Platelet motion near a vessel wall or thrombus surface in two-dimensional whole blood simulations

Decoding thrombosis through code: a review of computational models

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

Mechanobiology of the endothelium in vascular health and disease: in vitro shear stress models

In recent years, there has been growing evidence that vascular pathologies arise in sites experiencing an altered haemodynamic environment. Fluid shear stress (FSS) is an important contributor to vascular homeostasis and regulates endothelial cell (EC) gene expression, morphology, and behaviour through specialised mechanosensitive signalling pathways. The presence of an altered FSS profile is a pathological characteristic of many vascular diseases, with the most established example being the preferential localisation of atherosclerotic plaque development. However, the precise haemodynamic contributions to other vascular pathologies including coronary artery vein graft failure remains poorly defined. To evaluate potential novel therapeutics for the treatment of vascular diseases via targeting EC behaviour, it is important to undertake in vitro experiments using appropriate culture conditions, particularly FSS. There are a wide range of in vitro models used to study the effect of FSS on the cultured endothelium, each with the ability to generate FSS flow profiles through which the investigator can control haemodynamic parameters including flow magnitude and directionality. An important consideration for selection of an appropriate model of FSS exposure is the FSS profile that the model can generate, in comparison to the physiological and pathophysiological haemodynamic environment of the vessel of interest. A resource bringing together the haemodynamic environment characteristic of atherosclerosis pathology and the flow profiles generated by in vitro methods of applying FSS would be beneficial to researchers when selecting the appropriate model for their research. Consequently, here we summarise the widely used methods of exposing cultured endothelium to FSS, the flow profile they generate and their advantages and limitations in investigating the pathological contribution of altered FSS to vascular disease and evaluating novel therapeutic targets for the treatment and prevention of vascular disease.

Clinical Characteristics and Prognostic Risks of Philadelphia-Negative Myeloproliferative Neoplasms at Cipto Mangunkusumo General Hospital

Background

Philadelphia-negative myeloproliferative neoplasms (Ph-MPNs) are clonal hematopoietic cell malignancy that comprises polycythemia vera (PV), essential thrombocythemia (ET), and primary myelofibrosis (PMF). They prone to develop thrombosis, bleeding, fibrotic progression, and leukemic transformation. We aimed to study clinical characteristics, thrombosis complications, and prognostic risk in Indonesians with Ph-MPNs.

Methods

This was a single-center retrospective cross-sectional study, including patients with Ph-MPNs who attended Hematology and Medical Oncology outpatient clinic at Cipto Mangunkusumo General Hospital, Jakarta, between 2016 and 2021. Demographic data, clinical characteristics, previous antiplatelet treatment, baseline laboratory data, JAK2V617F mutation, and treatment were reviewed for analysis. The prognostic risk model was assessed for PV (IPSS), ET (IPSET-thrombosis), and PMF (IPSS and DIPPS) patients.

Results

One hundred forty-six patients were classified as PV (31.5%), ET (38.4%), and PMF (30.1%) with median ages of 54, 53.5, and 55 years, respectively. PMF presented with the most diverse clinical presentations. JAK2V617 mutations were detected in 82%, 42.5%, and 76.5% of PV, ET, and PMF patients. PV had the highest thrombosis event pre/at diagnosis (26.1%), with predominantly arterial thrombosis. Bleeding occurred more in PMF (20.5%). Phlebotomy and hydroxyurea are the only treatment available for Ph-MPNs in the government hospital in Indonesia. IPSS intermediate risk in PV (47.8%), IPSET-thrombosis low risk in ET (46.4%), and IPSS and DIPSS intermediate-2 in PMF (38.6% and 50% respectively) were the most common risk groups.

Conclusion

Essential thrombocythemia was the most prevalent Ph-MPNs in Indonesia. Arterial thrombosis was the highest thrombosis event pre/at diagnosis in PV despite IPSET-thrombosis low risk being the most common risk group. In JAK2V617 mutation-positive MPN population, thrombosis event was also the highest in PV.

