Effects of shear rate, confinement, and particle parameters on margination in blood flow

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

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

Label-free measurement of wall shear stress in the brain venule and arteriole using dual-wavelength third-harmonic-generation line-scanning imaging

Wall shear stress (WSS) is of fundamental physiological and pathological significance. Current measurement technologies suffer from poor spatial resolution or cannot measure instantaneous values in a label-free manner. Here we demonstrate dual-wavelength third-harmonic-generation (THG) line-scanning imaging, for instantaneous wall shear rate and WSS measurement in vivo. We used the soliton self-frequency shift to generate dual-wavelength femtosecond pulses. Simultaneous acquisition of dual-wavelength THG line-scanning signals extract blood flow velocities at adjacent radial positions for instantaneous wall shear rate and WSS measurement. Our results show the oscillating behavior of WSS in brain venules and arterioles at micron spatial resolution in a label-free manner.

Shear induced diffusion of platelets revisited

The transport of platelets in blood is commonly assumed to obey an advection-diffusion equation with a diffusion constant given by the so-called Zydney-Colton theory. Here we reconsider this hypothesis based on experimental observations and numerical simulations including a fully resolved suspension of red blood cells and platelets subject to a shear. We observe that the transport of platelets perpendicular to the flow can be characterized by a non-trivial distribution of velocities with and exponential decreasing bulk, followed by a power law tail. We conclude that such distribution of velocities leads to diffusion of platelets about two orders of magnitude higher than predicted by Zydney-Colton theory. We tested this distribution with a minimal stochastic model of platelets deposition to cover space and time scales similar to our experimental results, and confirm that the exponential-powerlaw distribution of velocities results in a coefficient of diffusion significantly larger than predicted by the Zydney-Colton theory.

Numerical Study of Particle Margination in a Square Channel Flow with Red Blood Cells

Red blood cells flow near the axis in a small vessel, known as axial accumulation. This causes a region called the cell-free layer, which does not contain red blood cells near the wall. Then, small particles such as platelets come out to the cell-free layer. This phenomenon is called platelet margination. In this study, related to this phenomenon, direct numerical simulations were conducted using the immersed boundary method. The effects of the shear rate, channel size, and hematocrit value were investigated on the pressure-driven flow in a straight tube with a square cross-section. The simulation results indicated that the margination rate, which is the ratio of the distance traveled in the flow direction to the margination distance in the wall direction, is independent of the shear rate. The effect of the channel size on platelet margination was found to be well scaled by introducing a dimensionless parameter, which included the shear rate and effective area of the particle movement. It was also found that the margination rate varied nonlinearly with the tube hematocrit. This was due to the volume exclusion effect of red blood cells, which facilitated or hindered the motion of particles depending on the hematocrit. The relationship between the stable position of the particles near the corner and the width of the cell-free layer was also found. Furthermore, velocity fluctuations normalized by wall shear rate in a cross-section collapsed to one curve in the presented simulations. This indicates that the lateral force acting on the particles increases linearly with the shear rate.

The interaction of vortical flows with red cells in venous valve mimics

The motion of cells orthogonal to the direction of main flow is of importance in natural and engineered systems. The lateral movement of red blood cells (RBCs) distal to sudden expansion is considered to influence the formation and progression of thrombosis in venous valves, aortic aneurysms, and blood-circulating devices and is also a determining parameter for cell separation applications in flow-focusing microfluidic devices. Although it is known that the unique geometry of venous valves alters the blood flow patterns and cell distribution in venous valve sinuses, the interactions between fluid flow and RBCs have not been elucidated. Here, using a dilute cell suspension in an in vitro microfluidic model of a venous valve, we quantified the spatial distribution of RBCs by microscopy and image analysis, and using micro-particle image velocimetry and 3D computational fluid dynamics simulations, we analyzed the complex flow patterns. The results show that the local hematocrit in the valve pockets is spatially heterogeneous and is significantly different from the feed hematocrit. Above a threshold shear rate, the inertial separation of streamlines and lift forces contribute to an uneven distribution of RBCs in the vortices, the entrapment of RBCs in the vortices, and non-monotonic wall shear stresses in the valve pockets. Our experimental and computational characterization provides insights into the complex interactions between fluid flow, RBC distribution, and wall shear rates in venous valve mimics, which is of relevance to understanding the pathophysiology of thrombosis and improving cell separation efficiency.

