Computational approaches to studying thrombus development

Shear stimulated red blood cell microparticles: Effect on clot structure, flow and fibrinolysis

BACKGROUND

Microparticles (MPs) have activity in thrombus promotion and generation. Erythrocyte microparticles (ErMPs) have been reported to accelerate fibrinolysis in the absence of permeation. We hypothesized that shear induced ErMPs would affect fibrin structure of clots and change flow with implications for fibrinolysis.

OBJECTIVE

To determine the effect of ErMPs on clot structure and fibrinolysis.

METHODS

Plasma with elevated ErMPs was isolated from whole blood or from washed red blood cells (RBCs) resuspended in platelet free plasma (PFP) after high shear. Dynamic light scattering (DLS) provided size distribution of ErMPs from sheared samples and unsheared PFP controls. Clots were formed by recalcification for flow/lysis experiments and examined by confocal microscopy and SEM. Flow rates through clots and time-to-lysis were recorded. A cellular automata model showed the effect of ErMPs on fibrin polymerization and clot structure.

RESULTS

Coverage of fibrin increased by 41% in clots formed from plasma of sheared RBCs in PFP over controls. Flow rate decreased by 46.7% under a pressure gradient of 10 mmHg/cm with reduction in time to lysis from 5.7 ± 0.7 min to 12.2 ± 1.1 min (p < 0.01). Particle size of ErMPs from sheared samples (200 nm) was comparable to endogenous microparticles.

CONCLUSIONS

ErMPs alter the fibrin network in a thrombus and affect hydraulic permeability resulting in decelerated delivery of fibrinolytic drugs.

Multiphysics and multiscale modeling of microthrombosis in COVID-19

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients’ fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis.

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. We employ a novel multiphysics and multiscale computational framework to investigate the underlying mechanism of the pathological formation of microthrombi and circulating cell clusters in COVID-19. We quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19, through which we identify the potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19.

Recent Advances in Computational Modeling of Biomechanics and Biorheology of Red Blood Cells in Diabetes

Diabetes mellitus, a metabolic disease characterized by chronically elevated blood glucose levels, affects about 29 million Americans and more than 422 million adults all over the world. Particularly, type 2 diabetes mellitus (T2DM) accounts for 90-95% of the cases of vascular disease and its prevalence is increasing due to the rising obesity rates in modern societies. Although multiple factors associated with diabetes, such as reduced red blood cell (RBC) deformability, enhanced RBC aggregation and adhesion to the endothelium, as well as elevated blood viscosity are thought to contribute to the hemodynamic impairment and vascular occlusion, clinical or experimental studies cannot directly quantify the contributions of these factors to the abnormal hematology in T2DM. Recently, computational modeling has been employed to dissect the impacts of the aberrant biomechanics of diabetic RBCs and their adverse effects on microcirculation. In this review, we summarize the recent advances in the developments and applications of computational models in investigating the abnormal properties of diabetic blood from the cellular level to the vascular level. We expect that this review will motivate and steer the development of new models in this area and shift the attention of the community from conventional laboratory studies to combined experimental and computational investigations, aiming to provide new inspirations for the development of advanced tools to improve our understanding of the pathogenesis and pathology of T2DM.

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.

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.

Utilizing Plasma Composition Data to Help Determine Procoagulant Dynamics in Patients with Thermal Injury: A Computational Assessment

INTRODUCTION

The development of methods that generate individualized assessments of the procoagulant potential of burn patients could improve their treatment. Beyond its role as an essential intermediate in the formation of thrombin, factor (F)Xa has systemic effects as an agonist to inflammatory processes. In this study, we use a computational model to study the FXa dynamics underlying tissue factor-initiated thrombin generation in a small cohort of burn patients.