Platelet-inspired nanomedicine in hemostasis thrombosis and thromboinflammation

Platelets are anucleate cell-fragments derived predominantly from megakaryocytes in the bone marrow and released in the blood circulation, with a normal count of 150 000-40 000 per μl and a lifespan of approximately 10 days in humans. A primary role of platelets is to aid in vascular injury site-specific clot formation to stanch bleeding, termed hemostasis. Platelets render hemostasis by a complex concert of mechanisms involving platelet adhesion, activation and aggregation, coagulation amplification, and clot retraction. Additionally, platelet secretome can influence coagulation kinetics and clot morphology. Therefore, platelet defects and dysfunctions result in bleeding complications. Current treatment for such complications involve prophylactic or emergency transfusion of platelets. However, platelet transfusion logistics constantly suffer from limited donor availability, challenges in portability and storage, high bacterial contamination risks, and very short shelf life (~5 days). To address these issues, an exciting area of research is focusing on the development of microparticle- and nanoparticle-based platelet surrogate technologies that can mimic various hemostatic mechanisms of platelets. On the other hand, aberrant occurrence of the platelet mechanisms lead to the pathological manifestation of thrombosis and thromboinflammation. The treatments for this are focused on inhibiting the mechanisms or resolving the formed clots. Here, platelet-inspired technologies can provide unique platforms for disease-targeted drug delivery to achieve high therapeutic efficacy while avoiding systemic side-effects. This review will provide brief mechanistic insight into the role of platelets in hemostasis, thrombosis and thromboinflammation, and present the current state-of-art in the design of platelet-inspired nanomedicine for applications in these areas.

A Hemodynamic Analysis of the Thrombosis Within Occluded Coronary Arterial Fistulas With Terminal Aneurysms Using a Blood Stasis Model

Objective: The aim of this study is to numerically evaluate thrombosis risk within occluded coronary arterial fistulas (CAF) with terminal aneurysms, and provide guidance in choosing occlusion positions, with clinical observations as reference. Method: Four patients with CAF were studied, with different occlusion positions in actual treatments. Hemodynamics simulations were conducted, with blood residue predicted using the blood stasis model. Three types of models (untreated model, aneurysm-reserved model and aneurysm-removed model) were studeid for each patient. Four metrics, i.e., proportion of high oscillatory shear index (OSI), area of high OSI, old blood volume fraction (OBVF)) and old blood volume (OBV) was obtained to distinguish the thrombosis risk of different treatments (proximal or distal occlusion), comparing with the follow-up CTA. Results: For all the postopertive models, the high OBVF, high OSI(>0.3) and low time-averaged wall shear stress (TAWSS) regions were mainly at the distal fistula, indicating these regions were prone to thrombosis. The regions where blood residue remains are roughly regions of high OSI, corresponding well with clinical observations. In contrast, TAWSS failed to distinguish the difference in thrombosis risk. Absolute values (area of high OSI, OBV) can better reflect the degree of thrombosis risk between treatment types compared with percentage values (proportion of high OSI, OBVF). By comparing with the actual clinical treatments and observations, the OBV is superior to the area of high OSI in determining treatment type. Conclusion: The OBV, a volumetric parameter for blood stasis, can better account for the CAF thrombosis and reflect the degree of blood stasis compared with OSI or TAWSS, is a more appropriate metric for thrombosis in the fistula. Together with morphological parameters, the OBV could guide clinicians to formulate more appropriate surgical plans, which is of great significance for the preoperative evaluation and treatment prognosis of CAF patients.

A two-fluid blood stasis model for false lumen thrombosis after type B dissection repair

The formation of thrombosis is a major concern in the false lumen (FL) for post-TEVAR (thoracic endovascular aortic repair) patients. Blood stasis is one of the key factors which lead to the formation of thrombosis in the arterial systems. This study proposed a computational model for blood stasis, using a two-fluid principle to track the locations of blood residual over time. The current study applied this novel model to evaluate blood stasis and thrombosis potential in four patient-specific post-TEVAR FLs of type B aortic dissection, with their follow-up in-vivo observations two years after TEVAR. The locations and topologies of residual blood in the FL predicted by the model agreed well with the in-vivo observations of thrombus. In addition, the results corresponded better with clinical observations in terms of interpatient comparison of degree of thrombosis, compared with conventional hemodynamic parameters. The blood stasis model serves as a valuable addition to conventional metrics to better predict thrombosis potential. Collectively, these metrics can provide an efficient non-invasive method for evaluating blood stasis and thrombosis potential in arterial system, and useful guidance for clinicians' operative planning and postoperative evaluation.

A multi-objective optimization of stent geometries

Stents are scaffolding cardiovascular implants used to restore blood flow in narrowed arteries. However, the presence of the stent alters local blood flow and shear stresses on the surrounding arterial wall, which can cause adverse tissue responses and increase the risk of adverse outcomes. There is a need for optimization of stent designs for hemodynamic performance. We used multi-objective optimization to identify ideal combinations of design variables by assessing potential trade-offs based on common hemodynamic indices associated with clinical risk and mechanical performance of the stents. We studied seven design variables including strut cross-section, strut dimension, strut angle, cell alignment, cell height, connector type and connector arrangement. Optimization objectives were the percentage of vessel area exposed to adversely low time averaged WSS (TAWSS) and adversely high Wall Shear Stress (WSS) assessed using computational fluid dynamics modeling, as well as radial stiffness of the stent using FEA simulation. Two multi-objective optimization algorithms were used and compared to iteratively predict ideal designs. Out of 50 designs, three best designs with respect to each of the three objectives, and two designs in regard to overall performance were identified.