Thrombosis and Hemodynamics: external and intrathrombus gradients

Distinct from dilute, isotropic, and homogeneous reaction systems typically used in laboratory kinetic assays, blood is concentrated, two-phase, flowing, and highly anisotropic when clotting on a surface. This review focuses on spatial gradients that are generated and can dictate thrombus structure and function. Novel experimental and computational tools have recently emerged to explore reaction-transport coupling during clotting. Multiscale simulations help bridge tissue length scales (the coronary arteries) to millimeter scales of a growing clot to the microscopic scale of single-cell signaling and adhesion. Microfluidic devices help create and control pathological velocity profiles, albeit at a low Reynolds number. Since rate processes and force loading are often coupled, this review highlights prevailing convective-diffusive transport physics that modulate cellular and molecular processes during thrombus formation.

Margination of Platelet-Sized Particles in the Red Blood Cell Suspension Flow through Square Microchannels

In the blood flow through microvessels, platelets show high concentrations near the vessel wall. This phenomenon is called margination of platelets and is closely associated with hemostasis and thrombosis. In the present study, we conducted in vitro experiments using platelet-sized fluorescent particles as platelet substitutes to investigate the cross-sectional distribution of these particles in the red blood cell suspension flowing through microchannels with a square cross section. Fluorescence observations were performed to measure the transverse distribution of particles at various heights from the bottom face with the use of a confocal laser scanning microscope system. In downstream cross sections of the channel, particles showed focusing near the four corners rather than uniform margination along the entire circumference of the cross section. The focusing of particles near the corners was more enhanced for higher hematocrits. On the other hand, particles in circular channel flows showed nearly axisymmetric uniform accumulation adjacent to the channel wall. The present result suggests that the segregation of suspended particles in the flow of multicomponent suspensions could have such heterogeneous 2D features of particle distribution in the cross section of channels, especially for rectangular channels often used in microfluidics.

Computational modeling of blood component transport related to coronary artery thrombosis in Kawasaki disease

Coronary artery thrombosis is the major risk associated with Kawasaki disease (KD). Long-term management of KD patients with persistent aneurysms requires a thrombotic risk assessment and clinical decisions regarding the administration of anticoagulation therapy. Computational fluid dynamics has demonstrated that abnormal KD coronary artery hemodynamics can be associated with thrombosis. However, the underlying mechanisms of clot formation are not yet fully understood. Here we present a new model incorporating data from patient-specific simulated velocity fields to track platelet activation and accumulation. We use a system of Reaction-Advection-Diffusion equations solved with a stabilized finite element method to describe the evolution of non-activated platelets and activated platelet concentrations [AP], local concentrations of adenosine diphosphate (ADP) and poly-phosphate (PolyP). The activation of platelets is modeled as a function of shear-rate exposure and local concentration of agonists. We compared the distribution of activated platelets in a healthy coronary case and six cases with coronary artery aneurysms caused by KD, including three with confirmed thrombosis. Results show spatial correlation between regions of higher concentration of activated platelets and the reported location of the clot, suggesting predictive capabilities of this model towards identifying regions at high risk for thrombosis. Also, the concentration levels of ADP and PolyP in cases with confirmed thrombosis are higher than the reported critical values associated with platelet aggregation (ADP) and activation of the intrinsic coagulation pathway (PolyP). These findings suggest the potential initiation of a coagulation pathway even in the absence of an extrinsic factor. Finally, computational simulations show that in regions of flow stagnation, biochemical activation, as a result of local agonist concentration, is dominant. Identifying the leading factors to a pro-coagulant environment in each case—mechanical or biochemical—could help define improved strategies for thrombosis prevention tailored for each patient.

