelet function under flow

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.

High-throughput assessment identifying major platelet Ca2+ entry pathways via tyrosine kinase-linked and G protein-coupled receptors

In platelets, elevated cytosolic Ca²⁺ is a crucial second messenger, involved in most functional responses, including shape change, secretion, aggregation and procoagulant activity. The platelet Ca²⁺ response consists of Ca²⁺ mobilization from endoplasmic reticulum stores, complemented with store-operated or receptor-operated Ca²⁺ entry pathways. Several channels can contribute to the Ca²⁺ entry, but their relative contribution is unclear upon stimulation of ITAM-linked receptors such as glycoprotein VI (GPVI) and G-protein coupled receptors such as the protease-activated receptors (PAR) for thrombin. We employed a 96-well plate high-throughput assay with Fura-2-loaded human platelets to perform parallel [Ca²⁺]_i measurements in the presence of EGTA or CaCl₂. Per agonist condition, this resulted in sets of EGTA, CaCl₂ and Ca²⁺ entry ratio curves, defined by six parameters, reflecting different Ca²⁺ ion fluxes. We report that threshold stimulation of GPVI or PAR, with a variable contribution of secondary mediators, induces a maximal Ca²⁺ entry ratio of 3-7. Strikingly, in combination with Ca²⁺-ATPase inhibition by thapsigargin, the maximal Ca²⁺ entry ratio increased to 400 (GPVI) or 40 (PAR), pointing to a strong receptor-dependent enhancement of store-operated Ca²⁺ entry. By pharmacological blockage of specific Ca²⁺ channels in platelets, we found that, regardless of GPVI or PAR stimulation, the Ca²⁺ entry ratio was strongest affected by inhibition of ORAI1 (2-APB, Synta66) > Na⁺/Ca²⁺ exchange (NCE) > P2×₁ (only initial). In contrast, inhibition of TRPC6, Piezo1/2 or STIM1 was without effect. Together, these data reveal ORAI1 and NCE as dominating Ca²⁺ carriers regulating GPVI- and PAR-induced Ca²⁺ entry in human platelets.

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.

Anti-GPVI Fab reveals distinct roles for GPVI signaling in the first platelet layer and subsequent layers during microfluidic clotting on collagen with or without tissue factor

The collagen receptor glycoprotein VI (GPVI) drives strong platelet activation, however its role at later stages of clotting remains less clear. Controlled timing of addition of anti-human GPVI Fab (clone E12) with microfluidic venous whole blood flow over collagen (± lipidated tissue factor, TF) produced distinct effects on platelets, fibrin, P-selectin exposure, and phosphatidylserine (PS) exposure. On collagen alone, Fab present initially potently reduced platelet deposition on collagen, while Fab added 90 s after initial platelet deposition, stopped subsequent platelet accumulation (despite the absence of fibrin). With thrombin generation via TF, Fab added at either t = 0 or 90 s had no effect on platelet deposition. However, Fab added initially, but not at 90-s, blocked fibrin formation. Gly-Pro-Arg-Pro ablated fibrin formation without effect on platelet accumulation (regardless of Fab added at t = 0 or 90 s), indicating thrombin signaling can suffice over GPVI signaling. Still, Fab moderately reduced P-selectin exposure with thrombin present and fibrin absent. On collagen/TF, Fab present initially ablated PS exposure, but had no effect when added 30 to 90-s later. The thrombin generated via PS exposure had an important role in driving platelet deposition in the presence of Fab, since inhibition of PS via annexin V binding in the presence of Fab significantly inhibited platelet deposition. We conclude GPVI signaling in the first platelet layer on collagen dictates thrombin and fibrin production, but the role of GPVI at subsequent times after formation of the first monolayer is obscured by thrombin-induced signaling.

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.

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.

Sensitivity analysis of a reduced model of thrombosis under flow: Roles of Factor IX, Factor XI, and γ'-Fibrin

A highly reduced extrinsic pathway coagulation model (8 ODEs) under flow considered a thin 15-micron platelet layer where transport limitations were largely negligible (except for fibrinogen) and where cofactors (FVIIa, FV, FVIII) were not rate-limiting. By including thrombin feedback activation of FXI and the antithrombin-I activities of fibrin, the model accurately simulated measured fibrin formation and thrombin fluxes. Using this reduced model, we conducted 10,000 Monte Carlo (MC) simulations for ±50% variation of 5 plasma zymogens and 2 fibrin binding sites for thrombin. A sensitivity analysis of zymogen concentrations indicated that FIX activity most influenced thrombin generation, a result expected from hemophilia A and B. Averaging all MC simulations confirmed both the mean and standard deviation of measured fibrin generation on 1 tissue factor (TF) molecule per μm2. Across all simulations, free thrombin in the layer ranged from 20 to 300 nM (mean: 50 nM). The top 2% of simulations that produced maximal fibrin were dominated by conditions with low antithrombin-I activity (decreased weak and strong sites) and high FIX concentration. In contrast, the bottom 2% of simulations that produced minimal fibrin were dominated by low FIX and FX. The percent reduction of fibrin by an ideal FXIa inhibitor (FXI = 0) ranged from 71% fibrin reduction in the top 2% of MC simulations to only 34% fibrin reduction in the bottom 2% of MC simulations. Thus, the antithrombotic potency of FXIa inhibitors may vary depending on normal ranges of zymogen concentrations. This reduced model allowed efficient multivariable sensitivity analysis.