A MATHEMATICAL MODEL OF PLATELET AGGREGATION IN AN EXTRAVASCULAR INJURY UNDER FLOW

We present the first mathematical model of flow-mediated primary hemostasis in an extravascular injury which can track the process from initial deposition to occlusion. The model consists of a system of ordinary differential equations (ODEs) that describe platelet aggregation (adhesion and cohesion), soluble-agonist-dependent platelet activation, and the flow of blood through the injury. The formation of platelet aggregates increases resistance to flow through the injury, which is modeled using the Stokes-Brinkman equations. Data from analogous experimental (microfluidic flow) and partial differential equation models informed parameter values used in the ODE model description of platelet adhesion, cohesion, and activation. This model predicts injury occlusion under a range of flow and platelet activation conditions. Simulations testing the effects of shear and activation rates resulted in delayed occlusion and aggregate heterogeneity. These results validate our hypothesis that flow-mediated dilution of activating chemical adenosine diphosphate hinders aggregate development. This novel modeling framework can be extended to include more mechanisms of platelet activation as well as the addition of the biochemical reactions of coagulation, resulting in a computationally efficient high throughput screening tool of primary and secondary hemostasis.

Simulation of blood flow in a sudden expansion channel and a coronary artery

In this paper, we numerically simulate the flow of blood in two benchmark problems: the flow in a sudden expansion channel and the flow through an idealized curved coronary artery with pulsatile inlet velocity. Blood is modeled as a suspension (a non-linear complex fluid) and the movement of the red blood cell (RBCs) is modeled by using a concentration flux equation. The viscosity of blood is obtained from experimental data. In the sudden expansion flow, the predicted velocity profiles for two different Reynolds numbers (based on the inlet velocity) agree well with the available experiments; furthermore, the numerical results also show that after the sudden expansion there exists a RBCs depletion region. For the second problem, the idealized curved coronary artery, it is found that the RBCs move towards and concentrate near the inner surface where the viscosity is higher and the shear stress lower; this phenomenon may be related to the atherosclerotic plaque formation which usually occurs on the inside surface of the arteries.

Magnetic Resonance Imaging Based Flow Field and Lagrangian Particle Tracking From a Left Ventricular Assist Device

This study explores the optimal left ventricular assist device (LVAD) cannula outflow configuration in a patient-specific replica of the aorta. The volumetric velocity field is measured using phase-contrast magnetic resonance imaging (PC-MRI) under a physiologically relevant steady flow. The effect of the LVAD outflow graft insertion site and anastomosis angle on the transport of embolic particles to cranial vessels is studied by solving the particle equation of motion for spheres in the range of 0.1-1.0 mm using the measured three-dimensional (3D) velocity field. Results show that for a given aorta anatomy, it is possible to design the cannula graft location and terminal curvature so that the probability of embolic transport to the cranial vessels is significantly minimized. This is particularly important since the complex flow pattern in each cannula case affects the embolic trajectories differently, and hence the common assumption that particles distribute by the volumetric flow division does not hold.

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

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

Platelet adhesion emulation: A novel method for estimating the device thrombosis potential of a ventricular assist device

Device thrombosis inside ventricular assist devices remains a limitation to their long-term clinical use. Thrombosis potential exists in almost all ventricular assist devices because the device-induced high shear stress and vortices can activate platelets, which then aggregate and adhere to the surfaces inside the ventricular assist device. To decrease the device thrombosis potential of long-term use of ventricular assist devices, a methodology entitled platelet adhesion emulation for predicting the thrombosis potential and thrombosis position inside the ventricular assist devices is developed. The platelet adhesion emulation methodology combines numerical simulations with in vitro experiments by correlating the structure of the flow passage components within the ventricular assist device with the platelet adhesion to estimate the thrombosis potential and location, with the goal of developing ventricular assist devices with optimized antithrombotic performance. Platelet adhesion emulation is aimed at decreasing the device thrombus potential of ventricular assist devices. The platelet adhesion emulation effectiveness is validated by simulating and testing an axial left ventricular assist device. The blood velocity relative to the surfaces of the flow passage components is calculated to estimate the platelet adhesion potential, indicating the probability of thrombus formation on the surfaces. Platelet adhesion emulation experiments conducted in a mock circulation loop with pump prototypes show the distribution of platelet adhesion on the surfaces. This methodology of emulating the device thrombosis distribution indicates the potential for improving the component structure and reducing the device thrombosis of ventricular assist devices.

