Platelet adhesive dynamics. Part I: characterization of platelet hydrodynamic collisions and wall effects

Platelet Biorheology and Mechanobiology in Thrombosis and Hemostasis: Perspectives from Multiscale Computation

Thrombosis is the pathological clot formation under abnormal hemodynamic conditions, which can result in vascular obstruction, causing ischemic strokes and myocardial infarction. Thrombus growth under moderate to low shear (<1000 s-1) relies on platelet activation and coagulation. Thrombosis at elevated high shear rates (>10,000 s-1) is predominantly driven by unactivated platelet binding and aggregating mediated by von Willebrand factor (VWF), while platelet activation and coagulation are secondary in supporting and reinforcing the thrombus. Given the molecular and cellular level information it can access, multiscale computational modeling informed by biology can provide new pathophysiological mechanisms that are otherwise not accessible experimentally, holding promise for novel first-principle-based therapeutics. In this review, we summarize the key aspects of platelet biorheology and mechanobiology, focusing on the molecular and cellular scale events and how they build up to thrombosis through platelet adhesion and aggregation in the presence or absence of platelet activation. In particular, we highlight recent advancements in multiscale modeling of platelet biorheology and mechanobiology and how they can lead to the better prediction and quantification of thrombus formation, exemplifying the exciting paradigm of digital medicine.

Platelet and endothelial cell responses under concurrent shear stress and tensile strain

Thrombosis can lead to significant mortality and morbidity. Both platelets and vascular endothelial cells play significant roles in thrombosis. Platelets' response to blood flow-induced shear stress can vary greatly depending on shear stress magnitude, pattern and shear exposure time. Endothelial cells are also sensitive to the biomechanical environment. Endothelial cell activation and dysfunction can occur under low oscillatory shear stress and low tensile strain. Platelet and endothelial cell interaction can also be affected by mechanical conditions. The goal of this study was to investigate how blood flow-induced shear stress, vascular wall tensile strain, platelet-endothelial cell stress history, and platelet-endothelial cell interaction affect platelet thrombogenicity. Platelets and human coronary artery endothelial cells were pretreated with physiological and pathological shear stress and/or tensile strain separately. The pretreated cells were then put together and exposed to pulsatile shear stress and cyclic tensile strain simultaneously in a shearing-stretching device. Following treatment, platelet thrombin generation rate, platelet and endothelial cell activation, and platelet adhesion to endothelial cells was measured. The results demonstrated that shear stress pretreatment of endothelial cells and platelets caused a significant increase in platelet thrombin generation rate, cell surface phosphatidylserine expression, and adhesion to endothelial cells. Shear stress pretreatment of platelets and endothelial cells attenuated endothelial cell ICAM-1 expression under stenosis conditions, as well as vWF expression under recirculation conditions. These results indicate that platelets are sensitized by prior shearing, while in comparison, the interaction with shear stress-pretreated platelets may reduce endothelial cell sensitivity to pathological shear stress and tensile strain.

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

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

Combined computational modeling and experimental study of the biomechanical mechanisms of platelet-driven contraction of fibrin clots

While blood clot formation has been relatively well studied, little is known about the mechanisms underlying the subsequent structural and mechanical clot remodeling called contraction or retraction. Impairment of the clot contraction process is associated with both life-threatening bleeding and thrombotic conditions, such as ischemic stroke, venous thromboembolism, and others. Recently, blood clot contraction was observed to be hindered in patients with COVID-19. A three-dimensional multiscale computational model is developed and used to quantify biomechanical mechanisms of the kinetics of clot contraction driven by platelet-fibrin pulling interactions. These results provide important biological insights into contraction of platelet filopodia, the mechanically active thin protrusions of the plasma membrane, described previously as performing mostly a sensory function. The biomechanical mechanisms and modeling approach described can potentially apply to studying other systems in which cells are embedded in a filamentous network and exert forces on the extracellular matrix modulated by the substrate stiffness.

Image-based flow simulation of platelet aggregates under different shear rates

Hemodynamics is crucial for the activation and aggregation of platelets in response to flow-induced shear. In this paper, a novel image-based computational model simulating blood flow through and around platelet aggregates is presented. The microstructure of aggregates was captured by two different modalities of microscopy images of in vitro whole blood perfusion experiments in microfluidic chambers coated with collagen. One set of images captured the geometry of the aggregate outline, while the other employed platelet labelling to infer the internal density. The platelet aggregates were modelled as a porous medium, the permeability of which was calculated with the Kozeny-Carman equation. The computational model was subsequently applied to study hemodynamics inside and around the platelet aggregates. The blood flow velocity, shear stress and kinetic force exerted on the aggregates were investigated and compared under 800 s-1, 1600 s-1 and 4000 s-1 wall shear rates. The advection-diffusion balance of agonist transport inside the platelet aggregates was also evaluated by local Péclet number. The findings show that the transport of agonists is not only affected by the shear rate but also significantly influenced by the microstructure of the aggregates. Moreover, large kinetic forces were found at the transition zone from shell to core of the aggregates, which could contribute to identifying the boundary between the shell and the core. The shear rate and the rate of elongation flow were investigated as well. The results imply that the emerging shapes of aggregates are highly correlated to the shear rate and the rate of elongation. The framework provides a way to incorporate the internal microstructure of the aggregates into the computational model and yields a better understanding of the hemodynamics and physiology of platelet aggregates, hence laying the foundation for predicting aggregation and deformation under different flow conditions.

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

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

Computational Biomechanical Modeling of Fibrin Networks and Platelet-Fiber Network Interactions

Fibrin deformation and interaction of fibrin with other blood components play critical roles in hemostasis and thrombosis. In this review, computational and mathematical biomechanical models of fibrin network deformation and contraction at different spatio-temporal scales as well as challenges in developing and calibrating multiscale models are discussed. There are long standing challenges. For instance, applicability of models to identify and test potential mechanisms of the biomechanical processes mediating interactions between platelets and fiber networks in blood clot stretching and contraction needs to be examined carefully. How the structural and mechanical properties of major blood clot components influences biomechanical responses of the entire clot subjected to external forces, such as blood flow or vessel wall deformations needs to be investigated thoroughly.

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.