Point of care whole blood microfluidics for detecting and managing thrombotic and bleeding risks

Point-of-care diagnostics of platelet and coagulation function present demanding challenges. Current clinical diagnostics often use centrifuged plasmas or platelets and frozen plasma standards, recombinant protein standards, or even venoms. Almost all commercialized tests of blood do not recreate the in vivo hemodynamics where platelets accumulate to high densities and thrombin is generated from a procoagulant surface. Despite numerous drugs that target platelets, insufficient coagulation, or excess coagulation, POC blood testing is essentially limited to viscoelastic methods that provide a clotting time, clot strength, and clot lysis, while used mostly in trauma centers with specialized capabilities. Microfluidics now allows small volumes of whole blood (<1 mL) to be tested under venous or arterial shear rates with multi-color readouts to follow platelet function, thrombin generation, fibrin production, and clot stability. Injection molded chips containing pre-patterned fibrillar collagen and lipidated tissue factor can be stored dry for 6 months at 4C, thus allowing rapid blood testing on single-use disposable chips. Using only a small imaging microscope and micropump, these microfluidic devices can detect platelet inhibitors, direct oral anticoagulants (DOACs) and their reversal agents. POC microfluidics are ideal for neonatal surgical applications that involve small blood samples, rapid DOAC testing in stroke or bleeding or emergency surgery situations with patients presenting high risk cofactors for either bleeding or thrombosis.

Multi-omics approaches for revealing the complexity of cardiovascular disease

The development and progression of cardiovascular disease (CVD) can mainly be attributed to the narrowing of blood vessels caused by atherosclerosis and thrombosis, which induces organ damage that will result in end-organ dysfunction characterized by events such as myocardial infarction or stroke. It is also essential to consider other contributory factors to CVD, including cardiac remodelling caused by cardiomyopathies and co-morbidities with other diseases such as chronic kidney disease. Besides, there is a growing amount of evidence linking the gut microbiota to CVD through several metabolic pathways. Hence, it is of utmost importance to decipher the underlying molecular mechanisms associated with these disease states to elucidate the development and progression of CVD. A wide array of systems biology approaches incorporating multi-omics data have emerged as an invaluable tool in establishing alterations in specific cell types and identifying modifications in signalling events that promote disease development. Here, we review recent studies that apply multi-omics approaches to further understand the underlying causes of CVD and provide possible treatment strategies by identifying novel drug targets and biomarkers. We also discuss very recent advances in gut microbiota research with an emphasis on how diet and microbial composition can impact the development of CVD. Finally, we present various biological network analyses and other independent studies that have been employed for providing mechanistic explanation and developing treatment strategies for end-stage CVD, namely myocardial infarction and stroke.

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.

Adrenaline May Contribute to Prothrombotic Condition via Augmentation of Platelet Procoagulant Response, Enhancement of Fibrin Formation, and Attenuation of Fibrinolysis

Background: Adrenaline is believed to play a role in thrombosis and hemostasis. The complex effect of its clinically relevant concentrations on thrombus formation, coagulation and fibrinolysis in human blood has never been specifically studied. Methods: Confocal microscopy was used to study thrombus formation under flow, exposure of phosphatidylserine (PS) in adhered platelets, to evaluate clots density, and to measure kinetics of fibrin formation and external fibrinolysis under flow. Flow cytometry was utilized to assess PS exposure in non-adhered platelets. Kinetics of clot formation and internal fibrinolysis was evaluated by thromboelastometry. Platelet aggregation was measured by optical aggremometry. Kinetics of clot retraction was assessed by using digital camera. Results: We found that adrenaline (1-10 nM) is able to enhance platelet activation evoked by subthreshold collagen (150 ng/ml), resulting in augmentation of platelet aggregation, thrombus formation under arterial flow conditions, platelet PS exposure, and formation of platelet-fibrin clots. The development of platelet procoagulant response evoked by adrenaline + low collagen was associated with the formation of denser platelet-fibrin clots and the decrease in rate of fibrinolysis despite whether lysis was initiated inside (internal fibrinolysis) or outside the clot (external fibrinolysis). The above phenomena were abolished by the α₂-adrenergic receptor antagonist, rauwolscine. Adrenaline-collagen synergism, expressed as PS exposure, was significantly reduced by cyclooxygenase inhibitor (acetylsalicic acid), GPIIb/IIIa receptor blocker (tirofiban), and P2Y₁₂ receptor antagonist (PSB 0739). Conclusion: Clinically relevant concentrations of adrenaline may significantly augment responses of human platelets in the presence of subthreshold concentrations of collagen, which should be considered during therapies involving adrenaline infusion. Routinely used antiplatelet drugs may reduce the prothrombotic state evoked by adrenaline-collagen synergism.