Advances in Computational Fluid Mechanics in Cellular Flow Manipulation: A Review

Recently, remarkable developments have taken place, leading to significant improvements in microfluidic methods to capture subtle biological effects down to single cells. As microfluidic devices are getting sophisticated, design optimization through experimentations is becoming more challenging. As a result, numerical simulations have contributed to this trend by offering a better understanding of cellular microenvironments hydrodynamics and optimizing the functionality of the current/emerging designs. The need for new marketable designs with advantageous hydrodynamics invokes easier access to efficient as well as time-conservative numerical simulations to provide screening over cellular microenvironments, and to emulate physiological conditions with high accuracy. Therefore, an excerpt overview on how each numerical methodology and associated handling software works, and how they differ in handling underlying hydrodynamic of lab-on-chip microfluidic is crucial. These numerical means rely on molecular and continuum levels of numerical simulations. The current review aims to serve as a guideline for researchers in this area by presenting a comprehensive characterization of various relevant simulation techniques.

Antimargination of Microparticles and Platelets in the Vicinity of Branching Vessels

We investigate the margination of microparticles/platelets in blood flow through complex geometries typical for in vivo vessel networks: a vessel confluence and a bifurcation. Using three-dimensional lattice Boltzmann simulations, we confirm that behind the confluence of two vessels, a cell-free layer devoid of red blood cells develops in the channel center. Despite its small size of roughly 1 μm, this central cell-free layer persists for up to 100 μm after the confluence. Most importantly, we show from simulations that this layer also contains a significant amount of microparticles/platelets and validate this result by in vivo microscopy in mouse venules. At bifurcations, however, a similar effect does not appear, and margination is largely unaffected by the geometry. This antimargination toward the vessel center after a confluence may explain earlier in vivo observations, which found that platelet concentrations near the vessel wall are seen to be much higher on the arteriolar side (containing bifurcations) than on the venular side (containing confluences) of the vascular system.

Red blood cell distribution in a microvascular network with successive bifurcations

Nonproportional RBC distribution is an important characteristic in microvascular networks, which can result in heterogeneity of oxygen supply that may cause ischemic death in severe cases. In this paper, we perform three-dimensional numerical simulations of a large number of RBCs in a microvascular network, by using a hybrid method of smoothed dissipative particle dynamic and immersed boundary method. The distribution of multiple RBCs in a T-bifurcation is first simulated as a validation study, and a reasonable agreement is observed both qualitatively and quantitatively on the RBC flux between our results and the previously published numerical and empirical results. Next, the distribution of a large number of RBCs in a microvascular network is investigated, including the effects of cell deformability, aggregation and tube hematocrit. The simulation results indicate that decreased deformability and increased aggregation strength have a similar effect on the RBC distribution: the large RBC flux becomes larger, but the small becomes smaller. A high hematocrit also causes a similar phenomenon that the RBCs are more apt to flow into a high RBC-flux branch, because they are arranged compactly into a rouleaux and difficultly broken up at a high hematocrit. These results imply that lower cell deformability, stronger aggregation or higher tube hematocrit would be conducive to the phase separation of hematocrit and plasma skimming processes in microcirculation.

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

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

Quantifying Platelet Margination in Diabetic Blood Flow

Patients with type 2 diabetes mellitus (T2DM) develop thrombotic abnormalities strongly associated with cardiovascular diseases. In addition to the changes of numerous coagulation factors such as elevated levels of thrombin and fibrinogen, the abnormal rheological effects of red blood cells (RBCs) and platelets flowing in blood are crucial in platelet adhesion and thrombus formation in T2DM. An important process contributing to the latter is the platelet margination. We employ the dissipative particle dynamics method to seamlessly model cells, plasma, and vessel walls. We perform a systematic study on RBC and platelet transport in cylindrical vessels by considering different cell shapes, sizes, and RBC deformabilities in healthy and T2DM blood, as well as variable flowrates and hematocrit. In particular, we use cellular-level RBC and platelet models with parameters derived from patient-specific data and present a sensitivity study. We find T2DM RBCs, which are less deformable compared to normal RBCs, lower the transport of platelets toward the vessel walls, whereas platelets with higher mean volume (often observed in T2DM) lead to enhanced margination. Furthermore, increasing the flowrate or hematocrit enhances platelet margination. We also investigated the effect of platelet shape and observed a nonmonotonic variation with the highest near-wall concentration corresponding to platelets with a moderate aspect ratio of 0.38. We examine the role of white blood cells (WBCs), whose count is increased notably in T2DM patients. We find that WBC rolling or WBC adhesion tends to decrease platelet margination due to hydrodynamic effects. To the best of our knowledge, such simulations of blood including all blood cells have not been performed before, and our quantitative findings can help separate the effects of hydrodynamic interactions from adhesive interactions and potentially shed light on the associated pathological processes in T2DM such as increased inflammatory response, platelet activation and adhesion, and ultimately thrombus formation.