A multiscale model for multiple platelet aggregation in shear flow

We developed a multiscale model for simulating aggregation of multiple, free-flowing platelets in low-intermediate shear viscous flow, in which aggregation is mediated by the interaction of αIIbβ3 receptors on the platelet membrane and fibrinogen (Fg). This multiscale model uses coarse grained molecular dynamics (CGMD) for platelets at the microscales and dissipative particle dynamics (DPD) for the shear flow at the macroscales, employing our hybrid aggregation force field for modeling molecular level receptor ligand bonds. We define an aggregation tensor and use it to quantify the molecular level contact characteristics between platelets in an aggregate. We perform numerical studies under different flow conditions for platelet doublets and triplets and evaluate the contact area, detaching force and minimum distance between different pairs of platelets in an aggregate. We also present the dynamics of applied stress and velocity magnitude distributions on the platelet membrane during aggregation and quantify the increase in stress in the contact region under different flow conditions. Integrating the knowledge from our previously validated models, together with new aggregation scenarios, our model can dynamically quantify aggregation characteristics and map stress and velocity distribution on the platelet membrane which are difficult to measure in vitro, thus providing an insight into mechanotransduction bond formation response of platelets to flow-induced shear stresses. This modeling framework, together with the tensor method for quantifying inter-platelet contact, can be extended to simulate and analyze larger aggregates and their adhesive properties.

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.

Validated model of platelet slip at stenosis and device surfaces

Platelets are central to thrombosis. However, it is unknown whether platelets slip at vascular or device surfaces. The presence of platelet slip at a surface would interrupt physical contact between the platelet and that surface, and therefore diminish adhesion and thrombosis. Unfortunately, no existing technology can directly measure platelet slip in a biological environment. The objective of this study was to explore whether microspheres-modeling platelets-slip at different vascular and device surfaces in an acrylic scaled-up model coronary artery. The microspheres (3.12 µm diameter) were suspended in a transparent glycerol/water experimental fluid, which flowed continuously at Reynolds numbers typical of coronary flow (200-400) through the model artery. We placed a series of axisymmetric acrylic stenoses (cross-sectional area reduction [CSAr], 20-90%) into the model artery, both without and with a central cylinder present (modeling a percutaneous interventional guide wire, and with a scaled-up Doppler catheter mounted upstream). We used laser Doppler velocimetry (LDV) to measure microsphere velocities within, proximal and distal to each stenosis, and compared to computer simulations of fluid flow with no-slip. For validation, we replaced the acrylic with paraffin stenoses (more biologically relevant from a surface roughness perspective) and then analyzed the signal recorded by the scaled-up Doppler catheter. Using the LDV, we identified progressive microsphere slip proportional to CSAr inside entrances for stenoses ≥60% and ≥40% without and with cylinder present, respectively. Additionally, microsphere slip occurred universally along the cylinder surface. Computer simulations indicated increased fluid shear rates (velocity gradients) at these particular locations, and logistic regression analysis comparing microsphere slip with fluid shear rate resulted in a c-index of 0.989 at a cut-point fluid shear rate of (10.61 [cm^-1]×mean velocity [cm×sec^-1]). Moreover, the presence of the cylinder caused disordering of microsphere shear rates distal to higher grade stenoses, indicating a disturbance in their flow. Finally, despite lower precision, the signal recorded by the scaled-up Doppler catheter nonetheless indicated slip at the entry into and at most locations distal to the 90% stenosis. Our validated model establishes proof of concept for platelet slip, and platelet slip explains several important basic and clinical observations. If technological advances allow confirmation in a true biologic environment, then our results will likely influence the development of shear-dependent antiplatelet drugs. Also, adding shear rate information, our results provide a direct experimental fluid dynamic foundation for antiplatelet-focused antithrombotic therapy during coronary interventions directed towards higher grade atherosclerotic stenoses.

A Multiscale Model for Recruitment Aggregation of Platelets by Correlating with In Vitro Results

Introduction

We developed a multiscale model to simulate the dynamics of platelet aggregation by recruitment of unactivated platelets flowing in viscous shear flows by an activated platelet deposited onto a blood vessel wall. This model uses coarse grained molecular dynamics (CGMD) for platelets at the microscale and dissipative particle dynamics (DPD) for the shear flow at the macroscale. Under conditions of relatively low shear, aggregation is mediated by fibrinogen via αIIbβ3 receptors.

Methods

The binding of αIIbβ3 and fibrinogen is modeled by a molecular-level hybrid force field consisting of Morse potential and Hooke law for the nonbonded and bonded interactions, respectively. The force field, parametrized in two different interaction scales, is calculated by correlating with the platelet contact area measured in vitro and the detaching force between αIIbβ3 and fibrinogen.

Results

Using our model, we derived, the relationship between recruitment force and distance between the centers of mass of two platelets, by integrating the molecular-scale inter-platelet interactions during recruitment aggregation in shear flows. Our model indicates that assuming a rigid-platelet model, underestimates the contact area by 89% and the detaching force by 93% as compared to a model that takes into account the platelet deformability leading to a prediction of a significantly lower attachment during recruitment.

Conclusions

The molecular-level predictive capability of our model sheds a light on differences observed between transient and permanent platelet aggregation patterns. The model and simulation framework can be further adapted to simulate initial thrombus formation involving multiple flowing platelets as well as deposition and adhesion onto blood vessels.

Extracting multivalent detachment rates from heterogeneous nanoparticle populations

Nanoparticles can form multiple bonds with target surfaces, thereby increasing adhesion strength and internalization rate into cells. This property has helped to drive interest in nanoparticles as delivery vehicles for drugs and imaging agents, but significant gaps in our understanding of multivalent adhesion make it difficult to control and optimize binding dynamics. In previous work, we experimentally observed that multivalent nanoparticle adhesion can exhibit a time-dependent detachment rate. However, simulations later indicated that the underlying cause was variability in the number of bonds that formed between individual nanoparticles within the population. Here, we use this insight to develop a simple model to isolate a series of constant detachment rates from such heterogeneous populations. Using simulations of experimental data to train the model, we first classified nanoparticles within a given population based on the most likely equilibrium bond number, which we termed the bond potential. We then assumed that each bond potential category would follow standard first-order kinetics with constant detachment rates. Model results matched the population binding data, but only if we further divided each bond potential category into two sub-components, the second of which did not detach. We then utilized bonding rates from the simulation to estimate detachment rates for the second, slower detaching sub-component. These results confirm our hypothesis that nanoparticle populations can be sub-divided based on bond potential, each of which could be characterized by a constant detachment rate. Finally, we established relationships between the new heterogeneous population detachment model and a time-dependent, empirical detachment model that we developed in previous work. This could make it possible to determine bond potential distributions directly from experimental data without computationally costly simulations, which will be explored in future work.