Influence of shear rate and surface chemistry on thrombus formation in micro-crevice

Thromboembolic complications remain a central issue in management of patients on mechanical circulatory support. Despite the best practices employed in design and manufacturing of modern ventricular assist devices, complexity and modular nature of these systems often introduces internal steps and crevices in the flow path which can serve as nidus for thrombus formation. Thrombotic potential is influenced by multiple factors including the characteristics of the flow and surface chemistry of the biomaterial. This study explored these elements in the setting of blood flow over a micro-crevice using a multi-constituent numerical model of thrombosis. The simulations reproduced the platelet deposition patterns observed experimentally and elucidated the role of flow, shear rate, and surface chemistry in shaping the deposition. The results offer insights for design and operation of blood-contacting devices.

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.

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).

An Introductory Overview of Image-Based Computational Modeling in Personalized Cardiovascular Medicine

Cardiovascular diseases account for the number one cause of deaths in the world. Part of the reason for such grim statistics is our limited understanding of the underlying mechanisms causing these devastating pathologies, which is made difficult by the invasiveness of the procedures associated with their diagnosis (e.g., inserting catheters into the coronal artery to measure blood flow to the heart). Likewise, it is also difficult to design and test assistive devices without implanting them in vivo. However, with the recent advancements made in biomedical scanning technologies and computer simulations, image-based modeling (IBM) has arisen as the next logical step in the evolution of non-invasive patient-specific cardiovascular medicine. Yet, due to its novelty, it is still relatively unknown outside of the niche field. Therefore, the goal of this manuscript is to review the current state-of-the-art and the limitations of the methods used in this area of research, as well as their applications to personalized cardiovascular investigations and treatments. Specifically, the modeling of three different physics – electrophysiology, biomechanics and hemodynamics – used in the cardiovascular IBM is discussed in the context of the physiology that each one of them describes and the mechanisms of the underlying cardiac diseases that they can provide insight into. Only the “bare-bones” of the modeling approaches are discussed in order to make this introductory material more accessible to an outside observer. Additionally, the imaging methods, the aspects of the unique cardiac anatomy derived from them, and their relation to the modeling algorithms are reviewed. Finally, conclusions are drawn about the future evolution of these methods and their potential toward revolutionizing the non-invasive diagnosis, virtual design of treatments/assistive devices, and increasing our understanding of these lethal cardiovascular diseases.

Clot Permeability, Agonist Transport, and Platelet Binding Kinetics in Arterial Thrombosis

The formation of wall-adherent platelet aggregates is a critical process in arterial thrombosis. A growing aggregate experiences frictional drag forces exerted on it by fluid moving over or through the aggregate. The magnitude of these forces is strongly influenced by the permeability of the developing aggregate; the permeability depends on the aggregate's porosity. Aggregation is mediated by formation of ensembles of molecular bonds; each bond involves a plasma protein bridging the gap between specific receptors on the surfaces of two different platelets. The ability of the bonds existing at any time to sustain the drag forces on the aggregate determines whether it remains intact or sheds individual platelets or larger fragments (emboli). We investigate platelet aggregation in coronary-sized arteries using both computational simulations and in vitro experiments. The computational model tracks the formation and breaking of bonds between platelets and treats the thrombus as an evolving porous, viscoelastic material, which moves differently from the background fluid. This relative motion generates drag forces which the fluid and thrombus exert on one another. These forces are computed from a permeability-porosity relation parameterized from experimental measurements. Basing this relation on measurements from occlusive thrombi formed in our flow chamber experiments, along with other physiological parameter values, the model produced stable dense thrombi on a similar timescale to the experiments. When we parameterized the permeability-porosity relation using lower permeabilities reported by others, bond formation was insufficient to balance drag forces on an early thrombus and keep it intact. Under high shear flow, soluble agonist released by platelets was limited to the thrombus and a boundary layer downstream, thus restricting thrombus growth into the vessel lumen. Adding to the model binding and activation of unactivated platelets through von Willebrand-factor-mediated processes allowed greater growth and made agonist-induced activation more effective.

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.

Predictive modelling of thrombus formation in diabetic retinal microaneurysms

Microaneurysms (MAs) are one of the earliest clinically visible signs of diabetic retinopathy (DR). Vision can be reduced at any stage of DR by MAs, which may enlarge, rupture and leak fluid into the neural retina. Recent advances in ophthalmic imaging techniques enable reconstruction of the geometries of MAs and quantification of the corresponding haemodynamic metrics, such as shear rate and wall shear stress, but there is lack of computational models that can predict thrombus formation in individual MAs. In this study, we couple a particle model to a continuum model to simulate the platelet aggregation in MAs with different shapes. Our simulation results show that under a physiologically relevant blood flow rate, thrombosis is more pronounced in saccular-shaped MAs than fusiform-shaped MAs, in agreement with recent clinical findings. Our model predictions of the size and shape of the thrombi in MAs are consistent with experimental observations, suggesting that our model is capable of predicting the formation of thrombus for newly detected MAs. This is the first quantitative study of thrombosis in MAs through simulating platelet aggregation, and our results suggest that computational models can be used to predict initiation and development of intraluminal thrombus in MAs as well as provide insights into their role in the pathophysiology of DR.

Platelet dysfunction during trauma involves diverse signaling pathways and an inhibitory activity in patient-derived plasma

BACKGROUND

Trauma-induced coagulopathy occurs in about 25% of injured patients and accounts for about 10% of deaths worldwide. Upon injury, hemostatic function may decline due to vascular dysfunction, clotting factor deficiencies, hyperfibrinolysis, and/or platelet dysfunction. We investigated agonist-induced calcium signaling in platelets obtained over time from trauma patients.