Computational studies aiming to model thrombosis often rely on an arterial wall injury. Collagen and other extracellular matrix components are exposed to the bloodstream, which facilitates platelet adhesion to the wall and subsequent clot formation. However, these models are not adequate to explain thrombosis in other settings where even in the absence of a focal lesion, clots may still form under certain flow conditions. Coronary artery aneurysm thrombosis following KD is an example of the need to understand the mechanisms of thrombus initiation in the absence of an extrinsic factor. This study provides a new framework to investigate thrombus initiation in KD from a patient-specific perspective, which integrates fluid mechanics and biochemistry and which could help quantify the pro-coagulant environment induced by the aneurysm and become a predictive tool. The work presented here has broad relevance to other clinical situations where flow stagnation and transport are driving factors in thrombus formation.

General sites of nanoparticle biodistribution as a novel opportunity for nanomedicine

The development of nanomedical devices has led to a considerable number of clinically applied nanotherapeutics. Yet, the overall poor translation of nanoparticular concepts into marketable systems has not met the initial expectations and led to increasing criticism in recent years. Most novel nano approaches thereby use highly refined formulations including a plethora of active targeting sequences, but ultimately fail to reach their target due to a generally high off-target deposition in organs such as the liver or kidney. In this context, we argue that initial nanoparticle (NP) development should not entirely become set on conventional formulation aspects. In contrast, we propose a change of focus towards a prior analysis of general sites of NP in vivo deposition and an assessment of how accumulation in these organs or tissues can be harnessed to develop therapies for site-related pathologies. We therefore give a comprehensive overview of existing nanotherapeutic targeting strategies for specific cell types within three of the usual suspects, i.e. the liver, kidney and the vascular system. We discuss the physiological surroundings and relevant pathologies of described tissues as well as the implications for NP-mediated drug delivery. Additionally, successful cell-selective NP concepts using active targeting strategies are assessed. By bringing together both (patho)physiological aspects and concepts for cell-selective NP formulations, we hope to show a novel opportunity for the development of more promising nanotherapeutic devices.

Mechanobiology of shear-induced platelet aggregation leading to occlusive arterial thrombosis: A multiscale in silico analysis

Occlusive thrombosis in arteries causes heart attacks and strokes. The rapid growth of thrombus at elevated shear rates (~10,000 1/s) relies on shear-induced platelet aggregation (SIPA) thought to come about from the entanglement of von Willebrand factor (VWF) molecules. The mechanism for SIPA is not yet understood in terms of cell- and molecule-level dynamics in fast flowing bloodstreams. Towards this end, we develop a multiscale computational model to recreate SIPA in silico, where the suspension dynamics and interactions of individual platelets and VWF multimers are resolved directly. The platelet-VWF interaction via GP1b-A1 bonds is prescribed with intrinsic binding rates theoretically derived and informed by single-molecule measurements. The model is validated against existing microfluidic SIPA experiments, showing good agreement with the in vitro observations in terms of the morphology, traveling distance and capture time of the platelet aggregates. Particularly, the capture of aggregates can occur in a few milliseconds, comparable to the platelet transit time through pathologic arterial stenotic sections and much shorter than the time for shear-induced platelet activation. The multiscale SIPA simulator provides a cross-scale tool for exploring the biophysical mechanisms of SIPA in silico that are difficult to access with single-molecule measurements or micro-/macro-fluidic assays only.

Development of margination of platelet-sized particles in red blood cell suspensions flowing through Y-shaped bifurcating microchannels

BACKGROUND

In the blood flow through microvessels, platelets exhibit enhanced concentrations in the layer free of red blood cells (cell-free layer) adjacent to the vessel wall. The motion of platelets in the cell-free layer plays an essential role in their interaction with the vessel wall, and hence it affects their functions of hemostasis and thrombosis.

OBJECTIVE

We aimed to estimate the diffusivity of platelet-sized particles in the transverse direction (the direction of vorticity) across the channel width in the cell-free layer by in vitro experiments for the microchannel flow of red blood cell (RBC) suspensions containing platelet-sized particles.

