Low micromolar intravascular cell-free hemoglobin concentration affects vascular NO bioavailability in sickle cell disease: a computational analysis

In sickle cell disease, the changes in RBC morphology destabilize the red blood cell (RBC) membrane and lead to hemolysis. Several experimental and clinical studies have associated intravascular hemolysis with pulmonary hypertension in sickle cell disease. Cell-free hemoglobin (Hb) from intravascular hemolysis has high affinity for nitrixc oxide (NO) and can affect the NO bioavailability in the sickle cell disease, which may eventually lead to pulmonary hypertension. To study the effects of intravascular hemolysis related cell-free Hb concentrations on NO bioavailability, we developed a two-dimensional mathematical model of NO biotransport in 50-μm arteriole under steady-state sickle cell disease conditions. We analyzed the effects of flow-dependent NO production and axial and radial transport of NO, a recently reported much lower NO-RBC reaction rate constant, and cell-free layer thickness on NO biotransport. Our results show that the presence of cell-free Hb concentrations as low as 0.5 μM results in an approximately three- to sevenfold reduction in the predicted smooth muscle cell NO concentrations compared with those under physiological conditions. In addition, increasing the diffusional resistance for NO in vascular lumen from cell-free layer or reducing NO-RBC reaction rate did not improve the NO bioavailability at the smooth muscle cell layer significantly for cell-free Hb concentrations ≥1 μM. These results suggest that lower NO bioavailability due to low micromolar cell-free Hb can disturb NO homeostasis and cause insufficient bioavailability at the smooth muscle cell layer. Our results supports the hypothesis that hemolysis-associated reduction in NO bioavailability may play a role in the development of pathophysiological complications like pulmonary hypertension in sickle cell disease that are observed in several clinical and experimental studies.     

Hydrodynamic interaction between erythrocytes and leukocytes affects rheology of blood in microvessels

Hydrodynamic interaction between erythrocytes (RBC) and leukocytes (WBC) in a microvessel of size 20-40 micron, typical of a postcapillary venule, is studied using a two-dimensional computational model. The model is based on immersed boundary method, and it takes into consideration the particulate nature of blood by explicitly modeling individual blood cell, and cell deformation. Due to their highly flexible nature, RBC drift away from the wall and toward the center of a vessel creating a cell-free layer. It is shown here that the lateral motion of RBC is strongly affected in presence of a WBC, and is dependent on whether the WBC is non-adherent or firmly adhered. When the WBC is non-adherent, some RBC, depending on their initial radial locations and vessel size, may be deflected closer toward the wall, resulting in a decrease in the cell-free layer. The apparent viscosity of the whole blood containing both RBC and WBC is computed, and shown to be much higher than that containing RBC only. The increased viscosity cannot be accounted for by the contribution due to WBC only. This observation is in agreement with a previous in vivo measurement. Here we show that the additional flow resistance is due to the decrease in the cell-free layer resulting from the WBC-RBC interaction. It can be accounted for by a two-layer model of blood when the reduced values of the cell-free layer thickness are used. When the WBC is firmly adhered, RBC easily move away from the wall, and the cell-free layer is not significantly changed. In such cases, the major contribution to whole blood viscosity comes from the WBC alone. The hydrodynamic interaction between WBC and RBC, though it exists, does not contribute significantly when WBC are adhered.     

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.     

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.     

Cellular determinants of low-shear blood viscosity

Low-shear viscometry is one of the methods commonly used to estimate the degree of red blood cell (RBC) aggregation in various bloods and RBC suspensions. However, it has been previously shown that alterations in RBC morphology and mechanical behavior can affect the low-shear apparent viscosity of RBC suspensions; RBC aggregation is also sensitive to these cellular factors. This study used heat treatment (48°C, 5 min), glutaraldehyde (0.005–0.02%) and hydrogen peroxide (1 mM) to modify cell geometry and deformability. Red blood cell aggregation was assessed via a Myrenne Aggregometer (“M” and “Ml” indexes), RBC suspension viscosity was measured using a Contraves LS-30 viscometer, and RBC shape response to fluid shear stresses (i.e., deformability) was determined by ektacytometry (LORCA system). Our results indicate that low-shear apparent viscosity and related indexes may not always reflect changes of RBC aggregation if cellular properties are altered: for situations where RBC aggregation has been only moderately affected, cellular mechanical factors may be the major determinant of low-shear viscosity. These findings thus imply that in situations which may be associated alterations of RBC geometry and/or deformability, low-shear viscometry should not be the sole measurement technique used to assess RBC aggregation.     