Cell-resolved blood flow simulations of saccular aneurysms: effects of pulsatility and aspect ratio

We study the effect of pulsatile flow on the transport of red blood cells (RBCs) and platelets into aneurysm geometries with varying dome-to-neck aspect ratios (AR). We use a validated two-dimensional lattice Boltzmann model for blood plasma with a discrete element method for both RBCs and platelets coupled by the immersed boundary method. Flow velocities and vessel diameters were matched with measurements of cerebral perforating arteries and flow was driven by a synthetic heartbeat curve typical for such vessel sizes. We observe a flow regime change as the aspect ratio increases from a momentum-driven regime in the small aspect ratio to a shear-driven regime in the larger aspect ratios. In the small aspect ratio case, we see the development of a re-circulation zone that exhibits a layering of high (greater than or equal to 7 s) and low (less than 7 s) residence cells. In the shear-driven regime, we see high and low residence cells well mixed, with an increasing population of cells that are trapped inside the aneurysm as the aspect ratio increases. In all cases, we observe aneurysms that are platelet-rich and red blood cell-poor when compared with their respective parental vessel populations. Pulsatility also plays a role in the small aspect ratio as we observe a smaller population of older trapped cells along the aneurysm wall in the pulsatile case when compared with a steady flow case. Pulsatility does not have a significant effect in shear-driven regime aspect ratios.

Synergistic Integration of Laboratory and Numerical Approaches in Studies of the Biomechanics of Diseased Red Blood Cells

In red blood cell (RBC) disorders, such as sickle cell disease, hereditary spherocytosis, and diabetes, alterations to the size and shape of RBCs due to either mutations of RBC proteins or changes to the extracellular environment, lead to compromised cell deformability, impaired cell stability, and increased propensity to aggregate. Numerous laboratory approaches have been implemented to elucidate the pathogenesis of RBC disorders. Concurrently, computational RBC models have been developed to simulate the dynamics of RBCs under physiological and pathological conditions. In this work, we review recent laboratory and computational studies of disordered RBCs. Distinguished from previous reviews, we emphasize how experimental techniques and computational modeling can be synergically integrated to improve the understanding of the pathophysiology of hematological disorders.

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.

Pressure and Flow Rate Changes During Contrast Injections in Cerebral Angiography: Correlation to Reflux Length

Cerebral angiography involves the antegrade injection of contrast media through a catheter into the vasculature to visualize the region of interest under X-ray imaging. Depending on the injection and blood flow parameters, the bolus of contrast can propagate in the upstream direction and proximal to the catheter tip, at which point contrast is said to have refluxed. In this in vitro study, we investigate the relationship of fundamental hemodynamic variables to this phenomenon. Contrast injections were carried out under steady and pulsatile flow using various vessel diameters, catheter sizes, working fluid flow rates, and injection rates. The distance from the catheter tip to the proximal edge of the contrast bolus, called reflux length, was measured on the angiograms; the relation of this reflux length to different hemodynamic parameters was evaluated. Results show that contrast reflux occurs when the pressure distal to the catheter tip increases to be greater than the pressure proximal to the catheter tip. The ratio of this pressure difference to the baseline flow rate, called reflux resistance here, was linearly correlated to the normalized reflux length (reflux length/vessel diameter). Further, the ratio of blood flow to contrast fluid momentums, called the Craya-Curtet number, was correlated to the normalized reflux length via a sigmoid function. A sigmoid function was also found to be representative of the relationship between the ratio of the Reynolds numbers of blood flow to contrast and the normalized reflux length. As described by previous reports, catheter based contrast injections cause substantial increases in local flow and pressure. Contrast reflux should generally be avoided during standard antegrade angiography. Our study shows two specific correlations between contrast reflux length and baseline and intra-injection parameters that have not been published previously. Further studies need to be conducted to fully characterize the phenomena and to extract reliable indicators of clinical utility. Parameters relevant to cerebral angiography are studied here, but the essential principles are applicable to all angiographic procedures involving antegrade catheter injections.

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.