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.

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.

Effect of circulating tumor cell aggregate configuration on hemodynamic transport and wall contact

Selectin-mediated adhesion of circulating tumor cells (CTCs) to the endothelium is a critical step in cancer metastasis, a major factor contributing to the mortality of cancer. The formation of tethers between tumor cells and endothelial selectins initiates cell rolling, which can lead to firm adhesion, extravasation and the formation of secondary metastases. Tumor cells travel through the bloodstream as single cells, or as aggregates known as circulating tumor microemboli (CTM). CTM have increased survivability and metastatic potential relative to CTCs, and the presence of CTM is associated with worse patient prognosis. The motion of cells and cellular aggregates in flow is a function of their size and shape, and these differences influence the frequency and strength of their contact with the endothelium. In this study, a computational model consisting of the hydrodynamic component of the Multiparticle Adhesive Dynamics simulation analyzed the effects of model aggregate conformation and orientation on adhesive binding potential. Model aggregates of the Colo205 colorectal cancer cell line were created, consisting of two, three, and four cells in simple geometrical conformations. Contact time, contact area, and time integral of contact area were measured as a function of fluid shear rate, initial centroid height, and initial orientation for model aggregates that experienced hydrodynamic collisions with the plane wall. It was found that larger CTM conformations with intermediate nonsphericities had the highest adhesion potential. The results of this study shed light on the correlation between environmental conditions and extravasation efficiency, which could inform the development of new anti-metastatic drugs.

Hydrodynamic repulsion of spheroidal microparticles from micro-rough surfaces

Isolation of microparticles and biological cells from mixtures and suspensions is a central problem in a variety of biomedical applications. This problem, for instance, is of an immense importance for microfluidic devices manipulating with whole blood samples. It is instructive to know how the mobility and dynamics of rigid microparticles is altered by the presence of micrometer-size roughness on walls. The presented theoretical study addresses this issue via computer simulations. The approach is based on a combination of the Lattice Boltzmann method for calculating hydrodynamics and the Lagrangian Particle dynamics method to describe the dynamics of cell membranes. The effect of the roughness on the mobility of spheroidal microparticles in a shear fluid flow was quantified. We conclude that mechanical and hydrodynamic interactions lift the particles from the surface and change their mobility. The effect is sensitive to the shape of particles.

The Effect of Hematocrit on Platelet Adhesion: Experiments and Simulations

The volume fraction of red blood cells (RBCs) in a capillary affects the degree to which platelets are promoted to marginate to near a vessel wall and form blood clots. In this work we investigate the relationship between RBC hematocrit and platelet adhesion activity. We perform experiments flowing blood samples through a microfluidic channel coated with type 1 collagen and observe the rate at which platelets adhere to the wall. We compare these results with three-dimensional boundary integral simulations of a suspension of RBCs and platelets in a periodic channel where platelets can adhere to the wall. In both cases, we find that the rate of platelet adhesion varies greatly with the RBC hematocrit. We observe that the relative decrease in platelet activity as hematocrit falls shows a similar profile for simulation and experiment.

In Vitro and Ex Vivo Approaches to Evaluate Next-Generation Tobacco and Non-Tobacco Products on Human Blood Platelets

Human blood platelets are major hemostatic regulators in the circulation and important in the mediation of chronic inflammation and immunomodulation. They are key elements that promote cardiovascular pathogenesis that leads to atherosclerosis, thrombosis, myocardial infarction, and stroke. New information on tobacco use and platelet dysregulation shows that these highly understudied vascular cells are dysregulated by tobacco smoke. Thus, platelet function studies should be an important consideration for the evaluation of existing and next-generation tobacco and non-tobacco products. Novel in vitro approaches are being sought to investigate these products and their influence on platelet function. Platelets are ideally suited for product assessment, as robust and novel in vitro translational methods are available to assess platelet function. Furthermore, the use of human biological systems has the advantage that risk predictions will better reflect the human condition.

Microfluidic measurement for blood flow and platelet adhesion around a stenotic channel: Effects of tile size on the detection of platelet adhesion in a correlation map

Platelet aggregation affects the surrounding blood flow and usually occurs where a blood vessel is narrowed as a result of atherosclerosis. The relationship between blood flow and platelet aggregation is not yet fully understood. This study proposes a microfluidic method to measure the velocity and platelet aggregation simultaneously by combining the micro-particle image velocimetry technique and a correlation mapping method. The blood flow and platelet adhesion procedure in a stenotic micro-channel with 90% severity were observed for a relatively long period of 4 min. In order to investigate the effect of tile size on the detection of platelet adhesion, 2D correlation coefficients were evaluated with binary images obtained by manual labeling and the correlation mapping method with different sizes of the square tile ranging from 3 to 50 pixels. The maximum 2D correlation coefficient occurred with the optimum tile size of 5 × 5 pixels. Since the blood flow and platelet aggregation are mutually influenced by each other, blood flow and platelet adhesion were continuously varied. When there was no platelet adhesion (t = 0 min), typical blood flow is observed. The blood flow passes through the whole channel smoothly, and jet-like flow occurs in the post-stenosis region. However, the flow pattern changes when platelet adhesion starts at the stenosis apex and after the stenosis. These adhesions induce narrow high velocity regions to become wider over a range of area from upstream to downstream of the stenosis. Separated jet-like flows with two high velocity regions are also created. The changes in flow patterns may alter the patterns of platelet adhesion. As the area of the plate adhesion increases, the platelets plug the micro-channel and there is only a small amount of blood flow, finally. The microfluidic method could provide new insights for better understanding of the interactions between platelet aggregation and blood flow in various physiological conditions.