METHODS

Platelets from trauma patients and healthy donors were monitored via intracellular calcium mobilization and flow cytometry markers (α2bβ3 activation, P-selectin display, and phosphatidylserine exposure) following stimulation with a panel of agonists (adenosine 5'-diphosphate sodium salt, U46619, convulxin, PAR-1/4 activating peptides, iloprost) used in isolation or in pairwise tests. Furthermore, healthy donor platelets were tested in heterologous plasma isolated from healthy subjects and trauma patients.

RESULTS

When exposed to agonists over the first 24 hours postinjury, trauma patient platelets mobilized less calcium in comparison to healthy platelets. Partial recovery of platelet activity was observed in about a third of patients after 120 hours, although not fully obtaining healthy baseline function. Flow cytometry markers of trauma platelets were similar to healthy platelets prior to stimulation, but were depressed in trauma platelets stimulated with adenosine 5'-diphosphate sodium salt or convulxin. Also, washed healthy platelets showed a significant reduction in calcium mobilization when reconstituted in plasma from trauma patients, relative to healthy plasma, at all plasma doses tested.

CONCLUSION

Platelet dysfunction in trauma patients included poor response to multiple agonists relevant to hemostatic function. Furthermore, the inhibitor effect of patient plasma on healthy platelets suggests that soluble plasma species may downregulate endogenous or transfused platelets during trauma.

A three-dimensional phase-field model for multiscale modeling of thrombus biomechanics in blood vessels

Mechanical interactions between flowing and coagulated blood (thrombus) are crucial in dictating the deformation and remodeling of a thrombus after its formation in hemostasis. We propose a fully-Eulerian, three-dimensional, phase-field model of thrombus that is calibrated with existing in vitro experimental data. This phase-field model considers spatial variations in permeability and material properties within a single unified mathematical framework derived from an energy perspective, thereby allowing us to study effects of thrombus microstructure and properties on its deformation and possible release of emboli under different hemodynamic conditions. Moreover, we combine this proposed thrombus model with a particle-based model which simulates the initiation of the thrombus. The volume fraction of a thrombus obtained from the particle simulation is mapped to an input variable in the proposed phase-field thrombus model. The present work is thus the first computational study to integrate the initiation of a thrombus through platelet aggregation with its subsequent viscoelastic responses to various shear flows. This framework can be informed by clinical data and potentially be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions.

Heterogeneity of Integrin αIIbβ3 Function in Pediatric Immune Thrombocytopenia Revealed by Continuous Flow Cytometry Analysis

Immune thrombocytopenia (ITP) is an autoimmune condition primarily induced by the loss of immune tolerance to the platelet glycoproteins. Here we develop a novel flow cytometry approach to analyze integrin α_IIbβ₃ functioning in ITP in comparison with Glanzmann thrombasthenia (GT) (negative control) and healthy pediatric donors (positive control). Continuous flow cytometry of Fura-Red-loaded platelets from whole hirudinated blood was used for the characterization of platelet responses to conventional activators. Calcium levels and fibrinogen binding were normalized to ionomycin-induced responses. Ex vivo thrombus formation on collagen was observed in parallel-plate flow chambers. Platelets from all ITP patients had significantly higher cytosolic calcium concentration in the quiescent state compared to healthy donors (15 ± 5 nM vs. 8 ± 5 nM), but calcium increases in response to all activators were normal. Clustering analysis revealed two subpopulations of ITP patients: the subgroup with high fibrinogen binding (HFB), and the subgroup with low fibrinogen binding (LFB) (8% ± 5% for LFB vs. 16% ± 3% for healthy donors in response to ADP). GT platelets had calcium mobilization (81 ± 23 nM), fibrinogen binding (5.1% ± 0.3%) and thrombus growth comparable to the LFB subgroup. Computational modeling suggested phospholipase C-dependent platelet pre-activation for the HFB subgroup and lower levels of functional integrin molecules for the LFB group.

Simulation of thrombosis in a stenotic microchannel: The effects of vWF-enhanced shear activation of platelets

This study was undertaken to develop a numerical/computational simulation of von Willebrand Factor (vWF) - mediated platelet shear activation and deposition in an idealized stenosis. Blood is treated as a multi-constituent mixture comprised of a linear fluid component and a porous solid component (thrombus). Chemical and biological species involved in coagulation are modeled using a system of coupled convection-reaction-diffusion (CRD) equations. This study considers the cumulative effect of shear stress (history) on platelet activation. The vWF activity is modeled as an enhancement function for the shear stress accumulation and is related to the experimentally-observed unfolding rate of vWF. A series of simulations were performed in an idealized stenosis in which the predicted platelets deposition agreed well with previous experimental observations spatially and temporally, including the reduction of platelet deposition with decreasing expansion angle. Further simulation indicated a direct relationship between vWF-mediated platelet deposition and degree of stenosis. Based on the success with these benchmark simulations, it is hoped that the model presented here may provide additional insight into vWF-mediated thrombosis and prove useful for the development of more hemo-compatible blood-wetted devices in the future.