MATERIALS AND METHODS

Plasma samples were collected upon admission (Hour 0) from nine subjects (five non-survivors) with major burn injuries and then at 48 hours. Coagulation factor concentrations (II, V, VII, VIII, IX, X, TFPI, antithrombin (AT), protein C (PC)) were measured and used in a computational model to generate time course profiles for thrombin (IIa), FXa, extrinsic tenase, intrinsic tenase and prothrombinase complexes upon a 5 pM tissue factor stimulus in the presence of 1 nM thrombomodulin. Parameters were extracted from the thrombin and FXa profiles (including max rate (MaxRIIa and MaxRFXa) and peak level (MaxLIIa and MaxLFXa)). Procoagulant potential was also evaluated by determining the concentration of the complexes at select times. Parameter values were compared between survivors and non-survivors in the burn cohort and between the burn cohort and a simulation based on the mean physiological (100%) concentration for all factor levels.

RESULTS

Burn patients differed at Hour 0 (p < 0.05) from 100% mean physiological levels for all coagulation factor levels except FV and FVII. The concentration of FX, FII, TFPI, AT and PC was lower; FIX and FVIII were increased. The composition differences resulted in all nine burn patients at Hour 0 displaying a procoagulant phenotype relative to 100% mean physiological simulation (MaxLIIa (306 ± 90 nM vs. 52 nM), MaxRIIa (2.9 ± 1.1 nM/s vs. 0.3 nM/s), respectively p < 0.001); MaxRFXa and MaxLFXa were also an order of magnitude greater than 100% mean physiological simulation (p < 0.001). When grouped by survival status and compared at the time of admission, non-survivors had lower PC levels (56 ± 18% vs. 82 ± 9%, p < 0.05), and faster MaxRFXa (29 ± 6 pM/s vs. 18 ± 6 pM/s, p < 0.05) than those that survived; similar trends were observed for all other procoagulant parameters. At 48 hours when comparing non-survivors to survivors, TFPI levels were higher (108 ± 18% vs. 59 ± 18%, p < 0.05), and MaxRIIa (1.5 ± 1.4 nM/s vs. 3.6 ± 0.7 nM/s, p < 0.05) and MaxRFXa (13 ± 12 pM/s vs. 35 ± 4 pM/s, p < 0.05) were lower; similar trends were observed with all other procoagulant parameters. Overall, between admission and 48 hours, procoagulant potential, as represented by MaxR and MaxL parameters for thrombin and FXa, in non-survivors decreased while in survivors they increased (p < 0.05). In patients that survived, there was a positive correlation between FX levels and MaxLFXa (r = 0.96) and reversed in mortality (r= -0.91).

CONCLUSIONS

Thrombin and FXa generation are increased in burn patients at admission compared to mean physiological simulations. Over the first 48 hours, burn survivors became more procoagulant while non-survivors became less procoagulant. Differences between survivors and non-survivors appear to be present in the underlying dynamics that contribute to FXa dynamics. Understanding how the individual specific balance of procoagulant and anticoagulant proteins contributes to thrombin and FXa generation could ultimately guide therapy and potentially reduce burn injury-related morbidity and mortality.

Strongly Coupled Morphological Features of Aortic Aneurysms Drive Intraluminal Thrombus

Over 75% of abdominal aortic aneurysms harbor an intraluminal thrombus, and increasing evidence suggests that biologically active thrombus contributes to the natural history of these potentially lethal lesions. Thrombus formation depends on the local hemodynamics, which in turn depends on morphological features of the aneurysm and near vasculature. We previously presented a hemodynamically motivated “thrombus formation potential” that predicts where and when thrombus might form. Herein, we combine detailed studies of the three-dimensional hemodynamics with methods of sparse grid collocation and interpolation via kriging to examine roles of five key morphological features of aneurysms on thrombus formation: lesion diameter, axial position, length, curvature, and renal artery position. Computational simulations suggest that maximum diameter is a key determinant of thrombogenicity, but other morphological features modulate this dependence. More distally located lesions tend to have a higher thrombus formation potential and shorter lesions tend to have a higher potential than longer lesions, given the same aneurysmal dilatation. Finally, movement of vortical structures through the infrarenal aorta and lesion can significantly affect thrombogenicity. Formation of intraluminal thrombus within an evolving abdominal aortic aneurysm thus depends on coupled morphological features, not all intuitive, and computational simulations can be useful for predicting thrombogenesis.