Evolution of Multivalent Nanoparticle Adhesion via Specific Molecular Interactions

The targeted delivery of nanoparticle carriers holds tremendous potential to transform the detection and treatment of diseases. A major attribute of nanoparticles is the ability to form multiple bonds with target cells, which greatly improves the adhesion strength. However, the multivalent binding of nanoparticles is still poorly understood, particularly from a dynamic perspective. In previous experimental work, we studied the kinetics of nanoparticle adhesion and found that the rate of detachment decreased over time. Here, we have applied the adhesive dynamics simulation framework to investigate binding dynamics between an antibody-conjugated, 200-nm-diameter sphere and an ICAM-1-coated surface on the scale of individual bonds. We found that nano adhesive dynamics (NAD) simulations could replicate the time-varying nanoparticle detachment behavior that we observed in experiments. As expected, this behavior correlated with a steady increase in mean bond number with time, but this was attributed to bond accumulation only during the first second that nanoparticles were bound. Longer-term increases in bond number instead were manifested from nanoparticle detachment serving as a selection mechanism to eliminate nanoparticles that had randomly been confined to lower bond valencies. Thus, time-dependent nanoparticle detachment reflects an evolution of the remaining nanoparticle population toward higher overall bond valency. We also found that NAD simulations precisely matched experiments whenever mechanical force loads on bonds were high enough to directly induce rupture. These mechanical forces were in excess of 300 pN and primarily arose from the Brownian motion of the nanoparticle, but we also identified a valency-dependent contribution from bonds pulling on each other. In summary, we have achieved excellent kinetic consistency between NAD simulations and experiments, which has revealed new insights into the dynamics and biophysics of multivalent nanoparticle adhesion. In future work, we will leverage the simulation as a design tool for optimizing targeted nanoparticle agents.

Minimum wound size for clotting: flowing blood coagulates on a single collagen fiber presenting tissue factor and von Willebrand factor

It is unknown if a lower size limit exists for human blood coagulation under flow over physiological vessel wall triggers as small as a single collagen fiber. Prior determinations of the smallest sized surface stimuli necessary for clotting of human blood, defined as the patch size threshold, have not deployed whole blood, hemodynamic flow, and platelet adhesive stimuli. For whole blood perfused in microfluidic devices, we report that steady venous flow (wall shear rate, 100 s(-1)) was sufficient to drive platelet deposition on 20 micron long zones of collagen fibers or on a single fiber. With tissue factor (TF)-coated collagen, flowing blood generated robust platelet deposits, platelet-localized thrombin, and fibrin on a single collagen fiber, thus demonstrating the absence of a physiological patch size threshold under venous flow. In contrast, at arterial wall shear rate (1000 s(-1)) with TF present, essentially no platelet or fibrin deposition occurred on 20 micron collagen zones or on a single collagen fiber, demonstrating a patch threshold, which was overcome by pre-coating the collagen with von Willebrand factor (vWF). For venous flows, human blood can clot on one of the smallest biological units of a single collagen fiber presenting TF. For arterial flows, vWF together with TF allows human blood to generate thrombin and fibrin on a patch stimulus as limited as a single collagen fiber. vWF-dependent platelet adhesion represents a particle-based sensing mechanism of micron-scale stimuli that then allows amplification of the molecular components of TF-driven thrombin and fibrin production under arterial flow.

Characterization of Nanoparticle Dispersion in Red Blood Cell Suspension by the Lattice Boltzmann-Immersed Boundary Method

Nanodrug-carrier delivery in the blood stream is strongly influenced by nanoparticle (NP) dispersion. This paper presents a numerical study on NP transport and dispersion in red blood cell (RBC) suspensions under shear and channel flow conditions, utilizing an immersed boundary fluid-structure interaction model with a lattice Boltzmann fluid solver, an elastic cell membrane model and a particle motion model driven by both hydrodynamic loading and Brownian dynamics. The model can capture the multiphase features of the blood flow. Simulations were performed to obtain an empirical formula to predict NP dispersion rate for a range of shear rates and cell concentrations. NP dispersion rate predictions from the formula were then compared to observations from previous experimental and numerical studies. The proposed formula is shown to accurately predict the NP dispersion rate. The simulation results also confirm previous findings that the NP dispersion rate is strongly influenced by local disturbances in the flow due to RBC motion and deformation. The proposed formula provides an efficient method for estimating the NP dispersion rate in modeling NP transport in large-scale vascular networks without explicit RBC and NP models.

Prediction of Molecular Interaction between Platelet Glycoprotein Ibα and von Willebrand Factor using Molecular Dynamics Simulations

AIM

The molecular mechanism of the unique interaction between platelet membrane glycoprotein Ibα (GPIbα) and von Willebrand Factor (VWF), necessary for platelet adhesion under high shear stress, is yet to be clarified.

METHODS

The molecular dynamics simulation using NAMD (Nanoscale Molecular Dynamics) package with the CHARMM 22 (Chemistry at Harvard Macromolecular Mechanics) force field were used to predict dynamic structural changes occurring in the binding site of A1 domain of VWF and N terminus domain of GPIbα under water soluble condition.

RESULTS

The mean distance between the mass center of A1 domain of VWF and GPIbα in the stable form was predicted as 27.3 Å. The potential of mean force between the A1 domain of VWF and GPIbα were calculated in conditions of various distances of the mass center between them. All the calculated values were fitted to the Morse potential energy function curve. The maximum adhesive force between A1 domain of VWF and GPIbα was predicted as 62.3 pN by differentiating the potential of mean force with respect to the molecular distance.

CONCLUSIONS

The molecular dynamics simulation is useful for predicting the dynamic structure changes of protein bonds involved in platelet adhesion and for predicting the adhesive forces generated between their interactions.

Effect of Pseudopod Extensions on Neutrophil Hemodynamic Transport Near a Wall

During inflammation, circulating neutrophils roll on, and eventually tether to, the endothelial lining of blood vessels, allowing them to exit the bloodstream and enter the surrounding tissue to target pathogens. This process is mediated by the selectin family of adhesion proteins expressed by endothelial cells. Interestingly, only 10% of activated, migrating neutrophils transmigrate into the extravascular space; the other 90% detach from the wall and rejoin the blood flow. Neutrophils extrude pseudopods during the adhesion cascade; however, the transport behavior of this unique cell geometry has not been previously addressed. In this study, a three-dimensional computational model was applied to neutrophils with pseudopodial extensions to study the effect of cell shape on the hydrodynamic transport of neutrophils. The collision time, contact area, contact force, and collision frequency were analyzed as a function of pseudopod length. It was found that neutrophils experience more frequent collisions compared to prolate spheroids of equal volume and length. Longer pseudopods and lower shear rates increase the collision time integral contact area, a predictor of binding potential. Our results indicate that contact between the neutrophil and the vessel wall was found to be focused predominantly on the pseudopod tip.