Reduced erythrocyte deformability alters pulmonary hemodynamics

Isolated rat lungs were perfused with suspensions containing normal and stiffened erythrocytes (RBCs) to assess the effect of altered RBC deformability on pulmonary hemodynamics. RBC suspensions were prepared using cells previously incubated in isosmolar phosphate-buffered saline with or without 0.0125 or 0.01875% glutaraldehyde. Washed RBCs were resuspended in isosmolar 4% albumin saline solution. Isolated rat lungs were perfused with control and stiffened cells by the use of a perfusion system that allowed rapid switching between suspensions. Pressure-flow (P/Q) curves were constructed by measuring pulmonary arterial pressure (Ppa) over a range of flow rates. In a second set of experiments, P/Q curves were generated for perfusion with control and stiffened cells (0.0125% glutaraldehyde) before and after vasoconstriction with a synthetic prostaglandin analogue (U 46619). RBC deformability was quantified in all experiments by determination of filtration time of a dilute cell suspension through a 4.7 microns Nuclepore filter. Incubation with 0.0125 or 0.01875% glutaraldehyde produced a 6 or 21% decrease in RBC deformability, respectively. These decreases in deformability were associated with significant increases in Ppa at each flow rate. The increases in Ppa correlated significantly with the degree of RBC stiffening. With 0.0125% glutaraldehyde, the P/Q curve was shifted upward without a change in slope, whereas incubation with 0.01875% glutaraldehyde resulted in a significant increase in slope. Vasoconstriction and perfusion with stiffened RBCs had additive effects on Ppa. These findings suggest that decreases in RBC deformability cause physiologically significant elevations in hemodynamic resistance in the pulmonary circuit independent of vasoactivity.     

Conductometric study of shear-dependent processes in red cell suspensions. II. Transient cross-stream hematocrit distribution

A novel experimental approach based on electrical properties of red blood cell (RBC) suspensions was applied to study the effects of the size and morphology of RBC aggregates on the transient cross-stream hematocrit distribution in suspensions flowing through a square cross-section flow channel. The information about the effective size of RBC aggregates and their morphology is extracted from the capacitance (C) and conductance (G) recorded during RBC aggregation, whereas a slower process of particle migration is manifested by delayed long-term changes in the conductance. Migration-induced changes in the conductance measured at low shear rates (< or =3.1 s(-1)) for suspensions of RBCs in a strongly aggregating medium reveal an increase to a maximum followed by a decrease to the stationary level. The ascending branch of G(t) curves reflects the aggregate migration in the direction of decreasing shear rate. A further RBC aggregation in the region of lower shear stresses leads to the formation of RBC networks and results in the transformation of the rheological behavior of suspensions from the thinning to the thickening. It is suggested that the descending branches of the G(t) curves recorded at low shear rates reflect an adjustment of the Hct distribution to a new state caused by a partial dispersion of RBC networks. For suspensions of non-aggregating RBCs it is found that depending on whether the shear rate is higher or lower compared with the prior value, individual RBCs migrate either toward the centerline of the flow or in the opposite direction.     

Geometrical focusing of cells in a microfluidic device: an approach to separate blood plasma

It is well known that when a suspension of cells flows in small vessels (arterioles or venules), there exists a cell-free layer of a few microns adjacent to the vascular walls. Using an in vitro model, we show experimentally that for a fixed flow rate a geometrical constriction in the flow can artificially enhance the cell-free layer. Also, we show that rapid variation of the geometry coupled to the deformability of the cells can dramatically modify their spatial distribution in the channel. The effects of the constriction geometry, flow rate, suspending fluid viscosity, cell concentration, and cell deformability are studied and the results are interpreted in terms of a model of the hydrodynamic drift of an ellipsoidal cell in a shear flow. We propose a microfluidic application of this focusing effect for separation of the red blood cells from the suspending plasma.     