METHODS

Fluorescence microscope observations were performed to measure the transverse distribution of spherical particles immersed in RBC suspensions flowing through a Y-shaped bifurcating microchannel. We examined the development of the particle concentration profiles along the flow direction in the daughter channels, starting from asymmetric distributions with low concentrations on the inner side of the bifurcation at the inlet of the daughter channels.

RESULTS

In daughter channels of 40 μm width, reconstruction of particle margination revealed that a symmetric concentration profile was attained in ∼30 mm from the bifurcation, independent of flow rate.

CONCLUSIONS

We presented experimental evidence of particle margination developing in a bifurcating flow channel where the diffusivity of 2.9-μm diameter particles was estimated to be ∼40 μm2/s at a shear rate of 1000 s-1 and hematocrit of 0.2.

Effect of cytosol viscosity on the flow behavior of red blood cell suspensions in microvessels

OBJECTIVE

The flow behavior of blood is strongly affected by red blood cell (RBC) properties, such as the viscosity ratio C between cytosol and suspending medium, which can significantly be altered in several pathologies (e.g. sickle-cell disease, malaria). The main objective of this study is to understand the effect of C on macroscopic blood flow properties such as flow resistance in microvessels, and to link it to the deformation and dynamics of single RBCs.

METHODS

We employ mesoscopic hydrodynamic simulations to investigate flow properties of RBC suspensions with different cytosol viscosities for various flow conditions in cylindrical microchannels.

RESULTS

Starting from a dispersed cell configuration which approximates RBC dispersion at vessel bifurcations in the microvasculature, we find that the flow convergence and development of RBC-free layer (RBC-FL) depend only weakly on C, and require a convergence length in the range of 25D-50D, where D is channel diameter. In vessels with D ≤ 20 μ m , the final resistance of developed flow is nearly the same for C = 5 and C = 1, while for D = 40 μ m , the flow resistance for C = 5 is about 10% larger than for C = 1. The similarities and differences in flow resistance can be explained by viscosity-dependent RBC-FL thicknesses, which are associated with the viscosity-dependent dynamics of single RBCs.

CONCLUSIONS

The weak effect on the flow resistance and RBC-FL explains why RBCs can contain a high concentration of hemoglobin for efficient oxygen delivery, without a pronounced increase in the flow resistance. Furthermore, our results suggest that significant alterations in microvascular flow in various pathologies are likely not due to mere changes in cytosolic viscosity.

Heterogeneous partition of cellular blood-borne nanoparticles through microvascular bifurcations

Blood flowing through microvascular bifurcations has been an active research topic for many decades, while the partitioning pattern of nanoscale solutes in the blood remains relatively unexplored. Here we demonstrate a multiscale computational framework for direct numerical simulation of the nanoparticle (NP) partitioning through physiologically relevant vascular bifurcations in the presence of red blood cells (RBCs). The computational framework is established by embedding a particulate suspension inflow-outflow boundary condition into a multiscale blood flow solver. The computational framework is verified by recovering a tubular blood flow without a bifurcation and validated against the experimental measurement of an intravital bifurcation flow. The classic Zweifach-Fung (ZF) effect is shown to be well captured by the method. Moreover, we observe that NPs exhibit a ZF-like heterogeneous partition in response to the heterogeneous partition of the RBC phase. The NP partitioning prioritizes the high-flow-rate daughter branch except for extreme (large or small) suspension flow partition ratios under which the complete phase separation tends to occur. By analyzing the flow field and the particle trajectories, we show that the ZF-like heterogeneity in the NP partition can be explained by the RBC-entrainment effect caused by the deviation of the flow separatrix preceded by the tank treading of RBCs near the bifurcation junction. The recovery of homogeneity in the NP partition under extreme flow partition ratios is due to the plasma skimming of NPs in the cell-free layer. These findings, based on the multiscale computational framework, provide biophysical insights to the heterogeneous distribution of NPs in microvascular beds that are observed pathophysiologically.