Simulation and Analysis of Tethering Behavior of Neutrophils with Pseudopods

P-selectin and P-selectin glycoprotein ligand-1 (PSGL-1) play important roles in mediating the inflammatory cascade. Selectin kinetics, together with neutrophil hydrodynamics, regulate the fundamental adhesion cascade of cell tethering and rolling on the endothelium. The current study uses the Multiscale Adhesive Dynamics computational model to simulate, for the first time, the tethering and rolling behavior of pseudopod-containing neutrophils as mediated by P-selectin/PSGL-1 bonds. This paper looks at the effect of including P-selectin/PSGL-1 adhesion kinetics. The parameters examined included the shear rate, adhesion on-rate, initial neutrophil position, and receptor number sensitivity. The outcomes analyzed included types of adhesive behavior observed, tether rolling distance and time, number of bonds formed during an adhesive event, contact area, and contact time. In contrast to the hydrodynamic model, P-selectin/PSGL-1 binding slows the neutrophil’s translation in the direction of flow and causes the neutrophil to swing around perpendicular to flow. Several behaviors were observed during the simulations, including tethering without firm adhesion, tethering with downstream firm adhesion, and firm adhesion upon first contact with the endothelium. These behaviors were qualitatively consistent with in vivo data of murine neutrophils with pseudopods. In the simulations, increasing shear rate, receptor count, and bond formation rate increased the incidence of firm adhesion upon first contact with the endothelium. Tethering was conserved across a range of physiological shear rates and was resistant to fluctuations in the number of surface PSGL-1 molecules. In simulations where bonding occurred, interaction with the side of the pseudopod, rather than the tip, afforded more surface area and greater contact time with the endothelial wall.

A phenomenological particle-based platelet model for simulating filopodia formation during early activation

We developed a phenomenological three-dimensional platelet model to characterize the filopodia formation observed during early stage platelet activation. Departing from continuum mechanics based approaches, this coarse-grained molecular dynamics (CGMD) particle-based model can deform to emulate the complex shape change and filopodia formation that platelets undergo during activation. The platelet peripheral zone is modeled with a two-layer homogeneous elastic structure represented by spring-connected particles. The structural zone is represented by a cytoskeletal assembly comprising of a filamentous core and filament bundles supporting the platelet's discoid shape, also modeled by spring-connected particles. The interior organelle zone is modeled by homogeneous cytoplasm particles that facilitate the platelet deformation. Nonbonded interactions among the discrete particles of the membrane, the cytoskeletal assembly, and the cytoplasm are described using the Lennard-Jones potential with empirical constants. By exploring the parameter space of this CGMD model, we have successfully simulated the dynamics of varied filopodia formations. Comparative analyses of length and thickness of filopodia show that our numerical simulations are in agreement with experimental measurements of flow-induced activated platelets. Copyright © 2015 John Wiley & Sons, Ltd.

A Multiple Time Stepping Algorithm for Efficient Multiscale Modeling of Platelets Flowing in Blood Plasma

We developed a multiple time-stepping (MTS) algorithm for multiscale modeling of the dynamics of platelets flowing in viscous blood plasma. This MTS algorithm improves considerably the computational efficiency without significant loss of accuracy. This study of the dynamic properties of flowing platelets employs a combination of the dissipative particle dynamics (DPD) and the coarse-grained molecular dynamics (CGMD) methods to describe the dynamic microstructures of deformable platelets in response to extracellular flow-induced stresses. The disparate spatial scales between the two methods are handled by a hybrid force field interface. However, the disparity in temporal scales between the DPD and CGMD that requires time stepping at microseconds and nanoseconds respectively, represents a computational challenge that may become prohibitive. Classical MTS algorithms manage to improve computing efficiency by multi-stepping within DPD or CGMD for up to one order of magnitude of scale differential. In order to handle 3-4 orders of magnitude disparity in the temporal scales between DPD and CGMD, we introduce a new MTS scheme hybridizing DPD and CGMD by utilizing four different time stepping sizes. We advance the fluid system at the largest time step, the fluid-platelet interface at a middle timestep size, and the nonbonded and bonded potentials of the platelet structural system at two smallest timestep sizes. Additionally, we introduce parameters to study the relationship of accuracy versus computational complexities. The numerical experiments demonstrated 3000x reduction in computing time over standard MTS methods for solving the multiscale model. This MTS algorithm establishes a computationally feasible approach for solving a particle-based system at multiple scales for performing efficient multiscale simulations.

Nanobiotechnology for the Therapeutic Targeting of Cancer Cells in Blood

During metastasis, circulating tumor cells migrate away from a primary tumor via the blood circulation to form secondary tumors in distant organs. Mounting evidence from clinical observations indicates that the number of circulating tumor cells (CTCs) in the blood correlates with the progression of solid tumors before and during chemotherapy. Beyond the well-established role of CTCs as a fluid biopsy, however, the field of targeting CTCs for the prevention or reduction of metastases has just emerged. Conventional cancer therapeutics have a relatively short circulation time in the blood which may render the killing of CTCs inefficient due to reduced exposure of CTCs to drugs. Nevertheless, over the past few decades, the development of nanoparticles and nanoformulations to improve the half-life and release profile of drugs in circulation has rejuvenated certain traditional medicines in the emerging field of CTC neutralization. This review focuses on how the principles of nanomedicine may be applied to target CTCs. Moreover, inspired by the interactions between CTCs and host cells in the blood circulation, novel biomimetic approaches for targeted drug delivery are presented.

Interaction of von Willebrand factor with platelets and the vessel wall

The initiation of thrombus formation at sites of vascular injury to secure haemostasis after tissue trauma requires the interaction of surface-exposed von Willebrand factor (VWF) with its primary platelet receptor, the glycoprotein (GP) Ib-IX-V complex. As an insoluble component of the extracellular matrix (ECM) of endothelial cells, VWF can directly initiate platelet adhesion. Circulating plasma VWF en-hances matrix VWF activity by binding to structures that become exposed to flowing blood, notably collagen type I and III in deeper layers of the vessel along with microfibrillar collagen type VI in the subendothelium. Moreover, plasma VWF is required to support platelet-to-platelet adhesion - i. e. aggregation - which promotes thrombus growth and consolidation. For these reasons, understanding how plasma VWF interaction with platelet receptors is regulated, particularly any distinctive features of GPIb binding to soluble as opposed to immobilized VWF, is of paramount importance in vascular biology. This brief review will highlight knowledge acquired and key problems that remain to be solved to elucidate fully the role of VWF in normal haemostasis and pathological thrombosis.