A dilution-filtration system for removing cryoprotective agents

In most cryopreservation applications, the final concentrations of cryoprotective agents (CPAs) must be reduced to biocompatible levels. However, traditional methods for removing CPAs usually have disadvantages of operation complexity, time consumption, and ease of contamination, especially for the applications involving large volumes of cell suspensions. A dilution-filtration system, which involves pure ultrafiltration for separation, was developed for continuous, automatic, and closed process of removing CPAs. To predict the optimal protocols under given experimental conditions, a theoretical model was established first. Cell-free experiments were then conducted to investigate the variation in CPA concentration during the process, and the experimental data were compared with the theoretical values for the validation of the model. Finally, ten units (212.9?ml/unit±9.5?ml/unit) of thawed human red blood cells (cryopreserved with 40% (w/v) glycerol) were deglycerolized using the theoretically optimal operation protocols to further validate the effectiveness and advantage of the system. In the cell-free experiments, glycerol was continuously removed and the concentration variations fitted the simulated results quite well. In the in-vitro experiments, glycerol concentration in RBC suspension was reduced to 5.57?g/l±2.81?g/l within an hour, and the cell count recovery rate was 91.19%±3.57%, (n=10), which proves that the system is not only safe for removing CPAs, but also particularly efficient for processing large-scale samples. However, the operation parameters must be carefully controlled and the optimal protocols should be specialized and various from case to case. The presented theoretical model provides an effective approach to find out the optimal operation protocols under given experimental conditions and constrains.     

The uptake and assimilation of sulphate by Thiobacillus ferrooxidans.

Sulphate was rapidly bound by cell suspensions of Thiobacillus ferrooxidans. The binding was depressed by tetrathionate but was unaffected by Group VI anions, cysteine or methionine. Increasing uptake of sulphate was observed in cell suspensions incubated in the presence of ferrous iron. The bulk of 35S-sulphate was removed from the organisms by washing with dilute sulphuric acid and the remaining label was incorporated into cold trichloroacetic acid-soluble compounds. 35S-labelled adenosine 5'-sulphatophosphate was produced from ATP and 35S-sulphate by cell suspensions and in cell-free extracts. There was no evidence for the production of adenosine 3'-phosphate 5'-sulphatophosphate assayed by a very sensitive bioluminescence method.     

Turbulent flow of red cells in dilute suspensions. Effect on kinetics of O2 uptake.

The turbulent flow properties of dilute (0.06% by volume) suspensions of human red blood cells in 4-mm-bore glass tubing were estimated by laser anemometry. The flow properties of the dilute red cell suspension were similar to those of a dilute suspension of polystyrene spheres (0.5 micron diameter) in isotonic NaCl solution. Flow was found to be laminar when the Reynolds number was below 2,000, transitional in the range of Reynolds numbers from 2,000 to 3,000, and fully turbulent above Reynolds number 3,000. These results differ from previous studies of more concentrated red cell suspensions. The length scales of the turbulence were also estimated: at a Reynolds number near 4,000 the macroscale is about 1.25 mm, the Taylor microscale is about 0.85 mm, and the Kolmogoroff scale is near 0.075 mm. The results are discussed in relation to previous measurements of the rate of oxygen uptake by dilute red cell suspensions in the flow-type rapid reaction apparatus. Our results suggest that under the conditions of most of these oxygen uptake measurements, the turbulent flow is characterized by eddies about 1 mm across, mixing with each other on a time scale of about 45 ms. Since most of the reported oxygen uptake measurements involve a similar time scale, it is possible that an effective "unstirred layer" influenced the reported rate of oxygen uptake.     