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.

Development of a platelet adhesion transport equation for a computational thrombosis model

Thrombosis is a significant issue for cardiovascular device development and use. While thrombosis models are available, very few are device-related and none have been thoroughly validated experimentally. Here, we introduce a surface adherent platelet transport equation into a continuum model to account for the biomaterial interface/blood interaction. Using a rotating disc system and polyurethane-urea material, we characterize steady and pulsatile flow fields using laser Doppler velocimetry. In vitro measurements of platelet adhesion are used in combination with the LDV data to provide further experimental validation. The rotating disc system is computationally studied using the device-induced thrombosis model with the surface platelet adherent transport equation. The results indicate that the flow field is in excellent agreement to the experimental LDV data and that the platelet adhesion simulations are in good agreement with the in vitro platelet data. These results provide good evidence that this transport equation can be used to express the relationship between blood and a biomaterial if the correct platelet adhesion characteristics are known for the biomaterial. Further validation is necessary with other materials.

Computational immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.

Development of a computational model for macroscopic predictions of device-induced thrombosis

While cardiovascular device-induced thrombosis is associated with negative patient outcomes, the convoluted nature of the processes resulting in a thrombus makes the full thrombotic network too computationally expensive to simulate in the complex geometries and flow fields associated with devices. A macroscopic, continuum computational model is developed based on a simplified network, which includes terms for platelet activation (chemical and mechanical) and thrombus deposition and growth in regions of low wall shear stress (WSS). Laminar simulations are performed in a two-dimensional asymmetric sudden expansion geometry and compared with in vitro thrombus size data collected using whole bovine blood. Additionally, the predictive power of the model is tested in a flow cell containing a series of symmetric sudden expansions and contractions. Thrombi form in the low WSS area downstream of the asymmetric expansion and grow into the nearby recirculation region, and thrombus height and length largely remain within 95 % confidence intervals calculated from the in vitro data for 30 min of blood flow. After 30 min, predicted thrombus height and length are 0.94 and 4.32 (normalized by the 2.5 mm step height). Importantly, the model also correctly predicts locations of thrombus deposition observed in the in vitro flow cell of expansions and contractions. As the simulation results, which rely on a greatly reduced model of the thrombotic network, are still able to capture the macroscopic behavior of the full network, the model shows promise for timely predictions of device-induced thrombosis toward optimizing and expediting the device development process.

A constitutive model for developing blood clots with various compositions and their nonlinear viscoelastic behavior

The mechanical properties determine to a large extent the functioning of a blood clot. These properties depend on the composition of the clot and have been related to many diseases. However, the various involved components and their complex interactions make it difficult at this stage to fully understand and predict properties as a function of the components. Therefore, in this study, a constitutive model is developed that describes the viscoelastic behavior of blood clots with various compositions. Hereto, clots are formed from whole blood, platelet-rich plasma and platelet-poor plasma to study the influence of red blood cells, platelets and fibrin, respectively. Rheological experiments are performed to probe the mechanical behavior of the clots during their formation. The nonlinear viscoelastic behavior of the mature clots is characterized using a large amplitude oscillatory shear deformation. The model is based on a generalized Maxwell model that accurately describes the results for the different rheological experiments by making the moduli and viscosities a function of time and the past and current deformation. Using the same model with different parameter values enables a description of clots with different compositions. A sensitivity analysis is applied to study the influence of parameter variations on the model output. The relative simplicity and flexibility make the model suitable for numerical simulations of blood clots and other materials showing similar behavior.