Fluid Mechanics of Blood Clot Formation

Intravascular blood clots form in an environment in which hydrodynamic forces dominate and in which fluid-mediated transport is the primary means of moving material. The clotting system has evolved to exploit fluid dynamic mechanisms and to overcome fluid dynamic challenges to ensure that clots that preserve vascular integrity can form over the wide range of flow conditions found in the circulation. Fluid-mediated interactions between the many large deformable red blood cells and the few small rigid platelets lead to high platelet concentrations near vessel walls where platelets contribute to clotting. Receptor-ligand pairs with diverse kinetic and mechanical characteristics work synergistically to arrest rapidly flowing cells on an injured vessel. Variations in hydrodynamic stresses switch on and off the function of key clotting polymers. Protein transport to, from, and within a developing clot determines whether and how fast it grows. We review ongoing experimental and modeling research to understand these and related phenomena.

Adhesive dynamics

Adhesive dynamics (AD) is a method for simulating the dynamic response of biological systems in response to force. Biological bonds are mechanical entities that exert force under strain, and applying forces to biological bonds modulates their rate of dissociation. Since small numbers of events usually control biological interactions, we developed a simple method for sampling probability distributions for the formation or failure of individual bonds. This method allows a simple coupling between force and strain and kinetics, while capturing the stochastic response of biological systems. Biological bonds are dynamically reconfigured in response to applied mechanical stresses, and a detailed spatio-temporal map of molecules and the forces they exert emerges from AD. The shape or motion of materials bearing the molecules is easily calculated from a mechanical energy balance provided the rheology of the material is known. AD was originally used to simulate the dynamics of adhesion of leukocytes under flow, but new advances have allowed the method to be extended to many other applications, including but not limited to the binding of viruses to surface, the clustering of adhesion molecules driven by stiff substrates, and the effect of cell-cell interaction on cell capture and rolling dynamics. The technique has also been applied to applications outside of biology. A particular exciting recent development is the combination of signaling with AD (so-called integrated signaling adhesive dynamics, or ISAD), which allows facile integration of signaling networks with mechanical models of cell adhesion and motility. Potential opportunities in applying AD are summarized.

Multiscale Particle-Based Modeling of Flowing Platelets in Blood Plasma Using Dissipative Particle Dynamics and Coarse Grained Molecular Dynamics

We developed a multiscale particle-based model of platelets, to study the transport dynamics of shear stresses between the surrounding fluid and the platelet membrane. This model facilitates a more accurate prediction of the activation potential of platelets by viscous shear stresses - one of the major mechanisms leading to thrombus formation in cardiovascular diseases and in prosthetic cardiovascular devices. The interface of the model couples coarse-grained molecular dynamics (CGMD) with dissipative particle dynamics (DPD). The CGMD handles individual platelets while the DPD models the macroscopic transport of blood plasma in vessels. A hybrid force field is formulated for establishing a functional interface between the platelet membrane and the surrounding fluid, in which the microstructural changes of platelets may respond to the extracellular viscous shear stresses transferred to them. The interaction between the two systems preserves dynamic properties of the flowing platelets, such as the flipping motion. Using this multiscale particle-based approach, we have further studied the effects of the platelet elastic modulus by comparing the action of the flow-induced shear stresses on rigid and deformable platelet models. The results indicate that neglecting the platelet deformability may overestimate the stress on the platelet membrane, which in turn may lead to erroneous predictions of the platelet activation under viscous shear flow conditions. This particle-based fluid-structure interaction multiscale model offers for the first time a computationally feasible approach for simulating deformable platelets interacting with viscous blood flow, aimed at predicting flow induced platelet activation by using a highly resolved mapping of the stress distribution on the platelet membrane under dynamic flow conditions.

Three-dimensional multi-scale model of deformable platelets adhesion to vessel wall in blood flow

When a blood vessel ruptures or gets inflamed, the human body responds by rapidly forming a clot to restrict the loss of blood. Platelets aggregation at the injury site of the blood vessel occurring via platelet-platelet adhesion, tethering and rolling on the injured endothelium is a critical initial step in blood clot formation. A novel three-dimensional multi-scale model is introduced and used in this paper to simulate receptor-mediated adhesion of deformable platelets at the site of vascular injury under different shear rates of blood flow. The novelty of the model is based on a new approach of coupling submodels at three biological scales crucial for the early clot formation: novel hybrid cell membrane submodel to represent physiological elastic properties of a platelet, stochastic receptor-ligand binding submodel to describe cell adhesion kinetics and lattice Boltzmann submodel for simulating blood flow. The model implementation on the GPU cluster significantly improved simulation performance. Predictive model simulations revealed that platelet deformation, interactions between platelets in the vicinity of the vessel wall as well as the number of functional GPIbα platelet receptors played significant roles in platelet adhesion to the injury site. Variation of the number of functional GPIbα platelet receptors as well as changes of platelet stiffness can represent effects of specific drugs reducing or enhancing platelet activity. Therefore, predictive simulations can improve the search for new drug targets and help to make treatment of thrombosis patient-specific.

Blood compatible materials: state of the art

Devices that function in contact with blood are ubiquitous in clinical medicine and biotechnology. These devices include vascular grafts, coronary stents, heart valves, catheters, hemodialysers, heart-lung bypass systems and many others. Blood contact generally leads to thrombosis (among other adverse outcomes), and no material has yet been developed which remains thrombus-free indefinitely and in all situations: extracorporeally, in the venous circulation and in the arterial circulation. In this article knowledge on blood-material interactions and "thromboresistant" materials is reviewed. Current approaches to the development of thromboresistant materials are discussed including surface passivation; incorporation and/or release of anticoagulants, antiplatelet agents and thrombolytic agents; and mimicry of the vascular endothelium.

Systems biology of platelet-vessel wall interactions

Platelets are small, anucleated cells that participate in primary hemostasis by forming a hemostatic plug at the site of a blood vessel's breach, preventing blood loss. However, hemostatic events can lead to excessive thrombosis, resulting in life-threatening strokes, emboli, or infarction. Development of multi-scale models coupling processes at several scales and running predictive model simulations on powerful computer clusters can help interdisciplinary groups of researchers to suggest and test new patient-specific treatment strategies.