Flow-induced segregation and dynamics of red blood cells in sickle cell disease

Blood flow in sickle cell disease (SCD) can substantially differ from normal blood flow due to significant alterations in the physical properties of the red blood cells (RBCs). Chronic complications, such as inflammation of the endothelial cells lining blood vessel walls, are associated with SCD, for reasons that are unclear. Here, detailed boundary integral simulations are performed to investigate an idealized model flow flow in SCD, a binary suspension of flexible biconcave discoidal fluid-filled capsules and stiff curved prolate capsules that represent healthy and sickle RBCs, respectively, subjected to pressure-driven flow in a planar slit. The stiff component is dilute. The key observation is that, unlike healthy RBCs that concentrate around the center of the channel and form an RBC-depleted layer (i.e. cell-free layer) next to the walls, sickle cells are largely drained from the bulk of the suspension and aggregate inside the cell-free layer, displaying strong margination. These cells are found to undergo a rigid-body-like rolling orbit near the walls. A binary suspension of flexible biconcave discoidal capsules and stiff straight (non-curved) prolate capsules is also considered for comparison, and the curvature of the stiff component is found to play a minor role in the behavior. Additionally, by considering a mixture of flexible and stiff biconcave discoids, we reveal that rigidity difference by itself is sufficient to induce the segregation behavior in a binary suspension. Furthermore, the additional shear stress on the walls induced by the presence of cells is computed for the various cases. Compared to the small fluctuations in wall shear stress for a suspension of healthy RBCs, large local peaks in wall shear stress are observed for the binary suspensions, due to the proximity of the marginated stiff cells to the walls. This effect is most marked for the straight prolate capsules. As endothelial cells are known to mechanotransduce physical forces such as aberrations in shear stress and convert them to physiological processes such as activation of inflammatory signals, these results may aid in understanding mechanisms for endothelial dysfunction associated with SCD.

Advances in mathematical models of the active targeting of tumor cells by functional nanoparticles

BACKGROUND AND OBJECTIVE

The process of nanoparticles (NPs) entering blood circulation to actively target tumor cells involves four stages-the transport of NPs in blood vessels, transvascular transport of NPs, transport of NPs in the tumor interstitial matrix and entry of NPs into tumor cells. These four stages are a complex process involving mechanical, physical, biochemical, and biophysical factors, the tumor microenvironment (TME) and properties of NPs play important roles in this process. Because this process involves a large number of factors and is very complex, it is difficult to study with conventional methods.

METHODS

Using mathematical models for simulation is suitable for addressing this complex situation and can describe the complexity well.

RESULTS

This work focuses on the theoretical simulation of NPs that target tumor cells to illustrate the effects of the abnormal microenvironment of tumors and properties of NPs on the transport process. Mathematical models constructed by different methods are enumerated. Through studying these mathematical models, different methods to overcome nanoparticle (NP) transport obstacles are illustrated.

CONCLUSIONS

It is necessary to construct a theoretical model of active targeting nanodrug delivery under the coupling of micro-flow field and specific binding force field, and to simulate and analyze the delivery process at mesoscopic scale using computational fluid dynamics (CFD) method, so as to reveal the law and characteristics of drug delivery and cell uptake in the micro-environment of tumors in vivo. The methods and techniques discussed can serve as the basis for systematic studies of active targeting of functional nanoparticles to tumor cells.

Occlusive thrombosis in arteries

Thrombus formation in major arteries is life threatening. In this review article, we discuss how an arterial thrombus can form under pathologically high shear stresses, with bonding rates estimated to be the fastest Kon values in biochemistry. During occlusive thrombosis in arteries, the growth rate of the thrombus explodes to capture a billion platelets in about 10 min. Close to 100% of all platelets passing the thrombus are captured by long von Willebrand factor (vWF) strands that quickly form tethered nets. The nets grow in patches where shear stress is high, and the local concentration of vWF is elevated due to α-granule release by previously captured platelets. This rapidly formed thrombus has few red blood cells and so has a white appearance and is much stronger and more porous than clots formed through coagulation. Understanding and modeling the biophysics of this event can predict totally new approaches to prevent and treat heart attacks and strokes.

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.