Regulation of Early Steps of GPVI Signal Transduction by Phosphatases: A Systems Biology Approach

We present a data-driven mathematical model of a key initiating step in platelet activation, a central process in the prevention of bleeding following Injury. In vascular disease, this process is activated inappropriately and causes thrombosis, heart attacks and stroke. The collagen receptor GPVI is the primary trigger for platelet activation at sites of injury. Understanding the complex molecular mechanisms initiated by this receptor is important for development of more effective antithrombotic medicines. In this work we developed a series of nonlinear ordinary differential equation models that are direct representations of biological hypotheses surrounding the initial steps in GPVI-stimulated signal transduction. At each stage model simulations were compared to our own quantitative, high-temporal experimental data that guides further experimental design, data collection and model refinement. Much is known about the linear forward reactions within platelet signalling pathways but knowledge of the roles of putative reverse reactions are poorly understood. An initial model, that includes a simple constitutively active phosphatase, was unable to explain experimental data. Model revisions, incorporating a complex pathway of interactions (and specifically the phosphatase TULA-2), provided a good description of the experimental data both based on observations of phosphorylation in samples from one donor and in those of a wider population. Our model was used to investigate the levels of proteins involved in regulating the pathway and the effect of low GPVI levels that have been associated with disease. Results indicate a clear separation in healthy and GPVI deficient states in respect of the signalling cascade dynamics associated with Syk tyrosine phosphorylation and activation. Our approach reveals the central importance of this negative feedback pathway that results in the temporal regulation of a specific class of protein tyrosine phosphatases in controlling the rate, and therefore extent, of GPVI-stimulated platelet activation.

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.

In vitro quantification of time dependent thrombus size using magnetic resonance imaging and computational simulations of thrombus surface shear stresses

Thrombosis and thromboembolization remain large obstacles in the design of cardiovascular devices. In this study, the temporal behavior of thrombus size within a backward-facing step (BFS) model is investigated, as this geometry can mimic the flow separation which has been found to contribute to thrombosis in cardiac devices. Magnetic resonance imaging (MRI) is used to quantify thrombus size and collect topographic data of thrombi formed by circulating bovine blood through a BFS model for times ranging between 10 and 90 min at a constant upstream Reynolds number of 490. Thrombus height, length, exposed surface area, and volume are measured, and asymptotic behavior is observed for each as the blood circulation time is increased. Velocity patterns near, and wall shear stress (WSS) distributions on, the exposed thrombus surfaces are calculated using computational fluid dynamics (CFD). Both the mean and maximum WSS on the exposed thrombus surfaces are much more dependent on thrombus topography than thrombus size, and the best predictors for asymptotic thrombus length and volume are the reattachment length and volume of reversed flow, respectively, from the region of separated flow downstream of the BFS.

A haemodynamic predictor of intraluminal thrombus formation in abdominal aortic aneurysms

Intraluminal thrombus (ILT) is present in over 75% of all abdominal aortic aneurysms (AAAs) and probably contributes to the complex biomechanics and pathobiology of these lesions. A reliable predictor of thrombus formation in enlarging lesions could thereby aid clinicians in treatment planning. The primary goal of this work was to identify a new phenomenological metric having clinical utility that is motivated by the hypothesis that two basic haemodynamic features must coincide spatially and temporally to promote the formation of a thrombus on an intact endothelium—platelets must be activated within a shear flow and then be presented to a susceptible endothelium. Towards this end, we propose a new thrombus formation potential (TFP) that combines information on the flow-induced shear history experienced by blood-borne particles that come in close proximity to the endothelium with information on both the time-averaged wall shear stress (WSS) and the oscillatory shear index (OSI) that locally affect the endothelial mechanobiology. To illustrate the possible utility of this new metric, we show computational results for 10 carotid arteries from five patients where regions of low WSS and high OSI tend not to be presented with activated platelets (i.e. they have a low TFP), consistent with the thrombo-resistance of the healthy carotid despite its complex haemodynamics. Conversely, we show results for three patients that high TFP co-localizes with regions of observed thin thrombus in AAAs, which contrasts with findings of low TFP for the abdominal aorta of three healthy subjects. We submit that these promising results suggest the need for further consideration of the TFP, or a similar combined metric, as a potentially useful clinical predictor of the possible formation of ILT in AAAs.