An investigation on platelet transport during thrombus formation at micro-scale stenosis

This paper reports on an investigation of mass transport of blood cells at micro-scale stenosis where local strain-rate micro-gradients trigger platelet aggregation. Using a microfluidic flow focusing platform we investigate the blood flow streams that principally contribute to platelet aggregation under shear micro-gradient conditions. We demonstrate that relatively thin surface streams located at the channel wall are the primary contributor of platelets to the developing aggregate under shear gradient conditions. Furthermore we delineate a role for red blood cell hydrodynamic lift forces in driving enhanced advection of platelets to the stenosis wall and surface of developing aggregates. We show that this novel microfluidic platform can be effectively used to study the role of mass transport phenomena driving platelet recruitment and aggregate formation and believe that this approach will lead to a greater understanding of the mechanisms underlying shear-gradient dependent discoid platelet aggregation in the context of cardiovascular diseases such as acute coronary syndromes and ischemic stroke.

Simulation of platelet, thrombus and erythrocyte hydrodynamic interactions in a 3D arteriole with in vivo comparison

Cylindrical blood vessels, ellipsoid platelets and biconcave-shaped deformable erythrocytes (RBCs) are important participants in hemostasis and thrombosis. However, due to the challenge of combining these components in simulation tools, few simulation studies have included all of them in realistic three-dimensional models. In the present study, we apply a recently developed simulation model to incorporate these components and analyze the flow in a thrombotic tubular arteriole, particularly the detailed hydrodynamic interactions between the thrombus shape, RBCs and platelets. It was found that at certain azimuth positions, the velocity drops in the proximity of both the upstream and downstream edge of the thrombus, which is accompanied by a rapid velocity increase in the narrowed region. The RBCs alter the flow profiles significantly from the typical low Reynolds (Re) number flow, and also enhance the deposition of free flowing platelets onto the thrombus. By evaluating the platelet-thrombus interaction and platelet-RBC interaction together, several mechanisms of platelet deposition augmentation are identified. With in vivo data comparison, our model illustrates the potential of future thrombosis studies that incorporate detailed receptor-ligand adhesion modules.

Platelet biology: the role of shear

Platelets are anucleated fragments produced by megakaryocytes that circulate in the blood. Platelets are involved in the initial cellular response to damaged endothelium and migrate to this area to prevent excessive bleeding. What is becoming more acknowledged over the last few decades is that blood flow (hemodynamics) plays a critical role in platelet function. The purpose of this review is to summarize the current understanding of platelet biology with particular focus on the role of hemodynamics. The emerging concept of shear microgradients, which are challenging the traditional model of platelet function, will also be introduced in the review.

Platelet size and density affect shear-induced thrombus formation in tortuous arterioles

Thrombosis accounts for 80% of deaths in patients with diabetes mellitus. Diabetic patients demonstrate tortuous microvessels and larger than normal platelets. Large platelets are associated with increased platelet activation and thrombosis, but the physical effects of large platelets in the microscale processes of thrombus formation are not clear. Therefore, the objective of this study was to determine the physical effects of mean platelet volume (MPV), mean platelet density (MPD) and vessel tortuosity on platelet activation and thrombus formation in tortuous arterioles. A computational model of the transport, shear-induced activation, collision, adhesion and aggregation of individual platelets was used to simulate platelet interactions and thrombus formation in tortuous arterioles. Our results showed that an increase in MPV resulted in a larger number of activated platelets, though MPD and level of tortuosity made little difference on platelet activation. Platelets with normal MPD yielded the lowest amount of mural thrombus. With platelets of normal MPD, the amount of mural thrombus decreased with increasing level of tortuosity but did not have a simple monotonic relationship with MPV. The physical mechanisms associated with MPV, MPD and arteriole tortuosity play important roles in platelet activation and thrombus formation.

Multiscale model of platelet translocation and collision

The tethering of platelets on the injured vessel surface mediated by glycoprotein Ibα (GPIbα) - Von Willebrand factor (vWF) bonds, as well as the interaction between flowing platelets and adherent platelets, are two key events that take place immediately following blood vessel injury. This early-stage platelet deposition and accumulation triggers the initiation of hemostasis, a self-defensive mechanism to prevent the body from excessive blood loss. To understand and predict this complex process, one must integrate experimentally determined information on the mechanics and biochemical kinetics of participating receptors over very small time frames (1-1000 µs) and length scales (10-100 nm), to collective phenomena occurring over seconds and tens of microns. In the present study, a unique three dimensional multiscale computational model, platelet adhesive dynamics (PAD), was applied to elucidate the unique physics of (i) a non-spherical, disk-shaped platelet interacting and tethering onto the damaged vessel wall followed by (ii) collisional interactions between a flowing platelet with a downstream adherent platelet. By analyzing numerous simulations under different physiological conditions, we conclude that the platelet's unique spheroid-shape provides heterogeneous, orientation-dependent translocation (rolling) behavior which enhances cell-wall interactions. We also conclude that platelet-platelet near field interactions are critical for cell-cell communication during the initiation of microthrombi. The PAD model described here helps to identify the physical factors that control the initial stages of platelet capture during this process.

Simulation of platelets suspension flowing through a stenosis model using a dissipative particle dynamics approach

Stresses on blood cellular constituents induced by blood flow can be represented by a continuum approach down to the μm level; however, the molecular mechanisms of thrombosis and platelet activation and aggregation are on the order of nm. The coupling of the disparate length and time scales between molecular and macroscopic transport phenomena represents a major computational challenge. In order to bridge the gap between macroscopic flow scales and the cellular scales with the goal of depicting and predicting flow induced thrombogenicity, multi-scale approaches based on particle methods are better suited. We present a top-scale model to describe bulk flow of platelet suspensions: we employ dissipative particle dynamics to model viscous flow dynamics and present a novel and general no-slip boundary condition that allows the description of three-dimensional viscous flows through complex geometries. Dissipative phenomena associated with boundary layers and recirculation zones are observed and favorably compared to benchmark viscous flow solutions (Poiseuille and Couette flows). Platelets in suspension, modeled as coarse-grained finite-sized ensembles of bound particles constituting an enclosed deformable membrane with flat ellipsoid shape, show self-orbiting motions in shear flows consistent with Jeffery's orbits, and are transported with the flow, flipping and colliding with the walls and interacting with other platelets.