Reduced model to predict thrombin and fibrin during thrombosis on collagen/tissue factor under venous flow: Roles of γ'-fibrin and factor XIa

During thrombosis, thrombin generates fibrin, however fibrin reversibly binds thrombin with low affinity E-domain sites (K_D = 2.8 μM) and high affinity γ’-fibrin sites (K_D = 0.1 μM). For blood clotting on collagen/tissue factor (1 TF-molecule/μm²) at 200 s^-1 wall shear rate, high μM-levels of intraclot thrombin suggest robust prothrombin penetration into clots. Setting intraclot zymogen concentrations to plasma levels (and neglecting cofactor rate limitations) allowed the linearization of 7 Michaelis-Menton reactions between 6 species to simulate intraclot generation of: Factors FXa (via TF/VIIa or FIXa), FIXa (via TF/FVIIa or FXIa), thrombin, fibrin, and FXIa. This reduced model [7 rates, 2 K_D’s, enzyme half-lives~1 min] predicted the measured clot elution rate of thrombin-antithrombin (TAT) and fragment F1.2 in the presence and absence of the fibrin inhibitor Gly-Pro-Arg-Pro. To predict intraclot fibrin reaching 30 mg/mL by 15 min, the model required fibrinogen penetration into the clot to be strongly diffusion-limited (actual rate/ideal rate = 0.05). The model required free thrombin in the clot (~100 nM) to have an elution half-life of ~2 sec, consistent with measured albumin elution, with most thrombin (>99%) being fibrin-bound. Thrombin-feedback activation of FXIa became prominent and reached 5 pM FXIa at >500 sec in the simulation, consistent with anti-FXIa experiments. In predicting intrathrombus thrombin and fibrin during 15-min microfluidic experiments, the model revealed “cascade amplification” from 30 pM levels of intrinsic tenase to 15 nM prothrombinase to 15 μM thrombin to 90 μM fibrin. Especially useful for multiscale simulation, this reduced model predicts thrombin and fibrin co-regulation during thrombosis under flow.

During blood clotting events, a complex series of reaction are involved. Simulation gives insights to the concentration of different enzymes which are at too low of concentration to be detected. However, the models are often large and difficult to solve for clotting under flow conditions. With a thin film approximation, we were able to simplify clotting under flow with parameters from literature, with only 3 adjusted in order to fit the experimental data. This model gave insights into the dynamics of the species involved, and the roles of γ’-fibrin and thrombin feedback activation. This reduced model may be useful in further multiscale simulations.

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.

A synthesis approach of mouse studies to identify genes and proteins in arterial thrombosis and bleeding

Antithrombotic therapies reduce cardiovascular diseases by preventing arterial thrombosis and thromboembolism, but at expense of increased bleeding risks. Arterial thrombosis studies using genetically modified mice have been invaluable for identification of new molecular targets. Because of low sample sizes and heterogeneity in approaches or methodologies, a formal meta-analysis to compare studies of mice with single-gene defects encountered major limitations. To overcome these, we developed a novel synthesis approach to quantitatively scale 1514 published studies of arterial thrombus formation (in vivo and in vitro), thromboembolism, and tail-bleeding of genetically modified mice. Using a newly defined consistency parameter (CP), indicating the strength of published data, comparisons were made of 431 mouse genes, of which 17 consistently contributed to thrombus formation without affecting hemostasis. Ranking analysis indicated high correlations between collagen-dependent thrombosis models in vivo (FeCl3 injury or ligation/compression) and in vitro. Integration of scores and CP values resulted in a network of protein interactions in thrombosis and hemostasis (PITH), which was combined with databases of genetically linked human bleeding and thrombotic disorders. The network contained 2946 nodes linked to modifying genes of thrombus formation, mostly with expression in megakaryocytes. Reactome pathway analysis and network characteristics revealed multiple novel genes with potential contribution to thrombosis/hemostasis. Studies with additional knockout mice revealed that 4 of 8 (Apoe, Fpr2, Ifnar1, Vps13a) new genes were modifying in thrombus formation. The PITH network further: (i) revealed a high similarity of murine and human hemostatic and thrombotic processes and (ii) identified multiple new candidate proteins regulating these processes.

High-throughput elucidation of thrombus formation reveals sources of platelet function variability

In combination with microspotting, whole-blood microfluidics can provide high-throughput information on multiple platelet functions in thrombus formation. Based on assessment of the inter- and intra-subject variability in parameters of microspot-based thrombus formation, we aimed to determine the platelet factors contributing to this variation. Blood samples from 94 genotyped healthy subjects were analyzed for conventional platelet phenotyping: i.e. hematologic parameters, platelet glycoprotein (GP) expression levels and activation markers (24 parameters). Furthermore, platelets were activated by ADP, CRP-XL or TRAP. Parallel samples were investigated for whole-blood thrombus formation (6 microspots, providing 48 parameters of adhesion, aggregation and activation). Microspots triggered platelet activation through GP Ib-V-IX, GPVI, CLEC-2 and integrins. For most thrombus parameters, inter-subject variation was 2-4 times higher than the intra-subject variation. Principal component analyses indicated coherence between the majority of parameters for the GPVI-dependent microspots, partly linked to hematologic parameters, and glycoprotein expression levels. Prediction models identified parameters per microspot that were linked to variation in agonist-induced α_IIbβ₃ activation and secretion. Common sequence variation of GP6 and FCER1G, associated with GPVI-induced α_IIbβ₃ activation and secretion, affected parameters of GPVI-and CLEC-2-dependent thrombus formation. Subsequent analysis of blood samples from patients with Glanzmann thrombasthenia or storage pool disease revealed thrombus signatures of aggregation-dependent parameters that were subject-dependent, but not linked to GPVI activity. Taken together, this high-throughput elucidation of thrombus formation revealed patterns of inter-subject differences in platelet function, which were partly related to GPVI-induced activation and common genetic variance linked to GPVI, but also included a distinct platelet aggregation component.