A continuum model for platelet plug formation, growth and deformation

A numerical framework for modelling platelet plug dynamics is presented in this work. It consists of an extension of a biochemical and plug growth model with a solid mechanics model for the plug coupled with a fluid-structure interaction model for the blood flow-plug system. The platelet plug is treated as a neo-Hookean elastic solid, of which the implementation is based on an updated Lagrangian approach. The framework is applied to different haemodynamic configurations coupled with different shear moduli of the plug. Results about plug growth, shape and size, as well as the stress distribution, are shown. Based on the simulations performed, we conclude that the deformability of the platelet plug is essential for its growth.

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.

Kinetic model facilitates analysis of fibrin generation and its modulation by clotting factors: implications for hemostasis-enhancing therapies

Current mechanistic knowledge of protein interactions driving blood coagulation has come largely from experiments with simple synthetic systems, which only partially represent the molecular composition of human blood plasma. Here, we investigate the ability of the suggested molecular mechanisms to account for fibrin generation and degradation kinetics in diverse, physiologically relevant in vitro systems. We represented the protein interaction network responsible for thrombin generation, fibrin formation, and fibrinolysis as a computational kinetic model and benchmarked it against published and newly generated data reflecting diverse experimental conditions. We then applied the model to investigate the ability of fibrinogen and a recently proposed prothrombin complex concentrate composition, PCC-AT (a combination of the clotting factors II, IX, X, and antithrombin), to restore normal thrombin and fibrin generation in diluted plasma. The kinetic model captured essential features of empirically detected effects of prothrombin, fibrinogen, and thrombin-activatable fibrinolysis inhibitor titrations on fibrin formation and degradation kinetics. Moreover, the model qualitatively predicted the impact of tissue factor and tPA/tenecteplase level variations on the fibrin output. In the majority of considered cases, PCC-AT combined with fibrinogen accurately approximated both normal thrombin and fibrin generation in diluted plasma, which could not be accomplished by fibrinogen or PCC-AT acting alone. We conclude that a common network of protein interactions can account for key kinetic features characterizing fibrin accumulation and degradation in human blood plasma under diverse experimental conditions. Combined PCC-AT/fibrinogen supplementation is a promising strategy to reverse the deleterious effects of dilution-induced coagulopathy associated with traumatic bleeding.

Modelling the influence of endothelial heterogeneity on the progression of arterial disease: application to abdominal aortic aneurysm evolution

We sophisticate a fluid-solid growth computational framework for modelling aneurysm evolution. A realistic structural model of the arterial wall is integrated into a patient-specific geometry of the vasculature. This enables physiologically representative distributions of haemodynamic stimuli, obtained from a rigid-wall computational fluid dynamics analysis, to be linked to growth and remodelling algorithms. Additionally, a quasistatic structural analysis quantifies the cyclic deformation of the arterial wall so that collagen growth and remodelling can be explicitly linked to the cyclic deformation of vascular cells. To simulate aneurysm evolution, degradation of elastin is driven by reductions in wall shear stress (WSS) below homeostatic thresholds. Given that the endothelium exhibits spatial and temporal heterogeneity, we propose a novel approach to define the homeostatic WSS thresholds: We allow them to be spatially and temporally heterogeneous. We illustrate the application of this novel fluid-solid growth framework to model abdominal aortic aneurysm (AAA) evolution and to examine how the influence of the definition of the WSS homeostatic threshold influences AAA progression. We conclude that improved understanding and modelling of the endothelial heterogeneity is important for modelling aneurysm evolution and, more generally, other vascular diseases where haemodynamic stimuli play an important role.

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.

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.

Biochemomechanics of intraluminal thrombus in abdominal aortic aneurysms

Most computational models of abdominal aortic aneurysms address either the hemodynamics within the lesion or the mechanics of the wall. More recently, however, some models have appropriately begun to account for the evolving mechanics of the wall in response to the changing hemodynamic loads. Collectively, this large body of work has provided tremendous insight into this life-threatening condition and has provided important guidance for current research. Nevertheless, there has yet to be a comprehensive model that addresses the mechanobiology, biochemistry, and biomechanics of thrombus-laden abdominal aortic aneurysms. That is, there is a pressing need to include effects of the hemodynamics on both the development of the nearly ubiquitous intraluminal thrombus and the evolving mechanics of the wall, which depends in part on biochemical effects of the adjacent thrombus. Indeed, there is increasing evidence that intraluminal thrombus in abdominal aortic aneurysms is biologically active and should not be treated as homogeneous inert material. In this review paper, we bring together diverse findings from the literature to encourage next generation models that account for the biochemomechanics of growth and remodeling in patient-specific, thrombus-laden abdominal aortic aneurysms.