Systems Analysis of Thrombus Formation

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

Binary agonist surface patterns prime platelets for downstream adhesion in flowing whole blood

As platelets encounter damaged vessels or biomaterials, they interact with a complex milieu of surface-bound agonists, from exposed subendothelium to adsorbed plasma proteins. It has been shown that an upstream, surface-immobilized agonist is capable of priming platelets for enhanced adhesion downstream. In this study, binary agonists were integrated into the upstream position of flow cells and the platelet priming response was measured by downstream adhesion in flowing whole blood. A nonadditive response was observed in which platelets transiently exposed to two agonists exhibited greater activation and downstream adhesion than that from the sum of either agonist alone. Antibody blocking of one of the two upstream agonists eliminated nonadditive activation and downstream adhesion. Crosstalk between platelet activation pathways likely led to a synergistic effect which created an enhanced activation response in the platelet population. The existence of synergy between platelet priming pathways is a concept that has broad implications for the field of biomaterials hemocompatibility and platelet activity testing.

Elevated hematocrit enhances platelet accumulation following vascular injury

Red blood cells (RBCs) demonstrate procoagulant properties in vitro, and elevated hematocrit is associated with reduced bleeding and increased thrombosis risk in humans. These observations suggest RBCs contribute to thrombus formation. However, effects of RBCs on thrombosis are difficult to assess because humans and mice with elevated hematocrit typically have coexisting pathologies. Using an experimental model of elevated hematocrit in healthy mice, we measured effects of hematocrit in 2 in vivo clot formation models. We also assessed thrombin generation, platelet-thrombus interactions, and platelet accumulation in thrombi ex vivo, in vitro, and in silico. Compared with controls, mice with elevated hematocrit (RBC^HIGH) formed thrombi at a faster rate and had a shortened vessel occlusion time. Thrombi in control and RBC^HIGH mice did not differ in size or fibrin content, and there was no difference in levels of circulating thrombin-antithrombin complexes. In vitro, increasing the hematocrit increased thrombin generation in the absence of platelets; however, this effect was reduced in the presence of platelets. In silico, direct numerical simulations of whole blood predicted elevated hematocrit increases the frequency and duration of interactions between platelets and a thrombus. When human whole blood was perfused over collagen at arterial shear rates, elevating the hematocrit increased the rate of platelet deposition and thrombus growth. These data suggest RBCs promote arterial thrombosis by enhancing platelet accumulation at the site of vessel injury. Maintaining a normal hematocrit may reduce arterial thrombosis risk in humans.

Multi-Constituent Simulation of Thrombus Deposition

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

A General Shear-Dependent Model for Thrombus Formation

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

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

Strongly Accelerated Margination of Active Particles in Blood Flow

Synthetic nanoparticles and other stiff objects injected into a blood vessel filled with red blood cells are known to marginate toward the vessel walls. By means of hydrodynamic lattice-Boltzmann simulations, we show that active particles can strongly accelerate their margination by moving against the flow direction: particles located initially in the channel center migrate much faster to their final position near the wall than in the nonactive case. We explain our findings by an enhanced rate of collisions between the stiff particles and the deformable red blood cells. Our results imply that a significantly faster margination can be achieved either technically by the application of an external magnetic field (if the particles are magnetic) or biologically by self-propulsion (if the particles are, e.g., swimming bacteria).

Computational fluid dynamics in the microcirculation and microfluidics: what role can the lattice Boltzmann method play?

Patient-specific simulations, efficient parametric analyses, and the study of complex processes that are otherwise experimentally intractable are facilitated through the use of Computational Fluid Dynamics (CFD) to study biological flows. This review discusses various CFD methodologies that have been applied across different biological scales, from cell to organ level. Through this discussion the lattice Boltzmann method (LBM) is highlighted as an emerging technique capable of efficiently simulating fluid problems across the midrange of scales; providing a practical analytical tool compared to methods more attuned to the extremities of scale. Furthermore, the merits of the LBM are highlighted through examples of previous applications and suggestions for future research are made. The review focusses on applications in the midrange bracket, such as cell-cell interactions, the microcirculation, and microfluidic devices; wherein the inherent mesoscale nature of the LBM renders it well suited to the incorporation of fluid-structure interaction effects, molecular/particle interactions and interfacial dynamics. The review demonstrates that the LBM has the potential to become a valuable tool across a range of emerging areas in bio-CFD, such as understanding and predicting disease, designing lab-on-a-chip devices, and elucidating complex biological processes.