Multiscale simulation of thrombus growth and vessel occlusion triggered by collagen/tissue factor using a data-driven model of combinatorial platelet signalling

During clotting under flow, platelets bind and activate on collagen and release autocrinic factors such as ADP and thromboxane, while tissue factor (TF) on the damaged wall leads to localized thrombin generation. Towards patient-specific simulation of thrombosis, a multiscale approach was developed to account for: platelet signalling [neural network (NN) trained by pairwise agonist scanning (PAS), PAS-NN], platelet positions (lattice kinetic Monte Carlo, LKMC), wall-generated thrombin and platelet-released ADP/thromboxane convection–diffusion (partial differential equation, PDE) and flow over a growing clot (lattice Boltzmann). LKMC included shear-driven platelet aggregate restructuring. The PDEs for thrombin, ADP and thromboxane were solved by finite element method using cell activation-driven adaptive triangular meshing. At all times, intracellular calcium was known for each platelet by PAS-NN in response to its unique exposure to local collagen, ADP, thromboxane and thrombin. When compared with microfluidic experiments of human blood clotting on collagen/TF driven by constant pressure drop, the model accurately predicted clot morphology and growth with time. In experiments and simulations at TF at 0.1 and 10 molecule-TF/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mu$\end{document}m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$^{2}$\end{document} and initial wall shear rate of 200 s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$^{-1}$\end{document}, the occlusive blockade of flow for a 60-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mu$\end{document}m channel occurred relatively abruptly at 600 and 400 s, respectively (with no occlusion at zero TF). Prior to occlusion, intrathrombus concentrations reached 50 nM thrombin, ~ 1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mu$\end{document}M thromboxane and ~ 10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$\mu$\end{document}M ADP, while the wall shear rate on the rough clot peaked at ~ 1000–2000 s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$^{-1}$\end{document}. Additionally, clotting on TF/collagen was accurately simulated for modulators of platelet cyclooxygenase-1, P2Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$_{1}$\end{document} and IP-receptor. This multiscale approach facilitates patient-specific simulation of thrombosis under hemodynamic and pharmacological conditions.

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.

Contact Pathway Function During Human Whole Blood Clotting on Procoagulant Surfaces

Microfluidic thrombosis assays allow the control of anticoagulation, hemodynamics, pharmacology, and procoagulant surfaces containing collagen ± tissue factor (TF). With corn trypsin inhibitor (CTI) ranging from low (1–4 μg/mL) to high levels (40–60 μg/mL), the function of Factor XIIa (FXIIa) can be modulated in the presence of low or high surface TF. With high CTI and no collagen/TF in the assay, no thrombin is generated during 15-min microfluidic perfusion. At low CTI (no TF), the generation of FXIa leads to fibrin polymerization at ~300 s after the initiation of flow over collagen, an onset time shortened at zero CTI and prolonged at high CTI. The engagement of FXIa was difficult to observe for clotting on high TF surfaces due to the dominance of the extrinsic pathway. Low TF surfaces allowed observable crosstalk between extrinsic pathway generation of thrombin and thrombin-mediated activation of FXIa, a feedback detected at >5 min and attenuated with polyphosphate inhibitor. From thrombin-antithrombin immunoassay of the effluent of blood flowing over collagen/TF, the majority of thrombin was found captured on intrathrombus fibrin. Additionally, extreme shear rates (>10,000 s⁻¹) can generate massive von Willebrand Factor fibers that capture FXIIa and FXIa to drive fibrin generation, an event that facilitates VWF fiber dissolution under fibrinolytic conditions. Finally, we found that occlusive sterile thrombi subjected to pressure drops >70 mm-Hg/mm-clots have interstitial stresses sufficient to drive NETosis. These microfluidic studies highlight the interaction of contact pathway factors with the extrinsic pathway, platelet polyphosphate, VWF fibers, and potentially shear-induced NETs.