Models for thrombin generation and risk of disease

Computational models can offer an integrated view of blood clotting dynamics and may ultimately be instructive regarding an individual's risk of bleeding or clotting. Appropriately, developed and validated models could allow clinicians to simulate the outcomes of therapeutics and estimate risk of disease. Computational models that describe the dynamics of thrombin generation have been developed and have been used in combination with empirical studies to understand thrombin dynamics on a mechanistic basis. The translation of an individual's specific coagulation factor composition data using these models into an integrated assessment of hemostatic status may provide a route for advancing the long-term goal of individualized medicine. This review details the integrated approaches to understanding: (i) What is normal thrombin generation in individuals? (ii) What is the effect of normal range plasma composition variation on thrombin generation in pathologic states? (iii) Can disease progression or anticoagulation be followed by understanding the boundaries of normal thrombin generation defined by plasma composition? (iv) What are the controversies and limitations of current computational approaches? Progress in these areas can bring us closer to developing models that can be used to aid in identifying hemostatic risk.

Challenges and opportunities in cardiovascular health informatics

Cardiovascular health informatics is a rapidly evolving interdisciplinary field concerning the processing, integration/interpretation, storage, transmission, acquisition, and retrieval of information from cardiovascular systems for the early detection, early prediction, early prevention, early diagnosis, and early treatment of cardiovascular diseases (CVDs). Based on the first author's presentation at the first IEEE Life Sciences Grand Challenges Conference, held on October 4-5, 2012, at the National Academy of Sciences, Washington, DC, USA, this paper, focusing on coronary arteriosclerotic disease, will discuss three significant challenges of cardiovascular health informatics, including: 1) to invent unobtrusive and wearable multiparameter sensors with higher sensitivity for the real-time monitoring of physiological states; 2) to develop fast multimodal imaging technologies with higher resolution for the quantification and better understanding of structure, function, metabolism of cardiovascular systems at the different levels; and 3) to develop novel multiscale information fusion models and strategies with higher accuracy for the personalized predication of the CVDs. At the end of this paper, a summary is given to suggest open discussions on these three and more challenges that face the scientific community in this field in the future.

A review of macroscopic thrombus modeling methods

Hemodynamics applied to mechanobiology offers powerful means to predict thrombosis, and to understand the kinetics of thrombus formation on areas of vascular damage in blood flowing through the human circulatory system. Specifically, the advances in computational processing and the progress in modeling complex biological processes with spatio-temporal multi-scale methods have the potential to shift the way in which cardiovascular diseases are diagnosed and treated. This article systematically surveys the state of the art of macroscopic computational fluid dynamics (CFD) Computational fluid dynamics techniques for modeling thrombus formation, highlighting their strengths and weaknesses. In particular, a comprehensive and systematic revision of the hemodynamics models and methods is given, and the strengths and weaknesses of those employed for studying thrombus formation are highlighted.

The computing platelet: integrating environmental cues

In this issue of Blood, Flamm et al combine high-throughput experimental methods and multiscale computer simulations to predict patient-specific thrombus formation potential.(1) Their studies reveal a novel thromboxane receptor mutation (TP-V241G) in humans that confers resistance to indomethacin.