Sub-cellular modeling of platelet transport in blood flow through microchannels with constriction

Platelet transport through arterial constrictions is one of the controlling processes influencing their adhesive functions and the formation of thrombi. We perform high-fidelity mesoscopic simulations of blood flow in microchannels with constriction, resembling arterial stenoses. The wall shear rates inside the constrictions reach levels as high as ≈8000 s(-1), similar to those encountered in moderate atherosclerotic plaques. Both red blood cells and platelets are resolved at sub-cellular resolution using the Dissipative Particle Dynamics (DPD) method. We perform a systematic study on the red blood cell and platelet transport by considering different levels of constriction, blood hematocrit and flow rates. We find that higher levels of constriction and wall shear rates lead to significantly enhanced margination of platelets, which may explain the experimental observations of enhanced post-stenosis platelet aggregation. We also observe similar margination effects for stiff particles of spherical shapes such as leukocytes. To our knowledge, such numerical simulations of dense blood through complex geometries have not been performed before, and our quantitative findings could shed new light on the associated physiological processes such as ATP release, plasma skimming, and thrombus formation.

Threshold of microvascular occlusion: injury size defines the thrombosis scenario

Damage to the blood vessel triggers formation of a hemostatic plug, which is meant to prevent bleeding, yet the same phenomenon may result in a total blockade of a blood vessel by a thrombus, causing severe medical conditions. Here, we show that the physical interplay between platelet adhesion and hemodynamics in a microchannel manifests in a critical threshold behavior of a growing thrombus. Depending on the size of injury, two distinct dynamic pathways of thrombosis were found: the formation of a nonocclusive plug, if injury length does not exceed the critical value, and the total occlusion of the vessel by the thrombus otherwise. We develop a mathematical model that demonstrates that switching between these regimes occurs as a result of a saddle-node bifurcation. Our study reveals the mechanism of self-regulation of thrombosis in blood microvessels and explains experimentally observed distinctions between thrombi of different physical etiology. This also can be useful for the design of platelet-aggregation-inspired engineering solutions.

Study of blood flow in several benchmark micro-channels using a two-fluid approach

It is known that in a vessel whose characteristic dimension (e.g., its diameter) is in the range of 20 to 500 microns, blood behaves as a non-Newtonian fluid, exhibiting complex phenomena, such as shear-thinning, stress relaxation, and also multi-component behaviors, such as the Fahraeus effect, plasma-skimming, etc. For describing these non-Newtonian and multi-component characteristics of blood, using the framework of mixture theory, a two-fluid model is applied, where the plasma is treated as a Newtonian fluid and the red blood cells (RBCs) are treated as shear-thinning fluid. A computational fluid dynamic (CFD) simulation incorporating the constitutive model was implemented using OpenFOAM® in which benchmark problems including a sudden expansion and various driven slots and crevices were studied numerically. The numerical results exhibited good agreement with the experimental observations with respect to both the velocity field and the volume fraction distribution of RBCs.

A comprehensive study on different modelling approaches to predict platelet deposition rates in a perfusion chamber

Thrombus formation is a multiscale phenomenon triggered by platelet deposition over a protrombotic surface (eg. a ruptured atherosclerotic plaque). Despite the medical urgency for computational tools that aid in the early diagnosis of thrombotic events, the integration of computational models of thrombus formation at different scales requires a comprehensive understanding of the role and limitation of each modelling approach. We propose three different modelling approaches to predict platelet deposition. Specifically, we consider measurements of platelet deposition under blood flow conditions in a perfusion chamber for different time periods (3, 5, 10, 20 and 30 minutes) at shear rates of 212 s⁻¹, 1390 s⁻¹ and 1690 s⁻¹. Our modelling approaches are: i) a model based on the mass-transfer boundary layer theory; ii) a machine-learning approach; and iii) a phenomenological model. The results indicate that the three approaches on average have median errors of 21%, 20.7% and 14.2%, respectively. Our study demonstrates the feasibility of using an empirical data set as a proxy for a real-patient scenario in which practitioners have accumulated data on a given number of patients and want to obtain a diagnosis for a new patient about whom they only have the current observation of a certain number of variables.

Pathological von Willebrand factor fibers resist tissue plasminogen activator and ADAMTS13 while promoting the contact pathway and shear-induced platelet activation

BACKGROUND

Under severe stenotic conditions, von Willebrand factor (VWF) multimerizes into large insoluble fibers at pathological shear rates.

OBJECTIVE

Evaluate the mechanics and biology of VWF fibers without the confounding effects of endothelium or collagen.

METHODS

Within a micropost-impingement microfluidic device, > 100-μm long VWF fibers multimerized on the post within 10 min using EDTA-treated platelet-free plasma (PFP) perfused at wall shear rates > 5000 s(-1) .