Deposition of sticky spheres in channel flow: Modeling of surface coverage evolution requires accurate sphere-sphere collision hydrodynamics

We analyzed the role of hydrodynamic interactions in a microfluidic channel flow containing a dilute suspension of micron-scale colloidal spheres (0.03%, 0.1%, 0.3% volume fraction) engineered to adhere onto a collector patch on the channel wall at wall shear rates of 9.3-930 s^-1. Particle-wall adhesion was mediated by single-stranded DNA oligomers grafted onto the spheres and the glass channel wall, producing well-defined interactions via DNA strand base pairing. Particle positions in the flow were evolved using Brownian dynamics simulations in which hydrodynamic interactions between moving particles and the channel walls and/or adhered particles were computed off-line using a series of local simulations that explicitly resolve the fluid flow at the particle scale. By systematically varying the nature of hydrodynamic interactions captured in the Brownian dynamics simulations, we find that the interactions between moving and adhered particles represents the single most important physical element in such models. Once captured sufficiently accurately, the resulting models are able to predict coarse variables such as the overall particle coverage evolution, as well as more subtle characteristics, such as the microstructural distribution of the adhered particles.

Platelet packing density is an independent regulator of the hemostatic response to injury

Essentials Platelet packing density in a hemostatic plug limits molecular movement to diffusion. A diffusion-dependent steep thrombin gradient forms radiating outwards from the injury site. Clot retraction affects the steepness of the gradient by increasing platelet packing density. Together, these effects promote hemostatic plug core formation and inhibit unnecessary growth.

SUMMARY

Background Hemostasis studies performed in vivo have shown that hemostatic plugs formed after penetrating injuries are characterized by a core of highly activated, densely packed platelets near the injury site, covered by a shell of less activated and loosely packed platelets. Thrombin production occurs near the injury site, further activating platelets and starting the process of platelet mass retraction. Tightening of interplatelet gaps may then prevent the escape and exchange of solutes. Objectives To reconstruct the hemostatic plug macro- and micro-architecture and examine how platelet mass contraction regulates solute transport and solute concentration in the gaps between platelets. Methods Our approach consisted of three parts. First, platelet aggregates formed in vitro under flow were analyzed using scanning electron microscopy to extract data on porosity and gap size distribution. Second, a three-dimensional (3-D) model was constructed with features matching the platelet aggregates formed in vitro. Finally, the 3-D model was integrated with volume and morphology measurements of hemostatic plugs formed in vivo to determine how solutes move within the platelet plug microenvironment. Results The results show that the hemostatic mass is characterized by extremely narrow gaps, porosity values even smaller than previously estimated and stagnant plasma velocity. Importantly, the concentration of a chemical species released within the platelet mass increases as the gaps between platelets shrink. Conclusions Platelet mass retraction provides a physical mechanism to establish steep chemical concentration gradients that determine the extent of platelet activation and account for the core-and-shell architecture observed in vivo.

Thrombosis in Cerebral Aneurysms and the Computational Modeling Thereof: A Review

Thrombosis is a condition closely related to cerebral aneurysms and controlled thrombosis is the main purpose of endovascular embolization treatment. The mechanisms governing thrombus initiation and evolution in cerebral aneurysms have not been fully elucidated and this presents challenges for interventional planning. Significant effort has been directed towards developing computational methods aimed at streamlining the interventional planning process for unruptured cerebral aneurysm treatment. Included in these methods are computational models of thrombus development following endovascular device placement. The main challenge with developing computational models for thrombosis in disease cases is that there exists a wide body of literature that addresses various aspects of the clotting process, but it may not be obvious what information is of direct consequence for what modeling purpose (e.g., for understanding the effect of endovascular therapies). The aim of this review is to present the information so it will be of benefit to the community attempting to model cerebral aneurysm thrombosis for interventional planning purposes, in a simplified yet appropriate manner. The paper begins by explaining current understanding of physiological coagulation and highlights the documented distinctions between the physiological process and cerebral aneurysm thrombosis. Clinical observations of thrombosis following endovascular device placement are then presented. This is followed by a section detailing the demands placed on computational models developed for interventional planning. Finally, existing computational models of thrombosis are presented. This last section begins with description and discussion of physiological computational clotting models, as they are of immense value in understanding how to construct a general computational model of clotting. This is then followed by a review of computational models of clotting in cerebral aneurysms, specifically. Even though some progress has been made towards computational predictions of thrombosis following device placement in cerebral aneurysms, many gaps still remain. Answering the key questions will require the combined efforts of the clinical, experimental and computational communities.

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.

Multiscale systems biology of trauma-induced coagulopathy

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

Mathematical Techniques for Understanding Platelet Regulation and the Development of New Pharmacological Approaches

Mathematical and computational modeling is currently in the process of becoming an accepted tool in the arsenal of methods utilized for the investigation of complex biological systems. For some problems in the field, like cellular metabolic regulation, neural impulse propagation, or cell cycle, progress is already unthinkable without use of such methods. Mathematical models of platelet signaling, function, and metabolism during the last years have not only been steadily increasing in their number, but have also been providing more in-depth insights, generating hypotheses, and allowing predictions to be made leading to new experimental designs and data. Here we describe the basic approaches to platelet mathematical model development and validation, highlighting the challenges involved. We then review the current theoretical models in the literature and how these are being utilized to increase our understanding of these complex cells.