Hydrodynamic interaction between a platelet and an erythrocyte: effect of erythrocyte deformability, dynamics, and wall proximity

We present three-dimensional numerical simulations of hydrodynamic interaction between a red blood cell (RBC) and a platelet in a wall-bounded shear flow. The dynamics and large deformation of the RBC are fully resolved in the simulations using a front-tracking method. The objective is to quantify the influence of tank treading and tumbling dynamics of the RBC, and the presence of a bounding wall on the deflection of platelet trajectories. We observe two types of interaction: A crossing event in which the platelet comes in close proximity to the RBC, rolls over it, and continues to move in the same direction; and a turning event in which the platelet turns away before coming close to the RBC. The crossing events occur when the initial lateral separation between the cells is above a critical separation, and the turning events occur when it is below the critical separation. The critical lateral separation is found to be higher during the tumbling motion than that during the tank treading. When the RBC is flowing closer to the wall than the platelet, the critical separation increases by several fold, implying the turning events have higher probability to occur than the crossing events. On the contrary, if the platelet is flowing closer to the wall than the RBC, the critical separation decreases by several folds, implying the crossing events are likely to occur. Based on the numerical results, we propose a mechanism of continual platelet drift from the RBC-rich region of the vessel towards the wall by a succession of turning and crossing events. The trajectory deflection in the crossing events is found to depend nonmonotonically on the initial lateral separation, unlike the monotonic trend observed in tracer particle deflection and in deformable sphere-sphere collision. This nonmonotonic trend is shown to be a consequence of the deformation of the RBC caused by the platelet upon collision. An estimation of the platelet diffusion coefficient yields values that are similar to those reported in experiments and computer simulations with multicellular suspension.

Determination of critical parameters in platelet margination

An investigation of margination dependence on hematocrit, platelet shape, and viscosity ratio of plasma to cytoplasm is presented. Whole blood is modeled as a suspension of deformable red blood cells (RBCs) and rigid platelets in a viscous liquid. The fluid phase is simulated using the lattice-Boltzmann method, the RBC membranes are modeled with a coarse-grained spectrin-link method, and the dynamics of rigid particles are updated using Newton's equations of motion for axisymmetric shapes. The results emphasize that an increase in hematocrit increases the rate of margination. The viscosity ratio between the interior cytoplasm and suspending fluid can considerably alter the rate of margination. The aspect ratio of surrogate platelet particles influences the rate of margination as well. Spherical particles tend to migrate more quickly than disks. Highly viscous or rigid RBCs slow down margination.

Multiscale systems biology and physics of thrombosis under flow

Blood clotting under hemodynamic conditions involves numerous multiscale interactions from the molecular scale to macroscopic vessel and systemic circulation scales. Transmission of shear forces to platelet receptors such as GPIbα, P-selectin, α(2)β(1), and α(2b)β(3) controls adhesion dynamics. These forces also drive membrane tether formation, cellular deformation, and mechanosignaling in blood cells. Blood flow results in red blood cell (RBC) drift towards the center of the vessel along with a near-wall plasma layer enriched with platelets. RBC motions also dramatically enhance platelet dispersion. Trajectories of individual platelets near a thrombotic deposit dictate capture-activation-arrest dynamics as these newly arriving platelets are exposed to chemical gradients of ADP, thromboxane, and thrombin within a micron-scale boundary layer formed around the deposit. If shear forces are sufficiently elevated (>50 dyne/cm(2)), the largest polymers of von Willebrand Factor may elongate with concomitant shear-induced platelet activation. Finally, thrombin generation enhances platelet recruitment and clot strength via fibrin polymerization. By combination of coarse-graining, continuum, and stochastic algorithms, the numerical simulation of the growth rate, composition, and occlusive/embolic potential of a thrombus now spans multiscale phenomena. These simulations accommodate particular flow geometries, blood phenotype, pharmacological regimen, and reactive surfaces to help predict disease risk or response to therapy.

Multiscale models of thrombogenesis

To restrict the loss of blood follow from the rupture of blood vessels, the human body rapidly forms a clot consisting of platelets and fibrin. However, to prevent pathological clotting within vessels as a result of vessel damage, the response must be regulated. Clots forming within vessels (thrombi) can restrict the flow of blood causing damage to tissues in the flow field. Additionally, fragments dissociating from the primary thrombus (emboli) may lodge and clog vessels in the brain (causing ischemic stroke) or lungs (resulting in pulmonary embolism). Pathologies related to the obstruction of blood flow through the vasculature are the major cause of mortality in the United States. Venous thromboembolic disease alone accounts for 900,000 hospitalizations and 300,000 deaths per year and the incidence will increase as the population ages (Wakefield et al. J Vasc Surg 2009, 49:1620-1623). Thus, understanding the interplay between the many processes involved in thrombus development is of significant biomedical value. In this article, we first review computational models of important subprocesses of hemostasis/thrombosis including coagulation reactions, platelet activation, and fibrin assembly, respectively. We then describe several multiscale models integrating these subprocesses to simulate temporal and spatial development of thrombi. The development of validated computational models and predictive simulations will enable one to explore how the variation of multiple hemostatic factors affects thrombotic risk providing an important new tool for thrombosis research.

Modelling platelet-blood flow interaction using the subcellular element Langevin method

In this paper, a new three-dimensional modelling approach is described for studying fluid-viscoelastic cell interaction, the subcellular element Langevin (SCEL) method, with cells modelled by subcellular elements (SCEs) and SCE cells coupled with fluid flow and substrate models by using the Langevin equation. It is demonstrated that: (i) the new method is computationally efficient, scaling as (N) for N SCEs; (ii) cell geometry, stiffness and adhesivity can be modelled by directly relating parameters to experimentally measured values; (iii) modelling the fluid-platelet interface as a surface leads to a very good correlation with experimentally observed platelet flow interactions. Using this method, the three-dimensional motion of a viscoelastic platelet in a shear blood flow was simulated and compared with experiments on tracking platelets in a blood chamber. It is shown that the complex platelet-flipping dynamics under linear shear flows can be accurately recovered with the SCEL model when compared with the experiments. All experimental details and electronic supplementary material are archived at http://biomath.math.nd.edu/scelsupplementaryinformation/.