Stochastic model of autocrine and paracrine signals in cell culture assays

Autocrine signaling systems are commonly studied under cell culture conditions. In a typical cell culture assay, a layer of liquid medium covers a random two-dimensional dispersion of cells, which secrete ligands. In a growing number of experiments, it is important to characterize the spatial range of autocrine and paracrine cell communication. Currently, the spatial distribution of diffusing signals can be analyzed only indirectly, from their effects on the intracellular signaling or physiological responses of autocrine cells. To directly characterize the spatial range of secreted ligands, we propose a stochastic model for autocrine cell cultures and analyze it using a combination of analytical and computational tools. The two main results derived within the framework of this model are 1), an expression for the fraction of autocrine trajectories, i.e., the probability for a ligand to be trapped by the same cell from which it has been secreted; and 2), an expression for the spatial distribution of trapping points of paracrine trajectories. We test these analytical results by stochastic simulations with efficient Brownian dynamics code and apply our model to analyze the spatial operation of autocrine epidermal growth factor receptor systems.     

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, nonsymmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes in RBC properties.     

Computational modeling of biomechanics and biorheology of heated red blood cells

Because of their compromised deformability, heat denatured erythrocytes have been used as labeled probes to visualize spleen tissue or to assess the ability of the spleen to retain stiff red blood cells (RBCs) for over three decades, e.g., see Looareesuwan et al. N. Engl. J. Med. (1987). Despite their good accessibility, it is still an open question how heated RBCs compare to certain diseased RBCs in terms of their biomechanical and biorheological responses, which may undermine their effective usage and even lead to misleading experimental observations. To help answering this question, we perform a systematic computational study of the hemorheological properties of heated RBCs with several physiologically relevant static and hemodynamic settings, including optical-tweezers test, relaxation of prestretched RBCs, RBC traversal through a capillary-like channel and a spleen-like slit, and a viscometric rheology test. We show that our in silico RBC models agree well with existing experiments. Moreover, under static tests, heated RBCs exhibit deformability deterioration comparable to certain disease-impaired RBCs such as those in malaria. For RBC traversal under confinement (through microchannel or slit), heated RBCs show prolonged transit time or retention depending on the level of confinement and heating procedure, suggesting that carefully heat-treated RBCs may be useful for studying splenic- or vaso-occlusion in vascular pathologies. For the rheology test, we expand the existing bulk viscosity data of heated RBCs to a wider range of shear rates (1–1000 s⁻¹) to represent most pathophysiological conditions in macro- or microcirculation. Although heated RBC suspension shows elevated viscosity comparable to certain diseased RBC suspensions under relatively high shear rates (100–1000 s⁻¹), they underestimate the elevated viscosity (e.g., in sickle cell anemia) at low shear rates (<10 s⁻¹). Our work provides mechanistic rationale for selective usage of heated RBC as a potentially useful model for studying the abnormal traversal dynamics and hemorheology in certain blood disorders.     

A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics

Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary.     

Mesoscale simulation of blood flow in small vessels

Computational modeling of blood flow in microvessels with internal diameter 20-500 microm is a major challenge. It is because blood in such vessels behaves as a multiphase suspension of deformable particles. A continuum model of blood is not adequate if the motion of individual red blood cells in the suspension is of interest. At the same time, multiple cells, often a few thousands in number, must also be considered to account for cell-cell hydrodynamic interaction. Moreover, the red blood cells (RBCs) are highly deformable. Deformation of the cells must also be considered in the model, as it is a major determinant of many physiologically significant phenomena, such as formation of a cell-free layer, and the Fahraeus-Lindqvist effect. In this article, we present two-dimensional computational simulation of blood flow in vessels of size 20-300 microm at discharge hematocrit of 10-60%, taking into consideration the particulate nature of blood and cell deformation. The numerical model is based on the immersed boundary method, and the red blood cells are modeled as liquid capsules. A large RBC population comprising of as many as 2500 cells are simulated. Migration of the cells normal to the wall of the vessel and the formation of the cell-free layer are studied. Results on the trajectory and velocity traces of the RBCs, and their fluctuations are presented. Also presented are the results on the plug-flow velocity profile of blood, the apparent viscosity, and the Fahraeus-Lindqvist effect. The numerical results also allow us to investigate the variation of apparent blood viscosity along the cross-section of a vessel. The computational results are compared with the experimental results. To the best of our knowledge, this article presents the first simulation to simultaneously consider a large ensemble of red blood cells and the cell deformation.     