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

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

A review of computational and mathematical modeling contributions to our understanding of Mycobacterium tuberculosis within-host infection and treatment

Tuberculosis (TB) is an ancient and deadly disease characterized by complex host-pathogen dynamics playing out over multiple time and length scales and physiological compartments. Computational modeling can be used to integrate various types of experimental data and suggest new hypotheses, mechanisms, and therapeutic approaches to TB. Here, we offer a first-time comprehensive review of work on within-host TB models that describe the immune response of the host to infection, including the formation of lung granulomas. The models include systems of ordinary and partial differential equations and agent-based models as well as hybrid and multi-scale models that are combinations of these. Many aspects of M. tuberculosis infection, including host dynamics in the lung (typical site of infection for TB), granuloma formation, roles of cytokine and chemokine dynamics, and bacterial nutrient availability have been explored. Finally, we survey applications of these within-host models to TB therapy and prevention and suggest future directions to impact this global disease.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Systems Analysis of Thrombus Formation

The systems analysis of thrombosis seeks to quantitatively predict blood function in a given vascular wall and hemodynamic context. Relevant to both venous and arterial thrombosis, a Blood Systems Biology approach should provide metrics for rate and molecular mechanisms of clot growth, thrombotic risk, pharmacological response, and utility of new therapeutic targets. As a rapidly created multicellular aggregate with a polymerized fibrin matrix, blood clots result from hundreds of unique reactions within and around platelets propagating in space and time under hemodynamic conditions. Coronary artery thrombosis is dominated by atherosclerotic plaque rupture, complex pulsatile flows through stenotic regions producing high wall shear stresses, and plaque-derived tissue factor driving thrombin production. In contrast, venous thrombosis is dominated by stasis or depressed flows, endothelial inflammation, white blood cell-derived tissue factor, and ample red blood cell incorporation. By imaging vessels, patient-specific assessment using computational fluid dynamics provides an estimate of local hemodynamics and fractional flow reserve. High-dimensional ex vivo phenotyping of platelet and coagulation can now power multiscale computer simulations at the subcellular to cellular to whole vessel scale of heart attacks or strokes. In addition, an integrated systems biology approach can rank safety and efficacy metrics of various pharmacological interventions or clinical trial designs.

Computer modeling of ischemic stroke

The occlusion of a blood vessel in the brain causes an ischemic stroke. Current treatment relies restoration of blood flow within 3 hours. Substantial research has focused on neuroprotection to spare compromised neural tissue and extend the treatment time window. Despite success with animal models and extensive associated clinical testing, there are still no therapies of this kind. Ischemic stroke is fundamentally a multiscale phenomenon where a cascade of changes triggered by loss of blood flow involves processes at spatial scales from molecular to centimeters with damage occurring in milliseconds to days and recovery into years. Multiscale computational modeling is a technique to assist understanding of the many agents involved in these multitudinous interacting pathways to provide clues for in silico development of multi-target polypharmacy drug cocktails.

Multi-Constituent Simulation of Thrombus Deposition

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

Microfluidic whole blood testing of platelet response to pharmacological agents

Platelets present a number of intracellular and transmembrane targets subject to pharmacological modulation, either for cardiovascular disease reduction or as an unintended drug response. Microfluidic devices allow human blood to clot on a defined surface under controlled hemodynamic and pharmacological conditions. The potencies of a number of antiplatelet and anticancer drugs have been tested with respect to platelet deposition on collagen under flow. Inhibitors of cyclooxygenase-1 (COX-1) reduce platelet deposition, either when added ex vivo to blood or ingested orally by patients prior to testing. Some individuals display a functional "aspirin-insensitivity" in microfluidic assay. When certain nonsteroidal anti-inflammatory drugs (NSAIDs) are taken orally, they block COX-1 acetylation by aspirin with concomitant reduction of aspirin efficacy against platelets in microfluidic assay. Both P2Y₁ and P2Y₁₂ inhibitors reduce platelet deposition under flow, as do NO donors and iloprost that target the guanylate cyclase and the prostacyclin receptor, respectively. In a microfluidic assay of 37 kinase inhibitors, dasatinib had potent antiplatelet activity, while bosutinib was less potent. Dasatinib and bosutinib have known profiles against numerous kinases, revealing overlapping and nonoverlapping activities relevant to their unique actions against platelets. Also, dasatinib caused a marked and specific inhibition of GPVI signaling induced by convulxin, consistent with a dasatinib-associated bleeding risk. Microfluidic devices facilitate drug library screening, dose-response testing, and drug-drug interaction studies. Kinase inhibitors developed as anticancer agents may present antiplatelet activities that are detectable by microfluidic assay and potentially linked to bleeding risks.

A General Shear-Dependent Model for Thrombus Formation

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

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

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.

Analysis of the lattice kinetic Monte Carlo method in systems with external fields

The lattice kinetic Monte Carlo (LKMC) method is studied in the context of Brownian particles subjected to drift forces, here principally represented by external fluid flow. LKMC rate expressions for particle hopping are derived that satisfy detailed balance at equilibrium while also providing correct dynamical trajectories in advective-diffusive situations. Error analyses are performed for systems in which collections of particles undergo Brownian motion while also being advected by plug and parabolic flows. We demonstrate how the flow intensity, and its associated drift force, as well as its gradient, each impact the accuracy of the method in relation to reference analytical solutions and Brownian dynamics simulations. Finally, we show how a non-uniform grid that everywhere retains full microscopic detail may be employed to increase the computational efficiency of lattice kinetic Monte Carlo simulations of particles subjected to drift forces arising from the presence of external fields.