RESULTS

von Willebrand factor fiber thickness increased to > 10 μm as a result of increasing the shear rate to 10,000 s(-1) . In a stress-strain test, fibrous VWF had an elastic modulus of ~50 MPa. The insoluble VWF fibers were non-amyloid because they rapidly dissolved in trypsin, plasmin or 2% SDS, but were resistant to 50 nm ADAMTS13 or 100 nm tissue plasminogen activator in plasma. Following fiber formation, perfusion of low corn trypsin inhibitor (CTI)-treated (4 μg mL(-1) ), recalcified citrated plasma at 1500 s(-1) caused fibrin formation on the VWF fibers, a result not observed with purified type 1 collagen or a naked micropost. During VWF fiber formation, contact pathway factors accumulated on VWF because the use of EDTA/D-Phe-Pro-Arg chloromethylketone (PPACK)/apixaban/high CTI-treated PFP during VWF fiber formation prevented the subsequent fibrin production from low-CTI, recalcified citrated PFP. VWF fibers displayed FXIIa-immunostaining. When PPACK-inhibited whole blood was perfused over VWF fibers, platelets rolled and arrested on the surface of VWF, but only displayed P-selectin if prevailing shear rates were pathological. Platelet arrest on VWF fibers was blocked with αIIb β3 antagonist GR144053.

CONCLUSIONS

We report VWF fiber-contact pathway crosstalk and mechanisms of thrombolytic resistance in hemodynamic settings of myocardial infarction.

Microparticle shape effects on margination, near-wall dynamics and adhesion in a three-dimensional simulation of red blood cell suspension

We present a 3D computational modeling study of the transport of micro-scale drug carriers modeled as microparticles of different shapes (spherical, oblate, and prolate) in whole blood represented as a suspension of deformable red blood cells. The objective is to quantify the effect of microparticle shapes on their margination, near-wall dynamics and adhesion. We observe that the near-wall accumulation is highest for oblate particles of moderate aspect ratio, followed by spherical particles, and lowest for very elongated prolate particles. The result is explained using micro-scale dynamics of individual particles, and their interaction with red blood cells. We observe that the orientation of microparticles in 3D space and the frequency of their collisions with red blood cells are the key factors affecting their margination. We show that due to repeated collisions with red blood cells in the presence of a bounding wall, the axes of revolution of oblate particles align near the plane of the shear flow, but those of prolate particles shift towards the vorticity axis with a wider distribution. Such specific orientations lead to more frequent collisions and a greater lateral drift for oblate particles than microspheres, but less frequent collisions and a reduced lateral drift for elongated prolate particles, resulting in the observed differences in their near-wall accumulation. Once marginated, the particle shape has an entirely different effect on the likelihood of making particle-wall contacts. We find that marginated prolate particles, due to their alignment along the vorticity axis and large angular fluctuations, are more likely to make contacts with the wall than spherical and oblate particles. We further simulate the adhesion between flowing microparticles and the wall in the presence of red blood cells, and observe that once wall contacts are established, the likelihood of firm adhesion is greater for disk-like particles, followed by elongated prolates, and microspheres. Consequently, this study suggests that the local hemorheological conditions near the targeted sites must be taken into consideration while selecting the optimum shape of micro-scale vascular drug carriers.

Platelet dynamics in three-dimensional simulation of whole blood

A high-fidelity computational model using a 3D immersed boundary method is used to study platelet dynamics in whole blood. We focus on the 3D effects of the platelet-red blood cell (RBC) interaction on platelet margination and near-wall dynamics in a shear flow. We find that the RBC distribution in whole blood becomes naturally anisotropic and creates local clusters and cavities. A platelet can enter a cavity and use it as an express lane for a fast margination toward the wall. Once near the wall, the 3D nature of the platelet-RBC interaction results in a significant platelet movement in the transverse (vorticity) direction and leads to anisotropic platelet diffusion within the RBC-depleted zone or cell-free layer (CFL). We find that the anisotropy in platelet motion further leads to the formation of platelet clusters, even in the absence of any platelet-platelet adhesion. The transverse motion, and the size and number of the platelet clusters are observed to increase with decreasing CFL thickness. The 3D nature of the platelet-RBC collision also induces fluctuations in off-shear plane orientation and, hence, a rotational diffusion of the platelets. Although most marginated platelets are observed to tumble just outside the RBC-rich zone, platelets further inside the CFL are observed to flow with an intermittent dynamics that alters between sliding and tumbling, as a result of the off-shear plane rotational diffusion, bringing them even closer to the wall. To our knowledge, these new findings are based on the fundamentally 3D nature of the platelet-RBC interaction, and they underscore the importance of using cellular-scale 3D models of whole blood to understand platelet margination and near-wall platelet dynamics.

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.

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.

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.