Quantitative Analysis of Mechanisms That Govern Red Blood Cell Age Structure and Dynamics during Anaemia

Mathematical modelling has proven an important tool in elucidating and quantifying mechanisms that govern the age structure and population dynamics of red blood cells (RBCs). Here we synthesise ideas from previous experimental data and the mathematical modelling literature with new data in order to test hypotheses and generate new predictions about these mechanisms. The result is a set of competing hypotheses about three intrinsic mechanisms: the feedback from circulating RBC concentration to production rate of immature RBCs (reticulocytes) in bone marrow, the release of reticulocytes from bone marrow into the circulation, and their subsequent ageing and clearance. In addition we examine two mechanisms specific to our experimental system: the effect of phenylhydrazine (PHZ) and blood sampling on RBC dynamics. We performed a set of experiments to quantify the dynamics of reticulocyte proportion, RBC concentration, and erythropoietin concentration in PHZ-induced anaemic mice. By quantifying experimental error we are able to fit and assess each hypothesis against our data and recover parameter estimates using Markov chain Monte Carlo based Bayesian inference. We find that, under normal conditions, about 3% of reticulocytes are released early from bone marrow and upon maturation all cells are released immediately. In the circulation, RBCs undergo random clearance but have a maximum lifespan of about 50 days. Under anaemic conditions reticulocyte production rate is linearly correlated with the difference between normal and anaemic RBC concentrations, and their release rate is exponentially correlated with the same. PHZ appears to age rather than kill RBCs, and younger RBCs are affected more than older RBCs. Blood sampling caused short aperiodic spikes in the proportion of reticulocytes which appear to have a different developmental pathway than normal reticulocytes. We also provide evidence of large diurnal oscillations in serum erythropoietin levels during anaemia.     

Simulation of a Single Red Blood Cell Flowing Through a Microvessel Stenosis Using Dissipative Particle Dynamics

The motion and deformation of a single red blood cell flowing through a microvessel stenosis was investigated employing dissipative particle dynamics (DPD) method. The numerical model considers plasma, cytoplasm, the RBC membrane and the microvessel walls, in which a three dimensional coarse-grained spring network model of RBC’s membrane was used to simulate the deformation of the RBC. The suspending plasma was modelled as an incompressible Newtonian fluid and the vessel walls were regarded as rigid body. The body force exerted on the free DPD particles was used to drive the flow. A modified bounce-back boundary condition was enforced on the membrane to guarantee the impenetrability. Adhesion of the cell to the stenosis vessel surface was mediated by the interactions between receptors and ligands. Firstly, the motion of a single RBC in a microfluidic channel was simulated and the results were found in agreement with the experimental data cited by [1]. Then the mechanical behavior of the RBC in the microvessel stenosis was studied. The effects of the bending rigidity of membrane, the size of the stenosis and the driven body force on the deformation and motion of red blood cell were discussed.     

A two-phase model for flow of blood in narrow tubes with increased effective viscosity near the wall

A two-phase model for the flow of blood in narrow tubes is described. The model consists of a central core of suspended erythrocytes and a cell-free layer surrounding the core. It is assumed that the viscosity in the cell-free layer differs from that of plasma as a result of additional dissipation of energy near the wall caused by the red blood cell motion near the cell-free layer. A consistent system of nonlinear equations is solved numerically to estimate: (i) the effective dimensionless viscosity in the cell-free layer (beta), (ii) thickness of the cell-free layer (1-lambda) and (iii) core hematocrit (H(c)). We have taken the variation of apparent viscosity (mu(app)) and tube hematocrit with the tube diameter (D) and the discharge hematocrit (H(D)) from in vitro experimental studies [16]. The thickness of the cell-free layer computed from the model is found to be in agreement with the observations [3,21]. Sensitivity analysis has been carried out to study the behavior of the parameters 1-lambda, beta, H(c), B (bluntness of the velocity profile) and mu(app) with the variation of D and H(D).