Defining the boundaries of normal thrombin generation: investigations into hemostasis

In terms of its soluble precursors, the coagulation proteome varies quantitatively among apparently healthy individuals. The significance of this variability remains obscure, in part because it is the backdrop against which the hemostatic consequences of more dramatic composition differences are studied. In this study we have defined the consequences of normal range variation of components of the coagulation proteome by using a mechanism-based computational approach that translates coagulation factor concentration data into a representation of an individual's thrombin generation potential. A novel graphical method is used to integrate standard measures that characterize thrombin generation in both empirical and computational models (e.g max rate, max level, total thrombin, time to 2 nM thrombin ("clot time")) to visualize how normal range variation in coagulation factors results in unique thrombin generation phenotypes. Unique ensembles of the 8 coagulation factors encompassing the limits of normal range variation were used as initial conditions for the computational modeling, each ensemble representing "an individual" in a theoretical healthy population. These "individuals" with unremarkable proteome composition was then compared to actual normal and "abnormal" individuals, i.e. factor ensembles measured in apparently healthy individuals, actual coagulopathic individuals or artificially constructed factor ensembles representing individuals with specific factor deficiencies. A sensitivity analysis was performed to rank either individual factors or all possible pairs of factors in terms of their contribution to the overall distribution of thrombin generation phenotypes. Key findings of these analyses include: normal range variation of coagulation factors yields thrombin generation phenotypes indistinguishable from individuals with some, but not all, coagulopathies examined; coordinate variation of certain pairs of factors within their normal ranges disproportionately results in extreme thrombin generation phenotypes, implying that measurement of a smaller set of factors may be sufficient to identify individuals with aberrant thrombin generation potential despite normal coagulation proteome composition.

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.

Multiscale model of fibrin accumulation on the blood clot surface and platelet dynamics

A multiscale computational model of thrombus (blood clot) development is extended by incorporating a submodel describing formation of fibrin network through "fibrin elements" representing regions occupied by polymerized fibrin. Simulations demonstrate that fibrin accumulates on the surface of the thrombus and that fibrin network limits growth by reducing thrombin concentrations on the thrombus surface and decreasing adhesivity of resting platelets in blood near thrombus surface. These results suggest that fibrin accumulation may not only increase the structural integrity of the thrombus but also considerably contribute toward limiting its growth. Also, a fast Graphics Processing Unit implementation is described for a multiscale computational model of the platelet-blood flow interaction.

Procoagulant activity in hemostasis and thrombosis: Virchow's triad revisited

Virchow's triad is traditionally invoked to explain pathophysiologic mechanisms leading to thrombosis, alleging concerted roles for abnormalities in blood composition, vessel wall components, and blood flow in the development of arterial and venous thrombosis. Given the tissue-specific bleeding observed in hemophilia patients, it may be instructive to consider the principles of Virchow's triad when investigating mechanisms operant in hemostatic disorders as well. Blood composition (the function of circulating blood cells and plasma proteins) is the most well studied component of the triad. For example, increased levels of plasma procoagulant proteins such as prothrombin and fibrinogen are established risk factors for thrombosis, whereas deficiencies in plasma factors VIII and IX result in bleeding (hemophilia A and B, respectively). Vessel wall (cellular) components contribute adhesion molecules that recruit circulating leukocytes and platelets to sites of vascular damage, tissue factor, which provides a procoagulant signal of vascular breach, and a surface upon which coagulation complexes are assembled. Blood flow is often characterized by 2 key variables: shear rate and shear stress. Shear rate affects several aspects of coagulation, including transport rates of platelets and plasma proteins to and from the injury site, platelet activation, and the kinetics of fibrin monomer formation and polymerization. Shear stress modulates adhesion rates of platelets and expression of adhesion molecules and procoagulant activity on endothelial cells lining the blood vessels. That no one abnormality in any component of Virchow's triad fully predicts coagulopathy a priori suggests coagulopathies are complex, multifactorial, and interactive. In this review, we focus on contributions of blood composition, vascular cells, and blood flow to hemostasis and thrombosis, and suggest that cross-talk among the 3 components of Virchow's triad is necessary for hemostasis and determines propensity for thrombosis or bleeding. Investigative models that permit interplay among these components are necessary to understand the operant pathophysiology, and effectively treat and prevent thrombotic and bleeding disorders.