Mesoscale simulation of soft particles with tunable contact angle in multicomponent fluids

Soft particles at fluid interfaces play an important role in many aspects of our daily life, such as the food industry, paints and coatings, and medical applications. Analytical methods are not capable of describing the emergent effects of the complex dynamics of suspensions of many soft particles, whereas experiments typically either only capture bulk properties or require invasive methods. Computational methods are therefore a great tool to complement experimental work. However, an efficient and versatile numerical method is needed to model dense suspensions of many soft particles. In this article we propose a method to simulate soft particles in a multicomponent fluid, both at and near fluid-fluid interfaces, based on the lattice Boltzmann method, and characterize the error stemming from the fluid-structure coupling for the particle equilibrium shape when adsorbed onto a fluid-fluid interface. Furthermore, we characterize the influence of the preferential contact angle of the particle surface and the particle softness on the vertical displacement of the center of mass relative to the fluid interface. Finally, we demonstrate the capability of our model by simulating a soft capsule adsorbing onto a fluid-fluid interface with a shear flow parallel to the interface, and the covering of a droplet suspended in another fluid by soft particles with different wettability.

The Margination of Particles in Areas of Constricted Blood Flow

Stroke is a leading cause of death globally and is caused by stenoses, abnormal narrowings of blood vessels. Recently, there has been an increased interest in shear-activated particle clusters for the treatment of stenosis, but there is a lack of literature investigating the impact of different stenosis geometries on particle margination. Margination refers to the movement of particles toward the blood vessel wall and is desirable for drug delivery. The current study investigated ten different geometries and their effects on margination. Microfluidic devices with a constricted area were fabricated to mimic a stenosed blood vessel with different extent of occlusion, constricted length, and eccentricity (gradualness of the constriction and expansion). Spherical fluorescent particles with a diameter of 2.11 μm were suspended in blood and tracked as they moved into, through, and out of the constricted area. A margination parameter, M, was used to quantify margination based on the particle distribution after velocity normalization. Experimental results suggested that a constriction leads to an enhanced margination, whereas an expansion is responsible for a decrease in margination. Further, margination was found to increase with increasing percent occlusion and constriction length, likely a result of higher shear rate and longer residence time, respectively. Margination decreases as the stenosis geometry becomes more gradual (eccentricity increases) with the exception of a sudden constriction/expansion geometry. The findings demonstrate the importance of geometric effects on margination and call for detailed numerical modeling and geometric characterization of the stenosed areas to fully understand the underlying physics.

Migration velocity of red blood cells in microchannels

The lateral migration of red blood cells (RBCs) in confined channel flows is an important ingredient of microcirculatory hydrodynamics and is involved in the development of a cell free layer near vessel walls and influences the distribution of RBCs in networks. It is also relevant to a number of lab-on-chip applications. This migration is a consequence of their deformability and is due to the combined effects of hydrodynamic wall repulsion and the curvature of the fluid velocity profile. We performed microfluidic experiments with dilute suspensions of RBCs in which the trajectories and migration away from the channel wall are analyzed to extract the mean behavior, from which we propose a generic scaling law for the transverse migration velocity valid in a whole range of parameters relevant to microcirculatory and practical situations. Experiments with RBCs of different mechanical properties (separated by density gradient sedimentation or fixed with glutaraldehyde) show the influence of this parameter which can induce significant dispersion of the trajectories.

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.

Influence of particle size and shape on their margination and wall-adhesion: implications in drug delivery vehicle design across nano-to-micro scale

Intravascular drug delivery technologies majorly utilize spherical nanoparticles as carrier vehicles. Their targets are often at the blood vessel wall or in the tissue beyond the wall, such that vehicle localization towards the wall (margination) becomes a pre-requisite for their function. To this end, some studies have indicated that under flow environment, micro-particles have a higher propensity than nano-particles to marginate to the wall. Also, non-spherical particles theoretically have a higher area of surface-adhesive interactions than spherical particles. However, detailed systematic studies that integrate various particle size and shape parameters across nano-to-micro scale to explore their wall-localization behavior in RBC-rich blood flow, have not been reported. We address this gap by carrying out computational and experimental studies utilizing particles of four distinct shapes (spherical, oblate, prolate, rod) spanning nano- to-micro scale sizes. Computational studies were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) package, with Dissipative Particle Dynamics (DPD). For experimental studies, model particles were made from neutrally buoyant fluorescent polystyrene spheres, that were thermo-stretched into non-spherical shapes and all particles were surface-coated with biotin. Using microfluidic setup, the biotin-coated particles were flowed over avidin-coated surfaces in absence versus presence of RBCs, and particle adhesion and retention at the surface was assessed by inverted fluorescence microscopy. Our computational and experimental studies provide a simultaneous analysis of different particle sizes and shapes for their retention in blood flow and indicate that in presence of RBCs, micro-scale non-spherical particles undergo enhanced 'margination + adhesion' compared to nano-scale spherical particles, resulting in their higher binding. These results provide important insight regarding improved design of vascularly targeted drug delivery systems.

Internal Viscosity-Dependent Margination of Red Blood Cells in Microfluidic Channels

Cytoplasmic viscosity-dependent margination of red blood cells (RBC) for flow inside microchannels was studied using numerical simulations, and the results were verified with microfluidic experiments. Wide range of suspension volume fractions or hematocrits was considered in this study. Lattice Boltzmann method for fluid-phase coupled with spectrin-link method for RBC membrane deformation was used for accurate analysis of cell margination. RBC margination behavior shows strong dependence on the internal viscosity of the RBCs. At equilibrium, RBCs with higher internal viscosity marginate closer to the channel wall and the RBCs with normal internal viscosity migrate to the central core of the channel. Same margination pattern has been verified through experiments conducted with straight channel microfluidic devices. Segregation between RBCs of different internal viscosity is enhanced as the shear rate and the hematocrit increases. Stronger separation between normal RBCs and RBCs with high internal viscosity is obtained as the width of a high aspect ratio channel is reduced. Overall, the margination behavior of RBCs with different internal viscosities resembles with the margination behavior of RBCs with different levels of deformability. Observations from this work will be useful in designing microfluidic devices for separating the subpopulations of RBCs with different levels of deformability that appear in many hematologic diseases such as sickle cell disease (SCD), malaria, or cancer.

Cellular Level In-silico Modeling of Blood Rheology with An Improved Material Model for Red Blood Cells

Many of the intriguing properties of blood originate from its cellular nature. Therefore, accurate modeling of blood flow related phenomena requires a description of the dynamics at the level of individual cells. This, however, presents several computational challenges that can only be addressed by high performance computing. We present Hemocell, a parallel computing framework which implements validated mechanical models for red blood cells and is capable of reproducing the emergent transport characteristics of such a complex cellular system. It is computationally capable of handling large domain sizes, thus it is able to bridge the cell-based micro-scale and macroscopic domains. We introduce a new material model for resolving the mechanical responses of red blood cell membranes under various flow conditions and compare it with a well established model. Our new constitutive model has similar accuracy under relaxed flow conditions, however, it performs better for shear rates over 1,500 s^-1. We also introduce a new method to generate randomized initial conditions for dense mixtures of different cell types free of initial positioning artifacts.

Shear-induced laning transition in a confined colloidal film

Using Brownian dynamics simulations, we investigate a dense system of charged colloids exposed to shear flow in a confined (slit-pore) geometry. The equilibrium system at zero flow consists of three well-pronounced layers with a squarelike crystalline in-plane structure. We demonstrate that, for sufficiently large shear rates, the middle layer separates into two sublayers where the particles organize into moving lanes with opposite velocities. The formation of this "microlaned" state results in a destruction of the applied shear profile; it also has a strong impact on the structure of the system, and on its rheology as measured by the elements of the stress tensor. At higher shear rates, we observe a disordered state and finally a recrystallization reminiscent of the behavior of bilayer films. We also discuss the system size dependence and the robustness of the microlaned state against variations of the slit-pore width. In fact, for a pore width allowing for four layers, we observe a similar shear-induced state in which the system splits into two domains with opposite velocities.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Prediction of Thrombus Growth: Effect of Stenosis and Reynolds Number

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